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Pulsating Flow Phenomena in Exhaust Manifolds
Christina Nikita Dipl. Ing.
This thesis is submitted for the degree of Doctor of Philosophy (Ph.D.)
Thermo fluids Division
Department of Mechanical Engineering
Imperial College London
July 2017
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Abstract
The objective of this work was to evaluate the accuracy of pressure losses predictions from
1-D gas dynamics models through the experimental study of the pressure wave action, the
interference of flow pulses amongst cylinders and the turbulent structures established in the
exhaust manifold flow. These phenomena have an effect on the exergy levels available at the
end of the manifold and, in the case of turbocharged engines, they reduce the amount of
energy in the exhaust gases that can be translated into useful work.
The evaluation of the accuracy of 1-D pressure loss models was done by reference to results
from a newly developed experimental apparatus which used pressurised air at ambient
temperature. The setup incorporated poppet valves that allowed the generation of pressure
pulses to propagate through a model T60o manifold. The downstream end of the manifold
was altered between open and 20% and 42% restricted ends; the latter two by the use of
orifice plates. Static pressure measurements were obtained across the junction area for open
end and restricted manifold end cases, at a range of engine speeds (950-2000rpm) and load
points. The parametric studies focused on the investigation of the behaviour of the acoustic
waves under a spectrum of different conditions. Velocity measurements using Particle Image
Velocimetry (PIV) were also obtained in the junction and outlet duct in the plane of
symmetry of the T60o manifold. The velocity measurements were used to evaluate the
contribution of the acceleration of the bulk flow, the diffusion losses and the acoustic
phenomena to the static pressure losses measured. An analysis of the predictions of two 1D
software packages (Gasdyn and GTPower) was also performed by reference to the pressure
measurements. Finally, the evaluation was extended by reference to CFD simulations
(OpenFOAM) of pulsating flow in T and Y manifolds.
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The copyright of this thesis rests with the author and is made available under a Creative
Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to
copy, distribute or transmit the thesis on the condition that they attribute it, that they do not
use it for commercial purposes and that they do not alter, transform or build upon it. For any
reuse or redistribution, researchers must make clear to others the licence terms of this work
I hereby declare that the work presented in this thesis is my own unless where the relevant
reference of others is mentioned.
Christina Nikita
London, 2017
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Acknowledgments
First and foremost I wish to thank my supervisors Prof. Yanni Hardalupas and Prof. Alex M
K P Taylor for giving me the opportunity to work on this project. Throughout the PhD
studies they did not only offer their academic and professional guidance but also expressed a
genuine interest for my physical and psychological wellbeing. I would also like to thank both
Yanni and Alex for always being enthusiastic about the project and willing to discuss for
long hours about all concerning scientific concepts.
I am also forever indebted to Daniel Pearce for his help and support in numerous technical
aspects whether it concerned the experimental facility or any software related issues. Dan
started his PhD studies at the same time with me and we shared offices, milestones and
occasional PhD frustration together, since day one. Dan was always keen to offer a hand, or
to help me out seek solutions for seemingly impossible obstacles to surpass. Above all he has
been a true friend to me and his way to always address problems with a positive mind has
been unparalleled, providing the psychological push I needed to keep on going in this,
otherwise lonely, path of obtaining a PhD. I would also like to thank both Dan and his
partner Rosie for their help towards the end of my studies.
I also wish to acknowledge the post-docs of the group Georgios Charalampous and Antonis
Sergis for their help with the optical setup. Particular mention also goes to the technicians at
the workshop and the laboratory, Eddie Benbow, Munasinghe Asanka and Tony Willis and
of course my external contractor Colin Hall. A big thank you also goes to the rest of the
students in the room, Kostis, Tony, Paul, Dimitris, Stathis and Konstantinos for making my
time at the office more enjoyable.
Aside of Imperial College, I wish to thank my flat mates Katerina and Yesna for being so
supportive and for being such good listeners whether it concerned technical issues or not. My
daily routine was so much better because of them.
I am also particularly grateful to my parents for their unconditional love and their
tremendous efforts to provide my life with all means possible to chase my dreams. I owe the
world to them not just for the comforting and encouraging words when I needed those the
most but also for teaching me that ethics, discipline and hard work are the key ingredients to
achieve my goals in life.
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Last but not least I would also like to thank my colleagues at Volvo Car Corporation for
funding the project and especially acknowledge Mattias Ljungqvist, Jian Zhu and Sofia
Ebermark for the fruitful collaboration that we had during my time at the company’s
headquarters in Gothenburg, Sweden.
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Contents Nomenclature ............................................................................................................................. 9
List of Figures .......................................................................................................................... 11
Chapter 1 ............................................................................................................................ 20
Introduction ...................................................................................................................... 20
1.1 Problem Considered .................................................................................................. 21
1.2 Previous Work ........................................................................................................... 23
1.2.1 One dimensional models for the prediction of exhaust flow ............................... 25
1.2.2 Experimental work in manifolds .......................................................................... 38
1.2.3 Turbocharger turbine modelling ........................................................................... 47
1.3 Present contribution .................................................................................................. 52
1.4 Thesis outline ............................................................................................................ 54
Chapter 2 ............................................................................................................................ 55
Experimental arrangement and instrumentation ....................................... 55
2.1 Introduction ................................................................................................................... 55
2.2 The experimental arrangement ..................................................................................... 56
2.2.1 General description ............................................................................................... 56
2.2.2 Pulse generator ...................................................................................................... 57
2.2.3 Test manifold ........................................................................................................ 59
2.3 Flow seeding and optical arrangement ......................................................................... 62
2.3.1 Flow seeding ......................................................................................................... 63
2.3.2 Particle Image Velocimetry (PIV) and optical arrangement ................................ 64
2.4 Test rig control and acquisition method ....................................................................... 65
2.4 Summary ....................................................................................................................... 67
Chapter 3 ............................................................................................................................ 68
Static Pressure and Velocity Measurements .................................................. 68
3.1 Pressure measurements ................................................................................................. 70
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3.1.1 Overview of the test cases .................................................................................... 70
3.1.2 Analysis of pressure signals in manifolds of finite length ................................... 71
3.1.3 Engine Speed Parametric Study ........................................................................... 75
3.1.4 Manifold Outlet Boundary Condition (BC) Parametric Study............................. 79
3.1.5 Operating Load Parametric Study - Pressure Losses ........................................... 81
3.2 Particle Image Velocimetry (PIV) Measurements ....................................................... 83
3.2.1 Introduction ........................................................................................................... 83
3.2.2 Cross Correlation Method for Velocity Vector Processing ................................. 86
3.2.3 Results ................................................................................................................... 89
3.3 Summary ..................................................................................................................... 113
Chapter 4 .......................................................................................................................... 115
1D Simulations of Branched Exhaust duct Flow ....................................... 115
4.1 Predictions by Gasdyn Software ................................................................................ 116
4.1.1 Model description and setup ............................................................................... 116
4.1.2 Pressure Loss model ........................................................................................... 118
4.1.3 Evaluation cases by reference to static pressure measurements - Gasdyn ......... 118
4.1.3 Summary ............................................................................................................. 125
4.2 Predictions using GT Power ....................................................................................... 125
4.2.1Model Description and setup ............................................................................... 125
4.2.2 Pressure Loss model ........................................................................................... 127
4.2.3 Evaluation cases by reference to pressure measurements - GT Power .............. 128
4.2.4 Summary ............................................................................................................. 133
4.3 Summary and Conclusions ......................................................................................... 134
Chapter 5 .......................................................................................................................... 135
Computational Fluid Dynamics ......................................................................... 135
5.1 Simulation setup ......................................................................................................... 135
5.1.1 The geometries .................................................................................................... 135
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5.1.2 Solution algorithm review .................................................................................. 136
5.1.3 Turbulence modelling and numerical discretisation .......................................... 137
5.1.4 Boundary conditions ........................................................................................... 138
5.1.5 Mesh generation and convergence ..................................................................... 141
5.2 Results and Discussion ............................................................................................... 142
5.2.1 Qualitative Results .............................................................................................. 142
5.2.2 Quantitative analysis ........................................................................................... 146
5.2.3 Pressure loss calculation comparison between CFD and 1D ............................. 150
5.2.4 Summary and conclusions of the comparative study ......................................... 154
Chapter 6 .......................................................................................................................... 157
Conclusion and Future work ................................................................................ 157
6.1 Summary and Conclusions ......................................................................................... 157
6.1.1 Summary ............................................................................................................. 157
6.1.2 Conclusions ......................................................................................................... 159
6.2 Future work ................................................................................................................. 161
Bibliography .......................................................................................................................... 163
Appendices............................................................................................................................. 169
A. Entropy generation .............................................................................................. 169
B. PIV data for 20% manifold end Restriction ........................................................ 171
C. Velocity profiles in outlet duct ............................................................................ 175
D. Input parameters for 1D simulation tools ............................................................ 176
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Nomenclature
A duct area 𝑚2
a speed of sound 𝑚/𝑠
b duct width 𝑚
c pressure wave speed 𝑚/𝑠
C static pressure loss coefficient _
dy square interrogation window side length 𝑚
f frequency 𝐻𝑧
F duct area 𝑚2
g gravitational acceleration 𝑚/𝑠2
h enthalpy 𝑘𝐽
𝒉𝒐 stagnation enthalpy 𝑘𝐽
H head loss 𝑚
K general stagnation pressure loss coefficient _
L duct length 𝑚
m mass 𝐾𝑔
�̇� mass flow rate 𝐾𝑔/𝑠
p static pressure 𝑃𝑎
𝒑𝒐 stagnation pressure 𝑃𝑎
q volumetric flow ratio of junction ducts _
q rate of heat transfer 𝐽/𝑠
Q volumetric flow rate 𝑚3/𝑠
T temperature 𝐾
u fluid velocity 𝑚/𝑠
�̅� average fluid velocity across duct width 𝑚/𝑠
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Greek letters
α Womersley number _
β flux correction factor _
Δ difference _
δ angle degrees
θ angle degrees
κ heat capacity ratio for real gas _
μ parameter to denote percentage of duct width _
μ dynamic viscosity 𝑘𝑔/(𝑚 ∙ 𝑠)
ξ energy loss coefficient _
ρ density 𝑘𝑔/𝑚3
ψ area ratio between two ducts of a junction _
ψ compressibility factor in OpenFOAM _
ω angular frequency 𝑟𝑎𝑑/𝑠
Subscripts
dat datum duct
C junction collector duct
j junction branch duct identification number
L junction feeding duct(s)
n junction fed duct(s)
s junction supplier duct
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List of Figures Figure 1: The graphical use of the Method of Characteristics (Fig2.8 on Benson et al. 1982):
(b) position diagram (x,t) where characteristic lines are drawn, (c) pressure at time t1, (d)
pressure at time t2 26
Figure 2: Flow types and loss coefficients as defined by Nichols 1984 28
Figure 3: Flow types at T-junctions classification according to experiments by (Benson et al.
1982) 30
Figure 4: Junction analysed using two major control volumes as of Hager (1984) 32
Figure 5: Control volume for modelling plena as in (Chapman et al. 1982) 36
Figure 6: Lamborghini 5 to 1 exhaust manifold 3D and 1D models (Onorati et al. 2005) 37
Figure 7: Pressure traces comparison between the 1D,1D-3D methods and measured data at
3000rpm and 6500rpm 38
Figure 8: Blair's experiments in a single cylinder two stroke engine as reported in Annand
and Roe (1974). 39
Figure 9: Branched pipe setup for steady flow tests (Bingham and Blair 1985) 40
Figure 10: Multi cylinder pulse generator of Benson Woollatt and Woods 1963 40
Figure 11: Geometry and pressure sensor positions of the shock tube test as in Pearson et al.
2006 41
Figure 12: Experimental and simulating pressure signals using two different models to
represent the behaviour in junctions (Pearson et al. 2006). 42
Figure 13: Visualisation of air flow through a T-90o junction showing weak shock waves at
the horizontal (outlet) pipe (at the point where the detachment is half the pipe’s width)
(Abou-Haidar, & Dixon, 1994) 43
Figure 14: Experimental apparatus in UMIST for the visualisation of shock waves in three
way junctions (Bassett et al. 1998) 44
Figure 15: Schlieren images of shock waves and their reflections on three way manifolds of
180o shape (left) and 45o shape with nozzle at the branch pipe (right). 44
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Figure 16: Experimental apparatus of a pulse generator with rotating plates (left) and the
results of the flow field (velocities in m/s) as obtained from the LDA technique -25mm and
12mm from the outlet pipe (right) (Snauwaert & Sierens 1987; Sierens & Flamang 1988). 45
Figure 17: PIV results of the flow field at the cross section downstream a 90o bend under
pulsating flow. Experimental setup (above), PIV results (below) (Kalpakli & Örlü 2013). 46
Figure 18: Operating loop in unsteady flow operation in comparison with the steady flow
characteristic (Szymko et al. 2005) 48
Figure 19: Different modelling ways for the turbocharger turbine volute. The rotor is
modelled as an orifice plate (Chiong et al. 2012) 49
Figure 20: Comparison of mean value and unsteady efficiency by adding harmonics (left).
Comparison of efficiency curves (right) (Hu & Lawless 2001) 50
Figure 21: Enthalpy-entropy diagram for the available energy in exhaust manifolds
(Winterbone and Pearson 1999) 51
Figure 22: Schematic of the experimental rig assembly 57
Figure 23: Engine head from single cylinder Honda BK-7 engine (left) and valve profiles
(right) (Yasuhiro Urata and Kazuo Yoshida at HONDA, personal communication, 2016). 58
Figure 24: Indexing plate to adjust the phasing between the heads every three degrees. 58
Figure 25: (Left) Isometric view of Perspex manifold assembly resulting in a three way
junction geometry with square ducts of 25mm x 25mm cross section. (Right) basic
dimensions at the top view of top surface along with sensor tapings where DIA=25mm 61
Figure 26: Pressure tapings (stations) that were used for the instantaneous pressure
measurements. The notation of ducts and stations of the present figure is also followed
throughout the thesis. 61
Figure 27: CAD top view manifold assembly mounted to the pulse generator 62
Figure 28: Transition part from the exhaust port to the manifold ducts (right). The chosen
profile (profile B-left) follows the guidelines of Bell and Mehta (1988) theory for gradual
contractions 62
Figure 29: Humidifier that produces the necessary mist to seed the flow inside the plena
(left), schematic with position inside the plenum 63
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Figure 30: Schematic of top view of optical arrangement. The circular beam was turned
through 90o by a mirror, then passing through a focusing convex lens (f=500mm) and a
concave lens (f=-12.5mm) that transformed the beam to a laser sheet 64
Figure 31: Field of view of the camera for position A (outlet pipe) and position (B)
(junction) 65
Figure 32: Pressure signal (red), laser timing TTL pulse (green) and acquisition triggering
TTL pulse (blue) for a fixed delay of 10ms(left) and 20ms(right) relative to the rising edge of
the triggering TTL pulse (blue). 67
Figure 33: Exhaust valve phasing scenarios; negative overlap (left) and positive overlap
(right) 70
Figure 34: Superposition of acoustic waves to the main exhaust blowdown pulses as seen on
the pressure signal obtained from the outlet duct (duct 3), at 1250rpm, low load with an open
end outlet boundary condition. 74
Figure 35: FFT analysis on the pressure signals obtained at station 3 shows the cycle
frequency at 10.25Hz, the valve opening frequency at 31Hz, the acoustic waves that are
superimposed on the main pulses at 123 and 134Hz respectively and 62Hz of the quasi-
sinusoidal motion at the end of the cycle. 75
Figure 36: Pressure signal during a cycle as obtained from the pressure transducer at station
1 at 950, 1250, 1650 and 2000rpm using an open end as outlet BC 77
Figure 37: Pressure signal along a cycle as obtained from pressure transducer at station 1 at
950, 1250, 1650 and 2000rpm using an orifice plate of 20% geometrical restriction as an end
outlet BC 78
Figure 38: Pressure signal along a cycle of as obtained from pressure transducer at station 1
at 950, 1250,1650 and 2000rpm using an orifice plate of 42% geometrical restriction as an
end outlet BC 79
Figure 39: Comparison of pressure traces obtained from pressure transducer at station 1
(lateral duct) for different BC at outlet duct end, namely open end, 20% Restriction and 42%
restriction. 80
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Figure 40: Pressure traces from pressure transducers at stations 1, 2 and 3 for low, medium
and high load operating points for the case of 20% restriction at the outlet BC.(Note the
change in y axis scale) 82
Figure 41: Sudden expansion due to geometrical step area change (left) and gradual
expansion due to partial blockage of duct owing to the formation of a recirculation region 84
Figure 42: Instances during the engine cycle at which images of the instantaneous flow
velocity field were acquired – Open End case and valve overlap scenario 87
Figure 43: Cross correlation method schematic for the calculation of correlation peak
between frames (LaVision Davis v7 software user manual) 87
Figure 44: Ensemble averaged velocity calculation for a number of N frame pairs A and B
(LaVision Davis v7 software user manual) 88
Figure 45: Ensemble averaged velocity for point A of the pressure pulse trace for the Open
End case 91
Figure 46: Ensemble averaged velocity for point B of the pressure pulse trace for the Open
End case 91
Figure 47: Ensemble averaged velocity for point C of the pressure pulse trace for the Open
End case 92
Figure 48: Ensemble averaged velocity for point D of the pressure pulse trace for the Open
End case 92
Figure 49: Ensemble averaged velocity for point E of the pressure pulse trace for the Open
End case 93
Figure 50: Ensemble averaged velocity for point F of the pressure pulse trace for the Open
End case 93
Figure 51: Ensemble averaged velocity for point G of the pressure pulse trace for the Open
End case 94
Figure 52: Ensemble averaged velocity for point H of the pressure pulse trace for the Open
End case 94
Figure 53: Ensemble averaged velocity for point I of the pressure pulse trace for the Open
End case 95
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Figure 54: Ensemble averaged velocity magnitude of the flow field at the mid plane of the
T60 junction at timestamp D. The pressure sensor position at the lateral duct is visible (10,-
35) due to its reflecting the laser light resulting in no valid vector calculation. The domain is
cropped at the lateral duct due to shadow of the straight duct projected to it as the laser light
was trespassing the manifold 96
Figure 55: Ensemble averaged velocity magnitude of the flow field at the mid plane of the
T60 junction at timestamp F. The pressure sensor position at the lateral duct is visible (10,-
35) as it was reflecting the laser light resulting in no valid vector calculation. The domain is
cropped at the lateral duct due to shadow of the straight duct projected to it as the laser light
was trespassing the manifold 97
Figure 56: PIV data points of the resultant velocity magnitude (blue) and fitted velocity
profile (moving average) (black) across the outlet duct. From the upper left, (a) and (b)
corresponding to profiles at cross sections at 5mm and 14mm are upstream of the
recirculation zone, (c) profile at 27mm is at the middle of the x-extent of the recirculation
region, and (d), (e) and (f) profiles at 40, 75 and 87mm respectively are downstream of the
recirculation region. 99
Figure 57: Calculation of the recirculation height from the integration of the velocity profile
to obtain the reverse and forward flowrates. The recirculation height is defined as the point
where the two areas become equal. 100
Figure 58: Flow streamlines (left) and velocity profile at the cross section of maximum
recirculation height (right). The specific imaging arrangement increases the spatial
resolution, resulting in the capture of the recirculation zone more accurately, but flow cross
sections after reattachment of the flow at the inner wall are outside the field of view. 102
Figure 59: Mass flow rate per unit depth along the outlet duct length as calculated by the
numerical integration of the velocity profiles derived from the PIV measurements at timestep
E 103
Figure 60: Mass flow rate per unit depth along the outlet duct length as calculated by the
numerical integration of the velocity profiles derived from the PIV measurements at timestep
A 104
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Figure 61: Non-dimensional cumulative mass flow rate with respect to the cross stream
coordinate at different streamwise stations within the outlet duct (15, 26, 27, 28, 65, 90mm)
using the no-slip condition hypothesis for the velocity at the wall. The height, where the
cumulative mass flow rate has reached 95% of the total value is taken to define the
recirculation zone maximum height. 106
Figure 62: Non-dimensional cumulative mass flow rate with respect to the cross stream
coordinate at different streamwise stations within the outlet duct (15, 26, 27, 28, 65, 90mm)
using a slip condition hypothesis for the velocity at the wall. The height, where the
cumulative mass flow rate has reached 95% of the total value is taken to define the
recirculation zone maximum height 107
Figure 63: Non dimensional cumulative mass flow rate for timestamps E-H at the cross
section where maximum recirculation height was observed. 108
Figure 64: Temporal variation of cross sectional average, phase average velocity magnitude
at three stream wise stations in the outlet duct (i.e. 10.5, 26.6 and 75mm). The magnitude
was calculated at the instances in phase that PIV measurements were obtained (A-I). 109
Figure 65: Pressure signals from stations 1(green) and 3(red) and pressure difference during
the cycle (blue). The blocked symbols are the calculated diffusion losses at the instances
when a recirculation zone was observed and are overlaid on the static pressure difference
trace. 110
Figure 66 : Values of velocity used for the estimation of the convection term of Equation
(37). The values refer to the velocity measurements at timestamp E 111
Figure 67: Overlay of the pressure signal obtained from stations 1 and 3 and the cross-
section average velocity magnitude at 75mm along the outlet duct during the cycle duration
113
Figure 68: Schematic representation of the 1D model of the experimental setup, as developed
in GasDyn software 116
Figure 69: Mesh sensitivity and discretisation method analysis on the static pressure
calculations at 1250rpm, low load conditions and open end BC for the outlet of the manifold.
The results show that mesh independency was reached using 1cm spacing. 117
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Figure 70 : Clockwise from upper left - Overlay of measured (dashed line) and Gasdyn-
computed (solid line) pressure signals at speeds of 950, 1250, 1650 and 2000rpm in the
lateral duct (duct 1) of the manifold at low load conditions and for the open end BC. 119
Figure 71 : Static valve profiles (dashed lines) (Yasuhiro Urata and Kazuo Yoshida at
HONDA, personal communication, 2016) and effective valve profiles (solid line). The latter
profiles were used in all simulations to improve the correlation with the experimental results.
They involve a 0.5mm increase in the valve lash. 121
Figure 72: Effect of the choice for valve lash in the 1D simulations. The comparison is based
on the static pressure measured on the lateral duct at medium load conditions, 1250rpm and
with open end BC at the manifold outlet. 121
Figure 73 : Illustration of a perturbation that travels along the manifold while the exhaust
valve is open. The boundary at the end of the manifold is an open end. A change to the
percentage opening of the valve at a given time stamp (2) determines the type of the
reflection and affects the overall wave dynamics, established in the manifold, during the
cycle 122
Figure 74 : Overlay of experimental (dashed lines) and computed (solid lines) traces for
pressure at duct 1 and 3 (left) and percentage pressure losses (right) for the open end case at
medium load conditions with valve overlap. 124
Figure 75 : Overlay of experimental (dashed lines) and computed (solid lines) traces for
pressure at duct 1 and 3 (left) and percentage pressure losses (right) for the 20% restricted
end case at medium load conditions with valve overlap. 124
Figure 76: Schematic representation of the 1D model of the experimental setup, as developed
in GT-ISE software 126
Figure 77: Setup of the junction sub-volume attribute in the GT-Power environment. Apart
from the geometrical orientation of the three ducts comprising the junction, additional
information on the expansion diameters in the junction volume and characteristic lengths for
each duct is required. 128
Figure 78: Clockwise from upper left - Overlay of measured (dashed line) and GT-Power
computed (solid line) pressure signals for speeds of 950, 1250, 1650 and 2000rpm observed
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at the lateral duct (duct 1) of the manifold at low load conditions and using an open end as
the manifold end BC. 129
Figure 79 : Clockwise from upper left - Overlay of measured (dashed line) and GT-Power
computed (solid line) pressure signals at speeds of 950, 1250, 1650 and 2000rpm observed at
the lateral duct (duct 1) of the manifold at low load conditions for 20% restriction at the
manifold end BC. 130
Figure 80: From top to bottom: the expansion diameter was calculated based on geometry,
in-phase flow correction and ad-hoc adjustment for partly in phase flow. The graphs on the
left show the overlay of experimental (dashed line) and computed (solid lines) traces for
pressure at duct 1 and 3 and on the right the percentage static pressure losses for the Open
end case at medium load conditions and at speed 1250rpm. 132
Figure 81: Overlay of experimental (dashed line) and computed (solid lines) traces for
pressure at duct 1 and 3 (left) and percentage pressure losses (right) for the 20% restricted
end case at medium load conditions and at speed 1250rpm. 133
Figure 82: The CFD simulations were performed using geometries of three way junctions of
Y and T shape; two Y junctions of 30 and 60 degrees branch angle respectively and one T
junction that resembles the experimental setup with 60 degrees branch angle. 136
Figure 83: Time varying pressure boundary condition, imposed at the inlet of duct 2 of the
computational domain. The dotted vertical lines represent the values of CAD at which
contours of velocity magnitude and density are presented in the following paragraph. 139
Figure 84: Evaluation of acoustic response of boundary conditions: open end, closed end and
wave transmissive in a 2D test case of a Y60o junction. A finite length plane pressure wave
was generated at the inlet of the branch duct on the left. 140
Figure 85: Mesh density at junction area (left) and outlet duct(right) for the T60o geometry.
There was a 2:1 geometrical grading at the streamwise direction that allowed for the
refinement of the mesh at the junction area. 142
Figure 86: Spatial distribution of the flow field with velocity magnitude contours in the plane
of symmetry in Y-30o, Y-60o and T-60o geometries during the propagation of the pressure
pulse. 143
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Figure 87: Spatial distribution of gas density in the plane of symmetry in the Y-30o, Y-60o
and T-60o geometries during the propagation of the pressure pulse. The colour scale had to
change to depict the density spatial variations for the Y-60o junction. 145
Figure 88: Pressure traces upstream and downstream of the junctions (a) Y30o, (b) Y60o, (c)
T60o. Sections AA' and BB' indicate the pressure rise or pressure drop for the same pressure
level upstream of the junction (5D from end of duct1). 147
Figure 89: Pressure and mass flow traces for junction geometries (a) Y30o, (b) Y60o and (c)
T60o at a location at the junction, which is at 5D from end of duct1 (inlet) and 5D from start
of duct3 (outlet). 149
Figure 90: Control volumes within plane of symmetry for the junction area of the T-60°
junction geometry, following the notation of (Bassett, Pearson, and Fleming 2003) 151
Figure 91: ΔP across the junction, as calculated by CFD and Bassett 1D model for constant
density assumption using (rho1) and using outlet duct density (rho3) values for the case of
T60o geometry 151
Figure 92: Static pressure traces of duct1, duct3 and ΔP for the T60o geometry, as calculated
from the CFD and the pressure trace of duct3 based on the model of Bassett et al (2003). 152
Figure 93: ΔP across the junction, as calculated by CFD and Bassett 1D model for a constant
density assumption (rho1) and outlet duct (rho3) density values for the case of Y60o junction
geometry. 153
Figure 94: ΔP across the junction, as calculated by CFD and Bassett 1D model for a constant
density assumption (rho1) and outlet duct (rho3) density values for the case of Y30o junction
geometry. 154
Figure 95: Ensemble averaged velocity for point F of the pressure pulse trace for the 20%
Restricted End case 173
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Chapter 1
Introduction
The transportation industry is greatly reliant on reciprocating engines for ground and sea
vehicles and also, although less extensively for aircrafts. The principle of the air breathing
reciprocating engine when it was first developed at the end of 19th century was to receive a
specific amount of air, provide the necessary fuel, retain a controlled combustion process
within its cylinders, and finally discard the exhaust gases so that the procedure can be
repeated. Through the years, this initial, simplified concept of reciprocating engines has
developed further, revealing the true potential of each individual process of the engine cycle.
The importance of the design of the exhaust manifold was revealed in the mid-20th
century as the primal aspect to affect the scavenging of cylinders. The engine is essentially a
pump that produces pulses containing the hot combustion products; these pulses carry almost
a third of the fuel energy originally in the cylinder after the portion of useful work is
deducted. Soon it was realised that the ability of an engine unit to provide an efficient gas
exchange process was dependent on the wave dynamics established in the manifold. An
increased engine breathing efficiency, as it is named, through a tuned manifold would result
in higher power output, compared to the same engine using a manifold of arbitrary
dimensions.
Lately, the demands for increasing power density, the need to meet stringent emission
regulations and to lower consumption levels has led to the re-visiting of the manifold design,
this time for energy recovery purposes. The turbocharger turbine uses the enthalpy of the
exhaust gases to drive a compressor that in turn can increase the density charge in the
cylinder. Initially at least, the turbine (either of axial or radial type) was developed to operate
under steady flow conditions, as on aircraft engines. In the case of ICEs, the turbocharger
P a g e | 21
turbine operates under unsteady (pulsed) conditions due to the opening and closing of the
exhaust valves. The magnitude of unsteadiness differs as the operating point of the ICE
changes and the exhaust manifold serves as the ‘connector’ between the source of
unsteadiness (i.e. the exhaust valves) and the turbine inlet. The optimisation of the turbine
matching to the engine unit is a rather challenging task for the engine manufacturers, and
nowadays relies on one dimensional software packages for the engine development process.
1.1 Problem Considered
The quantification of the energy transfer in exhaust gases through an engine manifold
under pulsating conditions can assist the prediction of the operation of a turbocharger
turbine. The energy available in the exhaust gases is transferred in a fragmented (unsteady)
manner through the blowdown process of each cylinder. This transfer is associated with
losses resulting in different energy levels between the exhaust valves and the outlet of the
manifold. The energy loss, apparent in every exhaust manifold, can be attributed to two
phenomena; (i) the direct heat losses due to temperature difference between the exhaust
gases and the manifold walls exposed to ambient conditions and (ii) mechanical losses,
which are related to the propagation of the exhaust gas pulses and the turbulent nature of the
flow. The pressure pulses generated at the exhaust valves upstream of the manifold are
essentially pressure waves that travel through the manifold branches. The wave dynamics in
the manifold describe the reflections and pressure losses generated at areas, such as pipe
bends and branching regions, i.e. the junctions of the manifold. The same areas also
aggregate the non-axisymmetric nature of the bulk flow resulting in flow detachment from
the manifold walls and in areas, where recirculating gas flow structures are formed.
The calculation of the aforementioned energy cascade in the manifold is of primal
importance at the design stage of the engine unit, not only for the overall engine efficiency
but also for the estimation of the maximum potential of a turbocharger turbine fitted at the
end of the manifold as an energy recovery unit. Accurate prediction of the pulsating flow
through the manifold requires extensive computational fluid dynamics simulations that
account for both the acoustics and the mean flow phenomena. A rigorous calculation is not
P a g e | 22
yet feasible for, the whole spectrum of the engine operation with reasonably available levels
of computational resources and time.
Industrial work still relies on one dimensional tools for the prediction of the engine
operation as a whole. In a one dimensional approach, the calculation is divided into two
processes, one responsible for the combustion process and one for the gas exchange and flow
travelling in the manifolds. One dimensional Euler equations for inviscid flows are used in
currently available software packages to calculate the flow characteristics in the exhaust
manifolds. Inherently, there is a loss of information when approximating a three dimensional
flow with a 1D model, since the complicated manifold shape, apart from generating pressure
reflections is also aggregating three dimensional flow structures. These two phenomena,
responsible for the reduction of the available energy in the manifold are known to
researchers, who have been studying the subject for the last 50 years. Extensive experimental
work has been carried out to help the calculation of the losses at the manifold junctions of
different geometries and under a range of operating points. The majority of the experiments,
which are presented in the following paragraphs, were carried out using water as the working
fluid and most of them under steady operating conditions. In recent years a number of
experiments have also taken place, using air as working medium, but again under steady
conditions. The measured pressure losses from the experiments were calculated by
comparing the pressure levels before and after the junctions and the comparison was
amongst a pair of pipes. The findings have led to the development of empirical and semi
empirical models to calculate the overall pressure losses in junctions based on pressure loss
coefficients. Inclusion of such models in one dimensional codes improved the accuracy of
the predictions for the manifold operation and helped to partly overcome the loss of
information, when the three dimensional flow (as the one in manifolds) is approximated by a
1D model. However, as it will be demonstrated in the following section, the empirical
models were developed using a series of experiments that were limited by the technology of
the era, which could not take into account a number of parameters, such as engine-like
pulsating conditions, interaction between pulses, compressible flow behaviour, mass
accumulation in pipes or the interaction with the turbocharger turbine as the outlet boundary
condition of the manifold.
The one dimensional models currently used in industry, their limitations and the areas
where predictions can be improved will be discussed in this thesis. In addition, a brief
P a g e | 23
summary of the experimental work available in the literature will be presented to
demonstrate the need for further investigation of the pulsating flow in manifolds using
contemporary methods.
1.2 Previous Work
Since the earliest attempts to perform a complete engine simulation, the importance of
predicting the behaviour of waves in engine manifolds has been well known: also well-
known is the challenge presented in the solution of digital computation, of appropriately
simplified forms of the associated governing equations. Work in the early 1960s used the one
dimensional (‘1D’) approximation embodied by the Method of Characteristics (MoC), (e.g.
Benson et al. 1982). The importance of wave actions on engine breathing was extensively
investigated at that time and subsequently by various researchers (Annand and Roe 1974;
Blair 1999), who reported on the use of tuning the manifold and scavenging process. The
MoC yielded significantly better results than the filling and emptying methods available for
the engine simulation (Kirkpatrick et al. 1994; Vandevoorde et al. 2000; Guardiola et al.
2012). Since that time, more adaptable, flexible and powerful approaches (namely finite
difference and finite volume techniques) have largely replaced the MoC.
Nowadays, engine design still heavily relies on 1D simulations despite the profound
advances in three-dimensional (3D) computational fluid dynamics (CFD) methods, which
can compute the complete flow field. In recent years, CFD coupled with 1D methods has
been made available in commercial and open source codes (e.g. Montenegro et al. 2007);
even this latter approach though is computationally expensive. The 1D approximation
remains the dominant framework, at least for development work in industry, and is likely to
remain so in the foreseeable future. The reduction of the equations describing the 3D flow to
a 1D description inevitably results in the need, in the case of manifolds, to have means of
representing their influence on the flow. In engine manifolds, one influence which is
important because it leads to pressure loss, is the branching or joining of flows at junctions.
A common approach used from the 1980s for the representation of the losses in the unsteady
flow passing through manifold junctions in the 1D calculation procedure is through the
P a g e | 24
inclusion of loss coefficients defined based on steady flow behaviour. Depending on the
methodology that was followed the loss coefficients were introduced either in the
momentum or the energy equation. The calculation procedure will be discussed in detail in
the following paragraphs. As a general remark here, it should be stated that the applicability
of these steady-flow-derived coefficients has already been evaluated in the literature by
experiment in the context of steady flows with widely varying junction angles and mass flow
rate splits between the pipes leading to the junction. The evaluation of coefficients as
described above was performed usually by reference to the mean pressure levels in the pipes,
and in unsteady flows (including shock tube tests) (Winterbone and Pearson 2000; Miller
1971; Bingham and Blair 1985). A brief overview of the available experimental work will be
given below, not only for the tests relevant to pressure losses, but also the ones focused on
the visualisation of the mean flow as it travels through the manifold.
The accurate quantification of the in-cycle pressure losses at junctions is important
because it is directly linked with the loss of energy in the manifold; and the need for
accuracy, or at least for the quantification of inaccuracy, is currently receiving increasing
attention for the determination of the operating parameters, for example, of a turbocharger’s
turbine fitted at the downstream end of a manifold. In such a case, the accurate prediction of
entropy level and pressure and energy losses as a function of time is necessary. Inaccuracies
in predictions which use these pressure loss coefficients can stem from three generic reasons,
which are apparent in the theoretical derivation of the form of the pressure loss coefficients.
These are: the use of a steady flow analysis to describe an unsteady flow; specifically (a)
neglecting the acceleration of the flow and (b) neglecting mass accumulation in the macro-
control volume (corresponding to the volume of the junction); incomplete, or incorrect,
specification of any spatial non-uniformities in the magnitude and direction of velocity, of
pressure and of density at the surface area of the macro-control volume. In the following
paragraphs, a more detailed analysis of the theoretical background of how the 1D codes treat
the flow in junctions of manifolds will be presented. Supporting experimental work that lead
to the development of widely used 1D codes will also be briefly exhibited, explaining the
reasons behind the motivation for further study which was undertaken in the present work.
P a g e | 25
1.2.1 One dimensional models for the prediction of exhaust flow
The complexity of models for the calculation of the flow in manifolds has increased along
with the increase in computer aided calculating capabilities. The simple 0D models and
emptying and filling methods were gradually replaced by 1D gas dynamics models that
could solve the conservation equations that describe the internal pipe flow. These for 1
dimensional (along x axis) non-steady and non-homentropic flow are as follows:
Continuity 𝜕𝜌
𝜕𝑡+ 𝜌
𝜕𝑢
𝜕𝑥+ 𝑢
𝜕𝜌
𝜕𝑥+
𝜌𝑢
𝐹
𝑑𝐹
𝑑𝑥= 0 (1)
Momentum: 𝜕𝑢
𝜕𝑡+ 𝑢
𝜕𝑢
𝜕𝑥+
1
𝜌
𝜕𝜌
𝜕𝑥+ 𝐺 = 0 (2)
where: 𝐺 = 𝑓𝑢2
2
𝑢
|𝑢|
4
𝐷 the friction loss term and 𝑓 =
𝜏𝑤1
2𝜌𝑢2
with tw the wall shear stress
Energy: (𝜕𝑝
𝜕𝑡+ 𝑢
𝜕𝑝
𝜕𝑥) − 𝑎2 (
𝜕𝜌
𝜕𝑡+ 𝑢
𝜕𝜌
𝜕𝑥) − (𝜅 − 1)𝜌(𝑞 + 𝑢𝐺) = 0 (3)
where q is the rate of heat transfer per unit time per unit mass and α the speed of sound
Wave action techniques, in general, are being studied for over 100 years. In the early 20th
century, Rayleigh (1910) was amongst the first to investigate the finite amplitude wave flow
and, some years later, Earnshaw (1910) proposed a solution for waves travelling in one
direction. Riemann in late 19th century developed an innovative technique to handle the
problem of wave propagation and the solution of the partial differential equations, the
Method of Characteristics (MoC). The concept was to transform the system of conservation
equations shown above by using algebraic manipulation to reduce the unknowns to only two,
the speed of sound, α, and gas particles velocity, u. Pressure-entropy relations were used for
this reason and the speed of sound and gas velocity are expressed as functions of x, t. The
solution for the new system was sought along characteristic lines of specific slope along
which the set of PDEs was transformed to a set of ODEs. Being essentially a graphical
method, MoC was able to predict the propagation of pressure waves and the formation of
steep wave fronts quite effectively due to the characteristic lines convergence (Figure 1).
P a g e | 26
Detailed analysis of the manipulation of the equations can be found in Benson et al. 1982.
The use of MoC became rather popular also for the calculation of channel flows and the
water hammer phenomenon in pipe lines. A detailed historical analysis for the use of MoC in
these systems can be found in the literature (Popescu, Arsenie, and Vlase 2003; Chaudhry
and Mays 2012) however, the discussion in this work pinpoints important marks in history
where MoC was used on the IC engine manifold flows. The graphical version of MoC was
appropriated in exhaust flows of IC Engines by De Haller (1945) and Jenny (1950).
The graphical nature of the method however made it time-consuming and completely
impractical for complex engine calculations until Shapiro (1954) and Benson et al. (1982)
managed an important step in history by introducing the numerical schemes and computer
aided solution of MoC in engine manifolds respectively. Benson proposed a complete
numerical technique including specific flowcharts and FORTRAN subroutines for the
solution of the hyperbolic equations using MoC in the context of engine manifold flow.
Since that time, the study of wave propagation methods for the purpose of exhaust manifold
design has been well established. The MoC has largely being replaced nowadays by more
Figure 1: The graphical use of the Method of Characteristics (Fig2.8 on Benson et al. 1982): (b) position diagram (x,t) where characteristic lines are drawn, (c) pressure at time t1, (d) pressure at time t2
P a g e | 27
generally applicable finite difference schemes that can achieve second order accuracy in
space and time like the Lax-Wendroff central differencing scheme (Lax and Wendroff 1960).
The downside of the use of these schemes was the appearance in the solution of artificial
overshoots at discontinuities (Kirkpatrick et al. 1994; Takizawa et al. 1982). Alterations to
the original scheme were developed later on to treat the overshoots with the inclusion of flux
limiters. Harten et al. (1983) suggested an upstream difference technique (Harten, Lax and
Leer-HLL) based on the Godunov’s solving scheme (Godunov 1959). A comparison and
evaluation of different numerical schemes is available in the bibliography by Kirkpatrick and
Blair (1994). Independently of which is the most suitable discretisation scheme for the
numerical solving of the equations, the principal aim of all 1D methods was always to
accurately predict, to the extent possible, the exhaust flow behaviour in the manifolds, which
becomes rather challenging at the junction regions.
Definition of coefficients
Although the flow in simple pipes can, in many cases, be well approximated as 1D, the same
cannot be said of junctions where complicated 2D and 3D flow structures are apparent. The
primary issue introduced by the junction is that of pressure loss. Developers of 1D codes
tried to account for this by implementing their effect on the flow characteristics. The general
approach is by introducing pressure loss coefficients in the conservation equations, either in
momentum or energy depending on the approach which was followed. Both approaches are
going to be briefly introduced in the following paragraphs. Over the years, pressure loss
coefficients have been calculated for numerous types of junctions under various operational
conditions and have also been evaluated against experimental data. A brief overview of the
experimental work on loss coefficients will also be given in this chapter.
The different methods used to calculate the pressure loss coefficients make it hard to form a
generic "lookup table" to be used as a subroutine in 1D codes. In addition, the combinations
of flow types and geometries are too many, so that, even if this table could be constructed to
account for all of these, it would be unwieldy. There is common ground on the notation and
the classification of flow patterns through junctions, although the methods with which the
coefficients are calculated vary. Nichols (1984) presents the 6 available flow types in a three
branch junction with two coefficients assigned to each one of these.
P a g e | 28
The general equation that gives the loss coefficient, K, if all data relating to the flow
upstream and downstream are available, is:
K =(pupstream+
1
2ρuupstream
2 )−(pdownstream+1
2ρudownstream
2 )
ρudownstream2 (4)
The first assumption is already evident in equation (4) in that the gas is regarded as
incompressible at the junction boundaries, so a common density through the junction volume
-as formed by the ends of the pipes comprising it- is used. Researchers have presented a
number of alternative forms of this equation based on a number of assumptions of the flow
field in the junction. These assumptions will be presented in this work and evaluated against
3D CFD data below. One of the aims of 1D engine simulations is to predict the exhaust flow
downstream of the junction at every time step as part of the engine cycle. The coefficient for
an arbitrary junction shape, which has not been experimentally tested, is not known
beforehand. This means that the applicability of coefficients against specific experimental
measurements is quite limited, when a 1D code handling the flow in manifolds of untested
shape is developed. The design of the manifold is usually in advance of the engine's
development; however, its importance to the engine breathing calculation is significant.
Therefore, the need of accurate pressure loss predictions comes before the ability to actually
measure them on the specific manifold on an engine test bed.
Figure 2: Flow types and loss coefficients as defined by Nichols 1984
P a g e | 29
How do coefficients appear in 1D flow equations?
1D simulations use the three governing equations (i.e. continuity, energy and momentum) for
any given junction to resolve the flow characteristics downstream. Although different
approaches exist, these rely on assumptions to allow for the calculation of the energy and
pressure levels in the pipes with flow direction going away from the junction, where the
boundary data (junction side) must be evaluated first before the solution can continue
downstream. These assumptions, which are discussed later in this work, are focused on only
two of the equations, the energy and momentum equations. The updated form of the two
equations after the assumptions take effect, contain the loss coefficients. These are then
combined with the continuity equation, which is solved iteratively until a pre-specified
convergence criterion is met. Over the years, different approaches for representing the
energy and momentum equations and hence the loss coefficients have been published and
two main categories can be identified. The first is where steady flow coefficients are
introduced in the momentum equation with specific assumptions being made for the energy
equation. This is necessary to form a complete set of equations, which can be solved. The
second is where the coefficients were developed from hydraulics theory and are introduced
in the energy equation. In the latter case, there is no need for further assumptions in the
momentum equation since the fluid is considered to be incompressible at the junction area.
The basic principles of these two methods will be briefly presented here, detailed derivation
of equations is left to the referenced literature.
Assumptions in energy equation - Coefficients in momentum equation
Benson et al. (1963) make the following assumptions regarding the energy equation:
(i) the sum of stagnation enthalpy over the three streams joining the junction is zero for
joining flows:
Joining: ∑ 𝑚ℎ𝑜𝑖= 03
𝑖=1 (5)
(ii) the stagnation enthalpy remains constant along a streamline for separating flows:
Separating: ℎ𝑜1=ℎ𝑜2=ℎ𝑜3 (6)
The terms joining and separating flows refer to the generally adopted notation of Nichols
(Figure 2)
P a g e | 30
For flow type C of Figure 3, the pressures at points P, P' of sections 1 and 3 (at the corner
between branch 1 and branch 3) are supposed equal, the argument being that these are too
close together for any pressure difference to arise. For flow type D, pressure is also found –
experimentally- to be almost equal between sections 1 and 2, based on steady flow
experiments on circular pipes as quoted on Benson.
The momentum equation for flow type C is written, for the x-direction (positive from left to
right horizontally across the page as on Figure 3),
(𝑝1 − 𝑝2)𝐹 = 𝑚2̇ 𝑢2 − 𝑚1̇ 𝑢1 (7)
�̇� = 𝜌𝑢𝐹 (8)
(𝑝1 − 𝑝2)𝐹 = 𝜌2𝑢22 − 𝜌1𝑢1
2 (9)
where F is the cross sectional area of the pipes (assumed to be of the same cross sectional
area).
For the y-direction (positive vertically up on Figure 3), the forces on the walls (R, S) are
unknown, so the momentum equation cannot be solved. However, based on Benson’s
assumption that 𝑝1=𝑝3, an extra equation can be formed and the system can be solved.
Figure 3: Flow types at T-junctions classification according to experiments by (Benson et al. 1982)
P a g e | 31
Because no either simple or readily generalisable assumptions can be made for the separating
flow types A and B, Benson constructed a new form of quasi-momentum equations to
express the pressure loss in the junction with the addition of a pressure loss coefficient.
For flow type A, we read:
x-momentum 𝑝1 − 𝑝2 = 𝐶1(𝜌2𝑢22 − 𝜌1𝑢1
2) (10)
y-momentum 𝑝1 − 𝑝3 = 𝐶2𝜌3𝑢32 (11)
Likewise, steady flow pressure loss coefficients have been experimentally obtained for all
the remaining types of flow and the derivation of equations is similar to the procedure listed
above. Benson observed that there was still need of a coefficient for the momentum theory to
match the experimental results at joining flows. However, the values of the joining flow
coefficients are close to unity, unlike the ones calculated for the separating flows.
Corberán (1992) argued that flow mixing occurs in the junction volume and so Benson's
assumption on stagnation enthalpy for separating flows was not valid. Corberán proposed
instead that the stagnation enthalpies of the flows leaving the junction are all the same, but
not the same with the one of the incoming flow, and that the entropy level in the pipes with
flow towards the junction remained unchanged.
Hydraulics theory - Coefficients in the Energy Equation
A different approach is based on hydraulics theory (Hager 1984), although it was later
applied to compressible flows as well (Abou-Haidar and Dixon 1992; Bassett, Pearson, and
Fleming 2003). According to this theory, a "dividing-streamline" separates the flow at a T-
junction in two major control volumes, namely the ‘directly through’ control volume, which
covers the main branch (considered to be the x direction), and the volume in the direction of
the lateral branch (considered to be the y direction) as shown in Figure 4. The ducts were of
rectangular cross section of width b and unity height.
P a g e | 32
Figure 4: Junction analysed using two major control volumes as of Hager (1984)
The assumptions on the energy head are as follows:
(i) The cross stream distributions of hydrostatic pressure and velocity are spatially uniform.
(ii) For the control volume of Figure 4a, the static pressure at point C approximately
corresponds to the energy head of inflow at "section1", as this is a stagnation point.
𝑝𝑠 = 𝑝1 +𝑄2
2𝑔𝑏2 (12)
where b is the duct’s width, Q is the flowrate and g the gravitational acceleration.
For the flow in the lateral branch, the control volume is divided into two sub-volumes (3->4)
and (4 ->5), as shown in Figure 4b. The first one contains converging streamlines, so the
energy head is known (Matthew 1985) to remain almost constant along these and equal to :
𝐻 = 𝑝 +𝑉2
2𝑔 (13)
where V is the magnitude of average cross sectional velocity. The additional mechanical loss,
denoted as ΔΗ from the change in pressure head for the lateral branch, appears only in the
diverging part.
P a g e | 33
Under these assumptions, energy equations are constructed for each direction (main branch,
lateral branch) and the local mechanical energy loss ΔΗ is represented in terms of the
velocity head with a coefficient, implemented in each of the equations.
The energy equation for the control volume of Figure 4a reads
𝑝1 +(𝑄−𝛥𝑄)2
2𝑔𝑏2(1−𝑞)2 = 𝑝2 +(𝑄−𝛥𝑄)2
2𝑔𝑏2 + 𝜉1𝑄2
2𝑔𝑏2 (14)
Energy equation for control volumes of Figure 4b :
converging sub-volume: 𝑝1+𝑝𝑠
2+
𝑄2
2𝑔𝑏2 = 𝑝4 +(𝛥𝑄)2
2𝑔𝜇2𝑏2 (15)
diverging sub-volume: 𝑝4 +𝛥𝑄2
2𝑔𝜇2𝑏2 = 𝑝5 +(𝛥𝑄)2
2𝑔𝑏2 + 𝜉2𝑄2
2𝑔𝑏2 (16)
where: q is the volumetric flow ratio of lateral to main duct ΔQ/Q, ξ1 and ξ2 are the loss
coefficients and the product 𝜇 ∙ 𝑏 denotes the effective width of the pipe if the separation
zone is neglected. μ is a parameter, which varies from 0 to 1, and subscript s relates to the
stagnation point of converging sub-volume as in Figure 4.
Combining the energy equations with the momentum equations for each volume the
definitions for the two coefficients ξ1 and ξ2 arise:
𝜉1 = 𝑞 (𝑞 −1
2) (17)
𝜉2 = 1 − 2𝑞 𝑐𝑜𝑠 (3
4𝛿) + 𝑞2 (18)
where δ is the branch angle of the junction. Hager reports that the flow in the lateral branch
diverts by an angle smaller than the geometrical angle δ. The deviation is reported to be δ/4
from the horizontal. This is a result of the separation zone formed on the lateral branch of the
junction as shown in Figure 4b. The above observation for the deviation of the direction of
flow was made for pipes of equal pipe areas.
P a g e | 34
Generalised models of junctions of N-branches
As stated before, there are numerous combinations of flow patterns and geometry
configurations for junctions limiting the ability of 1D codes to predict the losses downstream
of a junction that has not been tested and documented. This initiated the need of a
generalised model, which would perform well for junctions of more than three pipes.
Benson et al. (1982) implemented a computer subroutine in which the flow type is examined
at a given time step and depending on the classification (as in Figure 2), the corresponding
pair of equations was solved. Then, the continuity equation is either fulfilled or corrected to
repeat the solution procedure.
Bingham & Blair (1985) proposed an extension of Benson's calculation subroutine of the
three-way junction. He gathered experimental loss coefficients from T and Y junctions of
different branch angles and different flow types and formed an empirical generalised
coefficient, which would account for the geometry of any pair of pipes, independently of the
total number of the pipes comprising the junction. One of the pipes of the pair must always
be the one with the greatest mass fraction, which he denoted as supplier or collector,
depending on the flow type (separating or joining).
The generalised coefficient is given by the equation (19) below.
𝐶 = 1.6 − 1.6𝜃
167 (19)
Blair constructed two momentum equations, one each for the collector type junction and one
for the supplier following the work presented earlier by Benson .
For the calculation procedure he considered density to be constant in the junction region. To
avoid iterations, density and velocity were taken as the ones of the previous time step, as this
would still yield satisfactory results (Bingham and Blair 1985).
Supplier Type : 𝑝𝑠 − 𝑝𝑛 = 𝐶𝑛(𝜌𝑛𝑢𝑛2)𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑡𝑖𝑚𝑒 𝑠𝑡𝑒𝑝 (20)
Collector Type : 𝑝𝐿 − 𝑝𝑐 = 𝐶𝐿(𝜌𝑐𝑢𝑐2)𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑡𝑖𝑚𝑒 𝑠𝑡𝑒𝑝 (21)
P a g e | 35
where s denotes the supplier, n the pipes being fed and L the collector with c the feeding
pipes.
Bassett et al. (2003) combined the idea of Blair's maximum mass flow rate pipe with the
observations of Hager (1984) to introduce a different generalised model for N-way junctions.
This model accounts for junctions for arbitrary number of pipes, but it also includes arbitrary
pipe area ratios and any mass flow ratios. The pressure loss coefficient is developed from
hydraulics theory and is given by equation (22) below:
𝐶𝑗 = 1 −1
𝑞𝑗𝜓𝑗𝑐𝑜𝑠
3
4(𝜋 − 𝜃) (22)
𝑝𝑑𝑎𝑡 − 𝑝𝑗 = 𝐶𝑗(𝜌𝑢𝑗2) (23)
where j denotes the pipe in question, 'dat' is the datum branch, 𝑞𝑗 the mass flow rate ratio, 𝜓𝑗
the cross sectional area ratio. The angle π- θ represents the deviation of the flow that enters
the lateral branch as in Hager’s work. However, in the Bassett et al. (2003) model, it is the
momentum equation is written along the direction of the lateral branch as opposed to Hager’s
model that uses the energy equation. Winterbone & Pearson (2000) report that the
observation of Hager, regarding the deviation of the angle of the flow, was proven to match
experimental results satisfactorily even when ducts of different pipe areas are being used.
The coefficient of equation (22) can be used to calculate the stagnation losses through the
equation
𝐶𝑗 =1
2∙ {
𝐾𝑗
𝑞𝑗2𝜓𝑗
2 −1
𝑞𝑗2𝜓𝑗
2 + 1} (24)
where 𝐾𝑗 is the stagnation loss coefficient between the pair of pipes in question.
The coefficients are calculated, at each time step with regards to the pipe with the greatest
mass flow rate, towards the junction, which is denoted as the datum branch. Any pipe can be
the datum branch during the engine cycle, so the subroutine which calculates the pressure
losses checks all mass flow rates at the end of the time step before it continues with equation
(23). The latter model has been reported by researchers (Bassett, Pearson, and Fleming 2003;
Onorati et al. 2005) to give a fair agreement with results of pressure traces in shock tube tests
and a high speed racing engines.
P a g e | 36
Another approach, used in one of the most popular 1D codes available in industry (GT-
Power) is the one developed by Milt Chapman using the FRAM algorithm (Filtering Remedy
And Methodology) which is reportedly produces fewer non-physical oscillations in the
solution that the typical Lax-Wendroff scheme (Chapman 1981). An upwind differencing
scheme is used in Chapman's work (Chapman, Novack, and Stein 1982) and the governing
equations are constructed so that the energy term may be calculated for the control volume of
the junction as defined in Figure 5.
Figure 5: Control volume for modelling plena as in (Chapman et al. 1982)
A viscous momentum loss term is introduced in the junction pressure term, P, with Q
volumetric flow rate as follows:
𝑃1𝑛 = 𝑃 + 𝑄 (25)
𝑄 = 𝜌𝐶𝛥𝑙 ∇𝑈𝑖 (26)
where n is the current timestep, Ui is the velocity normal to the entrance of the junction
volume (Figure 5), ρ is the density at the junction and C is the pressure loss coefficient. Then,
the PdV work is calculated from a finite differencing approximation, which includes the
junction volume VL, so that the final equation for the specific integral energy can be
calculated for each of the pipes connected to the junction.
The above methodologies of pressure loss calculation are widely used in 1D codes for the
estimation of the flow parameters at junctions of engine manifolds. The background theory
indicates that each of the pressure loss models needs to rely on a number of assumptions for
P a g e | 37
the derivation of the appropriate governing equations. The cycle-, or pulse-averaged
behaviour of the junctions is usually documented as an integration in the whole-engine
calculation. This information is indeed essential for engine performance calculations but it
does not focus on the way the losses affect the available energy in the exhaust manifolds.
The latter, however, is vital for instance to the turbocharger turbine operation, where the
pulse amplitudes and frequencies determine its efficiency levels under unsteady conditions.
A correct estimation of energy levels would also be essential for heat recovery systems from
the manifolds.
Recent increases in computing capabilities have also led to another route of enhancing 1D
codes’ degree of calculation accuracy and this is the 3D-1D coupling method. In this form,
the most complex points of the manifold, where the directional effects are significant, can be
calculated by a 3D model and then inserted into the 1D code for the simulation of the
complete engine cycle. Piscaglia et al. (2007) published a joint method to calculate the
exhaust flow in a Lamborghini 5-1 manifold (Figure 6) in which data was continuously
passed between the 1D and 3D model. With this technique Piscaglia and his co-workers
managed to obtain better results in comparison with the traditional 1D schemes (Figure 7),
but the simulation cost was still quite high. Although this approach is still at a primitive
stage, it seems to have great potential and, given the rapid advances in computational
resources, it is likely to form the near future of air flow modelling in IC engines.
Figure 6: Lamborghini 5 to 1 exhaust manifold 3D and 1D models (Onorati et al. 2005)
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1.2.2 Experimental work in manifolds
The understanding of the pulsating nature of the flow in the manifolds of engines and the
validation of proposed one dimensional methods for relevant calculations were supported by
experimental work conducted throughout the 20th century. The aim was to arrive at a design
that would aid the scavenging of the combustion products from the cylinder (Annand and
Roe 1974; Blair and Johnston 1970; Blair 1999). Wave reflections are generated in any
geometrical change of the pipes where an incident wave is propagating. Thus, in the early
days of manifold development, researchers would experiment with exhaust pipes of constant
diameter to pipes of successive changes of cross section area. Figure 8 shows three different
designs of an exhaust pipe to demonstrate the generation of rarefaction and compression
reflected waves at the expansion and contraction of the pipe area respectively. Both single
cylinder 2 stroke engines and rotating plates linked to air compressors have served as pulse
generation devices in the experiments conducted in the past. Pressure transducers fitted at
various stations in the pipes would record the evolution of the pressure levels during the
blowdown process.
Figure 7: Pressure traces comparison between the 1D,1D-3D methods and measured data at 3000rpm and 6500rpm
P a g e | 39
Pipe area changes, as well as open and closed ends that can be met in a system of pipes, can
be considered to be simple boundary conditions. A multi-cylinder engine would involve a
more complicated manifold shape with branching regions where the wave reflections are not
as straight forward. For the study of junctions, a set of three joining pipes was needed. As
different geometries would lead to different wave reflections and, as a consequence, to
different levels of pressure losses, a universal approach was sought, where the apparatus
would be modular to account for different manifolds. Usually the test manifold would be a
separate part that would be connected to a series of reservoirs with pressurised air and
vacuum pumps to control the flow direction through the manifold. Steady flow tests were
conducted in this manner and the pressure loss coefficients, mentioned in the previous
paragraph, were derived for joining and separating flows. A typical example of such an
apparatus for the derivation of flow coefficients is given in Figure 9, as in Bingham & Blair
(1985).
Figure 8: Blair's experiments in a single cylinder two stroke engine as reported in Annand and Roe (1974).
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Benson, Woollatt, and Woods (1963), had already identified the importance of
compressibility effects as well as the difference between steady and unsteady behaviour of
the flow in three way junctions. An experiment consisting of single cylinder pulse generators
connected in a row was used to study the behaviour of pressure losses. The arrangement was
supplied with pressurised air and an external motor would drive the camshafts, through a
variable speed motor, over a range of rotational speeds between 520 and 670 rpm.
Figure 10: Multi cylinder pulse generator of Benson Woollatt and Woods 1963
Figure 9: Branched pipe setup for steady flow tests (Bingham and Blair 1985)
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Shock tube tests
Most of the validation work of the 1D codes in recent years was achieved through shock tube
tests. A thin diaphragm is introduced inside one of the pipes comprising a three way junction
Figure 11(Pearson et al. 2006). The pressure upstream of the diaphragm (and the junction),
was then increased until the diaphragm would burst open, producing a steep wave front, a
shock wave. Pressure transducers were fitted at the pipes comprising the junction to record
the pressure propagation against time until an equilibrium state was reached. Through these
tests, the pulsating behaviour at the junction area could be studied for a wide spectrum of
wave amplitudes. Although these tests were more simplified as compared with engine tests,
these would include easily modelled boundaries that could be handled with more confidence
through the 1D codes. Under the same principle, the shock tube setup was constructed by
pipes of increased length, so that there would be no additional interaction with the end
boundaries of the manifold during the time that the data from the junction area would be
acquired.
The correlations of results from shock tube tests with 1D predictions are generally
satisfactory (Figure 12). In reality though, it is rare for shock waves to be present in engine
exhaust manifolds. For the validation of computational methods though, shock waves are
easier for the code to handle as they create point reflections instead of a series of successive
ones that interact with each other. On a separate note, shock tube tests could also allow for
the visualisation of the wave fronts, as will be discussed in the section to follow.
Figure 11: Geometry and pressure sensor positions of the shock tube test as in Pearson et al. 2006
P a g e | 42
Visualisation of flow in branched systems
The development of calculation algorithms for the junctions of manifolds was primarily
based on the wave dynamics of finite pressure waves established in manifolds. Nevertheless,
researchers highlighted that the phenomena attributed to the motion of the bulk flow should
also be included in the derivation of the equations, although this was not always feasible.
Along with experiments on pressure monitoring, visualisation work was also conducted in
pipe systems consisting of junctions. Studies in this field however, were not new to
researchers. Either by passive observation of water flow in nature, such as rivers and lakes,
or later by conducting controlled experiments, researchers were able to identify patterns in
the flow of channels and canals with flowing liquids. Measuring the pressure upstream and
downstream of any non-axial fluid structure in steady flow tests revealed that the latter are
associated with pressure losses. Miller (1971) was one of the researchers to conduct a
substantial number of tests with flow through pipes with bends and branches resulting in
lookup tables with measured pressure losses. These tables would include losses measured for
pipes of different diameters and bend curvatures and different angles amongst the pipes
comprising the branching junctions.
Schlieren and shadowgraph methods were also used in the study of the flow in pipe systems.
In these, the flow is backlit and a camera captures images of the flow structures which are
indicated by local density variations. Experiments with liquids under steady conditions using
Figure 12: Experimental and simulating pressure signals using two different models to represent the behaviour in junctions (Pearson et al. 2006).
P a g e | 43
this imaging technique are available in the literature and show the patterns developing on
joining and separating flows in three way junctions. Similar experiments were conducted
with air as the working medium, again under steady conditions by Abou-Haidar and Dixon
(1994), who studied the compressibility effects of the flow passing through the junction with
visualisation of the flow detachment at the outlet pipe of the junction. They also report the
presence of weak shock waves normal to the pipe on the free stream of the flow (Figure 13).
They derived total pressure loss coefficients which are higher for dividing rather than joining
flows.
A limited number of studies also exist for periodic flows (change of bulk flow
direction, zero mean velocity), but these are usually for liquids (Karagoz 1993) or for
examination of the flow in branches of human aortas (Pedersen, Yoganathan, and Lefebvre
1992). In an internal combustion engine, the exhaust flow is highly unsteady but not
periodic, although weak backflow can be observed due to propagation of rarefaction waves.
The visualisation of the pulsating flow of compressible medium was achieved through the
shock tube tests mentioned in the previous paragraph. Researchers at UMIST (Bassett et al.
1998; Pearson et al. 2000), using the Schlieren technique, were able to capture the adverse
density gradients due to the shock waves propagation in three way junctions using the
apparatus shown in Figure 14. The test manifold was modular so that the waves in a range of
geometries could be captured.
Figure 13: Visualisation of air flow through a T-90o junction showing weak shock waves at the horizontal (outlet) pipe (at the point where the detachment is half the pipe’s width) (Abou-Haidar, & Dixon, 1994)
P a g e | 44
Figure 14: Experimental apparatus in UMIST for the visualisation of shock waves in three way junctions (Bassett et al. 1998)
Figure 15 shows two images of shock wave reflections in a 45deg and 180deg junction.
These experiments were used for the extension of the 1D code to a 2D simulation of the
wave propagation in the manifold, so that more accurate results can be obtained. The
superiority of the method against the 1D was evident as it could account for non-
axisymmetric propagation of the waves resulting to a higher degree of accuracy.
Figure 15: Schlieren images of shock waves and their reflections on three way manifolds of 180o shape (left) and 45o shape with nozzle at the branch pipe (right).
The aforementioned experiments were performed to explain the pressure losses measured
based on the qualitative observation of the bulk flow patterns in the junctions. In a
quantitative manner though, where the velocity profiles have been studied, experiments are
very limited. Snauwaert & Sierens (1987) and Sierens & Flamang (1988) studied the flow
P a g e | 45
patterns across the junction for steady flow using the LDA technique without including
pressure measurements. Then, using the pulse generator of Figure 16, the unsteadiness of the
flow patterns at the cross section of the outlet pipe downstream of a junction was also
studied. This proved the presence of flow non-uniformities, secondary flows in the plane of
the cross section, at the velocity front of a pulsating flow passed through a manifold that
would explain the limitations of the accuracy achieved through 1D models.
Kalpakli and Örlü (2013) have recently studied the aforementioned same secondary vortices
at the cross section of a pipe past a 90° bend by means of Particle Image Velocimetry (PIV).
The superiority of the PIV method over Schlieren is that the flow is seeded with particles, the
position of which can be tracked through time. This would allow for the calculation of
Figure 16: Experimental apparatus of a pulse generator with rotating plates (left) and the results of the flow field (velocities in m/s) as obtained from the LDA technique -25mm and 12mm from the outlet pipe (right) (Snauwaert & Sierens 1987; Sierens & Flamang 1988).
P a g e | 46
velocity magnitudes for the flow resulting in a quantitative analysis of the flow field. The
flow had pulses generated by a rotating slotted plate. Observations in Kalpakli's work
indicated that a single 90 degree bend would have an immediate effect on the velocity front
that enters the volute of a turbocharger turbine. These effects, along with the unsteady
turbocharger modelling in 1D software packages, will be discussed in the following
paragraph.
As a concluding remark, the experimental work available in the literature has quantified the
pressure loss coefficients and developed the empirical and semi-empirical models
incorporated in the 1D codes. Studies of shock waves and reflections in the pipes as well as
the effect of recirculation zones in the pressure losses of steady flows has highlighted the
Figure 17: PIV results of the flow field at the cross section downstream a 90o bend under pulsating flow. Experimental setup (above), PIV results (below) (Kalpakli & Örlü 2013).
P a g e | 47
importance of the inclusion of both phenomena for the accurate calculation of losses in
manifolds. As was demonstrated however, the available studies focus on the two phenomena
independently, targeting the unsteadiness with pulsations travelling through the manifold or
studying the bulk flow structures in steady conditions. Distinguishing the two was often not
possible owing to the limitation of experimental techniques used, or a deliberate
simplification so that the validation of the 1D codes could be made possible using
experimental setups that could easily and accurately be modelled using a 1D approximation.
The recent work using LDA and PIV techniques revealed the potential of further
investigations in the pulsating flow taking both phenomena into account. Experiments with
qualitative information about the unsteady pulsating compressible flow in manifolds are not
known to exist in the open literature. This is a topic, which will be addressed in the current
thesis.
1.2.3 Turbocharger turbine modelling
The turbocharger turbine, being essentially an energy recovery system, comprises the
downstream boundary condition of the exhaust manifold of most compression ignition
modern engines, and increasingly for spark ignition engines since the downsizing trend has
emerged; as such, it is the recipient of the pulsating flow travelling down the manifold.
Although the current thesis does not focus only on turbocharged engines, a brief summary on
the 1D modelling of turbines and their behaviour under pulsating manifold flow will be
given in this chapter to allow for a complete study of the utilisation energy available in
exhaust gases. The turbine volute and rotor constitute of a complex boundary condition that
responds to the exhaust pressure waves travelling downstream of the manifold. As it was
demonstrated in the previous paragraphs, the representation of complex boundaries in an 1D
approximation is not trivial, while assumptions for the flow are necessary for the closure of
the system of governing equations.
The turbocharger turbine operating principle is to utilise the enthalpy of the exhaust
gases to drive the compressor and it is designed and optimised for uninterrupted feeding flow
and under steady conditions. As a result, the study and development of turbochargers is
normally based on experiments carried out in steady flow gas stands. Characteristic maps are
produced through these tests which depict the measured pressure drop for a spectrum of
P a g e | 48
mass flow rates. The turbine characteristic map covers both low and high load points and it is
widely used by the IC engine manufacturers seeking a match between the engine and the
turbocharger. As might be expected, the turbo-matching is mainly a result of the comparison
of mean pressure levels upstream and downstream the turbine; i.e. exhaust manifold and
tailpipe. However, the pulsating flow that the turbine encounters when connected to the
engine exhaust manifold may give poorer efficiency and energy recovery capabilities
compared to the ones anticipated from the characteristic maps, since the available energy is
transported to the turbine in a fragmentary way. This observation initiated the interest of
wave propagation studies in the turbine itself, so researchers developed test rigs that could
generate pulsating flow upstream of the turbine (A. P. Dale 1990; Kalpakli 2012). One of
the first questions that needed to be clarified was how a pressure wave propagates through
the turbine, since until that time the turbine was assumed to operate on a quasi-steady
manner and it was being modelled as such. Dale & Watson (1986) published their work on
turbine testing under simulated engine conditions. They were among the first to overcome
technology restrictions and measure all parameters in a time-varying basis rather than mean
quantities. Their work proved that there are differences in the turbine’s performance between
steady and pulsating flow tests resulting in different operating characteristics. The most
obvious deviation was the operating loop of the characteristic maps, revealing that there is
accumulation and discharge of mass flow along a single pressure pulse (Figure 18). Thus, the
quasi-steady assumption used until then in simulations for the turbocharger had to be
rejected.
Figure 18: Operating loop in unsteady flow operation in comparison with the steady flow characteristic (Szymko et al. 2005)
P a g e | 49
The study of pulsating flow in turbines is a broad and still challenging topic for researchers.
As far as exhaust manifolds are concerned, the interaction of waves with the turbine is
important and the same is true for the time-varying (in-cycle) energy levels available at the
turbine inlet. The inclusion of the turbine in 1D codes is most commonly being done by
modelling the volute and the rotor independently; the volute being responsible for the wave
reflections and the rotor for the pressure drop. This was supported by the findings of
researchers, such as Yeo & Baines (1990), who measured velocity traverses and flow angles
on the rotor inlet of a turbine under steady and pulsating flow. These were found to be
comparable, therefore, a quasi-steady approach such as the emptying and filling methods
would be appropriate. Available work in the literature for the turbine volute modelling
usually uses a pipe of equivalent length, which can be either of constant diameter, tapered or
even curved (Chen, Hakeem, and Martinez-Botas 1996; Hamel, Abidat, and Litim 2012;
Chiong et al. 2012; Costall et al. 2011). The rotor is modelled as a point of pressure drop as
represented by an orifice plate. Each of the methods has some advantages compared to the
pure quasi-steady approach, but the results, as presented in the literature presented above, are
not entirely satisfactory for the accurate prediction of the instantaneous unsteady turbine
operation.
In the current state of 1D models, both filling and emptying methods as well as wave
theory are used in the calculation algorithm for the prediction of turbine operation. The
transition between the two methods so that both the reflections and the mass accumulation in
the volute can be modelled is not clear for each of the commercial packages available. The
transition, however, is dictated by the operating point of the engine, load and speed, and the
significance of the unsteadiness of the flow.
Figure 19: Different modelling ways for the turbocharger turbine volute. The rotor is modelled as an orifice plate (Chiong et al. 2012)
P a g e | 50
Abitat et al. (1998) worked on different amplitudes and frequencies of pulsating flows and
the conclusion was that the amplitude seems to have a stronger connection to the turbine’s
performance than the frequency. In fact, he observed that increasing amplitude over the same
frequency lead to a decreasing mass flow rate through the turbine, while he reported that the
output power seemed to be linked with both frequency and amplitude pulse characteristics.
Hu & Lawless (2001), during their experimental validation of unsteady turbine operation,
used Fourier decomposition to analyse the effect of the harmonics of unsteady inlet flow on
the efficiency of the turbine. They concluded that, even the addition of the 1st harmonic to
the steady flow inlet boundary condition, could alter the maximum efficiency level as well as
the mass flow rate where the maximum efficiency was observed (Figure 20).
In his review paper on the topic, Baines (2010) expressed the belief that the instantaneous
operation of turbine cannot be predicted in the form of characteristic maps as on Figure 18.
Instead a different approach must be sought, which relates more to the energy level or the
instantaneous work of the turbine rather than the swallowing capacity under specific pressure
ratios. Winterbone & Pearson (1999) suggested the so-called ‘turbine work function’, which
is calculated as the amount of the 'useful' energy, the exergy, of the exhaust gases at every
point inside the manifold upstream of the turbine. The turbine work function, which is
identical to the isentropic turbine power reads:
Figure 20: Comparison of mean value and unsteady efficiency by adding harmonics (left). Comparison of efficiency curves (right) (Hu & Lawless 2001)
P a g e | 51
�̇�𝑖𝑠 = �̇�𝑐𝑝𝛥𝑇𝑖𝑠 = �̇�𝑐𝑝𝑇1 {1 − (𝑝𝑜2
𝑝1)
(𝜅−1)/𝜅
} (27)
where suffix 2 relates to upstream conditions and suffix 1 relates to conditions downstream
of the turbine. If the turbine is of twin-scroll design, the overall turbine work function is the
sum of that from each entry.
The equation above represents the work that could be obtained from the exhaust gases from
any given point in the manifold (upstream of the turbine), if they could isentropically expand
to atmospheric conditions. Therefore, the upstream conditions (suffix 1) can be determined
to be directly at the turbine inlet or further upstream in the manifold (i.e. before a junction
point). Comparison between the two functions will give the energy loss in the manifold.
Figure 21 shows the enthalpy-entropy diagram for the flow in the engine.
Figure 21: Enthalpy-entropy diagram for the available energy in exhaust manifolds (Winterbone and Pearson 1999)
The suffix ‘c’ refers to in-cylinder conditions and the suffix ‘exh’ to the exhaust directly at
the inlet of the turbine. It can be seen that the amount of energy, which is unavailable, varies
with the entropy of the exhaust gases (Temperature / isothermal line). The more to the right
is hexh , the less energy will be available to be extracted from the turbine and therefore the
more energy will be lost in the exhaust manifold. In most studies, the pulsating behaviour
upstream of the turbocharger turbine is generated through rotating ball valves or slotted
P a g e | 52
plates that are incorporated in gas stand facilities. Although this approach is capable of
recreating unsteady periodic inlet boundary conditions, it is not clear whether these are
indeed representative of engine-like pressure pulses. The pressure pulses in ducting systems
of finite length are subjected to the acoustic waves which are superimposed to the main
exhaust pulses. The effect of the latter on the resultant shape of the pressure signals
generated by poppet valves will be studied in the present work. The energy losses inside the
manifold however are associated with the irreversibilities due to complicated flow structures.
The relative importance of the two phenomena and their effect on the pressure downstream a
junction of the manifold will also be addressed in the present work.
1.3 Present contribution
The limitations of the existing one dimensional tools for the calculation of pulsating exhaust
flow in manifolds along with the supporting experimental work for their validation were
presented in the previous section setting the framework for the current thesis. The inherent
loss of information due to the use of 1D approximations is tackled by the inclusion in the
governing equations of pressure loss coefficients and appropriate assumptions for the flow
behaviour. The majority of coefficients are obtained from experimental tests under steady
flow conditions. Experiments with unsteady flow are mostly limited to shock tube tests for
the calculation of pressure losses, while the bulk flow visualisation work available is limited
to observations of flow patterns in a qualitative manner; the latter being mostly focused on
incompressible media. Unsteady conditions in the non-shock tube experiments available in
the literature are usually formed by the use of pumps and reservoirs or rotating plates
producing pressure pulses with duration and amplitudes that may not be related to engine
conditions.
The motivation of the current work was to develop an experimental apparatus that can
more closely mimic the conditions met in exhaust manifolds of engines and overcome some
of the constraints of previous work regarding the validation of 1D algorithms against a wide
spectrum of engine-like pulses. For this reason, an experimental setup that contains single
cylinder engine heads with poppet valves has been developed and the measured data of the
pulsating flow acquired from a test three-way manifold include both pressure and velocity
measurements using the PIV technique. In this way, the experimental setup aimed to study
P a g e | 53
the energy losses in conjunction with pressure pulse propagation, rather than focusing only
on pressure. Such a study was made possible through the quantitative analysis of the flow
field from the PIV results of isothermal pulsating flow through the test manifold. In the
following chapters, the experimental data at a spectrum of load and speed points (950-
2000rpm) and for a range of outlet idealised manifold boundary conditions (open and partly
restricted end) were studied and compared with the simulation results produced by widely
used commercial 1D algorithms. The orifice restriction on the outlet boundary was chosen to
resemble, in an idealised way, the effect of the turbocharger turbine rotor as a point of
concentrated pressure loss. This choice stems from the analysis of the 1D modelling methods
that were presented in the previous section.
An open source computational fluid dynamics program was also used to simulate the 3D
compressible pulsed flow behaviour and the solution was compared with the experimental
findings. The results of the experimental work indicate that the deviations of the simulations
from experiments are mainly attributed to the acceleration of the flow and the mass
accumulation in the junction and pipes of the manifold depending on the phase of the pulsed
flows. Furthermore, the spatial non-uniformities of the magnitude and direction of velocity
and of pressure and density at the junction area also affect the accuracy of simulated results
in both 1D and 3D CFD. Pressure losses in all cases tested are calculated throughout the
duration of the exhaust pulses indicating the phases where the deviations are more severe.
The deviation is also presented in a time resolved manner.
As was stated in the literature review, the exhaust manifold is part of the energy recovery
system of the engine transmitting the exergy from the cylinder head to the components
downstream, including the turbocharger turbine. Correct quantification of energy losses is
vital for the design stage of the engine, which is primarily dependent on the accurate
calculation of pressure losses through the 1D codes. This thesis aims to give a more clear
view of the reasons for the deviation of the results currently obtained from 1D codes and to
link them with specific physical processes. It also presents quantitative pressure and velocity
results of the pulsed flow in junctions of manifolds. A fully 3D simulation of the flow
through the engine's air path system will remain computationally expensive in the near
future. Therefore, quantification of projected accuracy in 1D calculations, or at least the
quantification of the expected inaccuracies, is valuable.
P a g e | 54
1.4 Thesis outline
The thesis is divided in six chapters that cover the literature review, the experimental setup
and the measured data as well as the comparison with both 1D and 3D simulations.
The current chapter summarised the previous contributions to the development of 1D
codes and the experimental work both in terms of pressure measurements and flow
visualisation. A brief review of the turbocharger turbine modelling is also included, where
the relevant information to the manifold design and operation under pulsating flow are
presented.
The second chapter contains all the information regarding the development of the
experimental apparatus to mimic the pulsating flow inside an idealised three way manifold.
The instrumentation and the calibration of the rig are also presented in the same chapter.
The third chapter includes all the experimental results from the newly developed
experimental setup for pulsed flows in exhaust manifolds. It is divided in two main sections.
The first one is dedicated to the pressure measurements obtained for a spectrum of rotating
engine speeds (950-2000 rpm), load points and three different outlet boundary conditions.
The second section shows the velocity contours and profiles inside the exhaust ducts, as
obtained from the PIV technique.
Chapter four presents the comparison between the experimental results and simulations
with two widely used 1D software packages. These two packages use a different approach
for the calculation of the junction subroutine, therefore it was regarded necessary to include
both in the analysis. Deviations between experimental and simulated results are presented as
a function of time, so that the instantaneous behaviour of the flow and the pressure losses can
be studied.
The fifth chapter includes comparisons between experimental test cases and
computational results using the CFD software “OpenFoam”. The geometry of the test
manifold has been used to create the appropriate mesh for the cases in which the boundary
conditions are extracted from the experiments.
The final chapter summarises the findings of the present work both in terms of the
experimental results as well as presenting the conclusions from the comparisons with
simulations. It also discusses the potential of energy recovery from the exhaust gases in
engine manifolds along with proposals for future work.
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Chapter 2
Experimental arrangement and instrumentation
2.1 Introduction
The chapter presents the experimental facilities and instrumentation used in the current
research. As seen in the literature review, most of the experimental work in the field of
exhaust flow in manifolds relies on arrangements where the operating conditions often
deviate from those met in a typical Internal Combustion Engine (ICE). The most common
deviation is due to the generation of the pulsed flows, which is realised through bursting of
diaphragms, vacuum pumps or rotating plates, interrupting the flow through ducts. The
plates having slots placed at specific circumferential locations so that the duration of the
passage of the slot across the duct corresponds to that of the valve being lifted from its seat.
All these methods tend to generate pulsed flow, but which may have different shape and
initial amplitude of pressure that are different from those in the exhaust manifolds of ICEs.
In the current work, the use of poppet valves was considered necessary to better mimic the
flow structure and pulse shape that enters the exhaust manifold. This approach is known to
be used for the first time in the study of modelled exhaust gas pulsed flows.
The working medium was pressurised air coming from the laboratory facilities so that the
effect of compressible flow phenomena can be studied. The setup was modular to account
for a range of different manifold geometries. For the present work, a three-way manifold of
T60o shape was manufactured from transparent Perspex material for visualisation and PIV
purposes. For the latter reason, a mist of droplets was also introduced in the flow, upstream
of the pulse generator, to serve as the tracking particles for the PIV velocity measurements
P a g e | 56
and for visualisation purposes. Monitoring of instantaneous pressure was made possible
using high speed transducers at a number of positions along the manifold length. Overall, the
developed configuration fulfils the purpose of this research study to provide a comprehensive
view both in qualitative and quantitative manner of the apparent energy losses in junctions of
manifolds using the pressure data along with simultaneous measurements of the velocity
field on the symmetry plane of the junction.
2.2 The experimental arrangement
2.2.1 General description
The complete experimental configuration consisted of two independent engine single
cylinder heads positioned on two vertically mounted 'plena' that represent the cylinders
(Figure 22). An electric motor that rotated the camshafts was placed on the side of the engine
heads. A transparent planar test manifold of T60o geometry with square ducts was mounted
at the exhaust port of the engine heads. The dimensions and information on the
measurements obtained from the manifold will be given in the relevant section below. The
inlet valves of the engine heads were disabled so that the flow came through the plena. The
working medium was compressed air delivered from a central compressor with maximum
delivery of 1kg/s at 7 bar, which was fed to the lower part of the two plena through dedicated
pipework. The air is regulated through electrically actuated ball valves, which were
controlled through a custom written LabView programme. The optical arrangement for the
PIV measurements consisted of a laser head that emitted a circular laser beam at a
wavelength of 532nm, which was then transformed to a thin laser sheet through a series of
optical components. The details for all components of the experimental setup, control and
instrumentation will be presented separately in the following sections.
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Figure 22: Schematic of the experimental rig assembly
2.2.2 Pulse generator
For the pulse generation, two nominally identical engine heads from Honda BK-7 single
cylinder engines 4-valve were used. The engine heads were equipped with a pair of exhaust
and a pair of inlet valves with the latter being completely disabled (permanently closed) for
the purposes of the current study by removing the relevant rocker arms. The single cylinder
engines are identical with the cylinders of a 4 cylinder Honda VTEC engine with 1.4 L
capacity, allowing more accurate replication of engine pulse shapes than those produced by
rotating slotted plates or ball valves. Figure 23 shows the engine head and the valve profiles.
The two engine heads were connected through a pulley assembly with a 2:1 speed reduction
ratio to an electric motor (TECO) of 1.1kW Power and variable speed (up to 2800 rpm). The
motor was directly controlled through an ABB controller to limit any speed variations due to
fluctuations of the supplied current.
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A quadrature (X4) incremental rotary encoder (WDG58B, Wachendorff) delivering a TTL
signal was used to measure the rotational speed of the common shaft rotating the two
camshafts of the cylinder heads. The operating range of the encoder was 4.75-5.5V and it
was connected to a 9401 digital IO module giving an angular position accuracy of 0.1
degrees, when all channels A, B and Z were used. One of the two heads was also connected
to an indexing plate to indicate its phasing relative to the other engine head (Figure 24). The
indexing plate allowed for a phasing step of 3 degrees (camshaft) between the two heads, so
that different valve schemes (positive or negative overlap) that replicated the sequence and
interference of exhaust pulses of 3, 4 or 5-cylinder engines could be studied. The adjustment
of the valve phasing scheme was achieved manually by locking pin in the relevant position
of the indexing plate. Therefore the phasing was adjusted to the desired value (0 to 360
camshaft degrees) before the start of each experiment and not on-the-fly.
Figure 24: Indexing plate to adjust the phasing between the heads every three degrees.
Figure 23: Engine head from single cylinder Honda BK-7 engine (left) and valve profiles (right) (Yasuhiro Urata and Kazuo Yoshida at HONDA, personal communication, 2016).
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The two engine heads were placed on top of two plena of 30 litre volume each with vertical
exhausts. The bottom ends of these plena were connected to the compressed air supply of the
laboratory. In this sense, when the exhaust valves were closed, each plenum formed a closed
tank in which pressure rose until the following exhaust blowdown event occurred with the
opening of the poppet valves. The pressurised air supply of the facilities had a maximum
delivery of 1kg/s at 7 bar, which was enough to cover the cylinder pressure at the crank angle
corresponding to the opening of the exhaust valves near bottom dead centre of the expansion
stroke for the likely load points met in the exhaust manifold of an ICE. The volume of each
plenum was big enough to allow for the position of the flow seeding units (necessary for the
PIV method) and to allow for the attenuation of the pressure waves reflected from the
opening and the closing of the poppet valves. The latter would affect both the pressure
monitoring in the plena and the uninterrupted flow field around the seeding unit,
compromising the operation and potentially the accuracy of measurements. To control the
pressurised air supply inside the plena an electrically actuated ball valve (J3-2015, V-Flow
Solutions) was fitted in the pipe supplying the entrance to of each plenum. The ball valves
had a modulating position system and operated over an actuated voltage 0-10V DC. The two
valves were connected to the main Data Acquisition (DAQ) chassis to the 9215 16-bit
Analogue Input module and the 9263 16-bit Analogue Output module, in order to be able to
read the position and actuate the ball valve motor until the pressure inside each plenum
reached the desired level when the exhaust valve was closed. The pressure inside each
plenum was monitored through relative pressure transducers (PU5404, ifm electronics) with
0-10V output voltage, measuring a range of 0-10bar with a full scale accuracy of 0.5%. The
two pressure transducers were connected to the 9263 16-bit analogue module and had a
response time of 1ms resulting in 1kHz sampling rate, which was considered adequate for
the monitoring of the in-plenum pressure.
2.2.3 Test manifold
The experimental apparatus was modular, so that a range of different three way manifolds
could be tested. The distance between the two exhaust ports of the cylinder heads was fixed
at 250mm, which was the only dimensional constrained in the design. A T-shaped manifold
of 60 degrees branch angle was considered appropriate for the tests, since it is well
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documented in the literature and it also involves an impinging type of flow when the branch
pipe feeds the junction resulting in the flow deviating from the axisymmetric direction. The
test manifold was placed on the left hand side of the rig attached to the exhaust ports of the
two engine heads. The feeding pipes of the manifold had a constant square cross section of
25mm x 25mm throughout. The use of square ducts was selected to avoid the distortion of
images captured during the PIV measurements, as it will also be explained in the relevant
chapter. Furthermore, use of square ducts would result to the reduction of the phenomenon
under consideration essentially to two dimensions, which could not be achieved by the use of
circular pipes. This approach reduced the parameters that affect the accuracy of the
calculated flow resulting to a more direct comparison of the measured data with the results
from one dimensional models and CFD simulations.
The manifold was made of transparent Perspex material for visualisation purposes. It was
manufactured from two sheets of Perspex which formed the two walls parallel to the
symmetry plane while the walls perpendicular to this plan were fabricated as panels which
fitted into slots engraved into the T60° shape, as seen in Figure 25. Flanges at the upstream
entrances permitted the connection to the cylinder heads. The feeding pipes of the manifold
had a 2:1 length ratio and the outlet pipe was of 495mm long. A number of tapings for
pressure sensors were placed at the bottom wall of the manifold to allow for pressure
monitoring upstream and downstream of the junction; the exact stations are shown in Figure
25 as a function of the cross section width (DIA=25mm). High speed miniature (M5 size)
piezo-resistive absolute pressure transducers (4700C, Kistler) were used to measure the
instantaneous pressure simultaneously at three positions. Figure 26 shows the taping positions
that were selected and the notation used throughout this thesis. The sensors had a measuring
range of 0-10bar and sensitivity of <1% at FSO. Each sensor had its own amplifier unit,
which output 0-10V DC to a 9222 16-bit BNC Analogue Input module with 500kS/s
maximum sampling rate.
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Figure 26: Pressure tapings (stations) that were used for the instantaneous pressure measurements. The notation of ducts and stations of the present figure is also followed throughout the thesis.
To alter the boundary condition downstream of the junction orifice plates - of variable
diameter - could be attached at the exit of the 495 mm section manifold. As stated in Chapter
1, the turbocharger turbine is modelled in 1D calculations using a pipe extension to represent
the length and volume of the volute, so that the frictional losses and the overall length match,
to some extent, the actual design, while an orifice plate models the termination of the
acoustic waves reflections and also models the drop of pressure which occurs in the
turbocharger rotor. A similar approach was adopted for the experimental manifold design
where orifice plates were placed at the end of the Perspex manifold. Two different orifice
plates were used with 20 and 14.5mm hole diameters providing a geometrical restriction of
Figure 25: (Left) Isometric view of Perspex manifold assembly resulting in a three way junction geometry with square ducts of 25mm x 25mm cross section. (Right) basic dimensions at the top view of top surface along with sensor tapings where DIA=25mm
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20 and 42% respectively. A tailpipe of 40mm length was also placed at the end of the
Perspex manifold downstream the position where the orifice plates were.
To assemble the test manifold to the pulse generator a set of transition parts from the oval
shape exhaust port of the exhaust port to the smaller square duct manifold were necessary.
Figure 27 shows the top view of the design of the manifold assembly mounted to the pulse
generator where the position of the transition parts is visible.
Figure 27: CAD top view manifold assembly mounted to the pulse generator
To avoid flow separation inside this section of the flow, the theory for the design of low
speed small wind tunnels was used (Mehta and Bradshaw 1979; Morel 1977; Bell and Mehta
1989) and specifically the use of 5th order polynomials was implemented, as proposed by
(Bell and Mehta 1988), in order to design the appropriate curve profile for the contraction, as
seen in Figure 28.
2.3 Flow seeding and optical arrangement
Figure 28: Transition part from the exhaust port to the manifold ducts (right). The chosen profile (profile B-left) follows the guidelines of Bell and Mehta (1988) theory for gradual contractions
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2.3.1 Flow seeding
The seeding of the flow with particles, required for the PIV velocity measurements was
achieved with the use of humidifier units (AB SIBE International) that created a mist of
water droplets of approximate 3μm diameter. There was a separate seeder for each of the two
manifold branches, which were placed inside the lower part of each plenum respectively.
The mist of droplets was introduced in the flow upstream of the exhaust valves, so no
additional mass of air was added in the test manifold during the experiment past the
formation of the exhaust pulses, since this would result in deviation from the operation of
real engines. The seeders (Figure 29) produced a mist of droplets in a cone shape the angle of
which was adjusted to avoid direct impingement of the mist on the inner walls of the plenum,
since this would create liquid deposition inside the plena and form water films that could be
carried into the test manifold. The cone shape of the droplet mist was formed when the
already finely dispersed aerosol mist exiting from the nozzle impinged on the resonator tip at
high velocity. The optimal operating point of the seeders, as indicated by the manufacturer
was achieved for water flowrate of 50cm3/min and air flowrate of 40L/min at a working
pressure of at least 5bar.
Figure 29: Humidifier that produces the necessary mist to seed the flow inside the plena (left), schematic with position inside the plenum
The flow rates for the seeder operation were controlled through two nominally identical
circuits, one dedicated to each seeder. These circuits were equipped with pressure gauges for
both water and air lines. Two air supply rotameters were used with flowrate range of 0-
100Lmin-1, calibrated by the manufacturer (Roxspur Measurement & Control Ltd), which
gave an accuracy of 5% of full scale deflection. The water rotameters, also calibrated by the
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manufacturer (Key Instruments), had a flowrate range of 20-300cm3/min while giving an
accuracy of 4% at full scale deflection. The operating point of the seeders for optimum
quality of the mist also dictated the range of operating points of the pulsed flow rig.
2.3.2 Particle Image Velocimetry (PIV) and optical arrangement
The PIV system consists of a New Wave Nd:YAG double pulsed laser, rated at 120mJ
maximum energy, delivering a round beam of 4mm diameter at 15Hz repetition rate. The
laser beam was transformed to a thin laser sheet of approximately 100mm length and 2mm
wide. This was achieved by the use of a round convex lens of 25mm diameter and a focal
length of 500mm to focus the beam on the stream-wise axis of the main duct of the manifold
and a concave lens of -12.5mm focal length and 12.7mm diameter to transform the round
beam to a laser sheet at the horizontal plane of symmetry of the duct, as shown on Figure 30.
The laser sheet intersected the transparent manifold in the symmetry plane, upstream and
downstream of the junction area, so that the evolution of the flow in the manifold could be
measured.
Figure 30: Schematic of top view of optical arrangement. The circular beam was turned through 90o by a mirror, then passing through a focusing convex lens (f=500mm) and a concave lens (f=-12.5mm) that transformed the beam to a laser sheet
The illumination scattered by the seeding particles was captured with a CCD camera (non-
intensified LaVision Imager Intense) with a resolution of 1376 x 1040 pixels using a 35mm
1:1.8 lens with manual focus. A monochromatic band pass optical filter for 532nm
wavelength (Edmund Optics) with a bandwidth of 10 nm was attached to the camera lens to
eliminate any light emitted from other sources rather than the laser head. The field of view of
the camera and hence the image real dimensions were 95mm x 74.5mm and the resulting
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spatial resolution was around 71 μm/pixel. To capture both the upstream and, most
importantly, the downstream part of the junction area in the exhaust manifold, the camera
was moved between two positions giving the two overlapping fields of view, A and B, as
indicated in Figure 30. Capturing a larger area of the flow simultaneously would have been
possible, but at the expense of the final spatial resolution. As seen in Figure 31, there was an
overlap between the two fields of view which allowed the cross validation of the flow field
results as all test cases were repeated for both camera positions.
Figure 31: Field of view of the camera for position A (outlet pipe) and position (B) (junction)
The image processing was achieved through commercial software (LaVision Davis 7.2)
using a cross correlation method. The details of the method, including the selection of
interrogation windows and the multiple passes calculation procedure that was followed, will
be given in Chapter 3 that discusses the results from velocity measurements.
2.4 Test rig control and acquisition method
The overall control of the experimental setup apart from the adjustment of the valve phasing
(Figure 24) was achieved through a custom written LabView interface to operate a DAQ
acquisition system from National Instruments using a 9178 chassis, where all the relevant
modules were attached as outlined in the previous section.
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The rotational speed of the motor was set through the ABB controller and the encoder
signal was used to output, back to the LabView interface, the actual speed. The pressure
monitored from each plenum was controlled through adjustment of the position of the two
electrically actuated ball valves. Instantaneous pressure monitoring in the manifold was
sampled at 50kHz and the encoder at 200kHz. The three pressure signals (Figure 26) and the
encoder signal (1 per rev) were shared on the same graph. Prior to each set of experiments
the repeatability of the pressure pulses from the pulse generator was checked through an
algorithm in Matlab, which read the output pressure signals and the encoder signal to
produce an average pulse over a number of between 15 and 20 pulses in the sample. Then,
the average pulse was compared to arbitrary pulses of the same sample to check for the
presence of cycle-to cycle variations.
For the PIV measurements, the laser and the camera were triggered once per
camshaft revolution to obtain each pair of images. The process followed was the double
frame/single exposure in which the camera was triggered once, but there were two laser
pulses occurring, resulting in two images being stored. This is an established practice for
PIV measurements, where half of the camera sensor cells are used to capture each image so
that the end result is two different frames with a single camera exposure. The triggering of
the camera and laser was controlled through the LaVision Davis software (v7.2), which in
turn was externally controlled through a TTL signal, so that it can be correlated with the rest
of the experimental measurements. This TTL signal was provided from the Labview
interface giving a square pulse of 100ms pulse width once per camshaft revolution. The
specific approach enabled the acquisition of a pair of images once per revolution timed
according to the encoder signal of the camshaft. To achieve a statistically significant sample,
a number of pair of images between 300 and 500 was captured for each operating condition
and pulsed flow timing. In order to change the phasing of image triggering relative to the
pulse the Davis software generated a delay (tuned by the user) which was relative to the
initial triggering point (rising edge of the triggering TTL signal). Figure 32 shows the TTL
signal that triggers the Davis software as an overlay to the pressure signal of the lateral pipe
and the laser pulse occurrence with a 10ms and a 20ms of the aforementioned user defined
delay. The TTL signal for the acquisition triggering and the laser pulse signal were shared
with the 9222 Analogue Input module, where the pressure sensors were also connected. In
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this way, the overall data, stored during the acquisition, contained information not only for
the instantaneous pressure in the ducts but also the exact timing for the image capturing.
Figure 32: Pressure signal (red), laser timing TTL pulse (green) and acquisition triggering TTL pulse (blue) for a fixed delay of 10ms(left) and 20ms(right) relative to the rising edge of the triggering TTL pulse (blue).
2.4 Summary The present chapter outlined the experimental apparatus that was developed to study the
pulsating flow phenomena inside three way manifolds. The work in this thesis focused on the
study of a planar T60o manifold: however, the setup was modular so that the manifold could
be replaced by other geometries. The pressure pulses that propagated in the manifold were
generated through poppet valves of two independent single cylinder heads. The design
allowed for the phasing between the valves of the two heads to be altered by increments of 3
camshaft angle degrees so that effects of pulse interference in the manifold could be studied.
Three pressure transducers were used to obtain instantaneous pressure measurements from
each of the three ducts comprising the manifold to study the in-cycle pressure losses across
the junction. Seeding particles were introduced in the compressed air upstream of the
manifold. These were illuminated by a laser sheet and PIV images of the flow field were
captured at different instances/phases of the blowdown pulses. The images were obtained in
the plane of symmetry of the manifold so that the flow field through the junction could be
obtained. The processing of the results both from pressure and velocity measurements will
be presented in the corresponding sections of the following chapter.
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Chapter 3
Static Pressure and Velocity Measurements
Instantaneous static pressure measurements in the field of engine manifolds are amongst the
least intrusive types of measurement and hence it has been widely used for the development
and calibration of simulation tools for engine calculations. The same however is not always
true for parameters like total pressure or instantaneous temperature of the fluid. The present
chapter focuses on the experimental work in three way manifolds where non-intrusive types
of measurements of the exhaust flow were obtained i.e. static pressure measurements and 2D
Particle Image Velocimetry (PIV) velocity measurements of the pulsating exhaust flow in a
T60 planar manifold.
As was described in Chapter 1, static pressure measurements have been linked to the
calculation of pressure and energy losses in manifolds through the development of 1D
simulation tools that predict exhaust flow and turbocharger turbine performance. Full
characterisation of the exhaust flow requires information on pressure, velocity, density and
temperature of the fluid. Nevertheless, these parameters are not independent but related to
each other through conservation laws. It is common practice for simulations to focus on the
accurate prediction of static pressure while deriving the rest based on a number of
assumptions for the flow (as illustrated for different models in Chapter 1). A representative
example is the flow at a sudden step expansion where the static pressure does not fully
recover, resulting in the dissipation of mechanical energy into rise in fluid’s temperature.
The latter shows that the reduction of available energy (exergy) at the turbine inlet can be
estimated through the static pressure losses and the calculation of the remaining parameters
of the fluid.
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This chapter presents the static pressure measurements for the calculation of pressure losses
while it also employs PIV velocity measurements to explore the validity of assumptions for
exhaust flows commonly used in 1D model predictions. The results from the static pressure
measurements are presented first and include three parametric studies based on speed, load
and exhaust valves phasing. Orifice plates were placed and adjusted at the outlet of the
Perspex manifold so that the outlet boundary condition (BC) could be altered and its effect
on the propagation of the exhaust blow down pulses could also be studied. The interest in
studying the latter stems from the approach of the 1D algorithms outlined in Chapter 1,
where the pressure drop owing to the turbocharger’s turbine rotor, is modelled by using an
orifice plate (usually calibrated against the turbocharger’s map). The analysis of the results
from the static pressure measurements focuses on the effects these parameters (speed, load,
valve phasing and BC) have on the pulses’ shape and the pressure losses in the manifold
under the conditions tested.
The latter part of the chapter is dedicated to the velocity measurements as these were
captured through the 2D Particle Image Velocimetry (PIV) method. Following the BC study
performed for the pressure analysis, the PIV measurements were also obtained using orifice
plates attached at the outlet of the manifold. Comparative cases based on operating speed and
load were also performed for a fixed phasing between the exhaust valves. Images of the flow
field on the horizontal plane of symmetry of the manifold were acquired at a range of phases
during the pulse duration. Then, velocity vectors were computed through the cross
correlation method so that a quantitative analysis of the flow field could be obtained.
Particular focus was given to the outlet duct where separation of the flow arose due to the
geometry of the T60o manifold. The qualitative and quantitative analysis of the flow
separation with the formation and break-up of a recirculation region is also presented in this
part of the Chapter, which has the objective of calculating of the losses due to the diffusion
of the flow past the point of the maximum height of the recirculation region.
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3.1 Pressure measurements
3.1.1 Overview of the test cases
The propagation of pressure pulses in branched systems is primarily affected by the energy
contained in the incident wave (i.e. the exhaust pulse), the dimensions of the pipe system that
the pulse propagates through and especially the length of the pipes and any geometrical
changes where wave reflections occur, such as at changes in cross sectional area or junction
points. In the present study, as has also been stated in Chapter 2, the cross sectional area of
each duct in the manifold has been kept constant in an attempt to isolate the effect of the
junction as the main point of wave reflection before the outlet end. The ability of the
experimental setup to be adjusted for a range of phasing between the opening of the valves
by the use of the indexing plate allowed the study of the effect of pulse interference. Two
different scenarios were investigated, namely a negative and a positive overlap between the
two exhaust valves (Figure 33). In the first case, the second pair of valves opened 330 crank
angle degrees after the first one whereas for the overlapping scenario the second pair opened
192 crank angle degrees after the first one, as illustrated in Figure 33. Although the terms
valve overlap and valve interval are being used interchangeably throughout this work, they
refer to the overlap of the exhaust valves between two different cylinder heads as these were
used in the experimental installation. Hence, the terms should not be confused with the valve
overlap between the inlet and exhaust valves fitted on the same cylinder, which is a different
method that also aims at the effective scavenging of the combustion products from the
cylinder during the exhaust stroke.
Figure 33: Exhaust valve phasing scenarios; negative overlap (left) and positive overlap (right)
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For both valve phasing scenarios tested, parametric studies have been carried out on speed,
load and the manifold outlet boundary conditions and presented separately in the following
sections. The speed sweep was performed over four operating points from 950rpm to
2000rpm (equivalent crankshaft speed) for all three outlet boundary conditions (BCs),
namely Open End, 20% Restriction End and 42% Restriction End. The restrictions for the
outlet BCs were achieved by the use of orifice plates, as it was outlined in Chapter 2. The
load parametric study was performed at 1250rpm running speed for which the medium and
high load conditions were achieved by increasing the compressed air delivery rate to the
plena. The latter was controlled by the electrically actuated ball valves placed upstream of
the two plena. Increasing the flowrate through the control valves resulted in higher working
pressure upstream the exhaust valves, and hence higher load. A summary of the test cases
dedicated to static pressure measurements is given in Table 1 below.
Table 1: Summary of test cases run to obtain pressure measurements
Since Perspex is a pliant material, it was likely to be subjected to shape deformations when
the pressure level in the manifold increases. For this reason, the high pressure case related to
the 42% restriction (i.e. the 14.5 mm orifice plate) was not performed because the
backpressure in the manifold resulted in significant vibrations that were likely to impair the
measurement accuracy.
3.1.2 Analysis of pressure signals in manifolds of finite length
Acoustic waves can propagate in a stationary fluid as in the case of sound produced
by musical instruments that resonate or diaphragms that burst open in a pipe. As an acoustic
wave propagates through a stationary fluid, it disturbs the particles from their original
positions to generate fluid movement at a velocity u, namely the particles’ velocity. The
propagation speed c of the wave as discussed in Chapter 1 equals the local speed of sound
Medium Load
Overlap
High Load
Overlap
950 rpm 1250 rpm 1650 rpm 2000 rpm 1250 rpm 1250 rpm
Open End √ √ √ √ √ √
20% Restriction √ √ √ √ √ √
42% Restriction √ √ √ √ √ -
cases run Low Load - No Overlap & Overlap
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plus the fluid velocity u (c=a+u); if the particle velocity is very small the propagation speed
of the disturbance is equal to the speed of sound. In the case of exhaust manifolds, acoustic
pressure waves are generated by the unsteady motion of the exhaust valve releasing gases
which are at high pressure. This follows from the pressure discontinuity formed at the seat of
the valve as the exhaust valve opens or closes. The acoustic waves that are generated
propagate both upstream (into the cylinder) and downstream of the valve and into the
manifold. These waves are superimposed on the unsteady exhaust flow, which escapes from
the cylinder at first as a result of the difference in pressure between the inside and outside of
the cylinder and, later, due to the piston moving upwards. In this way, the acoustic waves in
an exhaust manifold travel in a non-stationary fluid as there is bulk flow moving in the same
or the opposite direction of the travelling waves. Engine exhaust pressure pulses are typically
of quasi-sinusoidal shape as a result of the lift profile of poppet valves (Figure 33). In reality
though, the shape of the pressure pulses measured in an engine manifold deviates from the
original quasi-sinusoidal form because of the superposition of acoustic waves on it. The
acoustic wave travels at the speed of sound and, as it meets the manifold end, it gets reflected
back towards the valve, at amplitudes which depend, to first order, on the magnitude of the
change in area. In typical engine manifolds the acoustic wave bounces between the valve and
the manifold end several times during an engine cycle. Therefore a pressure signal obtained
from the manifold is the result of the superposition of several ‘round trips’ of the acoustic
waves to the main blowdown exhaust pulses.
To better illustrate this behaviour, Figure 34 shows the static pressure signal obtained
from the outlet duct (sensor 3, Figure 26) of the experimental arrangement during one engine
cycle. The test case involved the valve overlap scenario, at 1250rpm using an open end as the
outlet BC of the manifold. The present test case is not part of the parametric studies that will
follow in the subsequent sections. Its purpose is to outline the procedure involved in the
analysis of the static pressure signals obtained from the manifold and to demonstrate the
effect of the acoustic waves in the manifold clearly. In the following paragraphs we will see
that depending on the operating conditions, this effect may be very difficult to observe.
Figure 34 shows the two main blowdown events between 90 and 500CAD; the first
pulse travels from the straight duct (duct 2) and the second from the lateral duct (duct 1). A
number of distinctive peaks that resemble a quasi-sinusoidal variation are superimposed on
each pulse. At the trailing edge of the pressure signal, after both valves have closed, there is
another damped quasi-sinusoidal motion. These motions are the result of the acoustic waves
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traveling in the manifold at the speed of sound. The peaks are equally spaced in time, at
approximately 57CAD for pulse 1, 60CAD for pulse 2 and 120CAD for the quasi-sinusoidal
motion at the end of the cycle. Figure 35 shows a spectral analysis of the pressure signal at
200kHz sampling frequency and using 400K samples (equivalent to 20 engine cycles). The
frequency of the engine cycle is the first spectral peak observed in Figure 35 at 10.25Hz,
which corresponds to 720CAD. The frequency spectrum, however, shows a number of
additional peaks apart from the engine cycle frequency. We can identify the frequencies of
the acoustic waves in the frequency spectrum. For pulse 1 and pulse 2 these were 134Hz and
123Hz respectively and for the quasi-sinusoidal motion after the end of the pulse the
frequency was 62Hz. The rest of the spectral peaks correspond to the higher order harmonics
of the cycle frequency and the valve opening time.
An explanation of the spectral analysis was performed taking into account the
overall length of the manifold. The distance between the valve attached to the straight duct
(duct 2) and the outlet of the manifold is approximately 1.25m, whereas the equivalent
distance through the lateral duct and up to the manifold end is 1.35m. In both cases, the
remaining duct (duct 1) was excluded from the calculation of the overall length. According
to acoustics theory, the fundamental frequency of a duct is calculated from the propagating
speed of the disturbance divided by a multiple of the overall length of the duct. The
propagating speed for acoustic waves equals the speed of sound. In cases where both ends of
the duct are open the fundamental frequency is given by equation (28):
𝑓 =𝑐
2𝐿 (28)
In the case of one end of the duct being closed the fundamental frequency is given by
equation (29):
𝑓 =𝑐
4𝐿 (29)
When the exhaust valve is open, the acoustic waves resonate at a frequency which is given
from equation (28), and when both valves are closed the frequency is calculated from
equation (29).
Since the experiment took place at atmospheric conditions, the speed of sound is expected to
be approximately 340m/s. Therefore based on the length of each branch of the manifold the
fundamental frequencies of the acoustic waves when the valves are open are estimated at 136
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and 126Hz respectively. After the second valve has closed the fundamental frequency is
calculated at 62.9Hz. The values obtained confirm that the origin of the oscillations seen on
the two blowdown pulses and the trailing edge of the cycle are the acoustic waves that act in
the manifold. When considering the acoustic wave travelling on pulse 1 from the straight
duct, the remaining feeding duct is likely to act as a Helmholtz resonator that extracts energy
out of the propagating wave (Dowling and Ffowcs Williams 1983; Kinsler et al. 1982). The
maximum attenuating capacity of the resonator arises when its fundamental frequency (based
on the quarter wavelength) matches the one of the acoustic wave propagating in the
manifold.
Figure 34: Superposition of acoustic waves to the main exhaust blowdown pulses as seen on the pressure signal obtained from the outlet duct (duct 3), at 1250rpm, low load with an open end outlet boundary condition.
The analysis presented above demonstrates the method that was followed throughout this
work in order to study the static pressure signals obtained from the manifold with emphasis
being given to the effect of the acoustic waves on the exhaust pulses. It will be shown that
the discrete characteristics of the pressure signals vary depending on the operating conditions
and there are cases when it is difficult to identify the acoustic waves in the pressure
measurements. In the present test case, the pressure inside the two plena remained at very
low levels (<1.1bar) so that the effect of the acoustic waves was clearly seen. The following
sections will demonstrate how the shape of the pressure signals measured at the manifold are
affected by the engine speed, by the load point as well as by the end boundary condition.
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Figure 35: FFT analysis on the pressure signals obtained at station 3 shows the cycle frequency at 10.25Hz, the valve opening frequency at 31Hz, the acoustic waves that are superimposed on the main pulses at 123 and 134Hz respectively and 62Hz of the quasi-sinusoidal motion at the end of the cycle.
3.1.3 Engine Speed Parametric Study
Instantaneous static pressure traces were obtained from the test manifold at pressure stations
1, 2 and 3 (positions as seen in Figure 26) for a range of engine speed conditions under the
same load. The valve phasing between the two engine heads was 165o in camshaft degrees
(330o in crank degrees). Figure 36 depicts the pressure traces, as measured at station 1 of the
lateral duct (duct1), at all engine speeds with an open end boundary condition. The pressure
signals obtained from the open end case show a number of distinctive peaks, including the
ones resulting from the two main blowdown pulses (seen approximately at 100CAD and
500CAD respectively). The remaining peaks and troughs observed are a result of the
acoustic waves acting in the manifold. The open end at the end of the manifold reflects the
incident pressure wave, which, in the case of exhaust pulses, is a compression wave,
resulting in troughs illustrating the presence of strong rarefaction waves. Although the valve
opening and closing time is fixed in CAD, it varies significantly in time in inverse proportion
to the engine speed. Hence, the time that the valve remains open at 950rpm is approximately
double that at 2000rpm (0.126sec at 950rpm in contrast to 0.06sec at 2000rpm). However, as
has already been mentioned, acoustic perturbations travel at the speed of sound c. The first
P a g e | 76
acoustic perturbation, generated as soon as the valve opens, travels to the outlet of the
manifold and is reflected at the open end boundary. Since the end boundary is the same in
the cases shown in Figure 36 and the load point is also the same, the perturbation is reflected
in the same way. This reflection then, in the case of an open end being a rarefaction wave,
travels backwards towards the valve seat. As the perturbation though arrives at the valve seat
(approximately 0.007sec after the exhaust valve opening-EVO), the valve is not at the same
lift position amongst the cases (of different engine speed) therefore the intensity of the
reflection by the valve will differ. In this way, the first reflection at the valve seat is bound to
be different between different running speeds, while all other parameters remain unchanged,
resulting in pressure signals that are not identical as a function of CAD. In Figure 36, we can
also observe that at 950rpm there are two peaks in between the main blowdown pulses,
which are not visible at higher speeds. This is related to more time being available between
the two valve openings at 950rpm for the wave reflections which act in the manifold to
become identifiable. As the running speed increases though, the dynamics change resulting
in the extra peaks appearing at different instances in terms of CAD, sometimes becoming
incorporated into the main blowdown pulses (i.e. pulse 2 at 1250rpm and pulse 1 at 1650rpm
and 2000rpm). Correct timing of the interaction of exhaust pulses with the acoustic waves
can aid the scavenging of the cylinder by lowering the pressure downstream of the valve
inside the manifold. Alternatively, it can increase the pressure amplitude of a pulse so that
more energy can be extracted if a turbocharger turbine is fitted at the end of the manifold. In
both cases, the manifold has to be tuned for a specific purpose. It can be seen that what is
considered a beneficial tuning of the pulses at a specific running speed may have the
opposite effect at a higher or lower speed.
The interpretation of pressure signals of Figure 36 is more complicated than in the test case
presented in the previous section. In the early studies of engine pulses, manifolds were
sufficiently long; long enough that the pressure measurement was obtained before the
reflection from the outlet end arrived back at the transducer. Such cases were largely
investigated by researchers (Annand and Roe 1974; Kirkpatrick et al. 1994) for the
characterisation of acoustic pressure losses in junctions of manifolds when the effect of the
outlet boundary was not present. However, the proximity of the outlet boundary to the valves
is vital to the study of the valve tuning and efficient breathing of the engine.
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Figure 36: Pressure signal during a cycle as obtained from the pressure transducer at station 1 at 950, 1250, 1650 and 2000rpm using an open end as outlet BC
The presence of a turbocharger turbine at the end of an exhaust manifold leads to pressure
reflections that are likely to differ from the ones generated at open ends. A turbocharger
turbine rotor can be considered to be a partially open end. It cannot be defined as fully open
due to its complex geometry and it is not fully closed as this would result in unrealistic
conditions (no engine scavenging). The nature of the reflection of a partially open end
depends on the restriction that it imposes at the duct exit (diameter ratio of restriction and
duct) and the pressure of the incident wave that arrives at the boundary. As such, a partially
open end may reflect a compression wave, either as a rarefaction wave or as another
compression wave. This leads to the realisation that there can be a combination of the two
parameters above (pulse amplitude and degree of duct restriction) that results to an anechoic
boundary, often referred to as an anechoic termination (Davies 1988; Durrieu et al. 2001).
Anechoic terminations are often useful in numerical simulations to diminish wave
interference due to reflection at the boundaries of the computational domain. Figure 37
presents the pressure traces equivalent to those of Figure 36 for the test cases of 20%
restricted end outlet boundary condition. The most distinct difference from the open end
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cases is that the shape of the main blowdown pulses resembles the valve lift profile rather
than having a steep descent during the second half of the pulse. The peaks intermediate to the
main pulses also deviate from what was observed with the open end cases at the respective
running speed. The deviations are due to the orifice plate behaving differently as an acoustic
termination, as opposed to the open end boundary.
For the case of 42% restricted outlet end (Figure 38), the effects of the travelling waves are
less evident since the overall backpressure on the manifold increases and, hence, the
amplitude of the main blowdown pulses also increases. The reflections are still occurring,
although the amplitude of the main pulse is substantially higher so that the superposition of
the travelling waves is not as evident as for the open end case.
Figure 37: Pressure signal along a cycle as obtained from pressure transducer at station 1 at 950, 1250, 1650 and 2000rpm using an orifice plate of 20% geometrical restriction as an end outlet BC
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Figure 38: Pressure signal along a cycle of as obtained from pressure transducer at station 1 at 950, 1250,1650 and 2000rpm using an orifice plate of 42% geometrical restriction as an end outlet BC
3.1.4 Manifold Outlet Boundary Condition (BC) Parametric Study
An open end condition that results into a shape inversion of the incident wave is rarely met
in manifolds of modern IC engines. A catalyst or a turbocharger turbine is usually fitted at
the end of the manifold, which will understandably give rise to different wave phenomena
from those at an open-end condition. Such mechanical components are also associated with
energy losses in the form of localised pressure losses. The concept of turbocharger turbine
representation using 1D approximations was introduced in Chapter 1 in detail and the
general approach only is repeated briefly here. The rotor of the turbocharger turbine can be
represented by the use of an orifice plate. In the open literature, there have been studies in
which a 50% reaction turbine was modelled by using two orifice plates, one for the rotor and
one for the stator (Payri, Benajes, and Reyes 1996; Serrano et al. 2008). However, the most
common approach in order to calculate correctly the reflections from the turbine is to use an
orifice plate for the rotor and a straight, tapered or curved duct for the volute (Baines 2010),
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while maintaining the same volume of the turbine’s geometry. The benefits of more detailed
representation of the volute geometry though did not result in notable changes to the 1D
calculations accuracy (Baines 2010).
In this work, the differences in the propagation of waves and the resultant pressure signals in
the manifold were studied by altering the downstream boundary condition of the test
manifold with the use of orifice plates. For the parametric study outlined in the current
section, the same load point was achieved amongst the cases (low pressure conditions –
Table1 page 71) and the valves’ phasing was that of negative overlap (Figure 33). The
overlay of the results for the case of 1250 rpm is shown in Figure 39. Apart from the overall
increase in the back-pressure, which was expected due to the end restriction, differences in
the pulse shape can also be observed as the downstream condition becomes more restricted.
In addition, the presence of strong rarefaction waves results in regions of sub-atmospheric
conditions, which are visible in the case of the open end BC, but become less substantial for
the slightly restricted BC and indistinguishable for the most restricted case. Although the
elimination of the rarefaction waves may impair the scavenging ability of the manifold, the
restriction also results in higher amplitude pressure at the turbine inlet. As the turbocharger
utilises the energy of the exhaust gases due to the pressure difference across its ends, higher
pressure at the inlet will also increase its efficiency. Evidently, a compromise between
scavenging and turbocharger efficiency should be sought for a specific application.
Figure 39: Comparison of pressure traces obtained from pressure transducer at station 1 (lateral duct) for different BC at outlet duct end, namely open end, 20% Restriction and 42% restriction.
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3.1.5 Operating Load Parametric Study - Pressure Losses
Static pressure losses across the T60 junction can be calculated for all test cases by
comparing the measured pressure signals obtained from the three sensors (Figure 26). The
pressure in the plena was altered to provide three different load points, which subsequently
resulted in three different amplitude pressure pulse cases in the manifold (low, medium and
high load points – Table 1 page 71). For these cases, the speed was held constant at 1250
rpm, the valve phasing was the one of positive overlap and pressure measurements were
acquired for all three boundary conditions. Figure 40 depicts the overlay of the three pressure
traces acquired from the manifold for the three load points with the slightly restricted end
BC. The first pulse on the graphs corresponds to the one propagating from the straight duct
(duct 2) and the second comes from the lateral duct (duct 1). Note that the y axes are not on
the same scale between the three graphs, this was to better illustrate the differences in static
pressure from the three sensors in all cases tests. As expected, the static pressure losses are
almost negligible for the pulse that comes from the straight duct, since the directionality of
the junction dictates that the blow-down pulse will continue straight to the outlet duct and the
reflections at the junction point are not strong enough to distort the signal.
For the pulse coming from duct 1 though, increased pressure losses can be seen, which are
associated with the impingement flow type from the lateral to the main duct outer wall. The
close matching of the signals obtained upstream of the junction (signals from duct 1 and duct
2) indicates that the bend at the beginning of duct 1 as well as the increased length compared
to duct 2 did not result in significant static pressure drop compared to the one observed when
the flow passes through the junction. This gives an indication of the significance of the
losses owing to bends as compared to the ones owing to branching regions. The change of all
pulse shapes with the load point should also be noted, as this is the resultant combination
between the wave actions and the increase of the bulk flow rate corresponding to different
load points. The percentage static pressure loss across the junction when the pulse travels
from the lateral duct increases with the load with maximum values that reach 4, 6 and 8%
respectively. The corresponding open end cases showed that significantly higher losses take
place across the junction with values up to 20% of the pressure upstream of the junction. An
insight into the respective changes to the flow field for all cases is required to decide on the
reasons behind the deviations observed amongst the cases. Such information will be
provided in the next section where the velocity measurements that were obtained from the
experimental setup are presented.
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Figure 40: Pressure traces from pressure transducers at stations 1, 2 and 3 for low, medium and high load operating points for the case of 20% restriction at the outlet BC.(Note the change in y axis scale)
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3.2 Particle Image Velocimetry (PIV) Measurements
3.2.1 Introduction
In this section the evolution of the flow field under pulsating conditions is studied through
the PIV results of three cases; an open end, a slightly restricted and a heavily restricted
downstream BC under the same speed and load point conditions. The static pressure
measurements, as presented in the previous chapter, capture the changes in pressure owing to
two different phenomena; wave dynamics and diffusion downstream of the maximum height
of the recirculation zone formed in the outlet duct (frictional losses are expected to be a small
contributor over such a small length). The latter physical mechanism has been used in the
development of the pressure loss model of Bassett et al. (2003) that was introduced in
Chapter 1. The Bassett et al. model is developed under the assumption of quasi steady
conditions, implying that the pulse can be discretised into a time series of steady flows
corresponding to the instantaneous pressure and velocity conditions. Under truly steady flow
conditions, a recirculation region is formed at the outlet duct of a three way manifold as the
flow separates from the duct wall, with the flow's boundary layer unable to negotiate the
adverse pressure gradient associated with the discontinuity in the magnitude of the wall
tangent at the junction. As a result the flow stream is restricted to a portion of the cross
section of the outlet duct passing through a vena contracta. This flow is associated with
pressure losses owing to the diffusion of the flow to cover the whole of the duct cross section
downstream of the recirculation region. There is a direct analogy between this pressure loss
and the well-known phenomenon of the pressure loss through a sudden expansion (Figure
41). For an inviscid fluid, the area expansion would result in velocity reduction with
subsequent static pressure recovery as predicted by Bernoulli's equation. However, such
pressure recovery is not achieved in viscous flows travelling in expanding ducts, (dU/dx<0)
as the Force-Momentum Theorem shows that the (viscous) diffusion associated with the
sudden expansion is also inevitably associated with mechanical energy losses, ultimately to
be translated into increased entropy due to eddies formed near the wall boundary.
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Figure 41: Sudden expansion due to geometrical step area change (left) and gradual expansion due to partial blockage of duct owing to the formation of a recirculation region
The energy dissipation at a sudden step expansion can be described through Equation 26
(below) that is derived from the conservation equation of momentum across a suitably
defined control volume. Equation (32) which is derived from the equation for the
conservation of energy applied to a control volume, ultimately can take a form which
appears to introduces an additional term to Bernoulli’s equation (although the equation is not
restricted to application along a stream, as is Bernoulli's) to represent the mechanical energy
loss due to sudden expansion, ΔH, which is expressed in terms of pressure head. The system
of governing equations for the flow configuration shown on in Figure 41is as follows when
applied to a rectangular control volume which for the sudden step expansion has its upstream
face at A1 (but its area is A2) and downstream face at A2 at which stations we assume the
velocity profile is a 'top hat' (or alternatively the overbar implies an appropriate cross
sectional bulk average), the pressures are uniform across the control volume faces, we
assume steady flow and we neglect wall friction for reasons suggested above:
Continuity: 𝐴1 ∙ �̅�1 = 𝐴2 ∙ �̅�2 (30)
Momentum: (𝑝1 − 𝑝2) ∙ 𝐴2 = 𝜌𝑎𝑖𝑟 ∙ 𝐴2 ∙ �̅�2(�̅�2 − �̅�1) (31)
Energy (‘extended’Bernoulli): 𝑝1
𝜌𝑔+
𝑢12
2𝑔=
𝑝2
𝜌𝑔+
𝑢22
2𝑔+ 𝛥𝛨 (32)
Combining and rearranging Equations (30) and (31), the loss term ΔH in equation (32) is
given by the following equation:
𝛥𝛨 =�̅�2
2
2𝑔(
𝐴2
𝐴1− 1)
2 (33)
And because 𝐻 =𝑝
𝜌𝑔
𝛥𝑃 = 𝜌𝑎𝑖𝑟�̅�2
2
2(
𝐴2
𝐴1− 1)
2 (34)
1 2
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When the analysis is extended to the flow with recirculation, we make effectively the same
assumptions. There are a number of assumptions under which the system of equations above
can be used for the calculation of losses when applied to a control volume which has its
upstream face at the maximum height of the recirculation zone and extends downstream to a
fully uniform profile; the flow should be incompressible, steady and with uniform
distributions of pressure and velocity at the cross sections of the control volume’s entrance
and exit. The applicability of those assumptions will be discussed in the following sections
by reference to the PIV measurements. We nevertheless mention that the assumption of
uniform pressure across the upstream control volume face, at the maximum height of the
recirculation zone is not as apparently poor as it may seem at first sight. While it is true that
streamline curvature is associated with a pressure gradient across the streamline, we expect
that the recirculation zone will be long relative to its maximum height and that, to a first
approximation at least, the cross stream pressure gradient will be relatively small. This is
because the pressure gradient is set by the curvature of the fastest moving streamlines
(centripetal force rises as the square of velocity) which will be those closest to the 'outer'
wall. There, the curvature is limited by the presence of the duct wall. A detailed analysis of
the procedure to obtain the velocity vector field in the manifold, the velocity profiles at the
cross sections of the outlet duct and finally the estimation of the pressure losses will also be
presented.
The governing equations (30) to (32) presented above are constructed using the profile
averaged velocities. Use of profile averaged velocities when the flow profile is not uniform
in the cross-stream direction may result in error arising on the momentum flux conservation
in which case a flux correction factor is introduced:
𝛽 =1
𝛢∫ (
𝑢
�̅�)
2𝑑𝐴 (35)
where A is the area that the velocity profile refers to, u is the actual velocity profile and �̅� is
the profile average velocity value. The flux correction factor is around 4/3 for laminar pipe
flow and ~1 in fully turbulent pipe flow. In the latter case it is therefore neglected and the
momentum equation is written as above (31). In the cases which are going to be presented in
this chapter the flow is turbulent with Reynolds numbers of around 30000 so the flux
correction factor has also been neglected as the resulting calculated values were in the range
of 1.01-1.03. It should be noted however, that flux correction factor was calculated “per unit
depth” as the velocity profiles were acquired only at the manifold’s horizontal plane of
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symmetry. Thus, the whole cross section is not adequately represented. Based on
unpublished CFD data, the underestimation of mass flow rate can be around 5% when using
data from the mid plane only rather than from the whole of the cross section. Although this
observation mostly concerns the cross sections upstream of the maximum recirculation
height, it is possible that there is some underestimation of the cross sectional averaged
velocity too. This topic is further discussed in the analysis of the PIV results given in the
following paragraphs.
The pressure loss analysis described by equations (30) to (34) requires an incompressible
fluid assumption. An estimation of the error arising from such an assumption can be made by
converting the head loss to entropy generation (Δs>0) and then compare it with the
corresponding entropy generation of a compressible flow case. More details on this approach
can be found in Appendix A. The entropy generation can also be linked with an exergy
analysis and the estimation of energy availability at the turbocharger turbine inlet. An
example of such analysis dedicated to manifolds can be found in Schmandt and Herwig
2011.
3.2.2 Cross Correlation Method for Velocity Vector Processing
The methodology for the image acquisition from the junction and outlet duct of the manifold
has been outlined in detail in Chapter 2. In this section, the vector processing procedure to
obtain the flow field from the raw images will be presented. As previously mentioned, the
image acquisition involved 500 pairs of images captured per point A-I (Figure 42) followed
by the calculation of the ensemble averaged velocity field. The PIV vector processing
follows the cross correlation method in which the position of illuminated particles between
two frames (one pair of images) is compared within a pre-specified small area (interrogation
window). The time delay between the frame capturing is an imposed variable, defined by the
flow characteristics, so that the velocity vector can be computed. The procedure is then
repeated across all interrogation windows and then along all pairs of images so that the
ensemble average velocity field can be obtained. Figure 43 and Figure 44 provide a visual
representation of the method as it results in the ensemble averaged velocity field starting
from the raw images.
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Figure 42: Instances during the engine cycle at which images of the instantaneous flow velocity field were acquired – Open End case and valve overlap scenario
Figure 43: Cross correlation method schematic for the calculation of correlation peak between frames (LaVision Davis v7 software user manual)
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Figure 44: Ensemble averaged velocity calculation for a number of N frame pairs A and B (LaVision Davis v7 software user manual)
Before the processing of the images, a correction routine for light intensity was
performed to normalize the light intensities scattered by the seeding particles. Following the
intensity correction, the cross correlation method was performed on each interrogation
window, the size of which is selected by the user. The method that was followed involves
multi-pass refinement in the calculation of the velocity vector field where on the first pass
the interrogation windows size was 256 x 256 pixels with an overlap of 75%. After the
calculation had been completed, the window was divided subsequently down to window
sizes of 32 x 32 pixels again of 75% overlap. The real dimensions of the windows were
calculated through the magnification factor of the imaging camera, which for the current
work results in a 72μm/pixel spatial resolution. Therefore, the 256 x 256 pixel window of the
first pass represents an area of 18.4 x 18.4mm, whereas the 32 x 32 pixel window
represented an area of 2.3 x 2.3mm. The smallest interrogation window that can be used is
that of 6 x 6 pixels and it is dictated by the software used for the post processing (LaVision
Davis v7). However, for the current experiment the resulting real dimensions were too small
resulting in seeding particles appearing stationary, thereby worsening the accuracy of the
calculation. For this reason, the last pass of the refinement process was selected to be the one
of 32 x 32 pixels. At each pass, a series of filtering processes were also performed during
which computed vectors were removed as erroneous if their correlation peak ratio was lower
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if the RMS values were significantly higher than the RMS values of neighbouring vectors.
Groups of such vectors could then be replaced with interpolated vectors.
The procedure described above was performed on all test cases run for the PIV study.
These were divided into the ones targeting the junction area and the ones where the camera
was moved to observe the flow field on the outlet pipe as described in Chapter 2. The load
point for the PIV measurements was chosen to be lower than those presented in the Pressure
Measurements section above in order to maintain the bulk flow velocity within appropriate
limits to obtain the PIV velocity measurements. The maximum velocity that could be
captured was calculated from the real dimensions of the smallest interrogation window and
the time difference between the two images of each pair. The time difference between the
images acquisition is fixed for steady flows, but needed to be adjusted for unsteady ones like
the pulsating flow studied in this work. Furthermore, keeping the working fluid delivery rate
low also helped to maintain the seeding particles at the appropriate amount, so that
condensation and fouling of the Perspex walls did not disturb the optical measurements.
3.2.3 Results
Velocity Contours at the Outlet Duct
In Figure 45 to Figure 53 the evolution of the ensemble-averaged flow velocity field during
the cycle (timestamps A-I, Figure 42) can be observed in the form of velocity contours of
absolute velocity vector magnitude in the horizontal mid plane of the manifold just
downstream of the junction area. The lateral duct was positioned directly before the area
captured by the PIV images at the inner wall of the outlet duct (the lower boundary on
Figures 45-53). The outlet BC for the manifold was an open end (the corresponding Figures
for the case of 20% restricted manifold end BC can be found in Appendix B). At the right
hand side of each figure, the sensor position can also be observed as its aluminum surface
was causing a strong reflection of the laser light. As a consequence, the luminosity of
seeding particles at that area was weak resulting in no valid vector calculation.
The flow field at timestamps A and B, depicted in Figure 45 and Figure 46,
corresponds to the exhaust event travelling from the straight duct (duct 2). The geometry of
the manifold favours the symmetric distribution of the flow, at least within the horizontal
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plane, along the centreline of the outlet duct as the pulse travels from duct 2. Nevertheless, it
is expected that the presence of the lateral duct on the inner wall (lower in the figures) of the
manifold should result in some disturbance. This disturbance might be seen in the form of a
shift of the flow towards the outer wall for a short length, yet still mostly parallel to the
main/outlet duct centreline. No recirculation region is formed within the outlet duct during
the pulse event travelling from the straight duct, as expected. The boundary layer formed at
the outer wall (the upper one in the figures) of the duct is also illustrated while its velocity
magnitude is progressively decreasing along the duct. Any change to the boundary layer
thickness is difficult to observe over the 100mm of the captured flow field length.
Figure 47 to Figure 53, corresponding to timestamps C-I, depict the flow field during the
exhaust event from the lateral duct (duct 1). The bulk flow travels through the lateral duct
and then it impinges on the outer wall of the junction and outlet duct. As the flow enters the
outlet duct at an angle of 60degrees to the horizontal axis (geometrically), a recirculating
region develops on the inner wall of the outlet duct. The free stream is initially directed
above this region before it diffuses to cover the full cross section of the duct further
downstream. This is clearly visible for timestamps E-H, in Figure 49 to Figure 52 that refer
to the part of the pulse where the pressure is decreasing in time. On the contrary, on
timestamps C and D which correspond to the pressure increasing and thus to an accelerating
flow, there is no formation of a recirculation region with the bulk flow giving the appearance
of being a jet directed towards the outer wall. This is because flow recirculation is associated
with flow - boundary layer - separation induced by an adverse (decelerating) pressure spatial
gradient. On the last timestamp, Figure 53, a clockwise recirculating region spans the whole
duct width and at least up to the pressure transducer position, lengthwise. The colour
contours also reveal that the maximum velocity magnitude is observed at timestamp E at
which the pressure had already started to decrease in time. It is well known in the acoustics
of ducts that there is a phase lag between the bulk flow and the pressure. This behaviour will
be discussed in more detail below by reference to the velocity temporal profiles as compared
to the pressure signals.
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Figure 45: Ensemble averaged velocity for point A of the pressure pulse trace for the Open End case
Figure 46: Ensemble averaged velocity for point B of the pressure pulse trace for the Open End case
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Figure 47: Ensemble averaged velocity for point C of the pressure pulse trace for the Open End case
Figure 48: Ensemble averaged velocity for point D of the pressure pulse trace for the Open End case
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Figure 49: Ensemble averaged velocity for point E of the pressure pulse trace for the Open End case
Figure 50: Ensemble averaged velocity for point F of the pressure pulse trace for the Open End case
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Figure 51: Ensemble averaged velocity for point G of the pressure pulse trace for the Open End case
Figure 52: Ensemble averaged velocity for point H of the pressure pulse trace for the Open End case
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Figure 53: Ensemble averaged velocity for point I of the pressure pulse trace for the Open End case
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Velocity Contours at the Junction
As discussed in the experimental setup chapter two positions of the camera were used to be
able to capture the pre and post junction flow field Figure 31. Figure 45 to Figure 53
presented above refer to position A. Figure 54 and Figure 55 below refer to position B and as
it can be seen the domain the computed velocity field is cropped at the lateral duct. The
reason is that the laser beam was entering the Perspex manifold at the mid plane from the
side of the straight and outlet ducts (Figure 30-top as seen on the page). This however,
created a shadow at the lateral duct from the point of 7mm and towards the left where
velocity vectors could not be computed. As with the case of the outlet duct, there was also
scattering alight due to sensor reflecting surface in the lateral duct. This is visible in Figure
54 and Figure 55 at approximately (10,-35mm).
Figure 54: Ensemble averaged velocity magnitude of the flow field at the mid plane of the T60 junction at timestamp D. The pressure sensor position at the lateral duct is visible (10,-35) due to its reflecting the laser light resulting in no valid vector calculation. The domain is cropped at the lateral duct due to shadow of the straight duct projected to it as the laser light was trespassing the manifold
P a g e | 97
Figure 55: Ensemble averaged velocity magnitude of the flow field at the mid plane of the T60 junction at timestamp F. The pressure sensor position at the lateral duct is visible (10,-35) as it was reflecting the laser light resulting in no valid vector calculation. The domain is cropped at the lateral duct due to shadow of the straight duct projected to it as the laser light was trespassing the manifold
Velocity profiles at different cross sections of the duct – Spatial velocity
distribution
As was mentioned in the introductory section to the PIV measurements, pressure losses
owing to the diffusion of the flow past a recirculation region can be evaluated -certainly
qualitatively- by reference to the modification to the theory of losses at a sudden area
expansion (Figure 41). To achieve this, knowledge of the fluid velocity is needed both at the
free stream above the recirculation region (the mass and momentum flow rates within the
recirculation zone are low and can be neglected to a first approximation) and at a cross
section further downstream when the flow has diffused to provide positive velocities
everywhere across the duct’s full width. In principle, the analysis should extend as far
downstream as the station where the flow is fully developed and hence no more diffusion
takes place, but this station is of the order of at least 20 duct diameters downstream and is
too long in the context of modern engine manifolds. There is, however, inevitably a
(quantifiable) error in using the upstream station. The pressure losses can then be estimated
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using Equation (34) which also requires the recirculation maximum height to be known so
that the effective cross section of the duct (A1) can be computed. The velocity profiles and
the recirculation height along the duct were calculated based on the data obtained from the
PIV measurements. The methodology and the results on the pressure loss estimation due to
flow diffusion are presented in the following sections.
The processed data from the PIV were stored as arrays of the planar coordinates (x,y) along
with the respective vector components (Vx and Vy). Axis x is the streamwise direction along
the duct centreline and axis y is the spanwise direction across the duct width. In this way,
the illustration of the complete flow field was possible, as in the case of velocity contours
presented above. The size of the array was determined by the number of the interrogation
windows examined in the final pass of the vector processing. The latter also defined the
spatial resolution of the data available.
Selecting the data points of the array at a fixed axial station, i.e. with the same x-coordinate,
allows for the presentation of the velocity profile across the width of the duct. Figure 56
shows the velocity profiles (resultant velocity vector magnitude) at cross sections located at
x equal to 5, 14, 27, 40, 75 and 87mm away from the junction end of the outlet duct at
timestamp E. The y axis is defined as the percentage of the duct width starting from the inner
wall. The gradual retardation of the velocity on the inner wall side can be observed between
the velocity profiles at 5 and 27mm, which results in a flow reversal and, hence, the
formation of the recirculation zone. Due to the presence of the recirculation region, the free
stream is gradually shifted towards the outer wall of the duct. Further downstream though, as
seen from profiles at 75 and 87mm, the flow reattaches to the inner wall and gradually
recovers from the effect of the recirculation zone. It needs to be noted that the velocity
profiles based on the streamwise component rather than the velocity magnitude were almost
identical to the ones of Figure 56 apart from stations a and b. The differences however are
presented in Appendix C for the interested reader.
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Figure 56: PIV data points of the resultant velocity magnitude (blue) and fitted velocity profile (moving average) (black) across the outlet duct. From the upper left, (a) and (b) corresponding to profiles at cross sections at 5mm and 14mm are upstream of the recirculation zone, (c) profile at 27mm is at the middle of the x-extent of the recirculation region, and (d), (e) and (f) profiles at 40, 75 and 87mm respectively are downstream of the recirculation region.
Height of Recirculation Region – Conservation of mass flow rate
The calculation of the recirculation zone height is based on the numerical integration of the
velocity profile along the duct width (y direction) starting from the inner wall (Figure 56).
The point, where the two areas, representing the local flowrate, of reversing and forward
velocity fields become equal, denotes the location of the separation streamline delineating
the recirculation zone height. The streamline that passes through that point is the locus of the
separation streamline, and separates the free stream from the recirculating region (Figure 57).
Two topics need to be addressed before the integration can be made. The first issue is related
to the nature of PIV measurements, which in this experiment did not allow for velocity
measurements to be obtained close to the wall. As a result, the first vector computed was
placed away from the wall at a distance equal to the size of the smallest interrogation
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window. To be able to integrate along the velocity profile, values for the velocity at the wall
must be estimated for the numerical integration to proceed.
Figure 57: Calculation of the recirculation height from the integration of the velocity profile to obtain the reverse and forward flowrates. The recirculation height is defined as the point where the two areas become equal.
The physically correct condition of zero velocity at the wall has been tested, as well as the
approximation that an acceptable approximation to the rapid 1/7 th power law and log-law
variation of the velocity profile between the last measurement point and the wall is that the
velocity value at the wall equals the value measured by the PIV just away from the wall. The
effect of these two approaches on the calculations, which would result in two estimates of
the mass flow rate between the wall and the last measurement point adjacent to the wall (the
real value), will be discussed further below. The second issue that needs to be addressed is
the relatively low velocities observed inside the recirculating region as compared to the
values encountered in the free stream. Adverse velocity magnitude gradients are challenging
for PIV measurements that require two frames of the flow field captured with a short time
delay between them. If the time delay is sufficient to capture the velocities of the slowly
recirculating region, the seeding particles that move in the free stream will have enough time
to travel beyond the interrogation window size. As a result, fewer particles will be captured
within each interrogation window, worsening the correlation factor between images and
increasing the uncertainty of the velocity vector calculation. On the other hand, a short time
delay between the frames will improve the accuracy of the velocity vector calculation in the
free stream, but the areas of recirculation will look stationary, ‘frozen’, as the velocities
observed in such regions are significantly smaller, sometimes even at an order of magnitude
difference. In the current study, the second approach was followed resulting in an
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underestimation of the velocities inside the recirculation region. An alternative approach
would have been to improve the spatial resolution of the images by moving the camera
closer to the testing facility or by using a zoom lens, which increases the magnification
factor. The compromise following this approach would have been that the overall length of
the duct visible on the images would be reduced. In this way the recirculation region would
be captured in greater detail but the downstream flow field and the recovery of the flow field
at the point of the sensor would not be included in the images. The latter approach has been
tested to verify the ability of the method to capture the recirculation zone. The spatial
resolution for this run was 50μm/pixel and the smallest interrogation window used was 8x8
pixels.
Figure 58 shows the complete velocity field computed across the junction and the velocity
profile at the position of the recirculation zone maximum height for timestamp E (Figure 41).
As compared to Figure 56(c), the recirculation region is captured in more detail, revealing
that its maximum height is extended further towards the duct centreline than shown in Figure
56(c). Were the aim of the measurements to study the recirculation region, this latter
approach would have been preferable. However, the aim of the measurements was to
estimate the diffusion losses due to the expansion, and the emphasis is on the use of the
continuity equation to determine the locus of the separation where the flow moves
unidirectionally, over the recirculation zone. The mass flow rate is conserved at any cross
section and we assume, for convenience, that the flow is the same in all planes above and
below the plane of the paper. Hence the PIV instantaneous images had to include the flow at
streamwise stations upstream of the recirculation zone, around the recirculation zone, as well
as downstream of the recirculation zone, where the flow had reattached to the duct wall. For
this reason, the optical arrangement of the imaging system changed to the one outlined in
Chapter 2, which captured instantaneously the spatial distribution that was presented in
Figure 45 to Figure 53.
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Figure 58: Flow streamlines (left) and velocity profile at the cross section of maximum recirculation height (right). The specific imaging arrangement increases the spatial resolution, resulting in the capture of the recirculation zone more accurately, but flow cross sections after reattachment of the flow at the inner wall are outside the field of view.
To quantify both the volumetric and the mass flow rate, the numerical integration of the
measured velocity profiles was initiated at the outer wall according to equation (36). This is
because the mass flow rate inside the recirculation zone is effectively zero therefore the mass
flow rate of the free stream must equal the mass flow rate downstream of the recirculation
zone. The point where the mass flow rate from the numerical integration at axial stations
within the recirculation zone equals the value downstream of the recirculation also denotes
the maximum recirculation height. Equation (36) below gives the mass flow rate per unit
depth of the duct:
�̇�
𝑤= 𝜌𝑎𝑖𝑟 ∫ 𝑢𝑑𝑦
ℎ
0= 𝜌𝑎𝑖𝑟 ∙ 𝑑𝑦 ∙ ∑ 𝑢𝑖 [
𝑘𝑔
𝑚]𝑁
𝑖=1 (36)
where w is the depth of the duct, 𝜌𝑎𝑖𝑟is the density of air, dy is the interrogation window
size, N the number of the equally spaced interrogation windows along the duct width,
including the extra points placed on the outer and inner (upper and lower) walls and ui the
corresponding velocity values. The calculation of mass flow rate through the discretised
equation above is feasible on the basis that the measured velocities indicate effectively
incompressible flow, since the Mach numbers are below 0.3.
Since the mass flow rate is preserved along the duct, the value at a cross section without
visible separation will be used as the reference value. This should be equal to the mass flow
rate of the free stream, above the separation streamline (provided that the flow is two
dimensional and the same at all planes normal to the plane of the paper; this may well be a
highly questionable assumption near the junction, however), and also at the areas where the
recirculation zone is present. Figure 59 shows the mass flow rate per unit depth along the
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outlet duct width for timestamp E. This was calculated using zero velocity at the wall,
although the second alternative aproximation, i.e. wall velocity being equal to the last
measured velocity above the wall, gave similar results. As can be seen, the mass flow rate
value increases up to 30mm from the duct start, while later stabilises at a value of
approximately 0.8kg/s/m. The same trend is observed at all timestamps that the recirculation
region appears in the flow field (E-H). On the contrary, when the exhaust event travels from
the straight duct (timestamps A,B), the mass flow rate is approximatelly at 0.8kg/s/m along
the whole outlet duct length (Figure 60). The expected error margin due to integration of the
PIV velocity measurements is 10%. This holds true for the measurements obtained when the
flow is travelling from the straight duct.
Figure 59: Mass flow rate per unit depth along the outlet duct length as calculated by the numerical integration of the velocity profiles derived from the PIV measurements at timestep E
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Figure 60: Mass flow rate per unit depth along the outlet duct length as calculated by the numerical integration of the velocity profiles derived from the PIV measurements at timestep A
At timestamp E however, up to 30mm along the duct length, the deviation from the mass
flow rate value downstream is up to 20%. There are two possible reasons for the increased
error which are linked to the possibility that the flow outside the measured plane is not
identical due to out of plane motion in the outlet duct due to the effect of the junction. The
PIV measurements have been obtained from the horizontal mid plane of the manifold, which
is the plane of symmetry for the square section ducts themselves. However, it is likely that
the flow in this plane is not representative of all the other planes outside the geometrical
symmetry plane. The engine head design used in the experiment incorporated poppet valves
and exhaust ports that direct the flow from the pent roof of the cylinder head to the plane
normal to the manifold entry. In order for this to be achieved, the ports had a bend of
approximately 60 degrees angle. As the valve opens, the flow is likely to have been directed
at the outer wall of the port bend rather than occupying the overall cross section of the port
(Wang et al. 2013). The flow is initially, at least, completely unaligned with the geometric
plane of symmetry of the square cross-sectioned ducts. Therefore we cannot expect the flow
in the plane of symmetry of the ducts, immediately downstream of the exit of the ports, i.e. at
entry to the ducts, to be representative of the flow outside the symmetry plane. This effect is
inevitably stronger in the proximity of the valve and the flow is expected to have recovered
to some extent at the upstream parts of the PIV measuring plane. A similar effect in
generating flow asymmetry, but applying on the perpendicular plane to the one mentioned
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before is likely to arise past the 30 degree bend located at the lateral duct. However, the
vector field on the end of the lateral duct just upstream of the junction showed that the flow
at the mid plane was occupying the whole duct width. A second reason that could impair the
accuracy of planar measurements is the development of strong secondary flows downstream
of a bend or the junction. As was discussed in Chapter1, these flows, also referred to as Dean
vortices (Dean 1927; Dean 1928) develop in pairs on the cross section of a pipe and they are
symmetrical with reference to the mid plane of the pipe. Similar structures were
experimentally observed for ducts of square cross section (Mees, Nandakumar, and Masliyah
2006). Dean vortices may depart from their symmetrical structure just downstream of a bend
(Kalpakli and Örlü 2013) and their shape is also affected in the case of pulsating conditions
in the pipe. (Renberg et al. 2014) report similar findings through numerical computations of
the Dean vortices past a T junction of 45 degrees. The latter studies indicate that the three
dimensionality of the flow in the junction is important and therefore the flow within the
geometrical plane of symmetry may not be fully representative for the flow field inside and
just after the junction. Nevertheless, the error in the calculation of the mass flow rate (Figure
59) decreases further downstream which suggests that the three dimensional effects are
significantly reduced as the flow enters the outlet duct. In addition, Figure 59 and Figure 60
show that increased error may be also associated with the presence of the recirculation
region, which spans from 10 to approximately 50 mm of the outlet duct length. The
recirculation region, which effectively partly blocked the cross section of the duct, appears to
act in a way similar to a flow conditioner redirecting the flow towards the centre of the duct.
The latter could also contribute to the reduced deviations on the calculation of the mass flow
rate observed past the 35mm station.
Figure 61 shows the non-dimensional cumulative mass flow rate with respect to the cross
stream coordinate at 6 different stations of the outlet duct at timestamp E, where the no slip
condition hypothesis has been used at the walls. As expected, for the cross sections within
the recirculation region, the cumulative mass flow rate reaches its maximum value away
from the wall, after which the cumulative value remains more or less constant, reflecting the
low velocities (either positive or negative) within the recirculation zone.
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Figure 61: Non-dimensional cumulative mass flow rate with respect to the cross stream coordinate at different streamwise stations within the outlet duct (15, 26, 27, 28, 65, 90mm) using the no-slip condition hypothesis for the velocity at the wall. The height, where the cumulative mass flow rate has reached 95% of the total value is taken to define the recirculation zone maximum height.
The difference in the behaviour of the profile of cumulative flowrate between the stream
wise stations within the recirculation region and the ones further downstream is also clearly
seen, with the latter continuously increasing until the wall boundary is met. A level of 95%
of the total mass flow rate was chosen as an indicative percentage of the flow travelling in
the free stream (above the recirculation zone), according to which the maximum height of
the recirculation zone was defined. This value was chosen as that at which the cumulative
profile within the recirculation zone started to deviate substantially from the quasi-linear
behaviour, as shown on Figure 61. The selection has been verified against the measurements
obtained with higher spatial resolution that result in the same values for the maximum height
of the recirculation.
As previously mentioned, an alternative hypothesis for the velocity at the wall has been
tested where the first and last nodes on the integration section had the same values as the last
measured velocities by the PIV. Figure 62 shows the non-dimensional cumulative mass flow
rate for a slip condition at the wall. It can be seen that it results in minor differences in the
behaviour of the cumulative mass flow rate profile from the duct centreline towards the inner
wall relative to that of Figure 61. The same observation applies to the maximum height of
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the recirculation region which changes by less than 1% by using the two different hypotheses
for the velocity at the wall. However, the observed differences at the outer wall indicate that
resolving the boundary layer close to the outer wall, where velocities are not negligible, is
associated with high level of ambiguity. Given also the pulsating conditions, a safe
estimation of the velocity close to the wall is subjected to the phase difference in the flow
between the boundary layer and the bulk flow. For these reasons, the no-slip condition was
considered as a more suitable assumption for the velocity at the wall.
Figure 62: Non-dimensional cumulative mass flow rate with respect to the cross stream coordinate at different streamwise stations within the outlet duct (15, 26, 27, 28, 65, 90mm) using a slip condition hypothesis for the velocity at the wall. The height, where the cumulative mass flow rate has reached 95% of the total value is taken to define the recirculation zone maximum height
Diffusion Losses
Estimation of the pressure losses owing to diffusion can be derived from the one-
dimensional analysis of flow through an area expansion as illustrated in the introduction. The
control volume to perform the calculations is defined by analogy to Figure 41 (right). The
entrance to the control volume was located at the stream-wise cross section of the duct that
the height of the recirculation region is at a maximum level. The exit of the control volume
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was defined to be 75mm away from the outlet duct entry. The present section discusses the
methodology to calculate the velocities at the two cross sections and the diffusion losses
within the control volume based on equations (30) to (34) presented in the introductory
section. These equations refer to incompressible steady flow across a suitably defined control
volume. They constitute the principles with which the Bassett et al. (2003) model addresses
the losses in pulsating flows in manifolds under the assumption of the existence of a
recirculating region in the outlet duct. Equation (34) was used to calculate the diffusion
losses at all timestamps involving a recirculating region (E-H) and compare them to the
measured pressure signals. The recirculating region height that is necessary to calculate the
flow expansion ratio for Equation (34) is obtained by the numerical integration of the non-
dimensional mass flow rate of Figure 61(no-slip condition at the walls). Figure 63 shows the
temporal evolution of the cumulative mass flow rate at the cross section of maximum
recirculation height between timestamps E and H.
The change in the absolute height between the different timestamps is of the order of 8%
indicating that the maximum height can be regarded as constant for as long as the
recirculation region is formed (timestamps E-H). As a result the ratio A2/A1 in Equation (34)
Figure 63: Non dimensional cumulative mass flow rate for timestamps E-H at the cross section where maximum recirculation height was observed.
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is practically constant. On the contrary, the temporal change of the cross sectional average
velocity �̅�2 undergoes significant changes during the pulsed flow, as opposed to the
maximum height of the recirculation zone. The cross section average velocity �̅�2 (Figure 41)
was obtained for the cross section located 75mm away from the duct entry, where the flow
was reattached to the inner wall (control volume exit). As can be seen in Figure 64, the
change in �̅� is of the order of 15% between timestamp F and G, but as much as between G
and H. Therefore, the average velocity downstream of the diffusion is the predominant
parameter in the calculation of pressure losses through Equation (34) as the remaining term
is constant during the pulse. An estimation of the diffusion losses can now be obtained using
the results of Figure 63 and Figure 64.
Figure 64: Temporal variation of cross sectional average, phase average velocity magnitude at three stream wise stations in the outlet duct (i.e. 10.5, 26.6 and 75mm). The magnitude was calculated at the instances in phase that PIV measurements were obtained (A-I).
Figure 65 (top) depicts the pressure signals from pressure transducers 1 and 3, which were
obtained simultaneously with the PIV measurements. The instantaneous pressure difference
between the two transducers during the cycle (Figure 65, bottom) has overlaid on it blocked
symbols which represent the calculated diffusion losses from Equation (34). As can be seen,
the diffusion losses constitute a small part of the measured static pressure difference. If the
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assumption of a quasi-steady flow is valid, the remaining pressure difference is presumably
due to the wave dynamics phenomena and the resulting transmitted wave from the junction
being of lower amplitude than the incident wave arriving at the junction.
Figure 65: Pressure signals from stations 1(green) and 3(red) and pressure difference during the cycle (blue). The blocked symbols are the calculated diffusion losses at the instances when a recirculation zone was observed and are overlaid on the static pressure difference trace.
To evaluate the validity of the quasi-steady assumption, the significance of the inertia effects
can be examined through the comparison of the spatial over the temporal acceleration terms
(convection, or spatial acceleration 𝑢𝑑𝑢
𝑑𝑥, over unsteadiness, or inertia 𝜕𝑢
𝜕𝑡) of the
incompressible Navier-Stokes momentum equation (with s, below, being the body forces ):
𝜌 (𝜕𝒖
𝜕𝑡+ 𝒖 ∙ ∇𝒖) = 𝒔 (36)
which along a direction (e.g. x direction): 𝜌 (𝝏𝒖
𝝏𝒕+ 𝑢
𝒅𝒖
𝒅𝒙) = 𝑠 (37)
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The order of magnitude of the two terms can be estimated from inspection of the PIV
velocity contours across the junction. The convection term is calculated based on the
acceleration of the flow from the end of the lateral duct and up to the point of maximum
recirculation height. The unsteady term is estimated based on the change in velocity at the
timescale of half the valve opening (120CAD). The unsteady term is estimated based on
values shown in Figure 66 at approximately 1000m/s2 and the convection term is around
5000m/s2. Although convection and unsteadiness terms were within the same order of
magnitude, they differ by a factor of 5 indicating that the flow was marginally quasi-steady.
This conclusion however is also related to the low running speed of the ‘crankshaft’ for the
PIV cases which was at 600rpm (5Hz). The unsteady term would be expected to become
comparable with the convection term at higher engine speeds at the same load (i.e. from
above 2800rpm). The convection term would be expected to not change in terms of order of
magnitude provided that the load (i.e. the pressure in the plena) was not changed because the
plenum pressure relates to the velocities which will be generated in the duct. In addition, it is
related to the Reynolds number of the flow is such that the flow should be Reynolds number
independent.
Figure 66 : Values of velocity used for the estimation of the convection term of Equation (37). The values refer to the velocity measurements at timestamp E
It is interesting to evaluate the Womersley number which relates transient inertia force due to
the pulsating nature of the flow to the viscous force with the dimensionless expression given
by Equation (38)
𝛼 = 𝐿√𝜔𝜌
𝜇 (38)
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where L is a characteristic length (the duct width in this case), ω is the angular frequency of
the oscillations, ρ is the density of the medium and μ is the dynamic viscosity of the fluid. For
values of α that approach 1, the viscous effects dominate whereas for higher values close to
10 pulsating effects dominate. The Womersley number was 𝑎 ≈ 16 , which suggests that the
transient inertia forces probably dominate viscous forces, although the latter are not
negligible and thus there may be a phase lag between velocity and pressure.
The velocity profile of Figure 67 shows pressure and velocity temporal profiles plotted
together. The importance of spatial acceleration reveals another aspect of the flow that can
lead to large pressure changes apart from the diffusion losses downstream of the
recirculation region. The spatial acceleration of the flow from the incoming duct up to the
maximum height of the recirculation zone implies, through Bernoulli's equation, that a
portion of the upstream total pressure finances the acceleration of the flow field so that the
static pressure decreases, into the outlet duct as far as the maximum height of the
recirculation zone. Then the flow decelerates downstream of the recirculation region, but due
to the diffusion losses the static pressure recovery is below that which erroneous application
of Bernoulli's theorem would indicate. The effect of the acoustic waves is superimposed onto
these phenomena and it also affects the pressure measurement readings. Estimates of both
the pressure decrease, due to the acceleration of the flow to the maximum height of the
recirculation bubble, and of the pressure rise associated with the diffusion of the mean
velocity profile downstream of the recirculation zone are both subject to some experimental
error. Thus, it is hard to know whether the existence of the acoustic waves contributes to the
measured pressure recovery. The waves represent waves of energy passing back and forth:
however, the strength of the incident waves on the junction must be stronger than the
reflected waves due to transmission losses both at the junction and at the open end, or even
at the partially open end. These losses must, presumably, be part of a loss of mean pressure
but it is not possible to say from the current results how strong this loss is.
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As an overall remark of the analysis presented in this section we can conclude that the static
pressure drop that is measured between the two pressure transducers at ducts 1 and 3 is the
combined effect of three phenomena. These are the pressure drop due to acceleration of the
flow (up to the station of the maximum height of the recirculation zone above the
recirculation zone), the diffusion losses downstream of the recirculation zone and the
transmission loss due to the acoustic waves that travel in the manifold.
3.3 Summary This Chapter focused on the analysis of the pressure and velocity measurements obtained
from the experimental arrangement. The results from the pressure measurements were
presented first. Three parametric studies on pressure measurements were presented based on
manifold end boundary condition (open and restricted end), load (low to high) and engine
speed (950 to 2000 rpm). In all cases the profile of the pressure signals was shaped both by
the blowdown pulses and the acoustic waves that act in the manifold superimposed on them.
The effects were stronger for all the cases that involved an open end as the manifold end
boundary condition because it was reflecting the acoustic waves more strongly. The effects
of the superimposed waves on the unsteady bulk flow of the blowdown event were less
Figure 67: Overlay of the pressure signal obtained from stations 1 and 3 and the cross-section average velocity magnitude at 75mm along the outlet duct during the cycle duration.
P a g e | 114
evident in the cases of the restricted manifold end that represented a turbocharger rotor
termination. As a result the shape of the pressure signal on the cases of the restricted end was
closer to the quasi-sinusoidal profile of the exhaust valve than it was for cases of an open end
BC. The signals were also not of identical shape amongst the different engine speeds as the
relative phase between the acoustic waves and the blowdown pulses was different. When the
load increased, it affected the shape of the pressure signals and it also affected the pressure
losses measured across the junction.
The second part of the chapter was dedicated to the velocity data obtained from the PIV
measurements at 9 instances/phases during the cycle duration (equivalent of 600 rpm). The
first two refer to the blowdown pulse travelling from the straight duct and the remaining 7
were timed according to the pulse travelling from the lateral duct. The vector field at the
horizontal plane of symmetry of the manifold revealed that there were two recirculation
zones formed when the blowdown pulse was travelling from the lateral duct. The first was
formed at the end of the straight duct blocking all of the duct’s width. Another recirculation
zone was formed at the inner wall of the outlet duct partly blocking the duct’s width
(approximately 30%). This arises as a result of the manifold geometry where the flow from
the lateral duct is entering the junction at a geometrical angle of 60 degrees on the horizontal
axis. As the flow passes over the recirculation zone it is accelerated and then it diffuses to
cover the original width of the duct. This motion is associated with losses owing to the
diffusion of the flow downstream of the maximum height of the recirculation zone. The
information from the PIV measurements about the recirculation region and the velocity
profiles at the manifold were used to evaluate the diffusion losses. The evaluation was
performed by reference to the theory of losses due to area expansion which is the basic
principle of the Bassett et al. model for the calculation of losses in junction in 1D analysis.
The results were compared to the pressure measurements obtained simultaneously with the
PIV measurements at the lateral and outlet duct. The analysis showed that the diffusion
losses constitute a relatively small part of the losses measured at the junction. The remaining
pressure difference is due to the acceleration of the flow up to the maximum recirculation
height and the transmission loss due to the acoustic waves that reflect at the junction. The
quasi-steady assumption that is used in the 1D model of Bassett et al. was valid for the case
studied in the PIV as it was performed at 600 rpm; however it is expected that it may be
violated at approximately 3000 rpm when the timescale of the unsteady valve motion will be
comparable to the timescale that the flow accelerates in the junction.
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Chapter 4
1D Simulations of Branched Exhaust duct Flow
The development of one dimensional algorithms to simulate the fluid flow in engines has
been useful for the automotive industry and it still dominates the early stages of engine
design. The prediction capability and reliability of one dimensional approximations,
however, remains a controversial topic. The advantages of 1D methods pinpoint the
numerous cases of successful matching of 1D simulations with experimental data. However,
anecdotal evidence suggests that successful matching is, in some cases, possible either after
the experiment has taken place and some re-adjustment of the model has been performed or
when extremely detailed information is available about the precise layout of ducting and
pipes. The aim of the current work is not to comment on the advantages or perceived
difficulties in using such an approach, but to rather study the predictions of flows through
junctions and in particular the prediction of junction pressure losses. The following chapter
presents the comparative study between the experimental data of Chapter 3 and 1-
dimensional simulations of pulsating flow in manifolds. Models of the experimental setup, as
it was outlined in Chapter 2, were developed using the software packages GT Power and
Gasdyn. The pressure loss predictions from each software package were evaluated using the
static pressure measurements obtained from the experiment. The two packages incorporate
different methods to treat the pressure losses at the junction. However, in both packages the
user defined parameters that were necessary to design the 1D representation of the
experimental setup were the same (see also Appendix D). The dimensions for all parts
followed those presented in Chapter 2. The material for all components was also defined in
both models for the calculation of friction coefficients. The material for the two plena and
engine heads was steel and for all manifold ducts was smooth plastic. Finally, the material
for the transition pieces between the engine heads and the manifold was aluminium. The
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inlet temperature was 300K and the pressure was varied according to the experimental case
being tested. The wall temperature was also imposed at 300K for all components. This was
considered adequate as there were no high gas temperatures in the experiments that would
necessitate the calibration of the models in terms of the convective and radiation heat transfer
coefficients. The solution process followed by each package will be presented in the relevant
section below.
4.1 Predictions by Gasdyn Software
4.1.1 Model description and setup
The Gasdyn 1D fluid dynamics software was developed at the Department of Energy of
Politecnico di Milano and it has been validated in both research and industrial applications
(e.g. Montenegro & Onorati 2009; Montenegro et al. 2007). In the present work, a 1D model
of the experimental setup of Chapter 2 was generated and the results of the computations
were compared with the static pressure measurements obtained from the experiment
(Hardalupas et al. 2016). Figure 68 shows the schematic of the model for the open-end case,
taken from the Gasdyn software environment. The model shares, as closely as possible, the
same dimensional characteristics with the experimental setup. It has also been customized to
allow for the piston to remain at a fixed position in the cylinders, so that the available
computational volume matches the experimental one (i.e. a plenum volume). The crankshaft
speed remained the driving time stamp for the calculations. The inlet valves were kept open
throughout the cycle and the calculated pressure traces were monitored at positions in the
ducts, which matched the pressure measuring stations of the experimental rig (Figure 26).
Figure 68: Schematic representation of the 1D model of the experimental setup, as developed in GasDyn software
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The simulations were carried out resorting to both first and second order methods. The two
step LaxWendroff scheme (second order in space and time) and the Riemann solver HLLC
(first order in space and time) methods have been applied to different mesh sizes. The mesh
spacing was uniformly set all over the domain, both downstream and upstream of the pulse
generator. Figure 69 shows a comparison between the LaxWendroff and the HLLC methods
for both 1 cm and 0.25 cm mesh spacing. It can be seen that, for 1 cm mesh spacing, the
results have already reached grid independency in terms of pressure pulsations. Due to the
nature of the pressure wave generation, shock waves were absent from inside the domain,
which led to reducing the advantage of having high resolution schemes. The boundary
condition that mimics the presence of the valves is based on the theory of Benson &
Whitehouse (1983); which is formulated from an approach based on the Method of
Characteristics. Thus the incident and reflected characteristics lines are computed at the
boundary, assuming the presence of a constant volume beyond the boundary. Non-isentropic
flow correlations are used to compute the state of the fluid at the restricted flow section,
where the flow area varies from time step to time step, and then suitably combined with the
state of the gas inside the duct (Benson and Whitehouse 1983). Since this approach is based
on the application of mass, momentum and energy conservation equations, it has been used
often in the literature and has been proven to excite the duct system from a point of view of
pressure wave propagation (Serrano et al. 2009).
Figure 69: Mesh sensitivity and discretisation method analysis on the static pressure calculations at 1250rpm, low load conditions and open end BC for the outlet of the manifold. The results show that mesh independency was reached using 1cm spacing.
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From an acoustic point of view, the usage of numerical schemes with high accuracy is
certainly an advantage for capturing high order harmonics contribution. However, the loss of
high frequency components, caused by the choice of a 1st order method, cannot be seen in a
time domain analysis.
4.1.2 Pressure Loss model
Gasdyn is one of the commercially available software packages that uses the Bassett et al.
(2003) theory for the calculation of pressure losses in junctions. Other programmes that
employ the same junction pressure loss model are the LES (Lotus Engine Simulation) and
the ONDAS (ONe Dimensional wave Action Simulation). As it was discussed in the
introductory chapter, the Bassett et al. (2003) model incorporates the losses due to diffusion
within the outlet duct for the estimation of the pressure loss coefficient at a junction. The
losses are associated with the flow ‘diffusing’ downstream of the maximum height of the
recirculation region which can be formed inside the outlet duct, just downstream of the
junction. In this sense, the effect of a multi-dimensional flow structure can be introduced
with the framework of a calculation procedure using a 1D approximation. The pressure
losses estimation is performed using equations (22) and (23) as in Chapter 1, which are also
repeated here.
𝐶𝑗 = 1 −1
𝑞𝑗𝜓𝑗𝑐𝑜𝑠
3
4(𝜋 − 𝜃)
𝑝𝑑𝑎𝑡 − 𝑝𝑗 = 𝐶𝑗(𝜌𝑢𝑗2)
where j denotes the pipe in question, 'dat' is the datum branch, 𝑞𝑗 the mass flow rate ratio, 𝜓𝑗
the cross sectional area ratio. The angle π- θ represents the deviation of the flow that enters
the outlet duct.
4.1.3 Evaluation cases by reference to static pressure measurements - Gasdyn
A selection of the results of comparing the pressure traces from the 1D calculations and
experimental setup are presented in this section. Figure 70 depicts the overlay of 1D
predictions and experimental pressure traces of the lateral duct (duct 1) for the open end case
at low load conditions and at four different speeds. The experimental results shown are for
the non-overlapping valve scenario with the blowdown pulse of the straight duct (duct 2)
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coming first followed by the pulse from the lateral duct. The experimental results of Figure
Figure 70 correspond to Figure 36 of Chapter 3, therefore the analysis in the present section
focuses only on the comparison with the 1D computations. The correlation is generally
satisfactory across the tested range of speeds.
As it can be seen, more evidently at speeds 1650rpm and 2000rpm, the 1D model predicts a
double pressure peak between 100 and 300CAD, which is associated with the blow-down
pulse of duct 1. However, in the experimental signal, such behaviour is not visible for the 1st
pulse. As discussed in Chapter 3, these intermediate peaks are associated with the acoustic
waves in the manifold that travel at the speed of sound and their effect is superimposed on
the blow down pulse from the exhaust valve. In the 1D predictions, these are more visible
than in the measurements, which may indicate that, although the calculation of the
propagation speed is satisfactory, there is not enough dampening of the energy as these
waves travel back and forth in the manifold.
Figure 70 : Clockwise from upper left - Overlay of measured (dashed line) and Gasdyn-computed (solid line) pressure signals at speeds of 950, 1250, 1650 and 2000rpm in the lateral duct (duct 1) of the manifold at low load conditions and for the open end BC.
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The establishment of the wave dynamics in the manifold is primarily affected by the overall
length of the duct system and all points of reflection. In the present arrangement, the main
points of reflection are the valves and the end BC at the end of the manifold. Numerical
experiments showed that both Gasdyn (and GT Power) were highly sensitive to the timing of
the valve events. The manufacturer of the cylinder heads reports a value of 0.25mm for the
valve lash (Yasuhiro Urata and Kazuo Yoshida at HONDA, personal communication, 2016);
that is to say the distance that the rocker arm of the overhead camshaft travels before the
valve starts to open. The purpose of the valve lash is to prevent the valves staying slightly
open in the case of material expansion due to high temperatures at certain running conditions
and as a result (depending on the design) it may vary according to running conditions.
Practically, the valve lash defines the actual (or effective) opening camshaft angle of the
valve, as opposed to the theoretical one described by the valve profile curve. Since the valve
lash was not measured on-the-fly, it is possible that it deviated from the nominal value given
by the manufacturer of the cylinder heads. It is quite common for the valve profiles, and this
also applies in the present work, to start and finish (valve lift < 1mm ) with a ramp of small
but constant slope. In the intermediate section, the profile is usually approximated by a
quasi-cosinusiudal shape. For convenience the manufacturer refers to the valve lash distance
as of negative sign (-0.25mm) so that the actual valves’ opening and closing timing (-VO,-
VC) correspond to 0mm lift rather than 0.25mm. The value for the valve lash was increased
in the computations to 0.5mm, so that the correlation in terms of pulse timing could be
improved. Figure 71 shows the differences at the valve profiles with nominal (labeled no
lash) and increased valve lash (0.5mm lash). An increase of 0.5mm in the valve lash resulted
in the decrease of the overall valve event by 60 CAD affecting also the percentage of valve
overlap in the cycle (the relative phasing of the EVO and EVC events remained the same).
Accordingly, the maximum lift of the valve was reduced. Apart from the valve lash
researchers as Rai et al. 2014 also report that the shape of the kinematic and dynamic valve
profiles differ from the static ones in aspects such as the radius contour or the eccentricity
between the rocker arm and the valve stem. Such deviations, however, are more common at
high loads or high engine speeds, and it was not considered to be the reason of the deviations
observed in the current work.
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Figure 71 : Static valve profiles (dashed lines) (Yasuhiro Urata and Kazuo Yoshida at HONDA, personal communication, 2016) and effective valve profiles (solid line). The latter profiles were used in all simulations to improve the correlation with the experimental results. They involve a 0.5mm increase in the valve lash.
Figure 72 compares the experimental static pressure trace obtained from the lateral duct with
the traces from 1D simulation1 using 0 and 0.5mm valve lash. The comparison is for
1250rpm and medium load conditions with an open end boundary condition at the manifold
outlet. The differences in timing correlation are more evident towards the opening and the
closing time of the valves.
1 1D simulations using GT-Power v7.4. The selection of 1D software however is not affecting the point being made about the effect of the valve lash on the accurate predictions using 1D tools.
Figure 72: Effect of the choice for valve lash in the 1D simulations. The comparison is based on the static pressure measured on the lateral duct at medium load conditions, 1250rpm and with open end BC at the manifold outlet.
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Differences are also observed in amplitudes and are mostly seen during the overlap region
and at the second pulse where the maximum pressure is underestimated. The differences
shown stem from the relation between the acoustic pressure waves and the percentage
opening of the valves at the specific time that the wave arrives at the valve seat. This relation
is explained through Figure 73 which illustrates the paramount importance of defining the
valve timing correctly for the calculation of the reflections occurring at the valve seat.
A partially open valve is considered to be an orifice type reflection. As such, the transmitted
and reflected waves at the valve seat are affected by the pressure level upstream and
downstream of the valve as well as the geometric ratio of the opening and the adjacent pipe
diameter. By changing the valve lash, the percentage opening of the valve and the valve lift
at a given time step in the cycle (time stamp 2 in Figure 73) are also affected. It can further
be seen, by reference to both Figure 71 and Figure 73, that the boundary at the valves
changes between partially open to closed end due to the truncation of the valve profiles. The
observations above reveal that the predictions of a 1D model are very sensitive to the
accurate representation of the experimental arrangement in terms of valve timing and overall
length of ducting.
Figure 73 : Illustration of a perturbation that travels along the manifold while the exhaust valve is open. The boundary at the end of the manifold is an open end. A change to the percentage opening of the valve at a given time stamp (2) determines the type of the reflection and affects the overall wave dynamics, established in the manifold, during the cycle
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As a concluding remark, it should be noted that the deviations shown in Figure 70 can only
be partly attributed to the 1D model's predicting capability. However, it supports the belief
that good comparisons may be facilitated if detailed knowledge of the experiment exists.
Pressure Losses at the T60o Junction
Figure 74 and Figure 75 show the overlay of measured and computed static pressure traces
for the open end and the 20% restricted end case respectively, at 1250rpm and medium load
conditions. The static pressure losses are substantially larger for the BC with the open end in
comparison to those for the restricted outlet BC case. The computed static pressure losses are
negligible for the pulse coming from duct 2 (20-200CAD), which is certainly not the case
observed experimentally. In addition, the second half of the pressure trace does not follow
the same steep downward trend observed at the measured profile. Since the junction is a T
shape, there is no expectation that a recirculation zone is formed in the outlet duct (duct 3)
when flow is fed from the straight duct. Therefore there are no readily identifiable sources of
diffusion losses in the outlet duct. The experimental values however, show up to 10%
pressure drop (Figure 74) that must be attributed to other processes, such as losses in the
junction area due to expansion and 3 dimensional effects.
For the pulse coming from duct 1 (200-400CAD), the calculations are in phase with the
measured pulse and follow the shape trend (Figure 74), as was the case for the 20 - 200 CAD
pulse. However, both magnitude of the absolute peak of the pulse, and also the
corresponding static pressure losses, are underestimated by the model. Since the valve
phasing scenario is the one of positive overlap between the two exhaust valves, there are no
intermediate peaks in between the pulses as there were in Figure 70. The amplitudes of the
sinusoidal motion present at the end of the cycle, which correspond to the quarter wave
mode, are overestimated by the 1D calculation. The maximum deviation observed between
the experimental and computed static pressure losses is higher for the open end case (10-
15%). In both cases, however, the static losses computed by the 1D model increase when the
pulse travels from the lateral duct. Overall, the attenuation of the pressure amplitudes
computed in the manifold is not as large as in the measured signals. Overall, the attenuation
of the pressure amplitudes computed in the manifold was not as large as in the measured
signals. This arises even after taking into account the so-called Rudinger's formulation for
the open end boundary condition at the outlet section (Piscaglia et al. 2010), which has
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proven to work better than the perfect reflection (isentropic) assumption. In such cases,
adjustment of the friction coefficients may be used. It is common practice for the nominal
values of friction coefficients to be selected, based on the ducts' material. Re-adjustment of
these values is possible, however, it is a measure of calibration of the model to match the
experimental data and does not necessarily reflect the actual cause for the deviation of
results.
Figure 74 : Overlay of experimental (dashed lines) and computed (solid lines) traces for pressure at duct 1 and 3 (left) and percentage pressure losses (right) for the open end case at medium load conditions with valve overlap.
Figure 75 : Overlay of experimental (dashed lines) and computed (solid lines) traces for pressure at duct 1 and 3 (left) and percentage pressure losses (right) for the 20% restricted end case at medium load conditions with valve overlap.
A safe estimation of the origin of the deviations may be achieved if the comparison is based
on additional parameters. The present chapter is focused on the comparison based on static
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pressure measurements only; however it is proposed that the work is extended to include
velocity and mass flow rate comparisons so that the energy contained in the pulses can be
estimated.
4.1.3 Summary
An analysis of the in cycle manifold pressure focusing on the calculation of static pressure
losses was performed using the 1D engine simulation software Gasdyn. The results were
evaluated by reference to the static pressure measurements that were presented in Chapter 3.
A temporal analysis revealed that the calculations are very sensitive to adjustments to the
valve lift events as these directly affect the reflections of the acoustic waves propagating in
the manifold. As the valve is considered an orifice type boundary, the percentage opening of
the valve at the time of arrival of the incident wave is crucial for the correct calculation of
the reflections. Good temporal matching was obtain by increasing the valve lash by 0.5mm
as compared to the value proposed by the manufacturer, an adjustment which is within the
bounds of plausibility. This affected both the opening duration of the valves and their
maximum lifts that were set for the experimental valve scenario. As far as the pressure losses
are concerned, Gasdyn uses the Bassett et al. model (2003) for the junction that includes
diffusion losses of the flow inside the outlet duct. The model underestimated the static losses
at the junction during both exhaust valve events by 4 and 15% respectively at the open end
BC case and by 1% and 4% in the case of a restricted end BC. Overall, the model predictions
were satisfactory in terms of pulse timing, but the maximum difference observed from the
experimental values was 15% and 4% at the open end case and restricted end case
respectively.
4.2 Predictions using GT Power
4.2.1Model Description and setup
GT-Power is a widespread commercial packages for 1D engine simulations. The schematic
of the model for the experimental is shown in Figure 76 taken from the GT-Power v7.4
software environment. The domain is split into components, which are further discretised to
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smaller sub-volumes. The discretised grid in GT-Power model had an equal spacing of
25mm with the exception of the transition parts that join the engine heads with the Perspex
manifold. For these components the grid spacing was 5mm.
Figure 76: Schematic representation of the 1D model of the experimental setup, as developed in GT-ISE software
The governing equations of the fluid flow, namely continuity, momentum and energy
equations, were solved in the bulk flow direction (in 1 dimension). A 5th order Runge Kutta
explicit integration scheme was used to determine the solution variables at the sub-volumes
as the time step advances. The explicit method is preferred, when accuracy on the pressure
pulsations is of high importance, although it is more time consuming since small time steps
are required. To retain solution stability, the relationship between the temporal and spatial
discretisation (time step over sub-volume size) is defined by the Courant number, which
dictates that:
𝛥𝑡∙𝑈𝑚𝑒𝑎𝑛
𝛥𝑥< 1 (39)
However, GT Power uses an alternative, yet similar, expression that ensures stability of the
simulation:
𝛥𝑡
𝛥𝑥(|𝑢| + 𝑐) < 0.8 (40)
where u is the bulk flow velocity and c is the speed of sound.
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4.2.2 Pressure Loss model
The computational approach of GT-Power for the pressure loss calculation at junctions
originates at the 1980s with the work of Morel et al. (1988). Although, extensive details of
the model are not available in the open literature, it is reported to work in a similar way to
the work of Chapman et al. (1982), which has already been discussed in Chapter 1. The
junction is represented in the algorithm by a sub-volume, the flowsplit that cannot be further
discretised. According to the description provided in the software's documentation, a
staggered approach is followed for the solution of the governing equations at the junction.
The scalar properties are computed at the centre of the volume, whereas the solution of the
momentum equation is carried out separately at each of the junction volume’s openings;
these are the boundaries with the adjacent pipes. The solution is performed iteratively so that
a single value is obtained for each of the scalar properties in the junction volume. The
flowsplit is characterised using three parameters, namely the characteristic length, the
expansion diameter and the relative angle between the pipes comprising the junction as in
Figure 77. It can be assumed that the first parameter determines the travelling distance of the
propagating waves within the junction and the second parameter is used to calculate flow
losses due to expansion of the flow as it enters the junction volume. In the case of flow
travelling towards the junction from only one duct at a time, the expansion diameter is
calculated from the geometrical characteristics of the junction volume. When there is in-
phase flow (overlap of blowdown events), the documentation of the software recommends
that the expansion diameter is reduced for each of the feeding ducts to only a portion of the
geometrical expansion diameter. Although, this treatment is intuitively correct, an
appropriate value for the reduction of the expansion diameter is to be sought through a trial
and error process. As will be discussed in more detail below, in the case of in-phase flow
(valve overlap scenario), the expansion diameter value was reduced at the lateral duct only,
improving the correlation with the experimental data. The software's documentation is also
reporting the work of Miller (1971) for the calculation of losses in bends, so it is possible
that the third parameter (i.e. the relative angle between the pipes) is used to include the effect
of the change in direction in the calculation of losses.
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The description presented above suggests, that the loss model used in GT-Power is
fundamentally different from the one implemented by the Gasdyn software. In the latter, the
system of the governing equations at the junction and the calculation of pressure losses are
constructed at a pair of branches. The procedure follows the work proposed originally by
Hager (1984) for incompressible flows which was discussed in detail in Chapter 1. It suffices
to repeat here, though, that one of the branches in this method is always the branch with the
maximum mass flow towards the junction. In the present case of a 3-way manifold, two pairs
are constructed and the solution progresses iteratively so that the continuity equation at the
junction is satisfied. Both modelling approaches can compute the pressure changes due to
wave motion. GT Power appears to also include losses due to irreversibilities from the
sudden flow expansion in the junction.
4.2.3 Evaluation cases by reference to pressure measurements - GT Power
The evaluation of the computations is focused on both the correct timing of the pulses as
well as the static pressure losses across the junction. Figure 78 and Figure 79 show the
correlation of results for the case of the open end boundary condition and 20% restricted end
respectively at the running speeds tested (Table 1 – page 71). The calculations follow the
trend of the experimental data satisfactorily in terms of pulse timing for both cases of end
boundary conditions. It can also be observed that the correlation is similar to the one
Figure 77: Setup of the junction sub-volume attribute in the GT-Power environment. Apart from the geometrical orientation of the three ducts comprising the junction, additional information on the expansion diameters in the junction volume and characteristic lengths for each duct is required.
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obtained from the Gasdyn software regardless of the differences in the setup of the two
models. This observation, however, does not imply that a one dimensional code is insensitive
to differences in the modelling approach in general. It rather illustrates that as long as the
overall dimensional relations between the experimental arrangement and the 1D
approximation are consistent between the two models, the results obtained for the
propagation speed of the pressure perturbations are bound to be similar.
In contrast, the way in which the energy of the pulsating flow in the manifold dissipates is
not as straight forward. A number of factors, including friction losses and losses due to
complicated flow structures like expansion losses, need to be considered. As was also seen in
Figure 78: Clockwise from upper left - Overlay of measured (dashed line) and GT-Power computed (solid line) pressure signals for speeds of 950, 1250, 1650 and 2000rpm observed at the lateral duct (duct 1) of the manifold at low load conditions and using an open end as the manifold end BC.
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Gasdyn computations, the pressure traces calculated from GT-Power show a number of more
distinct peaks superimposed on the blowdown exhaust pulses. This can be related to the
reflections of the waves at the outlet boundary being less dissipated than in reality. This view
can also be supported by the improved correlation between the 1D and experiment shown in
Figure 79.
Figure 79 : Clockwise from upper left - Overlay of measured (dashed line) and GT-Power computed (solid line) pressure signals at speeds of 950, 1250, 1650 and 2000rpm observed at the lateral duct (duct 1) of the manifold at low load conditions for 20% restriction at the manifold end BC.
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Pressure Losses at the T60o Junction
The evaluation of the 1D results on the static pressure losses is presented for both open end
and restricted end outlet BC in Figure 80 and Figure 81. The running speed was 1250rpm
under medium load conditions and for the valve overlap scenario. The setup of the junction
attribute in GT-Power requires an appropriate value to define the expansion ratio
encountered as the flow enters the junction. Since there is pulse interference for the scenario
of valve overlap, ducts 1 and 2 were both feeding the junction for a portion of the cycle.
Figure 80 shows the overlay of the predicted and experimental static pressure traces on the
lateral (duct 1) and the outlet duct (duct 3) and the corresponding percentage static pressure
change using three different approaches for the calculation of the expansion diameter. The
positions in the ducts at which the calculated static pressure traces are plotted are the same as
the positions of the pressure transducers on the Perspex manifold (Figure 26).As illustrated
in Figure 80, the model is sensitive on the selection of the appropriate values for the
expansion diameter. Flow expansion, based on the geometrical values, resulted in
underestimation of the static pressure losses by approximately 5% in both pulses, whereas
splitting the expansion diameter in two, as suggested by the software documentation for in-
phase flow, resulted in static pressure gain for the pulse travelling from the straight duct
(10% deviation from the experimental result). Finally, a smaller value for the effective
expansion diameter was selected (7% reduction) only for the flow coming from the lateral
duct (duct 1).
In the case of the 20% restricted end boundary condition, the same approach was followed
for the expansion diameter in the junction attribute. The results are presented in Figure 81,
where it can be seen that the percentage static pressure losses are in very good agreement
with the experimental values. However, the absolute values of the static pressure trace are
overestimated for the pulse coming from the lateral duct (duct 1). Therefore, reducing the
expansion diameter in the junction by inserting user defined values primarily affects the
predictions upstream of the junction. There is an increase of 'back pressure' before the
junction that results in higher amplitudes observed in the static pressure trace of duct 1. This
is in disagreement with the approach of Gasdyn for which the attempt to improve the
predictions was focused on the outlet duct.
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Figure 80: From top to bottom: the expansion diameter was calculated based on geometry, in-phase flow correction and ad-hoc adjustment for partly in phase flow. The graphs on the left show the overlay of experimental (dashed line) and computed (solid lines) traces for pressure at duct 1 and 3 and on the right the percentage static pressure losses for the Open end case at medium load conditions and at speed 1250rpm.
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Figure 81: Overlay of experimental (dashed line) and computed (solid lines) traces for pressure at duct 1 and 3 (left) and percentage pressure losses (right) for the 20% restricted end case at medium load conditions and at speed 1250rpm.
4.2.4 Summary
In cycle manifold pressure predictions from GT Power were compared against the
experimental static pressure data presented in Chapter 3. An analysis of the parameters
involved in the calculation of static pressure losses at the junction was attempted by
reference to the modelling attributes requested by the software for the junction. The junction
model is adjustable so that a better estimation of the pressure losses can be obtained. In the
present study, the values for the flow expansion in the junction when the pulse travels from
the lateral duct have been adjusted to improve the correlation with experimental data. As a
consequence, for the cases of the outlet end, the temporal correlation was very good and the
maximum deviation in percentage static pressure losses was about 5%. However, the
instantaneous absolute static pressure trace calculated for the pulse coming from the lateral
duct was offset from the experimental observation. For the case of restricted outlet BC, the
duration of the pulse coming from the straight duct was overestimated but the percentage
static pressure losses were within 3% difference from the experimental data. Overall, the
predictions from GT Power were satisfactory and, with fine adjustment of the junction
attributes, a very good correlation with the experimental results can be obtained.
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4.3 Summary and Conclusions The experimental arrangement presented in this work has been modeled using the 1D engine
simulation tools Gasdyn and GT Power. Evaluation of the models has been performed by
reference to the static pressure measurements obtained from the experiment, as these were
presented in the previous chapter. The two software packages implement different pressure
loss models, which also allowed for a comparative study of the static pressure losses across
the junction. A very good correlation with the experiment in terms of pulse timing was
obtained for both models in open and restricted end cases. This was achieved, by increasing
the valve lash from its nominal value given by the manufacturer. The effective valve
duration of both valves and the percentage of valve interference were therefore reduced,
demonstrating the importance of the valve profile timing in producing accurate results.
The predictions with Gasdyn revealed that the model was capable to follow the trend of the
static pressure traces in the straight duct satisfactorily, although some underestimation of the
peak amplitude was observed. Deviations between experiments and simulations were more
evident for the lateral duct. Computations using GT Power yielded similar results for the
straight duct. The GT Power pressure loss model improved the agreement with the
experiment for the lateral duct, as opposed to the predictions obtained by Gasdyn. This,
however, was achieved after some ad hoc adjustment of the parameters in the junction
attribute. In general the energy dissipation calculated by the 1D models was not as strong as
in the experiment and the maximum deviations observed for the static pressure losses were
of the order of 10% for the open end case and 4% for the restricted end case. The predictions
of the static pressure losses inside the junction and of the wave action in the three duct
branches could be improved by performing 3D simulation of the system. A more detailed
reconstruction of the domain, as mentioned in the analysis of the results, could be beneficial
for the prediction of the wave action. Additionally, the inclusion of viscous effects can
account for unforeseen interactions between vortices, generated at the passages of velocity
pulses through the junction, and the pressure probes.
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Chapter 5
Computational Fluid Dynamics
In this chapter simulation results of the unsteady, compressible, flow in model three-way
manifolds are presented. The simulations were performed using the open source CFD
software OpenFOAM employing the Finite Volume Method (FVM) for the numerical
approximations. The overview of the solution algorithm for the selected approach is
presented first followed by the results obtained from the CFD simulations on both Y and T
shape manifolds under pulsating inlet conditions. In contrast to the experimental results
shown in the previous chapter, the CFD simulations were focused on compressible flows
with Mach numbers above 0.3. The reason was to extend the evaluation of the assumptions
for incompressibility and perfect mixing of the flow at the junction which were used in the
derivation of the 1D pressure loss models in junctions. The evaluation was performed by
reference to qualitative analysis of the flow field and by comparing the predicted pressure
drop by an 1D macro-control volume analysis across the junction area of the manifold to the
corresponding pressure drop calculated from the CFD simulations.
5.1 Simulation setup
5.1.1 The geometries
The study of the three dimensional pulsating flow in engine manifolds was focused on three
way junctions of both Y and T geometries. T-junctions are more common in manifolds of
passenger cars, while the Y-junctions are more common in racing engines or motorbikes. A
schematic of the two geometries that were used is provided in Figure 82. The T shape
junction had a branch angle of 60 degrees, to match the experimental setup. For the Y
junction, two geometries were considered with 30 and 60 degrees branch angle respectively.
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Both Y and T shape junctions were modelled using square cross section ducts of 25 x 25
mm. The length of the two feeding ducts was 250mm (along their centreline) whereas the
outlet duct followed the dimensions of the Perspex manifold. The geometries did not include
exhaust valves and exhaust ports to allow for more simplified boundary conditions to be
applied at the inlets as it will also be discussed in the relevant section below.
Figure 82: The CFD simulations were performed using geometries of three way junctions of Y and T shape; two Y junctions of 30 and 60 degrees branch angle respectively and one T junction that resembles the experimental setup with 60 degrees branch angle.
5.1.2 Solution algorithm review
The solver selected was rhoPimpleFoam which is a transient solver for laminar and turbulent
compressible flows. It uses the PIMPLE algorithm (http://cfd.direct, 2017) which is a
combination of PISO (Issa 1986) and SIMPLE (Caretto et al. 1972) algorithms with the
addition of a number of outer correction loops. The values obtained on the last of the outer
loops are used as initial conditions to advance the simulation in time. As PIMPLE is a
pressure-velocity coupling algorithm, the solution is sought through an iterative procedure
where an initial pressure or velocity field is updated (corrected) while mass, momentum and
energy conservation laws are met (Ferziger and Peric 2002). For the conservation of energy,
the user may select between two alternative implementations; either using internal energy or
the total enthalpy of the fluid as the main parameter. In non-reacting compressible flows, as
in the case examined in this work, use of the enthalpy, h, is generally recommended:
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𝜕𝜌ℎ
𝜕𝑡+ ∇ ∙ (𝜌𝑼ℎ) +
𝜕𝜌𝛫
𝜕𝑡+ ∇ ∙ (𝜌𝑼𝐾) −
𝜕𝑃
𝜕𝑡= −∇ ∙ 𝒒 + ∇ ∙ (𝜏 ∙ 𝑼) + 𝜌𝒈 ∙ 𝑼 + 𝑆 (41)
The working fluid for the simulations was considered to be air which is a real gas and the
compressibility factor, ψ, of the fluid was given from:
𝜓 =1
𝑅𝑇 (42)
with R being the specific gas constant.
Sutherland's formula was used to calculate the dynamic viscosity μ, which includes the effect
of temperature changes:
𝜇 =𝛢𝑠√𝑇
1+𝑇𝑠𝑇
(43)
with As=1.4792x10-6 [kg/(msK1/2)] and Ts=116 [K] the Sutherland coefficients.
5.1.3 Turbulence modelling and numerical discretisation
Turbulence is a type of fluid motion consisting of eddies of a range of different scales that
succeed in stirring the fluid in a random and chaotic way (Durbin and Pettersson Reif 2001).
Direct computational resolution of the smallest scales of turbulence results in excessive
increase of the mesh size and computational effort. To avoid this, the time-averaged form of
the equations together with turbulence models exist in the open literature for a wide range of
engineering flows following the observation that the smallest scales bare similarities even
between macroscopically different flows (Tennekes and Lumley 1972). In the present work,
the standard form of the k-εmodel was used (Jones and Launder 1973; Launder and
Spalding 1972) which was developed for the Reynolds Averaged form of the Navier Stokes
and other transport equations (RANS). Large Eddy Simulation (LES) was also an option
with for the inclusion of turbulence in the simulation, however this was not adopted for two
main reasons. Firstly, the aim of the study was not to demonstrate the superiority of different
types of CFD simulations in representing the exhaust flow. In such case, it is expected that
direct numerical solving (DNS) of the transport equations including all scales of the
turbulent motion would be the sensible choice. The aim however was rather focused on
examining the validity of assumptions regarding the incompressibility and perfect mixing of
the working fluid in the junction area as these were used for the derivation of 1D models that
predict pressure losses in the junctions. The standard k-εmodel is widely validated in
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numerous engineering problems and it has been shown to perform well apart from
unconfined and highly swirling flows. It was therefore assumed that it would be adequate for
the current study given also the non-complex geometry of planar three way junctions and the
relatively simple boundary conditions. Furthermore, the increase in computational cost by
implementing LES or even performing a DNS simulation would not result in significant
benefit since direct comparison with experimental results of the flow field was not possible
due to limitations of the PIV setup that allowed only for image capturing in low Mach
numbers. Nevertheless, comparison of predictions between different CFD simulations and
validation over high speed PIV measurements could be performed in the future as possible
extension to this work.
The discretisation of equations for the numerical solving is performed through the finite
volume method as a standard practice in CFD simulations. It relies on the volume integration
of the equations across the cells that comprise the mesh and the substitution of the PDEs by a
set of linear, discretised algebraic equations based on the nodal points of the mesh. Since the
flow examined was transient, discretisation was performed both in space and time using a
central differencing scheme and the implicit Euler method respectively.
5.1.4 Boundary conditions
At the edges of the computational domain, the value or the derivative of the solution of the
discretised equations are specified through the boundary conditions. Usually, the pressure is
fixed and velocity gradient is set to zero at the inlet of the domain or the velocity is fixed and
the pressure gradient is set to zero (Hirsch 1991). In the case of the gas flow in a manifold, it
is not feasible to obtain velocity measurements at the exhaust valve seat. Static pressure
measurements are less intrusive and, therefore, more likely to be available for comparisons
against simulation results but again these are most probably to be available downstream of
the exhaust valve and exhaust port. If experimental values are not available for the specific
parameters, data from 1D engine models are used instead. Information on both velocity and
pressure are needed to fully characterise the inlet conditions, alternatively total pressure can
be prescribed as a boundary.
This latter approach was followed in the present work. The values obtained from the
experiment presented in Chapter 3 were not available at the time of the CFD computations.
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The boundary conditions for the geometries were supplied using data from a 1D model of a
2.0L Volvo engine (Johan Lennblad at Volvo VCC, personal communication, 2013) which
was calibrated to match the output data of the production engine. A time-varying total
pressure boundary condition was supplied at the one of the two inlets (feeding ducts) as
shown in Figure 83 to reflect the change in pressure during the blowdown pulse. The time
varying total pressure value was prescribed using data from the 1D model at 1500rpm and
part load conditions. The exhaust valve opening duration for this was 200 CAD, while the
maximum value of the pressure pulse was 1.75bar. At the exit (outlet duct end) static
pressure was set to atmospheric conditions (1bar) and the velocity gradient was set to 0. All
boundary faces were co planar to the end cross sections of the ducts. Finally, the walls were
treated as adiabatic and the no-slip condition was applied for velocity.
Figure 83: Time varying pressure boundary condition, imposed at the inlet of duct 2 of the computational domain. The dotted vertical lines represent the values of CAD at which contours of velocity magnitude and density are presented in the following paragraph.
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Before the comparative runs between the Y and T junctions, a 2D test case was also
performed to evaluate the acoustic behaviour of the boundary conditions at the duct ends.
For this test case, the geometry the Y shape manifold with 60 degrees branch angle was
selected. A finite wave of 1.2 bar amplitude was generated at the inlet of the branch duct on
the left hand side (Figure 84) and was left to propagate in the computational domain.
Figure 84: Evaluation of acoustic response of boundary conditions: open end, closed end and wave transmissive in a 2D test case of a Y60o junction. A finite length plane pressure wave was generated at the inlet of the branch duct on the left.
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The boundary at the feeding duct remained open to the atmosphere, the other side branch
was modelled to have a closed end boundary and the outlet duct had a wave transmissive
boundary condition. The latter type of boundary condition is typically used to represent long
ducts or to isolate the computational domain from reflections travelling inwards from the
outlet end. Alternatively, the wave transmission boundary can be regarded as the equivalent
of an anechoic termination. During the propagation of the wave both pressure and velocity
were monitored along all three ducts of the manifold. Figure 84 shows the position of the
wave(s) in the manifold and the pressure and velocity along the three ducts for two instances
in time, 0.5 and 1.65ms respectively. The predictions of the wave amplitudes as they were
reflected to the boundary faces were validated against analytical expressions. These are
available in the open literature (e.g. Benson, Horlock, and Winterbone 1982) for the
reflection of a finite plane wave that reaches an open or closed end of a duct.
5.1.5 Mesh generation and convergence
An orthogonal mesh was generated using the blockMesh utility of OpenFOAM which
divides the geometry in compartments that can have different mesh resolution. The initial
orthogonal mesh for all geometries comprised 100000 hexahedral cells. However, the mesh
size was later increased to approximately 250000 hexahedral to reach mesh independency
while y+ values at the walls remained in the log-law region to be in line with the use of the
k-ε turbulence model. The grid independence of the solution was evaluated by reference to
percentage changes in pressure and velocity cell values at a cross section 15D downstream
the junction. Apart from increasing the mesh resolution, a geometrical grading of the cells'
size was used in all compartments along the streamwise direction of each duct. This resulted
in a local refinement at the junction area with the cell size ratio between the free end and the
junction end of each duct being 2:1. Figure 85 shows the difference in mesh density at the
junction and outlet duct area as an example for the T60o geometry.
The time step, namely 5e-07s, or about 0.0025 CAD, was selected, so that the Courant
number remained below unity for the entire simulation. Low Courant number is not a
prerequisite for transient solvers convergence. However, it gives a good indication of mesh
quality. The simulations were repeated for three consecutive openings of the inlet valve to
achieve a repeatable flow pattern.
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5.2 Results and Discussion
5.2.1 Qualitative Results
In this section, the results of the OpenFOAM computations will be discussed for all the types
of tested junctions. Contour plots of the velocity magnitude and density field are shown in
Figure 86 and Figure 87 respectively for Y30o, Y60o and T60o junction types at selected time
steps during the flow pulse. The timing of the snapshots was selected, so that a direct
comparison between the accelerating and decelerating phases of the flow pulse could be
made. Because of the significant variations along the pulse, some of the contour scalings had
to be altered between the snapshots, so that the differences are more evident. As shown in
Figure 83, time steps, where the pressure amplitude at the inlet is the same but the pulse
phase differs, are available for comparison (i.e. region 20-80CAD). However, the plot of
Figure 83 represents the boundary condition at the inlet of the branch duct, so the points of
equal pressure, such as those calculated at the junction end of the branch duct, were at
different CADs. The pressure trace at the junction end of the branch duct was of the same
shape as that at the inlet, but it is phase shifted in time as a result of the pulse propagation in
that duct. The pressure development will be discussed in more detail in the quantitative
analysis that follows. The comparison between snapshots of similar pressure amplitudes
Figure 85: Mesh density at junction area (left) and outlet duct(right) for the T60o geometry. There was a 2:1 geometrical grading at the streamwise direction that allowed for the refinement of the mesh at the junction area.
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upstream of the junction is essential for identifying how losses are linked with the phase of
the pulse.
Based on the contour plots of Figure 86, a few observations can be made about the flow
field. In Y-junctions, there is only one recirculation zone formed inside the junction area,
which then expands solely into duct 2. In contrast, in the T-junction, two distinct
recirculation zones are evident, which also agree with the experiment. This is expected due
to the wall impingement type of flow at the junction.
Figure 86: Spatial distribution of the flow field with velocity magnitude contours in the plane of symmetry in Y-30o, Y-60o and T-60o geometries during the propagation of the pressure pulse.
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The recirculation zone at the outlet duct is significantly smaller than the one in the straight
duct (duct 2). The recirculation zones in duct 2 for both junction types expand substantially
towards the closed end as the pulse progresses and then collapse as the pressure pulse
amplitude decreases. However, the recirculation zones form again during the late phase of
the pulse, although weaker in intensity. The recirculation zone in the outlet duct of the T-
junction is established and maintained throughout the whole pulse duration, while its
thickness and length vary along the pulse but not significantly. This is in contrast with the
PIV measurements where, at lower pressure conditions the recirculation was formed only
during the decelerating part of the pulse. However, the establishment and size of the
recirculation region past an obstacle or a change of direction in a duct system are known to
be dependent on the value of the Reynolds number (Crane and Burley,1976). Since the
velocities obtained from the PIV measurements were 4-5 times smaller than the ones
computed in the CFD (due to the difference in the maximum pressure of the exhaust pulse),
the ratio of the Reynolds numbers is 6 between the CFD and experiment. Therefore, the
shape and size of the recirculation zones as calculated from the CFD were expected to differ
from those shown in the experimental results.
The next field value to be studied is the spatial variation of density in the junction
geometries. As Benson has stated (Benson, Horlock, and Winterbone 1982), some
compressibility effects were evident in his experimental results, although his method did not
account for these in the calculation of the pressure losses in three way junctions. The
methods of Hager (1984) and Bassett et al. (2003) are based on hydraulics theory and
incompressible fluids for the derivation of equations. Nevertheless, the latter reports a good
agreement of the method when compared with shock tube experimental data. Figure 87
shows the contours of the gas density field at the same temporal snapshots as those of the
velocity presented above.
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Figure 87: Spatial distribution of gas density in the plane of symmetry in the Y-30o, Y-60o and T-60o geometries during the propagation of the pressure pulse. The colour scale had to change to depict the density spatial variations for the Y-60o junction.
The density variations in the Y-junctions are significant in both phases of the pulse. The
calculations show that the gas density amongst the duct ends that form the Y-junction differs
by more than 10%. For the T-junction, the deviation of density is related to the selection of
the cross sections, where the comparison is made. What is evident for both geometries is that
the density field depicts non-uniformities both in proximity to the junction and further
downstream. Thus, the assumption of constant density (as in incompressible fluids) and the
assumption that the flow leaves the junction already mixed (Corberan 1992) are not
supported by the 3D CFD findings. The impact of the significant density variations however
should also be examined quantitatively. The analogy presented in the previous chapter
between the sudden step expansion and the flow past the maximum height of recirculation
region was based on the assumption of incompressible flow. In the following section, the
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results from the CFD computations were used to examine whether incorporating the density
values computed from the CFD to the 1D analysis affected the predictions of the 1D model.
5.2.2 Quantitative analysis
As stated earlier, a series of temporal snapshots were selected to depict the quantitative
difference in the flow field at the mid plane of the junction with regards to the pulse phase.
The spatially averaged static pressure trace along the cross section of the ducts before (end of
duct1) and after (start of duct3) the junction is shown in Figure 88 for the Y30o, Y60o and
T60o junctions. The cross section before the junction is located 1.5 diameters away of the
duct end. Since no recirculation zone appears at the outlet duct of the Y-junctions, the
downstream measuring point is 1 diameter away of the junction boundary with the outlet
duct (duct 3). For the T-geometries, the downstream cross section at which the pressure is
reported is further away from the junction boundary and at a point where the recirculation
zone thickness reduces to zero (5D away of junction end of the outlet duct).
For Y-junctions, there is a pressure gain at the outlet duct during the first phase of the
exhaust pulse and a pressure drop after 40CAD at the second phase while the pressure
amplitude decreases (Figure 88a, b). In contrast, for the T-junction (Figure 88 c) after about
40 CAD only pressure drop is observed between the pre and post junction cross sections.
However, the area between the two cross sections includes the recirculation zone which is
expected to result in additional pressure losses because of the diffusion of the flow past the
zone’s maximum height. The pressure drop between the two ducts is mostly observed at the
second phase of the pulse. It is also noted that, for the T shape junction only, the pre junction
pressure trace depicts no sub-atmospheric regions as opposed to the pressure trace from the
outlet duct. This behaviour is also supported from the experimental pressure measurements
obtained in the open end cases.
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Figure 88: Pressure traces upstream and downstream of the junctions (a) Y30o, (b) Y60o, (c) T60o. Sections AA' and BB' indicate the pressure rise or pressure drop for the same pressure level upstream of the junction (5D from end of duct1).
Figure 88 also shows two instances in time during the pulse, denoted as A and B with equal
pressure level at the branch duct. The two instances however are not associated with the
same phase of the pulse. At A the pressure amplitude is still increasing whereas at B the
pressure is decreasing. Points A’ and B’ denoted the pressure at the cross section
downstream the junction at the same instance in time. The difference between AA’ and BB’
reveal that the static pressure drop across the junction is dependent on the phase of the pulse.
In the light of this, coefficients that were developed based on steady state conditions taking
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into account only the geometrical features of the junction (Blair, Chapter 1) cannot
distinguish between the two phases of the pulse. Therefore the coefficient computed will be
the same between AA’ and BB’. As a result the difference observed in the pressure drop
between AA’ and BB’ using a 1D approximation of such coefficients will depend on the
mass flow at each duct.
In unsteady conditions, there is mass accumulation in the junction and into the closed end
duct (duct 2 in this case), which is then followed by the discharge of the same mass towards
the outlet duct. The closed-end branch forms a chamber, where part of the fluid is stored for
a period of time, which varies amongst manifolds of different geometry. During this period
the junction can be regarded as of a 'supplier type' based on Blair's notation. In the present
cases, the mass flow, that was initially stored in the closed end branch (duct 2), escapes into
the outlet duct. Subsequently, the junction type switches to a 'collector type', as the highest
mass flow rate is through duct 3, where the flow is away from the junction. This switch may
happen more than once during the overall pulse duration, although with less intensity. To
depict this behaviour, pressure traces and mass flow rates at the inlet and outlet ducts were
plotted against crank angle degrees (CAD) to further investigate the effect of mass flow rates
as the exhaust pulse travels through the junction (Figure 89). The mass flow traces are for
inlet duct1 and the outlet (duct3). The difference between these two over time is the mass
flow that escapes in the inlet duct 2 (𝑚2̇ ), where it accumulates during the first stage of the
pulse - this phase is indicated as ‘supplier’ in the graphs of Figure 89. The same mass will
then be discharged from inlet duct 2 towards the outlet, switching the junction type to that of
a collector. The transition between the supplier and the collector type occurs almost at the
same instant in time for all three junctions. That can be explained by the similarities of the
geometries. Ducts 1 and 2 are modelled to be of the same length and cross section resulting
in the same volume. What is also evident is that this transition happens as the upstream pulse
is reverting from positive to negative pressure gradients.
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Figure 89: Pressure and mass flow traces for junction geometries (a) Y30o, (b) Y60o and (c) T60o at a location at the junction, which is at 5D from end of duct1 (inlet) and 5D from start of duct3 (outlet).
Another, observation is that the flow field across the mid plane of the manifold also changes
during the blowdown pulse. Recirculation regions that form and collapse in the manifold
branches are expected to increase the overall losses observed in the manifold by an amount
equal to the diffusion losses as they were outlined in the previous Chapter. As a concluding
remark, Figure 88 and Figure 89 reveal that the pressure loss coefficient must follow an
approach that links both pressure and mass flow rate. Therefore the Bassett et al. model
(Eq.(22), Chapter 1) is expected to behave better than a coefficient that only relies on
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geometry and which is going to have a single value throughout the pulse. The evaluation of
the pressure losses predictions based on the Bassett et al. model will follow in the next
section.
5.2.3 Pressure loss calculation comparison between CFD and 1D
The correlation between CFD and 1D models for the calculation of pressure losses at the
junctions of all geometries tested are presented in this section. For the CFD cases, the static
pressure difference (ΔP) across the junction is estimated by spatially averaging the values at
two cross sections (i.e. upstream and downstream of the junction). Figure 90 shows a closer
representation of the cross sections locations for the T junction, where the presence of the
recirculation region was also taken into account. The cross sections A'' and C are selected so
that the streamlines are more or less parallel to the direction of the axis of the ducts (1.5
diameters upstream and 5 diameters downstream). For consistency in the calculation
procedure the cross sections downstream the junction for both Y and T geometries were
selected to be 5 diameters away from junction borders. For the 1D model, the calculation of
static pressure difference (ΔP) is performed using equations (22) and (23). As it was
indicated in the qualitative analysis, there is no recirculation zone formed in the outlet duct
of Y geometries. The Bassett et.al. (2003) model, as suggested by the authors, also applies in
cases where ξ value, (percentage of duct area free of recirculation zones-Figure 7), lies
between 0 and 1. That allows for the equations (22) and (23) to be also used for the pressure
loss calculation in Y geometries, where no recirculation is formed in the outlet duct. For the
comparison of the results, the Bassett et al. (2003) model was used both in its original form,
assuming a constant density across the junction, as well as with a realistic density - namely
the one calculated from the CFD at the outlet duct - imposed at the downstream branch.
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Figure 90: Control volumes within plane of symmetry for the junction area of the T-60° junction geometry, following the notation of (Bassett, Pearson, and Fleming 2003)
Figure 91 depicts the static pressure loss, as calculated for the T60° case. The 1D model
captures a significant portion of the losses quite well apart from two areas indicated by the
highlighted grey regions of Figure 91. It can be observed that the pressure loss ‘signal’ (ΔP)
has also the shape of a pulse, although shifted in time, as compared to the exhaust pulse that
is depicted in Figure 92.
Figure 91: ΔP across the junction, as calculated by CFD and Bassett 1D model for constant density assumption using (rho1) and using outlet duct density (rho3) values for the case of T60o geometry
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Figure 92: Static pressure traces of duct1, duct3 and ΔP for the T60o geometry, as calculated from the CFD and the pressure trace of duct3 based on the model of Bassett et al (2003).
Since the absolute value of the pressure difference is significantly smaller than the
background pressure in the manifold, the comparison is made based on ΔP to be more
informative and intuitive of the way losses occur during the evolution of the flow pulse. As
shown in Figure 91 and Figure 92, there is a sudden spike at the beginning of the static
pressure drop (ΔP) trace (10-20 CAD). This might be linked to the early stage of the exhaust
pulse, when the recirculation zone is being established in the outlet duct. The area where the
next discrepancy occurs is linked with the outlet duct being at sub-atmospheric pressure level
due to rarefaction waves travelling from the geometry outlet and upstream. The overall static
pressure losses are larger during the deceleration phase of the pulse flow (40CAD onwards),
as it was also suggested in Figure 88. Regarding the incompressibility assumption, using the
density value of the fluid from the CFD into the 1D model, the computed outlet duct still
fails to deliver a better agreement with the CFD results, although this is not visible at a
pressure trace comparison of Figure 92.
Figure 93 and Figure 94 depict the pressure losses for the two examined Y junction cases.
Again the 1D model follows the trend of the pressure loss trace produced from the CFD
results. The differences observed from the choice of an alternative density value for the 1D
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model are not significant because the density profiles do not vary to the same extent as
observed in the T junction geometries. It can also be observed that there are regions during
the pulse, where there is pressure gain at the outlet duct. This is consistent with what has
been reported by (Kirkpatrick et al. 1994) for steady flow experiments. The results indicate
that the correlation is better for the Y60o geometry than for the Y30o at which discrepancies
are evident more or less throughout the duration of the pulsed flow. It should also be noted
that the magnitude of the pressure losses for the Y geometries are smaller than in the T
geometry, which can be largely attributed to the absence of a recirculation region at the
outlet that does not impose a further restriction on the flow.
Figure 93: ΔP across the junction, as calculated by CFD and Bassett 1D model for a constant density assumption (rho1) and outlet duct (rho3) density values for the case of Y60o junction geometry.
In conclusion, it can be said that the 1D model, proposed by Bassett et.al., correlates well
with the data from the CFD along most of the exhaust pulse duration. The discrepancies are
mostly seen at the beginning of the pulse and during the deceleration phase. The latter might
be attributed to the amount of mass that accumulates at the junction region, which is used as
the control volume for the calculation. Since this is not infinitesimally small, mass
accumulation can be observed.
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Figure 94: ΔP across the junction, as calculated by CFD and Bassett 1D model for a constant density assumption (rho1) and outlet duct (rho3) density values for the case of Y30o junction geometry.
5.2.4 Summary and conclusions of the comparative study
The objective of this work was to evaluate the accuracy of pressure loss models for 1D
calculation of losses across a range of junctions by means of a 3D computational study
(CFD). One-dimensional codes calculate the flow characteristics at junctions based on
numerical and empirical models for the pressure losses. The pressure loss of the 1D model
used at the comparison with the CFD relies on assumptions, so that appropriate forms of
momentum and energy equations can be derived.
A series of simulations were carried out using a CFD program to solve the 3D, unsteady,
compressible, Reynolds-averaged equations for mass and momentum conservation for flows
in the three junction geometries of Y30o, Y60o and T60o. Pressure profiles of 1.75bar
amplitude at a frequency of 45Hz were collected from 2.0L engine data and introduced as
isothermal boundary conditions at one of the inlets of the junction. The other inlet was
treated as a closed end, since this is representative of engine like conditions, where the
exhaust valve of the cylinder in proximity with one at the exhaust stroke remains shut.
Study of the results obtained from the CFD indicated that some of the assumptions, that the
loss coefficient models rely on, are violated when a pressure pulse of wavelength comparable
to the ducts' length is propagating through a junction. In the current work, the importance of
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these violations was examined for the calculation of the pressure loss across the junction for
the tested geometries. More specifically, the following major remarks can be made:
1. Recirculation zones are formed in both branch ducts (1 and 2) for the T-junctions,
whereas in Y-junctions only one recirculation zone can be seen and it is located at the
closed branch duct2.
2. The recirculation zones within duct2 for all types of junctions are formed and collapse
more than once during the pulse duration.
3. Significant density variations are evident around the junction boundaries, which indicate
that an incompressible assumption for the junction, as that of hydraulics theory, may lead
to erroneous calculations (equation 20).
4. It was also found that the flow travelling away from the junction was not fully mixed as
it was stated in one of the assumptions (Corberan 1992).
5. The type of junction was found to change from ‘supplier’ to ‘collector’ during the pulse,
since a portion of the mass flow was at first stored and then released from the closed end
duct (duct 2).
6. The pressure difference across the junction during the exhaust pulse event was linked to
the phase of the pulse (i.e. accelerating or decelerating). For the same pressure level at
the inlet duct, the pressure downstream the junction differs accordingly. This is a clear
indication that the pulse cannot be represented by a sequence of steady state cases of
different pressure amplitudes, where only the effect of geometry is taken into account
(equation 16).
7. The direct comparison of pressure loss (ΔP) between the CFD and 1D models revealed in
which regions, along the pulse duration, the discussed 1D model can satisfactorily
calculate the pressure drop.
8. The Bassett et. al. (2003) pressure loss model, given by equation 20, allows for the mass
flow ratio effect to be considered in the calculation procedure. This contributes to a fair
agreement with the CFD during most of the pulse duration.
9. The Bassett et. al. 1D model using the incompressibility (constant density) assumption
was shown to yield better results for the T junction case compared to the results of the
same model using the density value for the downstream duct, calculated from CFD. For
Y junction cases, the density does not vary significantly between upstream and outlet
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ducts in the particular case considered in this paper so the results produced from the 1D
model were similar.
10. The discrepancies observed in the calculation of the pressure loss ΔP were at the
beginning of the pulse and in the decelerating part of the pulse.
The above observations identified the times and the locations within the ducts of the junction
that the estimation of the pressure losses can be compromised by the use of 1D models,
because of the violation of some of the assumptions these models rely on. The assumptions
concern the uniform mixing at the junction and the incompressibility of the fluid. The
quantification and importance of the violations was evaluated for the static pressure losses in
the T and Y shape geometries examined. Future work may also focus on the calculation of
the available energy of the exhaust gases in the manifold during the pulses, since a correct
estimation of this quantity is of vital importance for the prediction of the turbocharger
operating conditions, the amount of heat available for heat exchange systems and the overall
engine operation.
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Chapter 6
Conclusion and Future work
6.1 Summary and Conclusions
6.1.1 Summary
In this work a newly developed experimental arrangement was presented for the study of
pulsating flows in three way manifolds. The objective was to evaluate through experimental
data the predictions of widely used 1 dimensional analyses for the calculation of the pressure
losses across the junctions. The reduction of the equations describing the unsteady 3D flow
to a 1D description has a clear advantage in terms of speed of calculation but inevitably
results in the need, in the case of manifolds, of means of representing the effects of three
dimensionality on the flow in a 1D framework. In this process a number of assumptions are
adopted such as analysis using the quasi-steady flow and the use of the incompressibility
assumption. The present work studied the validity of these assumptions by reference to
experimental measurements of pressure and velocity.
The experimental setup used engine heads with poppet valves so that engine-like
pressure pulses could be generated as boundary conditions of the test manifold. This work
focused on the analysis of pulsating flow of pressurised air at room temperature through a
T60o manifold. The downstream boundary condition was altered between open and partially
restricted ends, the latter being a 1D model of the effects of the turbocharger turbine rotor.
The test manifold was of finite length so that the significance of the acoustic waves could be
established in the manifold during the engine cycle and their effect would be visible in the
static pressure measurements. This is generally in contrast to the work available in the open
literature (as presented in detail in Chapter 1), where the manifolds were sufficiently long so
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that there was no interference between the acoustic and the main pulses. In the experiments
carried out in this work the acoustic waves propagating in a finite length manifold were
superimposed on the main blowdown pulses generated by the unsteady motion of the valves.
The superposition of acoustic waves was identified both in temporal and frequency domain
using the static pressure signals obtained from the manifold during an exhaust blowdown
event. The analysis was then extended to parametric studies regarding the load (low to high),
the running speed (950 to 2000rpm) and the manifold end boundary condition (open and
partially restricted end).
The ability of 1D simulation tools to predict the engine manifold flow is usually
evaluated by reference to static pressure measurements. In the present study, the static
pressure measurements obtained were compared with the predictions of two 1D software
packages (Gasdyn and GT Power). The specific packages were selected as they incorporate
different models for the pressure loss calculation. Hence, the comparison between the
experimental results and 1D predictions was focused on the ability of each of the pressure
loss models to predict the static pressure losses across the junction.
In addition to the static pressure measurements, PIV velocity measurements allowed
for the quantitative study of the flow field at the horizontal plane of symmetry of the
manifold including both the junction and the outlet duct. The velocity measurements were
obtained at 5Hz (600rpm) and low load conditions for all three cases of different manifold
end boundary conditions. Flow structures developing in the manifold were more evident
during the blowdown event that travels from the lateral branch. The study was mostly
focused on the recirculation zone that was formed at the inner wall of the outlet duct as the
exhaust pulse was travelling from the lateral branch of the T60o manifold. The reason for this
was that the bulk flow motion above the recirculation region is associated with pressure
losses (partial pressure recovery) as a result of the diffusion of the flow downstream of the
maximum height of the recirculation zone. The diffusion losses were estimated at the
instances/phases of the pulse where the recirculation region was visible.
The PIV measurements were focused in low Mach number flows where the flow
could be regarded incompressible. The evaluation study of assumptions used in 1D models
was then extended to compressible flows by performing a series of CFD simulations on T60 o
and Y30o and Y60o junctions under pulsating flow inlet conditions. The density variations
and the non-uniformities of the flow were studied in both a qualitative and quantitative
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approach at the horizontal plane of symmetry of the junction. In an analogy to the PIV
measurements, the static pressure drop predictions from the CFD results were compared to
the 1D analysis of a macro-control volume of the junction. The conclusions of both the
experimental and computational studies are summarised in the following section.
6.1.2 Conclusions
1. The acoustic waves which are superimposed to the blowdown pressure pulse were
identified both on temporal and frequency domains using the static pressure
measurements obtained from the finite length manifold. The analysis presented, which is
rarely found in the literature, identified the effect of the acoustic waves motion in altering
(distorting) the main blowdown pulse shape by reference to instantaneous valve position
and organ pipe theory.
2. Analysis of the static pressure measurements on the parametric studies based on load,
speed and boundary conditions showed that the ability to ‘tune’ the effect of the acoustic
waves on the main pressure signal is decreased as the end boundary condition of the
manifold is restricted. This effectively means that the presence of a turbocharger turbine,
apart from increasing the overall back pressure of the manifold, also probably weakens
the effects of the acoustic waves on the pulse shapes. The higher the downstream
restriction the more the pressure pulses shape resemble the valves’ lift profile.
3. The static pressure difference across the junction, usually termed pressure loss, is
attributed to three phenomena;
a. the acceleration of the flow over the recirculation zone that is formed in the outlet
duct,
b. the diffusion losses downstream of the recirculation zone as the flow recovers and
c. the time-varying pressure difference due to the wave reflections at the junction
area and at the exit of the outlet duct.
The flow field computations from the 2D PIV along with the use of a macro control
volume analysis, allowed for the estimation of a and b above.
4. Analysis of the PIV results also allowed for the evaluation of the quasi-steady
assumption. The significance of the inertia effects were examined through the
comparison of the spatial over the temporal acceleration terms (convection, or spatial
P a g e | 160
acceleration 𝑢𝑑𝑢
𝑑𝑥, over unsteadiness, or inertia 𝜕𝑢
𝜕𝑡). It was shown that for low load and low
speed conditions (<3000rpm) the flow can be regarded as quasi-steady therefore more
testing is needed to evaluate the validity of the quasi-steady assumption above that
threshold.
5. The PIV results also revealed that the flow is three dimensional at the junction volume
and at the entry of the outlet duct. Hence, 1D approximations that incorporate a quasi-2D
analysis for the flow in the junction are likely to have an error arising from the three
dimensional nature of the flow. Further PIV measurements are needed, within successive
cross section planes of the manifold, to quantify the magnitude of the secondary flow
structures and their effect on the three dimensionality of the flow.
6. The commercial 1D software tools used in the work (Gasdyn and GT Power) were able
to closely replicate the pressure signals in terms of the temporal variation. The effect of
valve lash was proven to be important in the temporal matching since it affects the
behaviour of the 1D model in the calculation of the acoustic waves’ motion. The
predictions in terms of pressure amplitude deviated from the experimental traces. This
also affected the corresponding 1D predictions of static pressure losses at the junction.
The maximum deviations of the 1D models (Gasdyn and GT Power) from the
experimental values were 15% and 10% respectively. In both packages these
corresponded to the cases were the manifold end boundary condition was an open end.
7. The CFD simulations in compressible flow cases showed that there are substantial spatial
density variations both of the order of 20% both at the junction volume and directly
downstream of it. As a result, an incompressible assumption for the flow is not strictly
valid, although it is used in most 1D approximations to close the system of equations for
the characterisation of the junction. The error of using such an assumption is not as large
as might expected. This was confirmed by an attempt that was made to use an updated
1D macro control volume analysis where the density values were obtained from the CFD.
The improvement in the calculation of the pressure loss across the junction using the
updated 1D model was marginal. However, there may also be an effect of the spatial
averaging of the CFD cell values to perform the macro control volume analysis but this
was not determined in the work presented in this thesis.
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6.2 Future work
This work presented an experimental arrangement that can be used to evaluate the pressure
losses in three way manifolds under engine like pressure pulses. The setup is modular so that
manifolds of different shapes can be adjusted to the engine heads and it also allows for the
study of a range of pulse interference scenarios.
The work can be extended to include high temperature pulses by pre-heating the air that is
delivered to the plena. The results of experiments under different temperatures could be
compared with the ones of the ambient temperature flow to reveal the significance of
temperature gradients for the wave dynamics established in the manifold and the pressure
losses across the junction. If the temperature at the two plena is different and the two engine
heads are set to a valve overlap scheme, the effect of pressure discontinuities in the
propagation of the pulses can also be studied. Temperature discontinuities are expected to
also cause reflections of the acoustic waves affecting the gas dynamics in the manifold.
The work should also be extended to calculate the turbine work function as this was
described in chapter 1, and to also perform an exergy analysis. This follows the conclusion
that pressure differences calculated or measured in the manifold cannot be directly related to
energy loss; hence a form of calculating the irreversibilities will prove very useful for the
accurate prediction of the turbocharger turbine operation.
The PIV measurements could be extended to include cases of higher engine speeds so that
the validity of the quasi-steady assumption can be tested throughout the whole rpm spectrum
of a typical engine. Then the comparison with the 1D simulations can be performed also on
the velocity predictions in the engine cycle.
Thus, the PIV measurements obtained at the cross section of the ducts inside and
downstream of the junction will reveal if the origin of the mass flow rate deviations are
owing to the velocity vector having a significant component out of the horizontal plane . In
other words, PIV measurements could be obtained to study the secondary flows and the
portion of the total kinetic energy associated with them on the junction and outlet duct cross
sections.
Finally, a dynamic POD analysis on the images of the flow field can also be performed so
that the specific structures that are observed in the flow can be linked with the frequencies
P a g e | 162
obtained from the pressure transducers. This will also reveal the apparent effect that the
acoustic waves have on the bulk flow velocity as they travel back and forth in the manifold.
The image acquisition in this case should be changed to be at equal intervals during the
cycle. If high engine speeds are to be examined a high speed laser with repetition rates faster
than the cycle duration would be necessary.
P a g e | 163
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Appendices
A. Entropy generation
Below presents an attempt to estimate the entropy generation of an incompressible and
compressible flow case as described on Figure 41.
The change in internal energy of the fluid can be written as follows:
𝑑𝑢 = 𝑑𝑞 + 𝑑𝑤 →
𝑑𝑢 = 𝑇𝑑𝑠 − 𝑝𝑑𝑣 (1)
The change in enthalpy is
ℎ = 𝑢 + 𝑝𝑣 →
𝑑ℎ = 𝑑𝑢 + 𝑣𝑑𝑝 + 𝑝𝑑𝑣 (2)
For a compressible flow case, we can combine (1) and (2) as follows:
𝐶𝑝
𝑇𝑑𝑇 = 𝑑𝑠 +
𝑅
𝑝𝑑𝑝 (3)
and integration of (3) between two points leads to
𝐶𝑝 𝑙𝑛 (𝑇2
𝑇1) = (𝑠2 − 𝑠1) + 𝑅𝑙𝑛 (
𝑝2
𝑝1) (4)
As there is no change in entropy between stagnation and static conditions and if we further
assume that no work or heat transfer takes place, then the stagnation temperature remains
also constant.
(𝑠2 − 𝑠1) = 𝐶𝑝 ln (𝑇𝑜2
𝑇𝑜1) − 𝑅 𝑙𝑛 (
𝑝𝑜2
𝑝𝑜1) →
(𝑠2 − 𝑠1) = −𝑅 𝑙𝑛 (𝑝𝑜2
𝑝𝑜1) →
(𝑠2 − 𝑠1) = −𝑅 𝑙𝑛 (1 −𝛥𝑝𝑜
𝑝𝑜1) (5)
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For an incompressible flow case combining of equations (1) and (2) can be written as:
𝐶𝑝
𝑇𝑑𝑡 = 𝑑𝑠 +
𝑣
𝑇𝑑𝑝 (6)
If again, we consider stagnation conditions and assume To constant, then because of constant
density due to the incompressible fluid case the volume v is also constant. Hence (6) leads to
the following:
(𝑠2 − 𝑠1) = −𝑣
𝑇𝑜𝛥𝑝𝑜 (7)
or in terms of head loss:
(𝑠2 − 𝑠1) = −𝑔
𝑇𝑜𝛥𝛨𝜊 (8)
Equations (5) and (8) comprise one possible way of estimating the differences in entropy
generation by cause by a pressure drop in an incompressible and a compressible flow case. It
should be noted however, that in the present analysis only the entropy gain due to reversible
process is taken into account as du=Tds is only valid for those.
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B. PIV data for 20% manifold end Restriction
The selection of the optical setup for the PIV measurement cases was based on the maximum
number of images that could be acquired before the transparency of the Perspex walls was
compromised due to liquid film forming. Restricting the downstream end of the manifold
impacts on the scavenging capability resulting in more seeding droplets trapped at every
instance in time. For this reason, the image acquisition was limited to locations A and D-I.
The selection to avoid points B and C was made due to the similarities of the pressure trace
during the accelerating phase of the Open and Restricted end cases. On the contrary the
decelerating part of the pulsed flow differs amongst the cases, so it was regarded as more
important to measure the flow field.
Figure B1: Instances during the engine cycle that images have been acquired - 20% Restriction End case
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Figure B2: Ensemble averaged velocity for point A of the pressure pulse trace for the 20% restricted end case
Figure B3: Ensemble averaged velocity for point D of the pressure pulse trace for the 20% restricted end case
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Figure B4: Ensemble averaged velocity for point E of the pressure pulse trace for the 20% restricted end case
Figure B5: Ensemble averaged velocity for point F of the pressure pulse trace for the 20% restricted end case
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Figure B7 Ensemble averaged velocity for point H of the pressure pulse trace for the 20% restricted end case
Figure B6: Ensemble averaged velocity for point G of the pressure pulse trace for the 20% restricted end case
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C. Velocity profiles in outlet duct
Figure C 1: Magnitude velocity and component velocity profiles (moving average fitted to PIV data points) on outlet duct at 6 different streamwise stations. This Figure refers to Figure 56 on the main text.
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D. Input parameters for 1D simulation tools
All input parameters were the same between the models apart from the junction volume
representation. This is owing to the different models used by the 1D software packages.
Parameter Gasdyn GT power v7.4
Plenum diameter 200 mm 200mm
Plenum height 800mm 800mm Pre-engine head duct diameter 75mm 75mm Pre-engine head duct length 200mm 200mm
Exhaust port diameter (valve side) 31mm 31mm Exhaust port diameter (manifold side) 35mm 35mm Exhaust port length 60mm 60mm
Valve Cd coefficients (L/D and Cd) (Forward and Reverse Cd were the same)
0 0 0.035 0.164 0.069 0.306 0.104 0.427 0.138 0.525 0.173 0.602 0.207 0.656 0.242 0.689 0.277 0.70
0 0 0.035 0.164 0.069 0.306 0.104 0.427 0.138 0.525 0.173 0.602 0.207 0.656 0.242 0.689 0.277 0.70
30degree bend duct (Figure 27) diameter square 25mm square 25mm 30 degree bend duct (Figure 27) length 90mm 90mm Manifold ducts diameter Square 25mm Square 25mm
Straight duct length 125mm 125mm Lateral duct length 188mm 188mm Junction size See Chapter 4.1 See Chapter 4.2 Outlet duct length 495mm 495mm Exhaust duct length 400mm 400mm Exhaust duct diameter 35mm 35mm Components wall temperature 300K 300K
