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Proceedings of Shanghai 2017 Global Power and Propulsion Forum
30th October – 1st November, 2017 http://www.gpps.global
0200
Loss Mechanism and Assessment in Mixing Between Main Flow and Coolant Jets with DDES Simulation
Zhen Zhang, Tsinghua University
[email protected] Beijing, P. R. China
Xin Yuan Tsinghua University
[email protected] Beijing, P. R. China
Xinrong Su*
Tsinghua University [email protected]
Beijing, P. R. China
ABSTRACT
Film cooling has become one of the most important
cooling methods in gas turbines. The mass flow of the coolant
increases with the turbine inlet temperature and reaches
around 20% of main flow for advanced power plant gas
turbines. To understand the mixing loss mechanism and assess
the amount of loss are important for a cooling design. This
work simulated a fundamental mixing case and an Inlet Guide
Vane (IGV) with leading edge film cooling with Delayed
Detached Eddy Simulation (DDES), showing the flow
structures and turbulence properties of the mixing process and
analysing the loss mechanism from the aspect of entropy
production. Results show that the mixing processes are
unsteady. In the IGV case, leading edge jet flows are bended
towards the wall by the main flow and thus induce flow
separation, especially at the blade pressure side. Besides, loss
appears at the strong shear region near the wall and the vortex
interaction region downstream, which are caused by viscous
stress and Reynolds stress, respectively.
INTRODUCTION
Researches on film cooling in literature (Bogard and
Thole, 2006) mainly focused on the influence on film
effectiveness of the film cooling hole configurations (hole
shape, ratio of length and diameter, jet angle et al.), the coolant
jets parameters (blowing ratio, density ratio, velocity ratio and
mass flow ratio) and the main flow conditions (stream wise
pressure gradient, blade surface curvature and turbulence
intensity). These influences were discussed at different
regions of the flow passage. However, the loss due to the
mixing process in the interaction between jets and main flow
was less frequently discussed. In the limited researches in
literature, the mixing loss and its impact on the turbine
efficiency were investigated in three aspects: experiments in
cascades, analytical loss models and simulations.
Existing experiments mainly focused on the influence of
the position and intensity of coolant jets on the overall
efficiency. Ito (Ito, 1976) and Ito et al. (Ito et al., 1980)
measured the impact of coolant jets with different intensity
from one row of cooling holes at pressure or suction side of a
blade on the total pressure loss penalty downstream. Results
showed that jets from suction side induced transition at suction
side boundary layer and thus significantly increased loss. For
conditions with turbulent boundary layers, weak jets slightly
increased loss while strong jets decreased loss. Yamamoto et
al. (Yamamoto et al., 1991) studied the influence of coolant
jets from a slot at various position in axis direction on the
aerodynamic performance. Results showed that jets changed
the structure of secondary flow in the passage and thus
influenced loss. Jets from suction slot have less influence.
Similarly, Hong et al. (Hong et al., 1997) replaced the slot with
a row of cooling holes and got similar results. Day et al. (Day
et al., 1998; Day et al., 1999) used a different definition of
loss, which considered the total pressure of jet flows, to
evaluate the influence of coolant jets. They measure both
profile and endwall loss and showed that coolant jets
thickened the wake region and thus increase loss. Osnaghi et
al. (Osnaghi et al., 1997) studied the influence of jets from
various positions (leading edge, pressure side, suction side and
trailing edge) on the thermal dynamic loss. Results showed
that thermal dynamic loss increased with the momentum flux
of coolant jets and was independent of the density ratio of
coolant and main flow.
Denton (Denton, 1993) proposed to quantize the loss from
the aspect of entropy production. He analysed the loss sources
in a passage and gave empirical formulations to assess loss.
Some analytical loss models were put forward to estimate the
mixing loss in film cooing. Hertsel (Hartsel, 1972) presented
a control volume based loss model, which assumed the mixing
process was at a constant pressure and the mixing loss could
be added to the overall loss by a linear superposition.
Specifically, this loss model assumed mixing occurred in a
mixing layer, which was thicker than boundary layer. After the
mixing between jets and main flow in the mixing layer, fluids
inside and outside the mixing layer independently expended
to the exit pressure with an isentropic process, and then mixed
2
with each other. Urban (Urban et al., 1998) developed this
constant-pressure mixing model and used it in a cascade.
Based on Hertsel’s model, Lim et al. (Lim et al., 2012)
estimated the mixing loss in a turbine stage and showed that
mixing loss reduced the aerodynamic efficiency by 0.7%.
Numerical studies in literature focused less on the mixing
loss due to film cooling. Walters and Leylek (Walters and
Leylek, 2000) simulated the configuration of Ito’s ((Ito, 1976)
experiment. Different turbulence models were compared and
the Realizable k-ε (RKE) turbulent model was chosen. Results
showed that coolant jets influenced aerodynamic efficiency in
two ways: the first is the mixing between jets and main flow,
the second is that coolant jets changed the boundary layer
condition at blade surface. Lin et al. (Lin et al., 2016) used
RANS (SST turbulent model), DES and SAS to simulate film
cooling of a plate. The simulated total pressure penalty was
lower than experimental result at the downstream part of the
jet and higher at upstream part.
From the above discussion, film cooling has a significant
influence on the aerodynamic performance. However, existing
control volume based loss models totally ignore the flow
details in the mixing process, which are important for loss
production. Besides, RANS methods cannot precisely predict
the flow structures at small scale. The present work uses
DDES method to simulate a fundamental mixing case and
reveals both large scale flow structures and small scale
turbulence properties. Based on the understanding of the flow
field, the mixing loss mechanism is analysed. Results show
that the mixing loss appears at the strong shear region and the
downstream vortex interaction region and is related to viscous
and Reynolds stress, respectively. These analyses are adopted
in an IGV case with leading edge film cooling. Results show
that coolant jets at leading edge are bended towards the blade
surface by the interaction with main flow, which induces flow
separation downstream and increases loss. The mixing loss
due to the leading edge film cooling occurs at the strong shear
region near the hole exit and the vortex interaction region
downstream the hole exit. Besides, the mixing loss is related
to the velocity gradient of the instantaneous flow field.
NUMERICAL METHODS
Film cooling flow is characterized by strong mixing
between the main stream and the coolant, also a series of
vortices with different length scales. Various existing
literature show that it is difficulty to accurately predict the
small-scale flow structures and the turbulent fluctuation
properties in the film cooling process with current RANS
simulation tool. Benefiting from the rapid increase of the
computational resource, scale-resolving simulation, such as
Large Eddy Simulation (LES) or the hybrid RANS/LES
emerge as affordable and valuable tools in predicting complex
flow phenomena in turbomachinery. In this work, the DDES
type hybrid RANS/LES is employed to simulate the film
cooling in both a very simple case and an IGV case.
Current DDES simulation is conducted with a well-
proved in-house code which is based on the multi-block
structured finite volume method. The Navier-Stokes equation
can be expressed in the following integral form as
∂
∂t∫𝑈𝑑𝑉 + ∮𝐹𝑛𝑑𝐴 = ∮𝐺𝑛𝑑𝐴 (1)
where 𝐹𝑛 denotes the convective flux and 𝐺𝑛 the viscous
flux. In the current code the prefect gas is assumed and the
Sutherland law is used to get the molecular viscosity.
Current DDES simulation is based on the Spalart-
Allmaras one-equation turbulence model. The original
Detached Eddy Simulation was proposed by Spalart and
Allmaras which uses RANS model inside the boundary layer
and LES model elsewhere. To overcome the modelled-stress
depletion (MSD) issue in the original DES model, a shield
function is introduced to protect the boundary layer and the
new model is termed as DDES (Spalart et al., 2006).
For the DDES type simulation, the numerical dissipation
should be carefully kept at low value in order not to dissipate
the small scale turbulent structures. In this work, a high order
method is used to discretize the convective term defined in
Equation (1). It is based on a novel fifth-order method (Su et
al., 2013) which is verified to be accurate and stable. Also, in
order to further reduce the numerical dissipation, a vorticity
based parameter is used to automatically adjust the local
numerical dissipation and in this manner the highly vortical
region is resolved with minimal dissipation. In the unsteady
simulations, the dual time step method is employed and the
physical time step is chosen according to the unsteady
behaviour of the studied flow problem. The discretized
governing equation is solved with an efficient implicit time
marching method which permits the usage of large Courant–
Friedrichs–Lewy (CFL) number up to 1000. For further
convergence acceleration, multigrid method is also employed.
COMPUTATIONAL SETUP FOR THE FUNDAMENTAL CASE
Before the investigation of the interaction between main
flow and coolant jets in IGV, a simplified case with
experiments carried by Kacker and Whitelaw (Kacker and
Whitelaw, 1968a; Kacker and Whitelaw, 1968b; Kacker and
Whitelaw, 1969; Kacker and Whitelaw, 1971) was studied
first to delineate the fundamental mixing mechanism between
the main flow and jets. The configuration of the test rig is
shown in Fig.1 and the region enclosed by dashed lines was
chosen as the computational domain. The computational
domain starts 4D upstream of the slot outlet and ends 86D
downstream with height of 24D. The width and span of the lip
are 1.14D and 3D respectively. A structured mesh of 5M
points was generated with averaged y+ less than 1. To better
capture the coherent structures in the mixing region, the region
behind the lip was filled with nearly cubic elements.
Figure 1 Test rig configuration and computational domain
3
The inlet and outlet flow conditions are given in Table.1.
The slot width based Reynolds number, 12000, and the
blowing ratio, 1.25, are kept identical to and the Mach number
higher than the experiment. The walls of the lip and the bottom
wall of the domain are set to be no-slip wall condition and the
upper wall of the domain is set to be symmetric boundary
condition. Periodic conditions are forced at the lateral walls.
The SA-based DDES is applied with implicit time marching
scheme. The physical time step is 1e-5s for unsteady
simulation. The result was averaged for 5 flow through times
or 118 vortex shedding periods.
Table.1 Computational flow conditions
Tt_m
[K] Pt_m
[kPa] Tt_c
[K] Pt_ct
[kPa] Pout
[kPa]
300 100.93 280 101.178 100
RESULTS AND DISCUSSION FOR THE FUNDAMENTAL CASE
Figure 2 shows the comparison between numerical and
experimental results (Ivanova and Laskowski, 2014). As for
the turbulence property, DDES method gives good prediction.
Figure 2 Turbulent kinetics energy (x=10D)
To understand the large scale flow structure, the present
work gives the flow topology for mixing process, as shown in
Fig. 3, which is the abstraction of the time-averaged flow field.
In the mixing process, the flow field can be regarded as three
regions, from top to bottom: main flow region, mixing region
and jet flow region. The distribution of different velocity
components is shown in Fig. 4 and 5. In the mixing region, the
flow direction component is negative upstream and speeds up
to reach main flow velocity. As for the height direction
component, both scale and gradient are significant only in the
upstream part of the mixing region.
Figure 3 Flow topology for mixing process
Figure 4 Streamwise velocity distribution
Figure 5 Transverse velocity distribution
Figure 6 shows the distribution of turbulence kinetic
energy. The turbulence concentrates at the upstream part of
the mixing region, which implies that the turbulence is
produced by the free shear flows caused by the interaction
between jets and the main flow. To further discuss the
turbulence property, the present work choose three sets of
points from jet flow region, mixing region and main flow
region respectively and draw the corresponding Lumley
triangles (Lumley and Newman, 1977). The Lumley triangle
can reveal the anisotropy properties of the turbulence.
Comparison of Fig. 7 shows the the mixing process contains
various anisotropy properties. In main flow region, the
turbulence have two dominant directions. In jet flow region
and mixing region, the turbulence has one dominant direction,
which are in different directions for the two regions. In
existing RANS model, the linear Boussinesq relation is
adopted in which the Reynolds stress is assumed to be
isotropic. Fig. 7 explains why with existing RANS model it
always fails to accurately predict the film cooling
performance, mainly due to the missing of turbulent
anisotropic property.
4
Figure 6 Turbulence kinetics energy distribution
Figure 7 Lumley triangle for various positions: Jet flow region (up) mixing region (middle) main flow
region (bottom)
Figure 8 shows the total dissipation rate of the time
averaged flow field. From the integral results, 79.4% of the
mixing loss (out of the boundary layer) is located at the core-
mixing region (shown with a black rectangular). Figure 9 and
10 show the dissipation rates due to Reynolds and viscous
stress, respectively. The loss due to Reynolds stress is located
downstream the lip, where there are strong vortex interactions.
This part of loss accounts 90.7% of the mixing loss in the core
mixing region. The loss due to viscous stress is located at the
strong shear region close to the lip and accounts 9.3%.
Figure 8 Total dissipation rate
Figure 9 Dissipation rate due to Reynolds stress
Figure 10 Dissipation rate due to viscous stress
Figure 11 and 12 show the distribution of the Q criterion
and dissipation rate of an instantaneous flow filed. The loss
occurs at the strong shear region close to the lip and the vortex
interaction region downstream. The latter is due to the small
scale vortex because there is a noteworthy correspondence
between the Q criterion and the dissipation rate distributions.
Comparing with Fig. 10, we can conclude that mixing loss is
mainly due to the small vortex structures and the turbulent
fluctuations. After being averaged by time, the resource of this
part of loss shows in the form of Reynolds stress.
5
Figure 11 Instantaneous Q criterion
Figure 12 Instantaneous dissipation rate
Figure 13 and 14 compare the distribution of a component
of instantaneous dissipation rate (accounting 35.1%) and the
corresponding velocity gradient. Their relationship is shown
as
Φ12 = 𝜏𝑥𝑦𝜕𝑈
𝜕𝑌 (2)
where τxy, for instantaneous flow field, is determined by the
velocity gradient as
τxy =1
2𝜇(
𝜕𝑈
𝜕𝑌+
∂V
∂X) (3)
The instantaneous velocity gradient ∂U/∂Y dominates in
the mixing process. So we only consider the relationship
between Φ12 and ∂U/∂Y. The comparison in Fig. 13 and 14
reveals that the dissipation is determined by the velocity
gradient and for this case, the mixing loss is significantly
affected by the velocity gradient ∂U/∂Y close to and
downstream the lip.
Figure 13 Instantaneous Dissipation rate
component (Φ12)
Figure 14 Instantaneous velocity gradient (∂U/∂Y)
COMPUTATIONAL SETUP FOR THE IGV CASE
Film cooling is characterized by a mixing process
between jets and main flow near the wall. The fundamental
mixing case models and simplifies this kind of flow by
changing the mixing angle to be zero, thus only one dominate
mixing direction left. Based on this simplification, the
fundamental mixing case reveals the basic mixing loss
mechanism. Then the present work simulates another case,
which represents real turbine surroundings, to further discuss
the mixing loss in a turbine with film cooling. The simulated
object is an IGV with leading edge film cooling. Figure 15
shows the mesh at the symmetry plane of the calculation
domain. Detailed geometry data can be found in the
experiment report (Ardey and Wolff, 2001). The hole and
blade surfaces are set as non-slip wall. Periodic boundary
condition is set in azimuthal direction and symmetry boundary
condition in spanwise direction.
The total pressure is 196.2hPa at main flow inlet and
200.6hPa at the hole inlet. Total temperature is 303K at main
flow inlet and 300K at the hole inlet. Static pressure at outlet
is 145.9hPa. The physical time step is 2e-6s for unsteady
simulation. The result was averaged for 270 vortex shedding
periods or 174 characteristic times for pressure side hole.
Figure 15 Mesh for the IGV case
RESULTS AND DISCUSSION OF THE IGV CASE
Figure 16 shows the comparison between experimental
and numerical results of the blade surface pressure
distribution. The comparison shows the present work
precisely predicts the general parameters of the IGV case.
6
Figure 16 Blade surface pressure distribution
Figure 17 shows the flow structure at the blade leading
edge. There are two film cooling holes on both sides of the
stagnation point. The jets interact with main flow and are
bended to the blade surface. The bended jets induce flow
separation and the separation is more severe at the pressure
side. Figure 18 shows the limited stream lines at the blade
surface. The pressure side is on the left. From the limited
stream lines, the flow separation at the pressure side can be
observed. There exist several separation regions and their
boundaries are shown. Besides, the re-attaching point occurs
downstream.
Figure 17 Flow structure at leading edge
Figure 18 Limiting stream line near the leading edge
Figure 19 and 20 show the comparison between
instantaneous Q criterion and dissipation rate distribution. The
comparison shows that the flow structure in the IGV with film
cooling is more complicated. The loss mainly exists at hole
exits and the vortex interaction region downstream. The
results reveal that in this IGV case the loss appears mainly due
to the small-scale vortex structures. According to the analysis
of the fundamental case, the loss depends on the velocity
gradient caused by the interaction of jets and main flow.
Figure 19 Instantaneous Q criterion
Figure 20 Instantaneous dissipation rate
CONCLUSIONS
The present work uses DDES method to simulate a
fundamental mixing case and successfully captures both large
scale flow structures and small scale turbulence properties.
Based on the understanding of the flow field, the mixing loss
mechanism is analysed. Results show that the mixing loss is
related to both viscous and Reynolds stress at the strong shear
region and the downstream vortex region, respectively. These
analyses are adopted in an IGV case with leading edge film
cooling. Results show that coolant jets at leading edge are
bended towards the blade surface by the interaction with main
flow, which induces flow separation downstream and increase
loss. The mixing loss due to the leading edge film cooling
occurs at the strong shear region near the hole exit and the
vortex interaction region downstream the hole exit. Besides,
the mixing loss is related to the velocity gradient of the
instantaneous flow field. The present work reveals the detailed
flow structures and the loss mechanism of the mixing process,
7
covering the shortage of the widely used control volume based
loss models.
NOMENCLATURE
Pt_m: total pressure of the main flow
Pt_c: total pressure of the coolant flow
D: coolant jet outlet width
Tt_m: total temperature of the main flow
Tt_c: total temperature of the coolant flow
ACKNOWLEDGMENTS
The authors would like to express appreciation for the
support of the National Natural Science Foundation of China
(Project No. 51506107, Project No. 51476082 and Project No.
51136003).
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AGTB. Universität der Bundeswehr München, Fakultät für
Luft- und Raumfahrttechnik Institut für Strahlantriebe,
Institutsbericht LRT - Inst. 12 - 98/01
