[American Institute of Aeronautics and Astronautics 47th AIAA/ASME/SAE/ASEE Joint Propulsion...
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American Institute of Aeronautics and Astronautics
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Numerical computations of turbine blade aerodynamics;
comparison of LES, SAS, SST, SA and k-ε
Carlos Velez1, Patricia Coronado
2, Husam Al-Kuran
3 and Marcel Ilie
4
University of Central Florida, Orlando, FL, 32826
Numerical investigations of turbine blade are carried out using large-eddy simulation
(LES), Scale Adaptive Simulation (SAS), k-ε with extended wall function, Spalart-Allmaras
(SA), and Shear Stress Transport (SST). The goal of the present studies is to investigate the
turbine blade aerodynamics. The simulations are performed for a Reynolds number, Re =
3.67 x 106, based on the chord, c, of the airfoil and free-stream velocity. The computational
results reveal the dissipative nature, of SAS, associated with the turbulence modeling.
Cp = pressure coefficient
Cl = lift coefficient
Cs = Smagorinsky constant
c = chord of airfoil
Dwall = van Driest wall damping function
T = subgrid scale viscosity
ij = subgrid scale tensor
I. Introduction
HE boundary layer for the flow through a Low-Pressure Turbine (LPT) cascade is transitional in nature and the
transition location is not known a-priori. Furthermore, the separation process is highly unsteady with a wide
variation in the separation location. Both these factors tend to limit the predictive capability of the RANS approach
for this flow. Furthermore, conventional RANS simulations provide information only about the mean flow field, and
only limited insight regarding the dynamics of the unsteady separation process can be gained from these simulations.
Developments in computer technology hardware as well as in advanced numerical algorithms have now made it
possible to perform very large-scale computations of these turbine flow fields. Numerical methodologies based on
the large-eddy simulation (LES) technique have emerged as a viable means of investigating the transitional flow
through a LPT. In LES, the large-scale motion is simulated accurately, and the so-called subgrid-scales (SGS) are
modeled. Recent numerical studies of flow in a LPT used LES in conjunction with upwind-biased schemes.
Fujiwara et al. (2002) investigated the unsteady suction side boundary layer of a highly loaded low-pressure
turbine blade, TL10. Simulations were performed using a low-Reynolds number k-ε model and also compressible
LES with the Smagorinsky SGS model. The numerical computations, using the low Re k-ε model, were assumed to
be two-dimensional and steady, whereas the large-eddy simulations were three-dimensional and unsteady. For LES,
the three-dimensional compressible Navier-Stokes equations were solved by evaluating the convective terms using a
third-order upwind biased scheme and evaluating the viscous terms using a second-order central-difference scheme.
The study concerned the Reynolds number effect on the blade aerodynamics. Reynolds number, based on the axial
chord and exit velocity, varied in the range (0.99 ÷ 1.76) x105. The study showed that LES can predict the boundary
layer separation and reattachment process, and its Re-number dependence, while the 2D steady simulation with a k-ε
model cannot capture these flow phenomena. However, some difference between LES and experimental data were
1 Master Student, Department of Mechanical, Materials & Aerospace Engineering, AIAA Student Member
2 PhD Student, Department of Mechanical, Materials & Aerospace Engineering, AIAA Student Member
3 PhD Student, Department of Mechanical, Materials & Aerospace Engineering, AIAA Student Member
4 Assistant Professor, Department of Mechanical, Materials & Aerospace Engineering, AIAA Member
T
47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit31 July - 03 August 2011, San Diego, California
AIAA 2011-5880
Copyright © 2011 by Marcel Ilie. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
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observed at the reattachment point. Raverdy et al. (2003) employed the monotonically integrated large-eddy
simulation (MILES) approach to predict the transition process and its interaction with the wake dynamics for a
subsonic turbine blade configuration. The three-dimensional unsteady filtered Navier-Stokes equations were solved
using the finite-volume solver FLU3M, developed by ONERA. No explicit sub-grid scale model was used.
However, the numerical dissipation of the modified AUSM + (P) upwind scheme used to discretize the Euler fluxes
was assumed to transfer the energy from large scales to the small scales at a rate nearly equivalent to the one
provided by a conventional SGS model. The simulations were carried out for the T106 low-pressure turbine blade at
Re = 160,000 based on the exit isentropic velocity. They investigated the influence of the mesh resolution and the
spanwise extent, and concluded that the mean and turbulent quantities compared well with the available
experimental data. Although the numerical results, obtained using upwind-biased schemes, were in good agreement
with the experimental data, the energy in a substantial portion of the resolvable wave number range was damped out
due to the excessive numerical dissipation of the scheme.
According to Mittal and Moin (1997), LES gives good prediction only when is used in conjunction with energy-
conserving schemes such as spectral schemes or high-order central difference schemes. Mittal et al. (2001)
performed a computational study of a flow through a LPT cascade using LES with a dynamic SGS model. The study
employed a completely non-dissipative, mixed finite-difference–spectral spatial discretization scheme, with a
second-order central difference scheme and a Fourier spectral method. Simulations were carried out at Reynolds
numbers of 10,000 and 25,000 based on inlet velocity and axial chord. The spatial and temporal variations of the
flow through a LPT cascade were investigated by examining the mean streamwise velocity profiles and temporal
variation of the instantaneous streamwise velocity along various locations on the suction surface as well as in the
very near wake of the blade. It was observed that at relatively low Reynolds numbers, about 10,000, the dynamics of
the separation phenomenon on the suction surface is governed by the Karman-vortex type shedding behavior in the
wake, but this behavior was not observed for Re = 25,000. The study also concluded that, with the increase of
Reynolds number, the vertical and streamwise extent of the separation bubble on the suction surface decays. It is
worth to notice that the comparisons were based only on the LES results at two different Reynolds numbers, and no
comparison with the experimental data was performed.
Rizzetta and Visbal (2003) conducted a comprehensive numerical study to investigate the subsonic transitional
flow through a LPT cascade using the implicit large eddy simulation (ILES) technique. The ILES technique is
similar to the monotonically integrated large-eddy simulation (MILES). Unlike MILES, which introduces artificial
viscosity by applying a dissipative scheme to discretize the Navier-Stokes equations, in ILES, the truncation errors
of the higher-order accurate dispersive scheme are used to dissipate turbulent energy at the sub-grid scales which
cannot be supported by the computational grid. These studies were carried out for three different Reynolds numbers
2.5x104, 5.0x10
4 and 10.0x10
4. The study revealed the existence of differences between the computed blade-surface
pressure distribution and experimental data, and these differences were associated with the details of the
experimental configuration which were not accounted in the simulations. One of the main conclusions of this study
was that even two-dimensional simulations might provide useful information for preliminary design and parametric
studies.
In spite of the extensive LES studies, the numerical computations of LPT aerodynamics using LES still suffers
from the high grid refinement for resolving boundary layer. In the present study we employ the LES, SAS, Shear
Stress Transport (SST), k-ε and Spalart-Allmaras (SA) models. The comparison of the five turbulence models is
present in this study.
The structure of the paper is as follows. In Section 2 the computational method and models are introduced with
details regarding the numerical approach and computational domain. Section 3 presents the numerical results of the
aerodynamic and aeroacoustic studies. The conclusions regarding the present study are summarized in Section 4.
II. Computational Method and Models
A. Computational Method
In the present work, a LES, SAS, SST, k-ε and SA approaches are used for simulations. The quasi 3-D models
were performed for Re = 3.67x106, based on free stream velocity U and the chord length of the airfoil. The flow
field is solved using the filtered Navier-Stokes equations along with a standard subgrid scale (SGS) model and van
Driest wall damping.
The boundary conditions were assigned as follows. No slip boundary conditions are used at the airfoil wall. Free
slip boundary conditions are used at the top and bottom walls with opening at the end of the computational domain.
Large Eddy Simulation is a result of space averaging operation applied to Navier-Stokes equations. The filtered
Navier-Stokes equations are given by:
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0
i
i
x
u (1)
jj
i
j
ij
i
ji
j
i
xx
u
xx
puu
xt
u
2
Re
1 (2)
where ij is the subgrid scale (SGS) given by:
jijiij uuuu (3)
and is modeled. In the present work the SGS proposed by Smagorinsky and Lilly20-21
is used. In the present analysis
the value of Smagorinsky constant was set to 0.1. The SGS stresses are related to the strain rate tensor by SGS
viscosity, T:
ijTkkijij S 23
1 (4)
The SGS viscosity T is given by:
SDC wallsT
2)( (5)
where Cs is the Smagorinsky constant, Dwall represents the van Driest wall damping factor , is the filter width and
S represents the magnitude of the large-scale strain-rate tensor.
j
j
j
iij
x
u
x
uS
2
1 (6)
B. Simulation Domain
The Aachen 1-1/2 turbine rig stage is used as the case geometry. The turbine’s characteristic dimensions for the
rotor and stator are listed below in Table 1.
Table 1. Characteristic dimensions of blade geometry
Blade Characteristic Rotor Stator
Aspect Ratio 0.917 0.887
Pitch 41.8 mm 47.6mm
Blade # 41 36
RPM 3500 0
Tip Diameter 600mm 600mm
The models requires the definition of a y+ value in order to calculate the adequate distance of the nearest grid
point from the wall in order to resolve the boundary layer thickness. The y+ value is calculated through equation 7.
(7)
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Where, is the distance of the nearest grid point to the wall, is a reference velocity of the flow, is the
kinematic viscosity, is the reference length, and is a non-dimensional value. The corresponding values are
listed below in Table 2.
Table 2. Reference values for calculation
109.9557 m/s
0.3 m
1.038e-5
1
7.8e-6 m
A structured mesh, as seen in Fig. 1, is created with the corresponding y+ value and a span wise expansion ratio
of 1.309 is used to expand the cell width away from the boundary layer region. The entire mesh consists of 1.203e6
nodes split up into three separate blocks for each blade row. The stator blocks consists of 364k nodes each and the
rotor block consists of 475k nodes. The code allows for multi-staged blocks to interface between rotating and non-
rotating rows via a mixing region located at the interface of the stages.
Figure 1. Meshed turbine domain
The models key boundary conditions and settings are summarized below in Table 3.
Table 3. Model Description
Fluid Type Air (perfect Gas)
Axial , Radial, Tangential Flow velocity 109.95, 0, 0 m/s
Inlet Total Pressure 169,500 Pa
Inlet Total Temperature 900 K
Outlet Static Pressure 90,000 Pa
Turbulence Coefficients (k, ) 5
& 30,000
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III. Results and Discussion
Five different turbulence models were investigated and compared, LES, SAS, k-ε with extended wall function,
Spalart-Allmaras (SA), and Shear Stress Transport (SST), to study the effect on the temperature and pressure fields
of turbine blades. The simulations were carried out using in-house codes as well commercial CFD software
NUMECA, which is turbo machinery oriented software. NUMECA was used to carry out the SA, SST and k-ε
simulations, while an in-house code was used to simulate the LES and SAS models.
t = 0.1s
t = 0.2s
t = 0.3s
t = 0.4s
t = 0.5s
Figure 2. Time-dependent velocity magnitude, LES solution
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Figure 2 presents the time-dependent velocity magnitude from the LES computations at different instants in
time. The analysis of the velocity magnitude reveals the presence of the wake and the flow separation. The flow
accelerates at the upper surface of the airfoil and thus, a high velocity is identified at this location. As the flow
develops the separation line moves upward towards the leading edge of the airfoil. Highly turbulent flow is
identified at the trailing edge in the separation region. From Figure it can be seen that the wake remains highly
turbulent.
Figure 3 presents the wake evolution. The computations were carried out by means of Direct Numerical
Simulation using an Adaptive Mesh Refinement (AMR) technique. The analysis reveals the presence of relatively
large vertical structures in the wake of the blade. The flow separation region is well captured as well and in good
agreement with the LES computations.
t = 0.025s
t = 0.030s
t = 0.035s
t = 0.040s
t = 0.045s
Figure 3. Time evolution of the blade wake (DNS computations)
Figure 4 presents the comparison of the LES and SAS computations, based on the velocity magnitude. Overall,
the LES and SAS computations are in good agreement. However, the study reveals that dissipative nature of SAS.
Thus, the wake is smaller in the SAS computations when compared with the LES ones. The differences are well
captured in the vector field as well, as shown in Figure 5.
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a) LES b) SAS
Figure 4. LES/SAS comparison (magnitude velocity)
a) LES b) SAS
Figure 5. LES/SAS comparison (vector field)
Figures 6 and 7 provide a better insight into the differences between LES and SAS. The point wise comparisons
are conducted in the separation region where the difference between the two models is most significant. This
comparison emphasizes the dissipative nature of the SAS method. Although the computational time was reduced by
17% the SAS lacks of capturing the wake. The wake is an important component especially when the rotor-stator-
rotor configuration is employed.
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Figure 6. Comparison of velocity magnitude
Figure 7. Comparison of pressure
0
50
100
150
200
250
300
350
0 0.001 0.002 0.003 0.004 0.005 0.006
Ve
loci
ty [
m/s
]
t [s]
LES
SAS
-80000
-60000
-40000
-20000
0
20000
40000
60000
0 0.001 0.002 0.003 0.004 0.005 0.006
Pre
ssu
re [
Pa}
t[s]
LES
SAS
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Figure 8 presents the spanwise velocity, from LES computations. The analysis reveals a high velocity region at
the upper surface of the airfoil at the leading edge region. This trend remains valid for almost half of the airfoil
chord. In the second half chord of the airfoil the flow separation takes place and this is illustrated by the low values
of velocity, in this region vortices start to form. Close to the trailing edge the vortex formation become dominant
mechanism and thus enhanced flow separation is observed.
x/c = 0.001
x/c = 0.001
x/c = 0.001
x/c = 0.001
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x/c = 0.001
x/c = 0.001
Figure 8. Spanwise velocity magnitude (LES computations)
Figure 9 presents the static temperature distribution of the blade using k-ε with extended wall function. The
results show an average blade temperature of 890.122 K and an average blade pressure of 135,877 Pa, showing a
higher blade temperature at the leading edge. The static temperature distribution of both the trailing edge
and leading edge blade using k-ε are illustrated in Fig. 10.
The static temperature distribution of the blade using SA is presented in Fig. 11. The results show an average
blade temperature of 884.959 K and an average blade pressure of 136,042 Pa. The average temperature of the blade
is lower than that of the k-ε but still showing a higher blade temperature at the leading edge. The static
temperature distribution of both the trailing edge and leading edge blade using SA are illustrated in Fig.
12.
Figure 13 presents the static temperature distribution of the blade using SST. The results show an average blade
temperature of 885.685 K and an average blade pressure of 136,015 Pa, showing a higher blade temperature at the
leading edge. These values are relatively close to those for SA. The static temperature distribution of both
the trailing edge and leading edge blade using SST are illustrated in Fig. 14.
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Figure 9. Static temperature distribution of blade using k-ε
Figure 10. Static temperature distribution of LE and TE blade using k-ε
Leading Edge (LE)
Trailing Edge (TE)
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Figure 11. Static temperature distribution of blade using SA
Figure 12. Static temperature distribution of LE and TE blade using SA
Leading Edge (LE)
Trailing Edge (TE)
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Figure 13. Static temperature distribution of blade using SST
Figure 14. Static temperature distribution of LE and TE blade using SST
Leading Edge (LE)
Trailing Edge (TE)
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t=0.00011
t=0.00023
t=0.00034
a) SST- EWF b) SA c) k
Figure 15. Turbulence Model Comparison of Static Pressure
Figure 15 presents the comparison of static pressure for the SST, SA and k-ε turbulence models at three different
time steps. There is not a significant change in the results between the models. The main difference to note between
turbulence models was the time that the simulations took to be completed, the fastest one being the k-ε, then the SA
and finally the SST with extended wall function.
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t=0.000116
t=0.000232
t=0.000348
a) SST b) SA c) K-
Figure 16. Turbulence Model Comparison of Static Temperature
Figure 16 presents the comparison of static temperature for the SST, SA and k-ε turbulence models at three
different time steps. The results indicate that both the SA and k-ε turbulence models show a larger heat flux close to
the walls, where as the SST model has a more uniform heat distribution throughout the blade. Additionally, the SST
model shows a large drop in temperature towards the trailing edge of the rotor blade that is not found in the SA and
k-ε results.
IV. Conclusions
Numerical computations, using LES, SAS, SST, k-ε and SA approaches, are conducted to investigate the
aerodynamics of turbine blade. For all the computations we will employ the LES based models since it provides a
better prediction of the flow field. The dissipative nature of the SAS is evident in the results when compared to
turbulence models which model the SGS.
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