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UNIVERSITÀ DEGLI STUDI DI PARMA DIPARTIMENTO DI INGEGNERIA INDUSTRIALE Corso di Laurea Magistrale in Ingegneria Meccanica THREE DIMENSIONAL CFD SIMULATION OF A TURBOCHARGER TURBINE FOR MOTORSPORT APPLICATIONS SVILUPPO DI UN MODELLO DI SIMULAZIONE 3D CON UN CODICE DI CALCOLO CFD DI UNA TURBINA PER SOVRALIMENTAZIONE DESTINATA AD APPLICAZIONI MOTORSPORT Company Advisor: Ing. M. CHIODI (FKFS Stuttgart) Ing. P. ROBERTI (FKFS Stuttgart) Academic Advisor: Prof. Ing. A. GAMBAROTTA Candidate: CRISTIAN CAPILUPPI Anno Accademico 2011-2012

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UNIVERSITÀ DEGLI STUDI DI PARMA

DIPARTIMENTO DI INGEGNERIA INDUSTRIALE

Corso di Laurea Magistrale in Ingegneria Meccanica

THREE DIMENSIONAL CFD SIMULATION OF A

TURBOCHARGER TURBINE FOR MOTORSPORT APPLICATIONS

SVILUPPO DI UN MODELLO DI SIMULAZIONE 3D CON UN CODICE DI

CALCOLO CFD DI UNA TURBINA PER SOVRALIMENTAZIONE

DESTINATA AD APPLICAZIONI MOTORSPORT

Company Advisor:

Ing. M. CHIODI (FKFS Stuttgart)

Ing. P. ROBERTI (FKFS Stuttgart)

Academic Advisor:

Prof. Ing. A. GAMBAROTTA

Candidate:

CRISTIAN CAPILUPPI

Anno Accademico 2011-2012

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I

Index

Introduction ......................................................................................................................... 1 1

CFD tools: brief outlines ..................................................................................................... 2 2

Turbocharging fundamentals .............................................................................................. 5 3

Why turbocharging .......................................................................................................... 5 3.1

Supercharging technology and strategies ........................................................................ 6 3.2

3.2.1 Mechanical supercharger versus turbocharger .................................................................. 6

3.2.2 Layouts: the twincharger ................................................................................................... 10

3.2.3 Layouts: two stages twin turbocharger ............................................................................. 12

3.2.4 Layouts: the hybrid turbocharger...................................................................................... 14

Characteristics ............................................................................................................... 15 3.3

3.3.1 The turbine map ................................................................................................................ 15

Model description ............................................................................................................. 17 4

Geometry design ........................................................................................................... 17 4.1

4.1.1 Tomography results ........................................................................................................... 19

4.1.2 Previous CAD resetting ...................................................................................................... 21

Mesh design ................................................................................................................... 23 4.2

Preparing the surface ........................................................................................................ 23 4.2.1

Surface mesh setting ......................................................................................................... 24 4.2.2

Creating the volume mesh ................................................................................................ 28 4.2.3

The regions layout ......................................................................................................... 31 4.3

Interfaces creation between the parts .............................................................................. 32 4.3.1

Regions .............................................................................................................................. 33 4.3.2

Rotating motion specification ........................................................................................... 35 4.3.3

MRF Approach ............................................................................................................... 35 4.3.3.1

RBM Approach ............................................................................................................... 38 4.3.3.2

The boundaries definition .............................................................................................. 40 4.4

Mass flow inlet boundary .................................................................................................. 40 4.4.1

Pressure inlet boundary .................................................................................................... 43 4.4.2

Boundary and initial fluid conditions ............................................................................ 44 4.5

The GT-Power working point ............................................................................................. 44 4.5.1

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II

The fluid initial conditions ................................................................................................. 46 4.5.2

Physics definition .......................................................................................................... 47 4.6

Gas model .......................................................................................................................... 48 4.6.1

The continuum fluid domain ............................................................................................. 50 4.6.2

Simulations results ............................................................................................................ 54 5

Mesh size influence ....................................................................................................... 55 5.1

Inlet boundary type influence ........................................................................................ 57 5.2

Inlet geometry influence ................................................................................................ 59 5.3

Pressure and Temperature gradients through the blades ............................................... 61 5.4

Gas composition influence ............................................................................................ 65 5.5

Virtual test bench .......................................................................................................... 68 5.6

Outlet duct flow analysis ................................................................................................... 68 5.6.1

Building the turbine characteristic .................................................................................... 75 5.6.2

Choking mass flow rate refinement .................................................................................. 84 5.6.3

Ultimate turbine characteristic ......................................................................................... 86 5.6.4

Time calculation of the flow crossing the blades .......................................................... 93 5.7

Industrial CT analysis ....................................................................................................... 98 6

Technological signs ....................................................................................................... 98 6.1

Conclusions ..................................................................................................................... 100 7

References ....................................................................................................................... 102 8

Symbols and Abbreviations ............................................................................................ 103 9

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Introduction

1

Introduction 1

This master thesis work has been conducted at the research institute for automotive

engineering and engine technology Stuttgart (FKFS), with the virtual engine development

team. Its main purpose is to give the customers of projects and advanced analysis solutions,

through 3D-CFD tools.

Nowadays, the computational fluid dynamic applied to the optimisation of engines have

arose a leading role in the thermal design of powertrain systems, to compare different

layout solutions with reduced prototyping costs. These kinds of simulations are in facts very

required, since they can interact with the testing and prototyping steps and sustain them. To

complete the versatility of these tools, the 3D-CFD codes can interact with other simulation

approaches. For example, it’s possible to set a complex and detailed three dimensional flow

simulation with quite reliable data resulting from a real time or 1D-CFD analysis. These last

mentioned models are for sure more flexible in time calculation, but they only provide

signals or the mean values of thermal parameters in one spatial coordinate of the system

volume.

This work aim was to insert in this scenario the basis for the three dimensional fluid dynamic

simulation of a turbocharger for motorsport application, starting from the turbine

component.

Several steps in building the model are normally required, nevertheless bringing to its most

reliable behaviour aligned to the calibration values. The work abstracts are exposed along

the following chapters in a structured and methodical way, towards the most understanding

and precise improvement explanation, as well as inspire further development steps.

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CFD tools: brief outlines

2

CFD tools: brief outlines 2

Computational fluid dynamics, usually abbreviated as ‘CFD’, defines a branch of fluid

mechanics that uses numerical methods and algorithms to predict physical fluid flows and

heat transfer. Nowadays, the on-going research yields software achieving the accuracy and

speed of complex simulation scenarios (turbulent and unsteady flows): hence, CFD tools can

be used to calculate design mass-flow rates, pressure drops, heat transfer fluxes and fluid

dynamic forces. Once the fluid and its thermodynamic working properties are defined, CFD software can

simulate the interaction of liquids and gases with surfaces defined by boundary conditions:

this, through the numerical resolution of mathematical equations which govern these

processes, called indeed ‘governing equations’. The way to solve the problem is always by

numerical iteration, both in steady or unsteady flow (for which, the step time definition is

needed too).

After the simulation run, these software furnish advanced graphical interfaces and post

processing tools with the skill to isolate and analyse single specific phenomena for study; for

example the temperature distribution, rather than the kinetic energy or the pressure.

Furthermore, the flow study can be also in only one detailed region of interest and gives the

designers several comprehensive informations.

The CFD is spread in many science fields and for extreme wide range of industries. For

automotive in particular, CFD software provide large help to the cooling systems

prototyping, the passenger’s comfort analysis, the internal combustion simulation or, more

generically the whole intake and exhaust system design (fig.2.1).

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CFD tools: brief outlines

3

Fig. 2.1 CFD tools: internal combustion engine application.

Some example applications in which CFD is used are:

Aerospace: aerodynamics, wing design, missiles, passenger cabin

Biology: study of insect and bird flight

Biomedical: heart valves, blood flow, filters, inhalers

Building: clean rooms, ventilation, heating and cooling

Chemistry: mixing, reactions

Electrical: cooling systems

Environmental: pollutant control, fire management

Marine: wind and wave loading, sloshing, propulsion

Mechanical: pumps, fans, heat exchangers

Oceanography: flows in rivers, oceans

Power generation: boilers, combustors, furnaces

Sports equipment: cycling helmets, golf balls

Turbo-machinery: turbines, blade cooling, compressors

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CFD tools: brief outlines

4

Fig. 2.2 CFD analysis: example of external and internal flow application.

Especially for the industry, the CFD use for design purposes generally leads to fewer physical

prototypes being necessary during development and less testing: these aspects contain the

costs for physical experiments, which were traditionally the only way to extrapolate

essential engineering data for design.

Nevertheless, the improvement of this technology doesn’t eliminate the necessity to interact

with testing data towards the same models calibration. The last but not the least, the

solutions results and the experimental data set could always contain light gaps, because of

numerical approximations and the use of computational equations (being only the

mathematical representation of the real physics phenomena). The model boundaries

accuracy is anyway depending to the data used for the calibration, which are often

conditioned by measurement strategies and correction factors.

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Turbocharging fundamentals

5

Turbocharging fundamentals 3

Why turbocharging 3.1

In the last decades, charging the engine is an almost diffused strategy towards the

performance rise. Historically, this has always been done with a compressor before the

intake airbox increasing the air (or mixture) pressure and introducing an higher mass in the

cylinders; this is a great advantage, leading to the specific power amount. In fact, with the

same displacement it’s possible to have a higher power:

nmepVPe

(3.1)

Eq. (3.1) demonstrates that the two ways to increase the engine effective power (with the

same displacement) is acting on the mean effective pressure, or on the rotational speed. The

second idea is linked to the inertia effect of the rotating parts, being more influent if the

engine rotates faster: the design of lightweight special alloys components is recommended

to contain this effect, but for the costs is mainly in the racing applications applicable.

Therefore, to increase the engine power output, the mean effective pressure has to be

increased, e.g., raising the intake pressure (i.e., supercharging).

Supercharging has many advantages: the first one is to achieve the same power output with

a more compact engine, allowing to downsize it towards the reduction of dimensions, weight

and the manufacturing costs.

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Turbocharging fundamentals

6

Supercharging technology and strategies 3.2

3.2.1 Mechanical supercharger versus turbocharger

Fig. 3.1 Ways of charging.

The compressors usually employed are volumetric or centrifugal (fig. 3.1). The first

superchargers were realised with volumetric machines, mechanically driven with belt

transmissions directly from the engine camshaft (in the 1920’s Mercedes Benz became the

automotive supercharging pioneer, for racing engines design).

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Turbocharging fundamentals

7

Fig. 3.2 Volumetric compressors for automotive application (Roots and screw type).

This kind of compressor gives pulsating flow to the engine, but it has the benefit to give the

boost pressure to the air as soon as required, without delay. In this solution however, the air

mass flow rate to be boosted is always linked to the compressor displacement and rotational

speed:

Fig. 3.3 Example of volumetric compressor characteristic.

The last but not the least, this kind of compressor connection is always matter of mechanical

losses and the energy spent to rotate it is never recovered. For this ‘energetic’ reason,

another technology came on the market: the turbo supercharger, or simply turbocharger.

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Turbocharging fundamentals

8

Fig. 3.4 Turbocharger concept.

The turbocharger is a compact element, in which a radial turbine is linked to the centrifugal

compressor through a shaft. The idea is just exploiting and converting the exhaust gas

residual enthalpy into mechanical energy to let the compressor rotate. In the figure below,

the exhaust energy available for the compressor is represented by the triangle abc (fig 3.5).

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Turbocharging fundamentals

9

Fig. 3.5 Exhaust energy available (abc), represented on a pV diagram [2].

This contributes to obtain higher engine efficiency, because this energy is used and not

discharged.

Differently from the mechanically driven volumetric compressor, the turbocharger bane is

the so called “turbo lag”: or rather, the time needed for the turbocharger to generate the

required boost. Many factors contribute to have this exhaust system delay: among which the

rotating parts inertia, friction and compressor load. The traditional mechanical

superchargers don’t suffer of this, because their response is instantaneous to the driver

power request.

Moreover, a turbocharger can provide an appreciable boost to the engine only when the so

called ‘boost threshold’ is overcome. Especially at the low engine rotational speed, lower

exhaust mass flow rate crosses the turbine blades: they can’t spin enough to win the

frictions and the compressor load, so that also the desired response is not reached.

Another difficulty related to the turbocharger efficiency is the heat exchange: the exhaust

gases high temperature generates material stresses and due to its compactness, it could

transfer the heat to the compressor side and make the latter efficiency worse [7], as shown

below.

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Turbocharging fundamentals

10

To overcome this issue, the lubricating oil has the additional task to take away part of the

heat power.

Fig. 3.6. Heat transfer in a turbocharger.

.

3.2.2 Layouts: the twincharger

The comparison between the vantages and limits of the mechanical supercharging and the

turbocharging leads to new configurations, sometimes also with the combinations of these

two approaches to mitigate the weaknesses of both the systems.

The volumetric compressor can work at low engine rpm (at its maximum efficiency operating

area): this avoids the use of a turbocharger with turbo lag and gives a better torque

characteristic. On the other hand, a medium size turbocharger can be activated by the

engine control unit when the engine speed is higher. In the series configuration, the

volumetric compressor can be bypassed with a valve or in high power request, it continues

to work and supply the centrifugal compressor inlet, yielding so elevated boost. This layout is

really suitable for the engines in a spread rpm operating, because it can cover a good range.

The twincharger approach was firstly used by Lancia:

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Turbocharging fundamentals

11

Fig. 3.7 Lancia Delta S4 rally engine with “Volumex” twincharger (1985).

In these first applications, the electronic control hardware and strategies were not so able to

manage such a complex system. The complexity still nowadays remains one of this layout

disadvantages, even if many progress have been done. But nevertheless, the series market

too presents clear examples of the twincharger application, as the Volkswagen 1.4 l TSI

downsized engine (fig. 3.8).

Fig.3.8 Volkswagen 1.4 TSI twin charged engine.

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Turbocharging fundamentals

12

Fig. 3.9 Volkswagen 1.4 TSI twin charged engine.

The turbocharger has a wastegate valve to control the exhaust gas flow through the turbine,

while the roots supercharger can be controlled with an electromagnetic clutch. The intake

air can bypass the latter with the use of a control valve.

3.2.3 Layouts: two stages twin turbocharger

To reduce the turbo lag of a medium-high size turbocharger, this solution employs two

combined turbos. One smaller works at low engine rpm, having low turbolag and providing

already a good torque; at the medium rpm range, both the turbochargers operate together.

They’re in series, so that their boost pressures are multiplied. Since the exhaust mass flow is

continuously variable, the transition from one to the other is done proportionally and not

with an on-off control strategy.

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Turbocharging fundamentals

13

An example of this layout was applied on the Opel 2.0 l biturbo Diesel (fig.3.10 and 3.11).

Fig. 3.10 Opel 2.0 l Biturbo Diesel engine

Fig. 3.11 Opel 2.0 l Biturbo Diesel engine.

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Turbocharging fundamentals

14

3.2.4 Layouts: the hybrid turbocharger

This is another solution recently conceived and still on design and optimization:. An electric

machine is coupled with the turbocharger and is electronically driven by the engine control

unit: sometimes it works as motor or as generator.

Fig. 3.12 Electric assisted turbocharger example.

During the throttle opening request, it drives the compressor with an optimum response;

meanwhile, when no more power is needed, it can work as a generator collected to the

turbine in order to recover the compressor absorbed power through the exhaust enthalpy. If

at that instant the turbine provides more energy than the necessary, the excess fraction can

be saved in the battery storage and later supplied to the compressor.

The extreme flexibility is evident: indeed, this system has these two advantages. First, by

decoupling the turbine and compressor, the dynamic response limits of the traditional

turbochargers can be overcome. Furthermore, there’s the opportunity to manage the energy

rates in time.

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Turbocharging fundamentals

15

Characteristics 3.3

Both the turbine and the compressor are machineries which operating range is defined

through curves, precisely called characteristics. These characteristics are built by testing the

component in laboratory with different conditions of pressure ratio, mass flow rate and

rotational speed. Then, maps are drawn reporting the speed and mass flow rate as pseudo-

dimensional formulations, towards the comparison of different machines size on the same

diagram.

In this paragraph a brief sign about the characteristic building is presented, since in the

results chapter the Manufacturer’s turbine map has been compared to virtual ones.

3.3.1 The turbine map

The most common automotive turbocharger turbine is a radial flow machinery, often

manufactured in Inconel special alloy. The degree of reaction in automotive applications is

generally 0.5 [1]; It means that half of the overall enthalpy change occurs in the stator and

half in the rotor according to the R definition:

rotoutstin

rotoutin

rotst

rot

hh

hh

hh

hR

,,

)(

(3.2)

The turbine is characterized through the use of custom test benches and a relation between

the corrected mass flow rate and pressure ratio can be described:

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Turbocharging fundamentals

16

Fig. 3.13 Nozzle and radial turbine characteristics (respectively, left and right).

As the figure 3.11 shows, the radial turbine can be seen like a simple nozzle for the flow,

with the difference that there’s curves dependence from the rotational speed: particularly,

to obtain the same mass flow rate a higher pressure is required, as the turbine speed grows.

This aspect justification is that the exhaust flow meets more resistance to enter the blades

when the turbine turns fast. Furthermore, it’s to be noticed that reaching the choked flow

conditions, this correlation tends to be less meaningful: every iso-velocity characteristic

tends to be closer to the other. This effect is more pronounced in the axial turbines rather

than in these radial.

Further details on these topics are reported in [1].

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Model description

17

Model description 4

Geometry design 4.1

The first simulations were launched with a ‘hand-made’ housing geometry, having no precise

geometry references from the turbocharger producer (as a turbocharger for WRC rally

applications, no data were available on the web due to confidential reasons). The results

were obviously not enough accurate, so that to make a tomography analysis of the real

housing has been decided [A1].

Fig. 4.1 Turbine CAD assembly.

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Model description

18

Fig. 4.2 The assembly: multi-view of the last step modelled (Catia CAD software).

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Model description

19

4.1.1 Tomography results

The housing tomography results were furnished in “stl” format (Stereolitography extension).

So that, the software catiaV5 was not able anymore to modify this file extension and obliged

to directly import the housing in StarCCM+, as part. Since the CT file contained both the

surfaces (internal and external one), with the ‘surface repairing’ tool the external geometry

has been manually ‘peeled’ and removed.

Fig. 4.3 The ‘peeling’ and removing of the external housing surface from CT file.

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Model description

20

Fig. 4.4 The ‘peeling’ and removing of the external housing surface from CT file.

Since an STL extension is nothing more than a cloud of points and doesn’t contain any

reference system, it was not possible to make a common rapid prototyping and directly use

this geometry for the CFD importing.

Nevertheless, it has been discovered that Solidworks is able to transform Stereolitography

files into 3D cad files, with the tool ‘Scan to 3D’ (Surface Wizard): once a surface mesh is

created, the file could be into catia V5 imported. The way through the so called ‘reverse

engineering’ was too long in time, so that it has been abandoned. Since every STL file can be

normally opened in Solidworks and saved as IGES, this solution was preferred.

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Model description

21

4.1.2 Previous CAD resetting

A huge work of geometry building and manipulation has been done: the CAD housing

previously built has been totally reset in its sections and profiles, according to the reference

stl tomography geometry:

Fig. 4.5 Tomography reference geometry (left) and final CAD (right).

Fig. 4.6. The geometry reset.

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Model description

22

In Catia, the main issues were related to the multi-sections solid closure: so that, more

splines were added as guide lines.

Furthermore, to increase the model accuracy and precision, the space between the housing

and the impeller blades has been reduced.

Fig. 4.7 Superposition between the two housing surfaces: the internal is the reset one.

Unfortunately, importing the better geometry in Star CCM+ was more difficult as before; the

necessity to convert it in IGES extension and the reduced spaces between the future

boundaries reminded to reset the tessellating tolerance. Then, other problems in surface

recovering and merging between the parts occurred.

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Model description

23

Mesh design 4.2

Preparing the surface 4.2.1

As soon as geometry is imported, Star CCM+ directly creates a surface mesh from it, so

called ‘Initial geometry’. The quality of this mesh is often bad and needs to be refined before

launching the surface mesh generator. So that, before creating the regions from the part it’s

better to use the tool ‘repair parts’: with this surface diagnostics the free edges can be

closed, the no manifold vertices and edges have to be eliminated to let the beginning surface

remeshed. Furthermore, before doing this it’s recommended to check the feature curves

(important to let the surface remesher respect the boundaries definition).

Fig. 4.8 Surface diagnostics tool.

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Model description

24

Surface mesh setting 4.2.2

Once repaired, the initial surface can be automatically remeshed. A good surface mesh gives

better region boundaries, from which a more accurate volume mesh could be result. If the

surface is not correctly closed (free edges or intersecting faces), the volume meshing is not

possible. The remesher provides automatically to the closing proximity and poor quality

faces refinement and gives as output the worst face quality, so that the user can investigate

it.

Here the parameters mainly used in this work to set the surface mesher are presented:

Base size

The Base Size value is a characteristic dimension of the model. It should be set prior

to using any relative value parameters: for instance, the base size could be initially

set equal to the diameter of an inlet or whatever size is convenient in order for other

values to be scaled from it. If the mesh size is set with absolute values and not in

dependence of a reference length, no base size is needed.

Surface size

The Surface Size node allows the setting of the cells size next to the surface and

feature curves during surface and volume meshing. The min, max and target value

specifications are available. In this instance, the combination between the min and

target was preferred.

Within this specification, mesh models will try to achieve specified target size in the

absence of refinement from curvature/proximity effects, regardless of the local

triangle size of the input surface. Refinements from curvature and proximity will not

cause the surface size to go below specified minimum size.

Surface proximity

The Surface Proximity option allows the specification of cell refinement for the

surface mesh models based on a search distance (called the Search Floor) and the

number of ‘points in a gap’. That is, the ‘Search floor’ represents the minimum size

gap to be considered: if a gap is found with a distance less than the search floor

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Model description

25

value, it will not be considered for proximity to prevent unwanted refinement. The

‘Points in a gap’ value is used for specifying the refinement for surfaces that are in

close proximity to one another: a local size for triangles is determined by dividing the

distance from one face to another across a gap by the specified ‘points in a gap’

parameter, as long as the gap distance is not less than the search floor value.

Automatic Surface Repair

The enable automatic surface repair option provides an automatic procedure for

correcting a range of geometric type problems that may exist in the remeshed

surface once the surface remeshing process is complete. This procedure will

ensure that all triangles created by the process will have a quality equal to or

better than a specified value. This is achieved by allowing the mesher to change

feature edges if required, move feature vertices or avoid projecting vertices in

order to remove or improve faces whose quality is below the specified value. Up

to three different metrics are used: pierced faces (intersecting), surface proximity

and surface quality.

The surface repair follows two mechanisms:

a) Remeshing: growing out the problem area, deleting the local surface and

removing features (if required).

b) Patching: the remeshing procedure, including filling holes;

The remeshing will first be applied to a given problem area and if this succeeds in

eliminating the issue or improving the quality then no further action is taken and

the next problem area is addressed. If the remeshing step did not resolve the

problem, then the patching option will be applied to the original problem

definition.

The surface repair includes two nodes to be set:

o Minimum Proximity: can be used to specify the minimum proximity value

which all faces should have after fixing. It is defined as a percentage of the

average length of the edges in the triangle which is being checked. The

default value of 0.05 is sufficient for most fixing requirements and would

mean that any face of a neighbouring triangle would have to be a distance of

0.05 times the average edge length of initial triangle to pass the check.

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Model description

26

o Minimum Quality: it can be used to specify the minimum quality value which

all faces should have after fixing. The minimum quality property for the auto

surface repair is a value that ranges from 0 to 1, with 0 being the worst and 1

being perfect. The quality of a triangle is given by 2*(r/R) where r is the radius

of the circle that fits inside the triangle and R the radius of the circle that

passes through the three corner points of the triangle (the default value is

0.05):

Surface curvature (points/circle)

The Surface Curvature node allows cell refinement to be included for the surface

remesher mesh models, based on the number of points around a circle (#Pts/circle)

and the curvature deviation distance. The number of points around a circle value is

used for the specification of the basic curvature. For example, the default Pts/circle

value of 36 indicates that approximately 36 triangles (for a surface) or cells (for a

volume) would be used around a 360 degree cylindrical surface:

Increasing the value would increase the relative refinement of the cells next to the

curved surface.

2r

2R

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Model description

27

Surface grow rate

The surface growth rate parameter controls the rate at which triangle edges sizes can

vary from one cell to its neighbor. The parameter typically only comes into effect

when some sort of refinement (for example, curvature or proximity) is included.

Volumetric control

A volumetric control is a very important tool, both for surface and volume meshing. It

allows the mesh density increasing, based on a volume shape closed part. In the case

of the surface meshing tools, only the surfaces contained within the volumetric

control shape is affected. For volume meshing tools, the entire core and/or prism

layer volume contained within the volumetric control shape can be refined

depending on the options selected.

Once a volumetric control has been created, a supplied relative or absolute size value

determines the size of the cell faces that will be used for the isotropic volumetric

control.

In general, volumetric controls that need to influence the domain boundary should

extend a small distance beyond the geometry itself to ensure that that appropriate

sizes are included.

The size value used in a volumetric control can be less than the global minimum size,

so careful attention should be made to the size value and the units it is specified in

order to avoid generating unwieldy meshes by accident when using small values.

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Model description

28

Fig. 4.9 Volumetric control shape applied to the rotating region refinement.

To warranty a finer mesh (both surface and volume), a cylinder shape has been

selected as volumetric control, with a major radius than the outlet diameter: all the

mesh models are included under this control, avoiding too much difference between

the volume cells and the surfaces triangles sizes.

Creating the volume mesh 4.2.3

The models available for the volume mesh creations are the tetrahedral, trimmer and

polyhedral: for this model the third has been chosen, because it was considered more

accurate with the compact and complex geometry to fill. Furthermore, with the same

geometry, the number of polyhedral cells can be five times less than the tetrahedral one.

Moreover, other two models were ticked:

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Model description

29

- Prism mesh layer

The prism layer mesh model is used in conjunction with a core volume mesh to

generate orthogonal prismatic cells next to wall boundaries. A prism layer is mainly

defined in terms of its thickness and the number of cell layers within it.

Fig. 4.10 Prism layer definition mask in Star CCM+ and example applied to this work (inlet boundary).

These layers are largely used because necessary to improve the accuracy of the flow

solution. Indeed, numerical dissipation (represented by errors and discontinuities

embodied by large gradients in a finite volume) is minimized when the flow is aligned

with the mesh. In typical boundary layers, the flow is aligned with the wall, and the

largest gradients tend to be normal to the wall. The use of prism layers is an

approach that greatly improves accuracy, as a result of aligning the flow with the

mesh. In general, however, prism layers are critical to properly resolving turbulent

boundary layers.

- Extruder

This function has been included for example to create an out duct normal to the

outlet section, since fixing the outlet boundary conditions directly beyond the wheel

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Model description

30

was to problematic: the flow vortex is there still too high and needs space to be more

completely developed.

Under the outlet boundary it’s possible to activate the normal extruder mask, to set

the length, the number of layers and their stretching:

Fig. 4.11 Extruder settings.

Here the parameters mainly used in this work to set the volume mesher are presented:

Density (both polyhedral and tetrahedral)

A volume mesh growth and/or density factor can be applied to increase or decrease

the mesh density. The density value (1.0 by default) can be used to change the

overall density of the mesh, everywhere. Increasing the value to say 2.0 would

approximately double the number of cells generated, while decreasing it to 0.5

would approximately halve the number of cells.

The Growth Factor can be used to increase or decrease the mesh density of the core

mesh, by changing the rate at which cells grow from coarse to fine areas. Increasing

the value above the default of 1.0 would mean the cell sizes would grow faster,

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Model description

31

resulting in fewer cells. Conversely, decreasing the value below 1.0 would make the

cell sizes grow more slowly, resulting in more cells being created.

For example, if there are two opposing surfaces separated by a gap and the surface

mesh sizes are the same, then the growth factor will have no effect in this instance

and only the density factor could be used to change the volume mesh density. If the

surface mesh sizes differ in one surface to the other, then one or both factors could

be used in this instance to influence the resulting density.

Volume blending (both polyhedral and tetrahedral)

The global volume blending factor can be used to control the mesh density transition,

when volumetric controls are in close proximity to the surface mesh boundary or

interface. This is to avoid sharp transitions in mesh density, which could lead to

numerical instability during the analysis. The default value of 1.0 will provide a

reasonable transition between the cell size used for the volumetric control and the

surface mesh. Decreasing the value (to say 0.5) will provide a smoother transition by

making the local mesh size closer to the boundary/interface surface meshing size,

resulting in less cells in the core mesh (assuming that the volumetric control uses a

cell size smaller than the boundary/interface triangle edge size). Increasing the value

(to say 1.5) will provide a sharper transition by making the local mesh size closer to

the volumetric control mesh size, resulting in more cells in the core mesh (again

assuming that the volumetric control uses a cell size smaller than the

boundary/interface triangle edge size).

The regions layout 4.3

As previously mentioned, several steps of the work required a continuous remaking and

refinement of the imported geometry, but the main layout characteristics were always the

same. In this chapter the model is so explained in its parts and how the interfaces between

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Model description

32

them have been set. Furthermore, a brief list of every boundary belonging to them is

presented.

Interfaces creation between the parts 4.3.1

The first step is to import the Iges (or Stp) extension file as a new surface mesh, initialised as

soon as it’s opened. It’s strongly recommended to import the geometry as parts, repairing as

parts and let them imprinting.

Merge/Imprint surfaces tool

Fig. 4.12 Multi-part imprint mask (StarCCM+).

This procedure is the best to create a full precise contact between the parts sharing a

surface and edges. In difference with the single part imprint, the multi-part one is able to

calculate source and destination pairs automatically. The merge angle and tolerance

parameters are to be set in the case in which the tool doesn’t find some parts contact. Once

reset, the merging is activated with the command ‘imprint pair’.

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Model description

33

Once the part imprinting is done, it’s possible to create the regions and the interfaces from

these merged and repaired parts.

Regions 4.3.2

The model is composed of three different regions: the housing, the blades region and the

outlet one.

Fig. 4.13 The continuum: housing region (grey), blades region (brown), out duct region (blue).

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Model description

34

Fig. 4.14 Housing region detail.

Fig. 4.15 Rotating region detail.

Inlet boundary

Wall boundary

Interface boundary

Wheel Wall Interface with Housing

region

External Wall

Interface with Duct region

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Model description

35

Fig. 4.16 Outlet duct region detail.

Rotating motion specification 4.3.3

For the rotating systems modelling, StarCCM+ is equipped with two different approaches of

motion definition: the Rigid Body Motion (RBM), or the Moving Reference Frame (MRF). The

first approach consists of the vertices mesh motion according to a specified value, the

second uses the specified rotation to create a constant grid flux and no mesh vertices are

moving.

MRF Approach 4.3.3.1

The MRF approach is the most used for steady state flow analysis, so that it has been

adopted for this case. A rotating reference frame applied to a region permit to generate a

constant grid flux. This has to be defined under the node “tools” (fig. 4.17).

Interface with Blades region

Duct Wall

Outlet

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Model description

36

Fig. 4.17 Moving reference frame specification (StarCCM+).

The rotation axis has to be specified in its direction and origin, while the rotation rate can be

set as a constant, or as an interpolation of a data table.

In the previous modelling steps, the rotating speed was set as the working point constant

value, but due to numerical problems and floating points occurred this speed ratio value has

been then defined according to an input ramp given by the user (as csv table).

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Model description

37

Fig. 4.18 Velocity ramp.

This law is importable in StarCCM+, under the node ‘tables’ and then can be reminded to the

motion node with a little script (fig. 4.19).

Fig. 4.19 Script for the velocity ramp remind.

0

50000

100000

150000

0 500 1000 1500 2000 2500 3000

rota

tio

nal

sp

eed

[rp

m]

Iteration [-]

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Model description

38

Lots of simulations were done with different length ramps, to find the optimum number of

iterations in which the target value can be reached: it was necessary a trade-off between a

gradual ramp allowing no floating points (but increasing the simulation time) and a steeper

one, which could have saved time in calculus but with floating point occurring. After many

attempts, the value has been set to 160: from 160 to 200, the value remains constant.

For every iteration, the program makes a linear interpolation of the table data; the

simulation can continue for the next iterations over 200, keeping the last value of the table

(so, the target one).

RBM Approach 4.3.3.2

With the rigid body motion the procedure to identify the rotation is slightly different, since

to define the inertia of the rotating part is necessary and also the fact that here the whole

region mesh vertices rotate and not only a simple grid.

It has been decided not to delve into this approach, since it’s born for unsteady flow and

transient analysis. This philosophy could be the starting point to model the whole

turbocharger system: in this case the velocity is not imposed and the turbine is matched

with the compressor; the convergence on the velocity is given by the dynamical equilibrium

between the turbine and the compressor torque, only possible after a transient state.

Once the motion is defined, this has to be applied to the region of interest. In this model, it’s

always referred to the blades region (called precisely ‘rotating’, fig. 4.20).

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Model description

39

Fig. 4.20 Rotation motion specification: applying the rotating reference frame to the blades region.

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Model description

40

The boundaries definition 4.4

In the previous paragraph the regions layout and the boundaries are listed. Here the aim is

to explain how every chosen boundaries work and the combinations between them,

according to the thermodynamic definition of the global system.

Since as first simply step the turbine could be considered as a simple nozzle, to combine the

inlet/outlet boundaries in a compatible way it’s strongly required.

Along the several modelling steps, two were the layout adopted:

Mass flow specification (mass flow inlet)

Pressure ratio specification (pressure inlet)

The first philosophy has generated better results and a faster speed of convergence, but it

has to be considered as less real in its definitions. Since a mass flow is always generated by a

pressure ratio between the inlet and the outlet of every open system, when possible is

better to fix the boundary pressure conditions and let the system aligning on the mass flow

value.

Mass flow inlet boundary 4.4.1

As previously mentioned, this was the first philosophy adopted to model the flow through

the turbine: this paragraph contains a brief elucidation about this aspect. The mass flow rate

inlet could be combined only with a pressure outlet. This is due to the compatibility of the

physical quantities both required:

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Model description

41

Boundary type Physical quantities required

Mass flow Inlet Mass flow rate

Static Pressure: used only for supersonic conditions. For subsonic

flow, it’s extrapolated from the adjacent cell.

Total Temperature

Pressure Outlet Static Temperature: used only for inflow conditions. For the

outflow condition, it’s normally extrapolated from the adjacent cell.

Static Pressure: used in subsonic conditions, whereas a correction

is applied.

Table 4.1 Mass flow inlet boundary approach.

Since the temperatures are higher than the standard value of 298 K, the speed of sound is

higher too:

kRTa (4.1)

So that it’s more difficult for the flow to reach the sonic condition of Ma=1. Hence it’s

plausible to consider the flow conditions always as subsonic.

As noticed in the table, in subsonic flow conditions the system requires as inlet data the

mass flow rate and the total temperature; at the same time, at the outlet only the pressure

is required. The temperature outlet specification is redundant, excepting the situation in

which some cell calculates an inflow direction. The thermodynamic reason of this setting

could be justified in the following passages.

Considering as first instance an isentropic expansion, it could be:

k

k1

out

in

in

out

p

p

T

T (4.2)

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Model description

42

In which the subscripts ‘in’ ‘out’ are respectively referring to the inlet and outlet sections.

At the inlet section, the flow velocity can be determined since the geometry and the mass

flow rate are known:

m c

.

(4.3)

The density is known too, because it comes from the ideal gas equation (for the physic

definition see the next paragraph):

RT

pρ (4.4)

The inlet static pressure p is determined, since taken from the nearest cells. The inlet static

temperature is related to the total temperature, given by the definition of total isentropic

enthalpy:

(4.5)

Since all these quantities are determined, the thermodynamic inlet state is completely

defined.

At the outlet section, the hypothesis of averaged outflow can be done (only some cells will

calculate local inflow velocity vectors).

In this conditions, the density is derived from the same ideal gas equation (the static

pressure is given by the user and the temperature is taken from the nearest cells). Besides

this, if the continuity equation is satisfied the mass flow rate is the same as specified at the

inlet by the user. Having the section area too, the outlet velocity can be calculated.

2

c ΔhΔh

2

sttot

ΔTcΔh_

pst

p

2

totstc2

cTT

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Model description

43

Pressure inlet boundary 4.4.2

In difference with the first simpler approach, this one is slightly different.

Boundary type Physical quantities required

Pressure Inlet (working always in inflow)

Static Temperature: being in inflow, it’s always used.

Static Pressure: used in subsonic conditions.

Pressure Outlet Static Temperature: used only for inflow conditions. For the

outflow conditions, it’s normally extrapolated from the adjacent

cell.

Static Pressure: used in subsonic conditions, whereas a correction

is applied.

Table 4.2 Pressure inlet boundary approach.

The inlet is here set as a ‘pressure outlet’, which always works in inflow conditions. In fact,

due to the higher inlet pressure rather than the outlet one, a decreasing pressure gradient is

fixed and also the mass flux direction is generated. In this solution, as before mentioned, the

mass flow is calculated as a consequence of fixing the pressure ratio (according to the Saint

Venant formulation for isentropic nozzle outflow). The density on both the boundaries

comes from the ideal gas equation, being the pressures and the temperatures already

known.

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Model description

44

Boundary and initial fluid conditions 4.5

The GT-Power working point 4.5.1

The values to set the inlet and outlet boundaries have been extrapolated from a GT-Power

turbocharged engine 1D CFD model (in these kinds of models, the quantities involved are

averages across the flow direction). The data were furnished as averaged on the engine

cycle: in fact, the real engine thermodynamic parameters in dependence of the crank angle

are always pulsating.

In the GT-Power model it’s possible to isolate the turbine component and read the most

important quantities.

3500 rpm engine speed point

Hence, at a precise engine speed value:

Pressure (inlet and outlet)

Temperature (inlet and outlet)

Mass flow rate (the fraction bypassed through the external wastegate is already

subtracted)

Turbocharger rotational speed

Turbine real power

Turbine efficiency

Everything then has been managed in an excel table, calculating the remaining reference

data for the 3D StarCCM+ simulation (as the torque and the power, table 4.3).

p in [bar] 1.830

p out [bar] 1.080

ε 1.7

n t [rpm] 149053

T in [K] 1067

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Model description

45

T out [K] 945

R air [J/kg*K] 287.05

Runiv [J/mol K] 8.314

R exh [J/kg*K] 296.93

mexh [g/mol] 28

ρ in [kg/m^3] 0.578

ρ out [kg/m^3] 0.385

mass flow rate [kg/s] 0.12

real power [W] 14900 ideal power [W] 20523

real torque [Nm] 0.955 ideal torque [Nm] 1.316

Efficiency 0.726

delta h [J/kg] 124167 ideal delta h [J/kg] 171028

cp in,out [J/kgK] 1017.8

Delta T[K] 122 ideal Delta T [K] 168

ideal T4[K] 899

Table 4.3 Reference parameters calculations.

The densities are calculated with the ideal gas equation (4.4), where R is the mass constant

of the exhaust gases, calculated as:

exhmR

(4.6)

(m exh is the molecular mass of the gas mixture and R is the universal gas constant).

With the equation 60

n 2πCP t

(4.7), it’s easy to find the real torque value.

To estimate the ideal power and the ideal torque, there’s only to divide both the real

quantities for the turbine efficiency given by GT-Power:

t

realideal

η

PP

t

realideal

η

CC

(4.8)

From the real power and the mass flow rate, the real specific enthalpy variation can be

obtained according to the relation:

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Model description

46

realreal hmP.

(4.9)

Since, under the hypothesis of ideal gas, the enthalpy difference between inlet and outlet

could be defined as follows

)T(TcΔh outin

_

outin, preal (4.10)

Furthermore, as before, is:

t

realideal

η

ΔhΔh

(4.11)

Then the average specific capacity between inlet and outlet can be extracted.

The fluid initial conditions 4.5.2

The regions fluid must be set in its initial conditions, at least pressure and temperature, to

encourage the calculus convergence. For this reason, under the fluid definition the pressure

and temperature values have been reset and intermediate values between the inlet and

outlet were adopted.

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Model description

47

Fig. 4.21 Fluid initial conditions set.

For the n=3500 rpm working point:

p= 1.5 bar;

T=1000 K;

Physics definition 4.6

An important step in a CFD model building is to specify all the parameters and equations

concerning the physical definition of the fluid analysed. In particular, the main points to

focus on are:

Gas model

The continuum fluid domain type

In this paragraph a brief description of these points is presented, just to specify the basics.

Deeper dissertations on these topics are discussed in several books on fundamental of fluid

dynamics.

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Model description

48

Gas model 4.6.1

Star CCM+ allows the user to choose trough different real fluid definitions, among them the

simplest one which has been adopted in this work: the ideal gas model.

This model refers to the equation RTpv , where the constant R is for the specified gas and

related to the universal one by the gas molecular weight (4.6).

By default, the software leaves the setting as compressible gas so that no further

modifications were needed about this aspect.

But another important feature revealing itself fundamental for the correct gas definition is

the specific heat: for a CFD simulation, even in the simplest approach the specific heat

modelling as a constant is too restrictive because this parameter can differ according to the

temperature and the species involved: from the output of QuickSim, an innovative tool

giving StarCD CFD code more flexibility [5], this quantity trends can be seen in figure 4.22.

Fig. 4.22 Exhaust species specific heat.

800900

100011001200130014001500160017001800190020002100220023002400250026002700280029003000310032003300

200 700 1200 1700 2200 2700 3200 3700 4200 4700

cp [

J/kg

K]

Temperature [K]

cp (T) exhaust species

cp-N2 [J/kgK] cp-CO2 [J/kgK]cp-H20 [J/kgK] cp-Air [J/kgK]

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Model description

49

These kinds of correlations are already included for every chemical species in StarCCM+

database, taken from the Janaf tables and fitted with a five coefficient polynomial (fig. 4.23).

Fig. 4.23 CO2 Specific Heat definition: polynomial fitting the Janaf tables.

A polynomial in T could be defined entirely by the user too, specifying the intervals number,

the input variable ranges (in this case, the Temperature), how many coefficient terms fitting

and the coefficient values: but in this case, the definition of the reference temperature and

the enthalpy of formation should be specified.

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Model description

50

The continuum fluid domain 4.6.2

The previous results of this work were obtained with the simplest fluid model: ideal gas. The

type has been selected as single component, the air. The next steps required a better

alignment in the comparison with the GT-Power reference data, so that a new multi-

component fluid definition has been created. The gas model remained ideal, but the mixture

composition depends on the ratio between the exhaust species generated by the

combustion reaction.

Hence, considering that in this full load engine working point the mixture is a little bit richer,

there is no oxygen excess in the exhaust gas and the combustion reaction could be in this

way written:

22222mn N4

mn

21

79OH

2

mnCON

4

mn

21

79O

4

mnHC

(4.12)

For a common gasoline [3], the mass fraction composition could be 0.86C and 0.14H, or

better:

fuel

c

kg

kg 0.86C and

fuel

H

kg

kg 0.14H

The molecular weight of the involved species is:

mol

g

mol

g

mol

g

mol

g

N

O

H

C

14

16

008.1

011.12

The molecular weight of the fuel is so:

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Model description

51

HCfuel mn (4.13)

Since in the reaction there’s only one mole of fuel as reactant, it’s possible to write:

fuelfuel m

Then is

139.0

072.0

fuel

fuel

m

n

A correct ratio for a common gasoline is 1.876n

m so that it could be defined as n 1.876nHC .

From the Heywood tables [2], it’s known thatmol

gfuel 110 ; making some algebraic

passages, the value 7.912n is obtained. The chemical formula of the gasoline could be

written as 14.8437.912HC .

As consequence, the products are:

222 43.724NO7.422H7.912CO

The sum of the products moles is mol 59.058n exh

The moles percentage is:

CO2: 13.40%

H2O: 12.57%

N2: 74%

The products molecular weights are:

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Model description

52

mol

g

mol

g

mol

g

N

OH

CO

013.28

016.18

011.44

2

2

2

So, the product mass is:

1706.770gm

1224.840gμnm

133.715gμnm

348.215gμnm

exh

NNN

OHOHOH

COCOCO

222

222

222

The mass percentage for each component is:

CO2: 20.4 %

H20: 7.8 %

N2=71.8 %

The mass fraction of each component can be then in StarCCM+ defined, being careful to

order the species with an increasing mass fraction criterion. In fact, for calculation reason,

the highest mass fraction species in the mixture must be at the end: the list order must be

so H20, CO2 and N2.

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Model description

53

Fig. 4.24 Gas mixture setting.

In the previous steps with the multi-component mixture set up, this order was not respected

and the ‘Biconjugate gradient stabilized method’ non convergence occurred (for

explanations, see [6] the AMG solver chapter.

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Simulations results

54

Simulations results 5

In this section, the simulations results are presented in a structured way to comment on the

tested parameters, whereby the runs and the outputs were so sensitive.

Fig. 5.1 Factors that have a significant influence on the simulations results and model reliability.

Model optimisation

Inlet boundary type

Mesh size Inlet geometry

Gas composition

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Simulations results

55

Mesh size influence 5.1

Since a coarser mesh can save much computational time, it’s a good thing to optimize the

volume mesh cells size in order to have a trade-off number that ensures good model

reliability too.

Some testing simulations with different kind of surface mesh refinement (and consequently,

volume mesh size too) have been run and they demonstrated a coarser mesh can give the

same results as a finer one. Furthermore, it confirmed a finer mesh can give more instability

in calculations, as it can be seen in the figures 5.2 and 5.3.

Fig. 5.2 Coarser mesh gave less numerical instability; torque has been estimated by integration of the pressure

forces on the wheel surface.

Δ=3.6% Δ=4.7 %

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Simulations results

56

These two simulations were done with the same regions layout and imposing the mass flow

rate at the inlet boundary (not the pressure). It’s to be noticed that the outlet mass flow rate

has been estimated by integration of the term ρc (density*velocity), on the outlet flow area.

Fig. 5.3 The continuity is well verified: the mass flow rate at the outlet boundary is aligned with the target

imposed at inlet.

The convergence values are more or less the same and the signal dynamic on the torque is

even better with the half of the cells number. For this reason, the setting with 800000 cells

has been abandoned. In the last simulations the optimization brought to have even less than

300000 cells (from 230000 to 255000, depending on the inlet length).

The same tests were done with the pressure inlet boundary rather than the mass flow

specification and the effect was the same: a finer mesh could not bring meaningful

enhancements.

Δ=0%

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Simulations results

57

Another aspect to be mentioned in this parenthesis is the prism layers: these are necessary

to have reliability in the mass flow rate value and respect the continuity equation. Especially,

the layer thickness must have more or less the same dimensions of the nearest volume cells.

Inlet boundary type influence 5.2

As previously discussed, in this work two approaches for the inlet boundary description were

adopted: one time specifying the mass flow rate, the other time the static pressure. In the

second approach, the simulations were very difficult to converge and the dynamics was

definitely the worst. The figures 5.4 show the comparison between the two strategies

adopted, keeping the same geometry (no additional inlet duct).

Fig. 5.4 With pressure inlet boundary type, the numerical instability is higher.

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Simulations results

58

Fig. 5.5 With pressure inlet boundary type, the numerical instability is higher.

When the mass flow is imposed, the torque stable value is reached more or less after 2500

iterations (around 3.6% error in respect of the GT-Power target). Imposing the pressure at

the inlet, the numeric fluctuations hold over: as a consequence of the mass flow bad

dynamic behaviour, the torque too is oscillating.

An explanation of this behaviour could be the following: the pressure inlet specification is

unreliable when the inlet boundary is too much closed to the turbine wheel, region in which

the fluid has more vorticity and difficult to be solved.

Fixing a pressure boundary is anyway a more real approach than imposing the mass flow,

because from a theoretical point of view, the mass flow rate through a nozzle is always a

consequence of a given pressure ratio; but to follow this redline, some geometrical device is

required.

Δ=3.6%

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Simulations results

59

In fact, it must be mentioned that all three dimensional CFD models are always set with one

dimensional boundaries: for example, at the inlet and the outlet the p,T quantities are

averaged on the sections. This simplification influences the calculations.

So, to avoid this as more as possible and give more reliability to the model, it’s better to fix

the inlet boundaries farther (as done at the outlet).

Inlet geometry influence 5.3

To obtain the convergence with the pressure inlet boundary type too, an inlet duct has been

created with the extruder mesh tool (as the one built previously for the outlet).

Fig. 5.6 Inlet duct.

The number of layers has been calibrated in function of the duct length, to have the same

layer thickness of the outlet ones (5 mm).

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Simulations results

60

Different simulations were run, changing the inlet duct length. Within the trade-off between

inlet duct length and numerical stability, the best compromise was 100 mm, since it has

been verified that 5 mm still gives rise to some problems and 300 mm is too much

conservative, because it doesn’t enhance the convergence so meaningfully in respect of the

100 mm duct case.

Fig. 5.7 The 100 mm inlet duct proved to be the best compromise to have the best stability.

Δ=4%

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Simulations results

61

Fig. 5.8 Longer inlet solved numerical problems, but the gap on the torque remains.

From one side (figure 5.7), having a farther pressure inlet generates a better numerical

behaviour, but the mass flow rate value decreased (as a consequence, the torque too). In a

first instance, this was supposed due to the gas friction losses near to the housing wall; but

since the results didn’t change with the length duct variation, this was not retained the

cause anymore.

Pressure and Temperature gradients through the blades 5.4

StarCCM+ allows several reports that the user can easily associate to a derived part. This tool

was very useful in this instance of the work, to investigate how the pressure and the

temperature decrease meanwhile the flow passes across the turbine blades.

Different sections were set as derived, along the x axis direction (fig.5.9).

Δ=14.7%

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Simulations results

62

Sections (from x=0)

x=1 mm

x=5 mm

x=10 mm

x=15 mm

x=20 mm

x=25 mm

5.9 Sections specifications under the "Derived parts" option.

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Simulations results

63

Each section has been linked with an average surface report: this has the task to read a user

specified quantity for every iteration step and send it to a monitor (from which it’s possible

to export or tabulate the value). Ten reports were created, five for the absolute pressure

monitoring and the others for the temperature.

After the simulations, these outputs were post-processed and it has been possible to realise

the following plots (5.10 and 5.11), demonstrating the gradients through the blade in every

approach: original and 50 mm length inlet as geometry, mass flow or pressure as inlet

boundary type.

Fig.5.10 The inlet pressure value changed with reference to the inlet boundary type adopted.

On the pressure gradient, there’s a little gap between the inlet values: when the pressure

inlet is imposed, the value is correct (1.83 bar, according to the GT-Power reference) but the

mass flow rate is underestimated. On the contrary, imposing the correct mass flow rate the

model overestimated the inlet pressure (1.6%). In the further steps of the model

Outlet (545 mm)

Inlet

1 mm

5 mm

10 mm

1.6%

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Simulations results

64

development, to delve on this aspect could bring to a fundamental reduction with the

reference data gap.

Furthermore, the presence of the constant section duct seems to give the flow a sort of back

pressure, obliging it to decrease the velocity.

Fig. 5.11 Specifying the pressure as inlet boundary, the temperatures are higher than in the other approaches.

Concerning the way in which the temperature decreases, the 20K regain is due to the

adiabatic duct presence too (figure 5.11): in fact, at this state of the art no convection heat

exchange was considered and the heat from gas friction losses near the walls was not

dissipated.

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Simulations results

65

Gas composition influence 5.5

In the GT-Power reference model, the exhaust mixture gas flows from the engine manifolds

to the turbine: its composition depends by several factors, for example λ and the

combustion efficiency. Hence, in order to better align this model to the reference one, a

multi-component gas mixture simulation has been done in comparison with a pure Nitrogen

gas simulation (species highly concentrated in air and exhaust too).

As in the chapter 4 described, the mixture mass fractions have been estimated simply with

the perfect and complete combustion hypothesis.

Furthermore, even if these rally gasoline engines work with mixtures that are often rich, for

more simplicity calculation a stoichiometric air/fuel ratio (λ=1) has been considered. So,

there are no unburned gas and no oxygen excess.

The results of these two simulations are here in the figures 5.12 and 5.13 reported. Through

their comparison, the model sensitivity on the gas multi-component mixture description is

presented.

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Simulations results

66

Fig. 5.12 Pressure inlet boundary type: with multi-component exhaust mixture, underestimation in mass flow

rate is higher.

Δ=5%

Δ=7.5%

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Simulations results

67

Fig. 5.13 Pressure inlet boundary type: the multi-component exhaust mixture introduced a gap reduction on

the torque.

Δ=9.5% Δ=13%

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Simulations results

68

Virtual test bench 5.6

Outlet duct flow analysis 5.6.1

This 3D CFD model could be very well used as ‘virtual test bench’: as specified in chapter 1,

the experimental conditions can be applied to this virtual component, which solution is good

to justify the measurements done by test engineers on a real bench and overcome the

aspects that couldn’t be so clearly seen. An application of this is here below explained.

The aim of this analysis was to study the temperature, pressure and velocity profiles at

different distances along the outlet.

To reproduce the laboratory test devices, instead of the classical sections, a series of thirty

punctual sensors has been set on six steps along the x axis (one point on every 2 mm in the

vertical direction, fig. 5.14).

Fig. 5.14 Point sensors position.

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Simulations results

69

Taking as example the temperature measurement, this is equal to move an ideal

thermocouple and taking 30 samples for every x. Proceeding in this way, these obtained

profiles are shown in figure 5.14.

Temperature

Fig. 5.15 Outlet temperature profiles.

Fig. 5.16 Outlet temperature profiles.

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Simulations results

70

Fig. 5.17 Outlet temperature profiles.

The temperature gradient on the sections is going to decrease approaching to the outlet.

But these are very interesting trends especially because they’re asymmetric and the highest

value of every plot seems to oscillate in the x direction, as if a portion of hot gas were

moving helically.

This is totally confirmed in figure 5.18.

Fig. 5.18 The temperature outlet wall pattern justifies the profiles obtained by point measurement (5.14).

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Simulations results

71

The helicoidal reflects the velocity flow trends, as follows.

Velocity

As expected, where the gas reaches the highest velocity the temperature is the lowest. In

figure 5.18, the blue helical is also the track of the fastest flow.

Fig. 5.19 Velocity outlet profiles.

Fig. 5.20 Velocity outlet profiles.

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Simulations results

72

Fig. 5.21 Velocity outlet profiles.

The temperature profiles aren’t decreasing near the walls because they have been

considered as adiabatic, hence no heat transfer is contemplated. But on the contrary the

velocity tends to decrease in the proximity of the duct walls and this effect is going to be

more relevant along the duct: this is sensible because no slip option has been selected and

friction effects are taken into account, dissipating kinetic energy.

Moreover, on the z=0 level the velocity magnitude is always from 0.7-1 m/s tends to the rest

at the outlet and the gradient is high as on the 100 mm section, immediately after the

turbine.

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Simulations results

73

Pressure

Fig. 5.22 Pressure outlet profiles.

Fig. 5.23 Pressure outlet profiles.

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Simulations results

74

Fig. 5.24 Pressure outlet profiles.

In the outlet walls a lower increase in static pressure has been observed: on the rotational

axis the pressure is lower due to the vorticity of the flow. There’s a slightly asymmetry of the

profile on the pressure plots too, but in minor relevance. They are more similar between

them and having more or less the same gradient (from 1.075 to 1.11 bar): only at the out

section the pressure rises more uniformity.

Fig. 5.25 On the duct walls there are practically no remarkable pressure differences.

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Simulations results

75

Building the turbine characteristic 5.6.2

The model was calibrated by comparison with data referring to one particular condition

),(.

m and a quite good reliability has been reached. As following step of this work, the

challenge was to build a virtual turbine characteristic at constant rotational speed and

compare it with the characteristics given by the Manufacturer, in order to quantify shifts. To

build these curves several simulations were run, each of them with a different pressure

ratio.

Fig. 5.26 The Garrett GTR 2560R turbine characteristic.

Among these curves, the 138900 rpm one has been chosen as sample.

The first testing series were conducted with the exhaust gas mixture model, whose

composition has been in chapter 4 described.

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Simulations results

76

To move on the x axis, the pressure ratio or more precisely the inlet pressure has been

changed. The inlet temperature has been maintained constant: 1045K, from the GT-Power

reference point used to calibrate the model.

Once the simulation has been run, pressure values have been virtually “measured”

immediately upstream and downstream the turbine, with two surface average reports

(figure 5.27).

Fig. 5.27 Definition of the “virtual” measuring sections.

This has been done in order to insert the real modelled ε values on the turbine map: as a

matter of fact, usually pressures and temperatures are measured not very far from the

turbine housing (figure 5.28).

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Simulations results

77

Fig. 5.28 Typical turbocharger test bench.

Contrary to the real test bench in figure 5.28, the mass flow rate has been measured on the

upstream turbine cross section, since on this reference the mass flow signal is generally

more accurate than the downstream one (it has less fluctuations).

On the turbine characteristic the reduced mass flow rate must be reported:

int,

int,

.

.

redp

Tmm

(5.1)

Where the total inlet temperature and pressure are so defined:

p

2

inint,c2

cTT

dcρcpp

in

int,

inint,

(5.2)

The reduced mass flow rate has been obtained within a simple Excel sheet:

pressure (y 60mm) 1.59 bar 159247.1 Pa pressure

tot 16007 Pa epsilon 1.369

pressure (x 50mm) 1.16 bar

P, T turbine measurement

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Simulations results

78

temperature (y 60mm) 1045.0 K temperature

tot 1047 K

R_exh 287.84 J/kgK cp 1319 J/kgK

density 0.529 kg/m^3

Inlet area 0.0019625 m^2 inlet

diameter 0.05 m

mass flow rate 0.077 kg/s

velocity 74.26 m/s

m rid 0.01552 (kg/s)*(K^0.5)/kPa

Table 5.1 Reduced mass flow rate calculation.

Obtained values were inserted in the turbine map (figure 5.29).

Fig. 5.29 Turbine characteristic at 138900 rpm: comparison between the reference data (Target) and the model

output.

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Simulations results

79

For lower inlet pressures, the gap between reference and calculated data is very small but it

increases with ε: from 1.6 on, it’s around the 5% (figure 5.30).

Fig. 5.30 Errors evaluation.

An evaluation of the measurement errors related to the reference curves was done to show

the accuracy range of the experimental data. To this extent, measured points were

highlighted (fig. 5.29).

To estimate the measurement errors on ε, as attempt it has been assumed that both the

pressure sensors have a precision of 0.1% full scale (where the latter is 2 bar for the inlet

and 1 bar at the outlet). The error calculation must follow the errors theory description.

Using the total differential theorem:

out2

out

in

out

inout

out

in

in

Δpp

p

p

ΔpΔp

δp

δεΔp

δp

δεΔε

(5.3)

With:

Δpout= 0.001 bar, Δpin= 0.002 bar, pout=1 bar and outin pεp the results are:

100target

model-targetE(%)

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Simulations results

80

Pressure ratio [-] Epsilon error [-] Epsilon error [%]

1.32534 0.00332534 0.250904674

1.44879 0.00344879 0.238046232

1.56358 0.00356358 0.227911588

1.71452 0.00371452 0.216650724

2.00362 0.00400362 0.199819327

2.60694 0.00460694 0.176718298

Table 5.2 Error on the pressure ratio measurement.

The error bars on ε proved to be very narrow in the plot of fig. 5.29.

The same procedure has been applied for the reduced mass flow rate error calculation.

int,2

int,

int,

.

int,

int,int,

..

int,

int,rid

.

Δpp

TmΔT

pT2

mmΔ

p

TmΔ

(5.4)

This valuation was a little bit more complicate, since the .

m values were not known. Hence,

it has been so obtained:

int,

int,red

.

.

T

pmm

(5.5)

The kinetic term to be added to the static pressure and temperature inlet has been

evaluated from the model, having no specifications about the inlet and outlet velocity in the

testing conditions.

Considering:

%1.

m (assumed from experimental experience)

inint pp ,

inint TT ,

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Simulations results

81

m_reduced

[kg/s*K^0.5/bar]

mass flow rate

[kg/s]

m_error [kg/s] m_reduced error

[kg/s*K^0.5/bar]

m_reduced error

[%]

1.32534 0.05967734 0.000596773 0.01523991 1.149886835

1.772 0.087649838 0.000876498 0.020137809 1.136445193

1.986 0.106933425 0.001069334 0.022349377 1.125346269

2.176 0.129032965 0.00129033 0.024236639 1.113816141

2.356 0.164066783 0.001640668 0.025843366 1.096917068

2.5 0.224992945 0.002249929 0.026874808 1.074992313

Table 5.3 Errors on the reduced mass flow rate.

For the reduced mass flow rate the error is higher, because the mass flow measurement

depends on several parameters [equation 5.5].

Last but not the least, the difference between the real walls and the model has to be

considered: in the real conditions, the housing internal surface roughness is decisive and the

dilation with the temperature could be another aspect not to neglect.

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Simulations results

82

With the same procedure, several points at 153600 rpm have been considered: obviously,

changing the velocity ramp in the model (paragraph 4.3.3).

Fig. 5.31 Turbine characteristic at 153600 rpm: comparison between reference data (Target) and the model

output.

The gap on the reduced mass flow rate has been evaluated for this 153600 rpm too. With

the exception of the first point in which the mass flow rate is overestimated, the other two

simulations presented a gap of 5% more or less.

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Simulations results

83

Since on the most common test benches the turbine is characterised with air and not engine

exhaust, this could have an influence on the shift obtained. Hence, the 5.31 figure curve has

been rebuilt running simulations with air (fig. 5.32).

Fig. 5.32 Turbine characteristic at 153600 rpm: when the air is selected, the gap with the reference data is

smaller.

As forecast, testing the model with the air has brought a gap reduction (averaged on 3%); for

this reason, the comparison with the experimental data has been taken on with this option.

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Simulations results

84

Fig. 5.33 Errors evaluation.

Choking mass flow rate refinement 5.6.3

In the following step of the work, the attention has been focused on a point in choked flow

conditions (ε= 2.88) and many attempts were done to reduce as much as possible the mass

flow rate model error.

In the previous simulations, the walls were all set as adiabatic. But this is not so real in

comparison to a real test bench condition. Hence, setting on the walls a constant external

ambient temperature of 300 K the heat exchange coefficient has been gradually increased

until the reasonable value of 150 W/m^2K, being the limit between natural and forced

convection exchange.

It has been so proved that the convection on the housing and duct walls could give a

beneficial amount on the flow rate: this is logical, since as the flow temperature decreases

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Simulations results

85

due to the heat exchange, at the same pressure ratios the average air density must increase

and so the mass flow rate too.

Another meaningful factor for the mass flow convergence is the volume mesh layer

thickness: normally, that’s suggested to have the same size of the nearest internal volume

cells dimension.

Fig. 5.34 Volume mesh layer thickness reduction.

In the previous simulations this was 4 mm thick and in the further it has been set as 2.5mm,

with plain improvements on the results:

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Simulations results

86

Fig. 5.35 Gap reduction with the layer thickness optimization and the inclusion of convection, in the choked

flow condition.

The best compromise resulted to be the thicker mesh layer combined with the highest

possible convection heat exchange (figure 5.35).

Ultimate turbine characteristic 5.6.4

To investigate these factors effect on other working points, a new series has been simulated

and as before post-processed, showing this trend from which the gap is evaluated (fig. 5.36).

2.4

2.41

2.42

2.43

2.44

2.45

2.46

2.47

2.48

2.4 2.6 2.8 3

Re

du

ced

mas

s fl

ow

rat

e

[kg/

s*K

^0.5

/bar

]

Pressure ratio [-]

Factors influencing the reduced mass flow rate

TARGET

25 W/m^2K

100 W/m^2K

No Convection

150 W/m^2K

100 W/m^2K, 2.5 mm mesh layers

150 W/m^2K, 2.5 mm mesh layers

1.83% 2.27 %

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Simulations results

87

Fig. 5.36 Turbine characteristic at 153600 rpm: contribute of thinner layers and convection exchange.

.

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Simulations results

88

Fig. 5.37 Errors on the mass flow rate calculations.

The convection effect allows to improve theoretical results of mass flow rate up to ε=1.8,

reaching the smallest gap of 1.83%. But under this pressure threshold, the alignment seems

to be better without convection exchange (figure 5.37).

The further step was to redefine in a more correct way the convective heat exchange:

)(.

wallaverage TTSQ

(5.6)

As first attempt, the convection heat flux was introduced only with the variation of the heat

exchange coefficient α, keeping the ambient temperature at 300 K. This was not so

reasonable, since the ambient temperature for the flow means not the laboratory one but is

referring to the walls. Hence, as experience assumption, the external walls surface

temperature has been set 50 K less of the average flow temperature and 30 K less for the

wheel surfaces. Precisely, the turbine wheel has been considered with a less convective heat

-1

0

1

2

3

4

5

6

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2

[%]

Pressure ratio [-]

Error (%) on the reduced mass flow rate

Air, 150 W/m^2K, 2.5 mm layers

Air, no convection, 4 mm layers

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Simulations results

89

exchange, compared with the external walls: the former was set to exchange only the 1% of

the turbine power, meanwhile the latter convective ratio is around the 17%.

Torque 2.67876577

rotating speed [rpm] 153600 16076.8

Turbine power [W] 43066

External walls

Q [W] 7.09E+03 % of turbine power 16.47

Surface walls area [m^2] 1.45E-01

T in [K] 8.73E+02

T average [K] 813

Twall [K] 763

alfa convection [W/m^2K] 974.8

Turbine walls

% of turbine power 1.00

Q [W] 430.66

Surface walls area [m^2] 1.05E-02

Twall [K] 783

alfa convection [W/m^2K] 1367.9

Table 5.4 Convective heat exchange calculation on the walls.

The surface walls areas were taken from the StarCCM+ reports; the average temperature

has been evaluated between the inlet and outlet turbine cross sections. Fixing higher walls

temperatures than before forced the ΔT to be more realistic and, in order to obtain the

same power, α has grown (table 5.4).

Therefore, a new characteristic curve was built, but with a different measurement strategy

too. In fact, the test methods are usually conducted not through the average pressure and

temperature calculations on the inlet/outlet cross sections, but with a point sensor

measurement according to the testing prescriptions. As matter of that, two point sensors

have been positioned (figure 5.38).

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Simulations results

90

Fig. 5.38 Point sensors placement references on the inlet and outlet turbine cross sections.

The results confirmed the expected forecast.

From the pressure acquisition side, the measurement of the inlet and outlet turbine as

averaged rather than punctual is not so forceful: in fact, the inlet pressure is more or less

uniform on the cross section and the outlet one presents 50 mbar range of variation (from

1.07 to 1.12 bar). On the temperature side, measuring an average value or a punctual one

could generate different results because the temperature distribution can be more variable

than the pressure one.

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Simulations results

91

Fig. 5.39 Turbine characteristic at 153600 rpm: effect of the point sensors measurement and error evaluation

on the target test bench curve.

Another important issue that should be considered in the presented comparison is related to

the reduced mass flow rate calculation, i.e. if static or total values of T, p were used.

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

2.6

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2

Re

du

ced

mas

s fl

ow

rat

e [

kg/s

*K^0

.5/b

ar]

Pressure ratio [-]

Turbine map: target and 3D-CFD model

153600 rpm (Target)

StarCCM+: AIR, alfa 150, 2.5 mm layers

StarCCM+: AIR, convection optimised , 2.5 mm layers (pointmeasurements)

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Simulations results

92

Fig. 5.40 Turbine characteristic at 153600 rpm: effect of the static reduced mass flow rate evaluation.

If static values of p,T are considered in evaluation of reduced mass flow rate parameter, the

characteristic curve changes as reported in figure 5.40.

This aspect has to be investigated, since up to now no information were available.

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

2.6

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2

Re

du

ced

mas

s fl

ow

rat

e [

kg/s

*K^0

.5/b

ar]

Pressure ratio [-]

Turbine map: target and 3D-CFD model (static p,T)

153600 rpm (Target)

StarCCM+: AIR, convection optimised , 2.5 mm layers(point measurements)

StarCCM+: AIR, alfa 150, 2.5 mm layers

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Simulations results

93

Time calculation of the flow crossing the blades 5.7

As post processing step, an interesting aspect to delve on is how many revolutions the

turbine makes meanwhile a particle of gas crosses a blades duct. This, obviously, it’s

expected to change in function of the flow velocity entering the turbine wheel (and so, from

the pressure ratio fixed).

The length the gas could cover has been in CAD estimated, drawing two splines and

measuring them, for the description of two different flow paths: in fact, the flow particles

could follow several directions entering the turbine wheel.

Fig. 5.41 Gas particle track definition in turbine wheel.

High spline: 33.4 mm

Low spline: 34.5 mm

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Simulations results

94

Since the length is not so different, the green one has been considered for this calculation.

As simulation report, the average flow velocity between the housing and the rotating region

can be calculated: this value, for a pressure ratio of 3 and air without convection influence, is

more or less 420 m/s. So, considering the flow having constant velocity, the time necessary

for the gas particle to pass through the blades vane is:

s82s108.214420

0.0345t 5

The number of revolutions the wheel does during the whole passage of the particle is given

by:

32.115360030

10214.830

5ntrev

For rotational speed of 153600 rpm, the particle makes around one revolution before

leaving the turbine wheel. This parameter influences without doubts the flow helicoids in

the outlet duct and depends on the gas velocity entering the turbine, so from the mass flow

rate and indirectly from the pressure ratio stabilised.

Hence, a relation between the pressure ratio and the number of these revolutions has been

sought; the gas track length is always the same, as the turbine rotational speed (steady

state). From the simulations reports, plotting the average inflow velocity in function of the

increasing pressure ratio a proportion has been found (fig. 5.42).

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Simulations results

95

Fig. 5.42 Average radial velocity and particle crossing time depend on the pressure ratio.

Hence the expected results is that as the inlet pressure rises, the flows crosses faster the

turbine wheel and recovers a minor rotational angle, finding itself with a more little

tangential velocity vector. Having simulations results at different pressure ratios, it’s possible

to see the number of revolutions trend (fig. 5.43).

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Simulations results

96

Fig. 5.43 The turbine revolutions covered by the particle depend on the pressure ratio fixed.

Making some examples, when the pressure ratio is around 1.5, the gas exits from the turbine

wheel after 2.1 revolutions, meanwhile in chocked flow conditions this number is around

1.3. This is reasonable and the previous expectations are justified.

Lower is the pressure ratio, lower is the average flow velocity and the mass flow rate. Hence,

to cross the same track more time is required and in this longer interval, the turbine covers

more angular distance.

In other words, when the gas flow is in steady state conditions and the turbine speed is

constant, the outflow vorticity depends directly to the upstream pressure and this can be

seen also in the StarCCM+ streamlines scenes. In the following table is reported the

measured flow wavelength for different pressures ratios (fig. 5.44).

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Simulations results

97

1.47ε : 12 cm

1.98ε : 19 cm

2.65ε : up to 40 cm

2.88ε : up to 40 cm

Fig. 5.44 Pressure ratio influence on the streamlines wavelength.

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Appendix

98

Industrial CT analysis 6

Industrial CT (computed tomography) scanning is a process which uses X-ray equipment to

produce three-dimensional representations of components, both externally and internally.

The CT scanning was originally used only for medicine applications, but then it has been

applied in many areas of industry too, for internal inspection of components.

Technological signs 6.1

This device uses x-ray beams, in order to create an image to be captured by a detector. The

part to be analysed is fixed on a rotating stage and the source is too moving along the

vertical/horizontal axis, so that a complete three dimensional scanning can be obtained.

More powerful is the x-ray emission, more it can flow through thicker materials substrates

(for the housing walls depth, a medium voltage machine was needed to have a sufficient

intense beam).

Fig. 6.1 Industrial CT device concept.

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Appendix

99

Fig. 6.2 Some machines can have the fixed stage and the source/detector system rotating: the result is the

same.

Some of the main sectors in which CT scanning is used are for example failure analysis, metrology,

assembly analysis and the so called ‘reverse engineering’.

In fact, CT scanning can be useful to analyse every single product or assembly quality, without

destructive test or disassembly. It’s so easier to compare the product with the original CAD, or to test

eventual imperfections in every production piece. Furthermore, generating a file from the CT data

set is particularly useful in reverse engineering applications and product development. Exported CAD

file formats are recognized by many types of software. The CAD file created by CT scanning doesn’t

only show the external components, but the internal as well. This allows for first-time rapid

prototyping of internal components. This last application is just this work aim; having no reference

geometry or design data about the internal surface of the volute, it’s necessary to scan the real

component and extract the reference geometry, from which it’s possible to compare the CAD

previously built.

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Conclusions

100

Conclusions 7

This thesis work aim has been the building of a 3D-CFD motorsport turbine model. First, the

housing geometry was CAD designed taking as target the real internal housing surface,

obtained from an industrial CT analysis. Subsequently to the assembly between the internal

housing and the turbine wheel, the CFD model has been set in its regions layout and

interfaces optimization between them.

The model calibration occurred on a single steady state condition, using a GT-Power engine

1D model for the boundary conditions generation. Since in GT-Power a real exhaust flow

involves the turbine, a basic multicomponent exhaust fluid definition was proposed to be

more aligned.

Two main inlet boundary types have been compared: imposing the mass flow rate instead of

the pressure at the turbine inlet, the numerical system response is better; but in order to

consider the mass flow as a consequence of a given pressure ratio, the pressure inlet

approach has been for the further steps preferred. According to these first options, the

mesh size and the inlet length influences on the simulations have been estimated: coarser is

the volume mesh, more is the numerical stability. The same could be said about the inlet

length variation; in fact, it has been proved that too short inlet ducts generate mass flow

divergence, so that it’s recommended to fix the inlet and outlet boundary conditions as

further as possible to the wheel region.

In the second part of the work, a ‘virtual’ test bench has been built: varying the pressure

ratio and calculating the mass flow rate, different turbine model characteristic were

extracted. In particular, the alignment with the experimental conditions is very important,

especially the reference temperature. The gap between the experimental turbine map and

the model one has been reduced with the introduction of the convective heat exchange and

the optimisation of the walls volume mesh layers thickness. Furthermore, the comparison

with the experimental map valued with static p,T quantities has brought to an additional

refinement.

Other investigations have been conducted, as the turbine outflow characterization and its

wavelength variation in function of the inlet turbine pressure.

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Conclusions

101

This state of the art is considered a good starting point for the next development: especially,

to check the complete alignment with the Manufacturer’s declared testing conditions.

Another two relevant effects could be the axial turbine positioning to the housing and a

more detailed definition of the heat exchange with the walls.

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References

102

References 8

[1] N. Watson, M.S. Janota - Turbocharging the internal combustion engine – Ed. Wiley

(1982).

[2] J. Heywood – Internal combustion engines fundamentals – Ed. McGraw-Hill (1988).

[3] G. Ferrari – Motori a combustione interna – Ed. Il Capitello (1988).

[4] C. Caputo – Le turbomacchine – Ed. Cea (1994).

[5] M. Chiodi – An innovative 3D-CFD approach towards virtual development of internal

combustion engines – Ed. Vieweg+Teubner (2010).

[6] StarCCM+ user guide - www.cd-adapco.com

[7] S. Shaaban, J.R. Seume - Analysis of turbocharger non-adiabatic performance - 8th

International Conference on Turbochargers and Turbocharging (London 2006).

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Symbols and Abbreviations

103

Symbols and Abbreviations 9

Symbol Description Unit

a Speed of sound m/s

Ma Mach number: ratio between the flow velocity and the speed sound -

k Ratio between the specific heat capacity at constant pressure and constant

volume -

c Flow velocity m/s

ε Pressure ratio -

mep Mean effective pressure Pa

Abbreviation Description

in, out Inlet and Outlet subscripts

st, tot Static and Total conditions subscripts

CFD Computational Fluid Dynamics

1D,3D One dimensional, three dimensional

t Turbine subscripts

exh Exhaust mixture subscripts