[American Institute of Aeronautics and Astronautics 47th AIAA/ASME/SAE/ASEE Joint Propulsion...

American Institute of Aeronautics and Astronautics

1

Aerodynamic Aspects and Cooling Techniques of Turbine Blade;

Numerical Studies using LES, SAS, SST, SA and k-ε

Carlos Velez1, Patricia Coronado

2 , Husma 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 and blade cooling techniques. 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.

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

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

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 2011-5817

Copyright © 2011 by Marcel Ilie. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


2

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:

0

i

i

x

u (1)


3

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 (Cs = 0.1 in the present work), 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 47.6 mm

Blade # 41 36

RPM 3500 0

Tip Diameter 600mm 600mm

The models require 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 Eqn. 7.

(7)

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.


4

Table 2. Reference values for

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,e) 5

& 30,000

To investigate the performance and flow physics involved in hub cooling a comparison study was created which

varies the mass flow rate of a hub based cooling jet at a fixed position 10mm in front of the leading edge of the rotor

blade. Additionally, a comparison of LES, SAS, SST, k-ε and SA turbulence models is completed to study the effect

of turbulence models on the temperature field. The initial simulations compare the temperature profile of the blade

for a cooling mass flow rate of 0.1, 0.2 and 0.3 kg/s with 100 cooling jets each with a diameter of 0.001 meters

which are equally spaced along the hub. The cooling jets exhaust cold air at 273K in the radial direction from hub to

tip.


5

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.

Figure 2 presents the wake evolution. The computations were carried out by means of Direct Numerical

Simulation using an Adaptive Mesh Refinement (AMR) technique without injection as a reference to the

performance of the injection system. 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


6

t = 0.05s

Figure 2. Time evolution of the blade wake (DNS computations)

Figure 3 compares the time evolution of the wake between the cases of no jet and impinging jet, the analysis

reveals that the wake becomes highly dynamic in the presence of the injectors.

t =

0.02

5s

t =

0.03

0s


7

t =

0.03

5s

t =

0.04

0s

t =

0.04

5s

t =

0.05

s


8


The vortex dynamics is well illustrated in the temperature plots. Figure 4 shows the influence of the impinging jet on

the blade surface and its wake.

t =

0.025

s

t =

0.030

s


9

t =

0.035

s

t =

0.040

s


1

0

t =

0.045

s

t =

0.05s



1

1

Figure 5 presents the velocity magnitude for the case thin film cooling, at various cutting planes form the wall.

The blowing ratio (BR) is 3:1. The analysis reveals the presence of highly dynamic vertical structures at the exit of

the injecting holes, near the wall surface. Distancing from the wall the flow becomes more dynamic and thus,

vertical structures are identified at the surface of the airfoil. The study reveals a wake of low velocity. Increasing the

distance from the wall the wake is shrinking and a high velocity region is identified.

x/c= 0.0001

x/c= 0.0002

x/c= 0.0004

x/c= 0.0005

x/c= 0.0006

x/c= 0.0007


1

2

x/c= 0.0008

x/c= 0.0009

Figure 5. Time-dependent velocity magnitude (LES)

x/D=0.5

x/D=0.51


1

3

x/D=0.52

x/D=0.53

Figure 6. Spanwise velocity (LES)

Figure 6 presents the spanwise velocity from LES computation for the case on injecting flow. The analysis

reveals the presence of highly dynamic vertical structures close to the wall surface. Close to the trailing edge the

vertical structures are the most dynamic. Their influence is reflected in the normal direction velocity. The plume of

cold air is entrained in the mean stream flow. Distance from the trailing edge of the injecting hole the influence of

the jet starts to diminish. The effect of the jet, on the flow field, is well illustrated in the vorticity field as well. Thus,

the analysis of Fig. 7 shows the presence of highly dynamic vertical structures. These vertical structures are highly

dynamic in the region close to the wall. Their effect on the upper flow field is well illustrated in the plots. The

highly dynamic region corresponds to the leading edge of the blade. The jet impinges on the leading of the blade.

The effect of the cooling jet is well captured in the DNS computations as shown in Figure

x/D=0.5

x/D=0.51


1

4

x/D=0.52

x/D=0.53

Figure 7. Spanwise vorticity (LES)

Figure 8 below shows the temperature field of the rotor blade when the cooling jet is injected from the hub

towards the tip. A variation of the cooling mass flow rate shows a considerable effect on the blade temperature. The

variation shows a positive and negative effect on the blade temperature, which shows that the cooling effectiveness

if not solely a function of the cooling mass flow rate.

In the case where the cooling mass flow rate is equal to 0.1 kg/s the average blade temperature and pressure are

respectively, 868.12K and 136,635 Pa. The temperature field appears very uniform in comparison to the other two

mass flow rates, insinuating that the correct jet velocity is used to cool the entire blade surface. In all three cases a

large temperature gradient is encountered at the blades leading edge where the blade meets the hub. This large

temperature difference is the result of the cooling jets inability to cool close to the hub, which can be attributed to

too high of a jet velocity. A max temperature of 1823K is encountered in this region which is approximately double

the inlet static temperature.

When the mass flow rate is increased to 0.2 kg/s, similar results are found. An increase in the cooling jet velocity

reduces the blade temperature closer to the shroud then the hub. This results in a lower peak temperature of 1312K

which is distributed throughout a larger region where the hub and blade intersect. The average blade temperature

and pressure are respectively, 878.924K and 137,085Pa. Thus, a higher cooling mass flow rate has produced higher

blade temperatures with a more distributed blade temperature profile.

As the cooling mass flow rate is increase to 0.3 kg/s, similar results are encountered. An increase in the cooling

jet velocity reduces the peak temperature to 1180K and distributes the high temperature upon a larger region away

from the hub. The average blade temperature and pressure are respectively, 862.122K and 138,513Pa, which is the

lowest average blade temperature of the three mass flow rates.


1

5

Cooling Mass Flow Rate = 0.1 kg/s



Figure 8. Blade Temperature Profile vs. Cooling Mass flow rate

In order to study the effects of a varying cooling mass flow rate from a quantitave perspective. The blade leading

and trailing edge temperature profiles have been plot in comparison to the three different mass flow rates, as shown

in Fig. 9.


1

6

Figure 9. Temperature plot of blade leading and trailing edges

Table 4. Average blade temperature and pressure for different turbulence models

Turbulence Model Mdot=0.3 Average Blade Temperature Average Blade Static Pressure

K-Omega 876.39 K 138114 Pa

Shear Stress Transport 862.35 K 138513 Pa

SST – Extended Wall Function 866.19 K 138520 Pa

The resulting temperature distribution along

the blade’s leading and trailing edges show a

considerable difference with varying cooling

mass flow rate. In the case where the cooling

mass flow rate is equal to 0.1 m/s very high

heat flux is found near the hub, where the

largest temperature changes are found. The

slow cooling jet has contributed to 100 K

difference between the leading and trailing

edges. In the case where the cooling mass flow

rate is raised to 0.2 kg/s a very small

temperature difference between leading and

trailing edges is found close to the hub. It can

be seen that a larger temperature difference

between edges occurs closer to the shroud.

In both cases there is a point where the leading

and trailing edge temperatures are equal, which

is a characteristic location for the effectiveness

of the hub based cooling jets.

Additionally, a comparison of four

turbulence models is completed. The effect on

the blade average pressure and temperature is

compared in Table 4 to determine an adequate

model for accurate results which are not

computationally expensive.


1

7

t=0.00011

t=0.00023

t=0.00034

a) SST- EWF b) SA c) k

Figure 10. Turbulence Model Comparison of Skin Friction Coefficient

Figure 10 presents the comparison of skin friction coefficient for the SST, SA and k-ε turbulence models at three

different time steps. The results show that there is not a significant change between the models.


1

8

t=0.00011

t=0.00023

t=0.00034

a) SST- EWF b) SA c) k

Figure 11. Turbulence Model Comparison of Static Pressure

Figure 11 presents the comparison of static pressure for the SST, SA and k-ε turbulence models at three different

time steps. Same as with the skin friction coefficient results, there is not a significant change 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.

IV. Conclusions

Numerical computations, using LES, SAS, SST, k-ε and SA approaches, are conducted to investigate the

aerodynamics and cooling techniques of turbine blade. The performance of a hub based cooling jet is analyzed

through the variation of the cooling jet mass flow rate. The temperature field is analyzed in regards to different mass

flow rates and the initial results are documented. Additionally, a comparison of five different turbulence models is

completed, which show negligible changes in the temperature field when comparing LES and SAS based turbulence

models.

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