[american institute of aeronautics and astronautics 43rd aiaa aerospace sciences meeting and exhibit...

American Institute of Aeronautics and Astronautics

1

A Scale-Adaptive Simulation Model using Two-Equation

Models

F.R. Menter1 and Y. Egorov

2

ANSYS CFX Germany, 83624 Otterfing, Germany

The Scale-Adaptive Simulation (SAS) concept is based on the introduction of the von

Karman length-scale into the turbulence scale equation. The information provided by the

von Karman length-scale allows SAS models to dynamically adjust to resolved structures in

a URANS simulation, which results in a LES-like behavior in unsteady regions of the

flowfield. At the same time, the model provides standard RANS capabilities in stable flow

regions. The introduction of the von Karman length-scale is based on the reformulation of

Rottas’s equation for the integral length-scale. In the current paper, the term containing the

von Karman length-scale is transformed to the SST turbulence model. It allows the SST

model to be operated in a SAS mode.

I. Introduction

HERE is a continuously increasing demand in all areas of CFD for unsteady flow simulations. In

aerodynamics, the unsteady fluctuations of the flow field can have a significant influence on stalled flow

characteristics, or on the forces acting on different parts of the aircraft. Unsteady flowfields are also required for the

reliable prediction of aerodynamic noise generation from cavities or protruding surfaces. In non-aerodynamic flows,

there is a multitude of mixing problems (piston engines, turbine blade cooling, chemical engineering) where steady

RANS (Reynolds Averaged Navier-Stokes) solutions are not adequate. Even more complex applications require the

simulation of the unsteady interaction of the flow with additional physical effects, like cavitation or combustion. For

many of these problems, the simple switch from steady RANS to (unsteady) URANS has proven to be insufficient.

The reason is that URANS solutions typically do not display the correct spectrum of turbulent scales, even if the

numerical grid and the time step would be of sufficient resolution. This is the result of the overly dissipative

character of standard URANS methods, which prevents the formation of a turbulence cascade starting from the large

URANS structures. The use of LES methods on the other hand is often not practical, as the resolution of attached

boundary layers and internal flows (pipe or channel flows) would be prohibitive.

Due to the deficiencies of standard URANS methods an alterative was developed by Spalart et al. (1997), Spalart

(2000), Strelets (2001) using a combination of RANS and LES techniques defining the DES methodology (Detached

Eddy Simulation). DES relies on the comparison of the turbulent length-scale computed from the turbulence model

and the local grid spacing. In case the grid spacing is sufficiently lower than the turbulent length-scale, the model

switches to the grid spacing as the defining length-scale. The argument being that under those conditions, the grid is

sufficiently fine for resolving the turbulent structures. From a practical standpoint, the use of the grid spacing

reduces the eddy-viscosity and allows the formation of a three-dimensional turbulent spectrum in detached flow

regions. The original concept of DES was intended for flows with a clear separation of attached and detached flow

regions, where the RANS model would be active in the attached boundary layers and the LES method in the

detached regions. Recently, DES is also being applied as a layered model inside attached flows, where the near wall

region is covered by the RANS portion and the outer part by the LES formulation (see e.g Davidson & Dahlström

2005). In the authors’ understanding, the second use of the DES method was not originally intended and is also not

providing the savings in computational costs required in today’s CFD simulation. This is not to say that this

application of DES will not develop into an attractive engineering tool in the future.

1 Head of Software Development Dept., ANSYS Germany, Staudenfeldweg 12, 83624 Otterfing, Germany. 2 Software Development, ANSYS Germany, Staudenfeldweg 12, 83624 Otterfing, Germany.

T

43rd AIAA Aerospace Sciences Meeting and Exhibit10 - 13 January 2005, Reno, Nevada

AIAA 2005-1095

Copyright © 2005 by ANSYS Inc. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


2

The present interpretation refers to the original proposal of computing large unsteady detached flows. In this

meaning, DES has already been applied successfully to numerous engineering flow problems and is therefore an

enrichment of the spectrum of models available to a practitioner. On the downside, DES does require the application

of strict rules for grid generation to obtain a consistent solution. Of particular concern during grid generation is that

the grid may not exceed a critical level of refinement, as otherwise the underlying RANS solution will be

compromised. Guidelines have been defined by Spalart (2001) for avoiding this situation. However, the principle

problem remains, that standard DES solutions will deteriorate under systematic grid refinement, which is an

unsatisfactory situation in numerical analysis, where one expects a convergence of the solution (for unsteady flows

at least in a statistical sense) under grid- and timestep refinement. As a consequence, quality assurance procedures,

using systematic grid refinement cannot be applied to classical DES computations. This is not a hypothetical

argument, as quality assurance is one of the strongest weapons for avoiding numerical errors in industrial CFD

simulations. From the perspective of general-purpose CFD codes, it is often not possible to satisfy the grid

requirements demanded by DES, as numerous other constraints have to be considered (physical and geometrical).

From the same perspective, it is also difficult to ensure that all users of a general purpose CFD code are informed

about and follow such procedures. In order to remedy the situation, Menter et al. (2002) have proposed a zonal

formulation of the SST-DES model to protect the boundary layer from the DES limiter. A number of successful

applications of this technique have been reported. Nevertheless, even the zonal DES approach does not avoid the

resolution issue, but shifts the problem to finer grid limits. In addition, the method has to rely on the ability of the

SST blending functions to switch from RANS to DES mode.

In an alternative approach, Menter and Bender (2003), Menter and Egorov (2004) have investigated the

development of improved URANS methods, which can provide a LES-like behavior in detached flow regions. The

first such model was based on the KE1E one-equation model for the eddy-viscosity (Menter and Bender, 2003). The

KE1E model is a direct result of the transformation of the high Reynolds number version of the k-ε model to a one-

equation model, using equilibrium assumptions. During the transformation, the von Karman length-scale, LvK,

appears in the equation in the sink term. It turns out that this new term introduces a dynamical behavior into the

model, which was not present in the underlying two-equation model. Instead of producing the large-scale

unsteadiness, typically observed in URANS simulations, the model adjusts to the already resolved scales in a

dynamic way and allows the development of a turbulent spectrum in the detached regions. It therefore behaves in a

way much similar to a DES model, but without the explicit grid dependence in the RANS regime. The concept was

called Scale-Adaptive Simulation (SAS), as the model adjusts automatically to the resolved flow field. It is to be

noted that the KE1E-SAS model is derived on classical (U)RANS arguments. Its ability to act in an LES-like

fashion in certain flow regions does therefore pose questions concerning the URANS concept as a whole (Menter

and Bender, 2003).

The von Karman length-scale, LvK, entered the KE1E model as a result of the transformation from the k-ε model. An

open question is therefore, if LvK could also be derived naturally within the more general two-equation framework. It

was shown by Menter and Egorov (2004) that the exact transport equation for the turbulent length-scale, as derived

by Rotta (1972), does actually introduce the second derivative of the velocity field and thereby LvK into the turbulent

scale equation. In Menter and Egorov (2004), a two-equation turbulence model was presented using a k-νt

formulation, which can be operated in RANS and SAS mode. While the further development of this model is still

ongoing, it was considered desirable to investigate, if the SAS term in the k-νt model could be transformed to

existing two-equation models. The target two-equation model in the present paper is the SST model (Menter, 1993,

Menter et al., 2003), using the ω-equation as the second scale equation. The transformation of the SAS term to the

SST model will be presented in the next section. The calibration and application of the model will be described in

the testcase section.

II. Turbulence Model Formulation

Starting point of the transformation to the SST model is the k-νt formulation as given in Menter and Egorov (2004).

The following two equations have been derived there for the variables k and Lk=Φ :


3

∂

∂

∂

∂+

Φ−=

∂

∂+

∂

∂

y

k

y

kcP

x

kU

t

k

k

t

k

j

jσ

µρ

ρρµ

2

4/3

∂

Φ∂

∂

∂+−

Φ−=

∂

Φ∂+

∂

Φ∂

Φ yyk

kUSP

kx

U

t

t

tk

j

j

σ

µρζµζ

φζ

ρρ32/3

2

21 ''ˆ

Φ= 4/1

µν ct

(1)

with:

=

κζζ

';maxˆ

22

LcSAS

; jjj

i

k

i

x

L

x

LL

x

U

x

UU

∂

∂

∂

∂=

∂

∂

∂

∂= ';''

2

2

2

2

(2)

where S is the absolute value of the strain-rate, Pk the production rate of the turbulent kinetic energy and

41.0,09.0 == κµc .

The determination of the constants followed mainly Rotta’s estimates resulting in 8.01 =ζ and

0326.03 =ζ . 51.32 =ζ comes from the demand that the equations have to satisfy the logarithmic law of the wall.

The diffusion constants are chosen as 3/2== Φσσ k to ensure a proper behaviour of the equations at a viscous-

inviscid interface. The constant cSAS allows the model to adjust to a given resolved length-scale of the mean flow. In

the k-νt model a value of cSAS~0.5 was found optimal.

The SAS-relevant term in the equation for Φ is the term with the second derivative ''U . As a result of this term, the

length-scale, L, predicted by the above model is largely proportional to the von Karman length-scale:

22 /

/

yU

yULvK

∂∂

∂∂= κ

(3)

It has been demonstrated by Menter and Egorov (2004) that the ''U term is the result of the exact length-scale

equation of Rotta. It therefore has a strong theoretical foundation and is one of the central terms in Eq.1. It has also

been shown that this term allows the model to operate in a scale-adaptive simulation (SAS) mode. The reason is that

LvK adjusts to the already resolved scales in a simulation and provides a length-scale, which is proportional to the

size of the resolved eddies. Standard turbulence models, on the other hand, always provide a length-scale

proportional to the thickness of the shear layer. They do not adjust to the local flow topology and are therefore

overly diffusive.

In order to provide the SAS capability also to the SST model, the Φ-equation is transformed to the k-ω framework

using:

ωµ

k

c4/1

1=Φ

(4)

The resulting ω−equation reads:

−

∂

∂

∂

∂+

+

∂

∂

∂

∂−

∂

∂

∂

∂+

∂

∂

∂

∂+−=

∂

∂+

∂

∂

ΦΦ

Φ

σσσ

νρω

κρζωω

ω

ω

ωσ

ρ

ω

σ

µβρωαρ

ρωρω

ω

11

~12 2

22

22

kj

t

j

vKjjjj

j

t

jj

j

x

k

xk

L

LS

xx

k

xx

k

xxS

x

U

t

(5)


4

with SASc⋅= 22

~ζζ and )/(

25.0 ωµckL = . Note that the L’- term in the max function of Eq. 2 was neglected as it is

dominated by cSAS in the SAS regime. The first three terms on the right hand side of Eq.5 are the standard terms of

the original Wilcox model (see Wilcox, 1993). The term

jj xx

k

∂

∂

∂

∂

Φ

ω

ωσ

ρ 12

(6)

is the cross-diffusion term, which would also result from the transformation of the k-ε model to the k-ω model. It is

already included in a zonal way in the SST model and helps the model to prevent the freestream sensitivity of the

Wilcox model (Menter, 1993). The last term in parenthesis is zero, as both, the k-ω and the k-Φ model use identical

diffusion constants in both equations. The remaining terms are therefore:

vKjj

SASSSTL

LS

xx

kF

2

22

~2κρζ

ωω

ωσ

ρ+

∂

∂

∂

∂−=

Φ

−

(7)

It is the goal of the transformation to preserve the SST model in the RANS regime and to activate the SAS capability

in URANS regions. In RANS regime (and particularly in boundary layers) the two terms on the right hand side of

Eq.7 are of the same size, whereas the LvK term dominates in the SAS regime:

vKjj L

LS

xx

k 2

22

2κρζ

ωω

ωσ

ρ≈

∂

∂

∂

∂

Φ

RANS regime

vKjj L

LS

xx

k 2

22

2κρζ

ωω

ωσ

ρ<

∂

∂

∂

∂

Φ

SAS regime

In order to preserve the SST model in the RANS region, the FSST term is modeled as follows (note that the

jj x

k

x

k

k ∂

∂

∂

∂2

1 term has little influence in the SAS regime, as it is also dominated by the 2

~ζ term.

∂

∂

∂

∂

∂

∂

∂

∂⋅−⋅=

Φ

− 0,1

,1

max2~

max22

2

2

jjjjvK

SASSASSSTx

k

x

k

kxxk

L

LSFF

ωω

ωσκζρ

(8)

The constants are taken from the k-Φ model with minor adjustments:

3/2;755.1~

;25.1 22 ==⋅== Φσζζ SASSAS cF

(9)

The constant FSAS has been introduced for the calibration of the SAS term in the SST environment. Finally, the term

FSST-SAS is added to the right hand side of the ω-equation of the SST model.

It should be noted that the details of the formulation of the second derivative term are important. In order to

reproduce the calibration given in the following sections, the term has to be formulated as given in Eq. 2. Simpler

formulations, based on the strain rate are not representative of the smallest scales in the SAS regime; e.g.:

jjj

i

k

i

x

S

x

S

x

U

x

UU

∂

∂

∂

∂≠

∂

∂

∂

∂=

2

2

2

2

''

(10)

as can easily be verified by assuming a harmonic variation of the velocity field down to the grid limit.


5

III. Numerical Treatment

Similar to the DES formulation, the SAS model also benefits from a switch in the numerical treatment between the

steady and the unsteady regions. In DES, this is achieved by blending functions as proposed by Strelets (2001),

which allow the use of a second order upwind scheme in RANS regions and a second order central scheme in

unsteady regions. The blending functions are based on several parameters, including the grid spacing and the ratio of

vorticity vs. strain rate. No effort has currently been made for reformulating these functions for the SAS model. A

future development will be the formulation of numerical blending functions without the explicit use of the grid

spacing. However, this is not essential, as the current functions have proven adequate for a range of geometrically

and physically diverse flows.

All simulations have been carried out with the commercial flow solver CFX-5 using a second order backward Euler

time integration and the blended second order space discretisation.

IV. Test Cases

1) Decaying Homogenous Isotropic Turbulence (DHIT)

The An important test case for the model calibration is the decay of homogenous isotropic turbulence (DHIT). The

set-up is based on the experiment from Comte-Bellot and Corrsin (1971). For the simulation, generic turbulence is

produced in a box using an equidistant grid of 323

volumes. The turbulence is generated by an inverse Fourier

transformation using a tool provided by Strelets in the framework of the DESIDER project. The turbulence level and

structure is designed to match the experiment in terms of the energy content and the spectral information. The

relatively coarse resolution was chosen, both for efficiency reasons, but also as it matches best the real situation in

industrial SAS simulations, where the grid resolution is typically not sufficient to deeply resolve the turbulent

spectrum.

Initial conditions for the turbulence model are produced by running the SST-SAS model on the frozen initial

velocity field from the Fourier transform. This is a non-trivial operation, as standard (U)RANS models would not

provide an initial field under such conditions. The reason is that standard models do not have any information on the

resolved length-scale or the grid spacing. As the length-scale determined by standard turbulence model is

proportional to the thickness of the turbulent layer under consideration, no such scale can be obtained from the

current set-up, due to the periodicity of the flow. In the author’s judgment, this is unnatural, as the current flow field

does have clearly defined resolved structures with given length-scales. In the SAS model, the von Karman length-

scale allows the model to adjust to these structures dynamically. It converges therefore for the frozen velocity field

to a steady state solution, with a turbulent length-scale, L:

vKLL ~

(11)

Assuming source term equilibrium (zero convection and zero diffusion), the model produces:

−= α

β

β

ζ *

2

~1

SAS

vKF

LL

(12)

and an eddy-viscosity of:

SLF

vK

SAS

t

2

2

*

2

~1

ραβ

β

ζµ ⋅

−=

(13)

This formulation can be interpreted as a subgrid scale model, where the length-scale is not the grid spacing, but the

length-scale of the resolved structures. In this respect, the model is a dynamic subgrid-scale model, as it

automatically adjusts to the scales of the resolved flow. It provides LvK as a length-scale and S (shear rate of the

resolved scales) as a frequency scale. In other words, the model assumes a scale similarity between the resolved and


6

the unresolved scales. This is the reason for the models ability to act in a LES-like fashion, once unsteady structures

appear in the simulation. Contrary to a dynamic LES model, the current formulation has however a RANS fallback

position, for stable (steady flows), like boundary layers or channel flows, etc.

Figure 1 shows the energy spectrum for the DHIT case after a non-dimensional time of t=0.87 for different values of

FSAS. It should be noted that the DHIT case does not provide the ultimate test for the calibration of LES/DES/SAS

models. It is known from standard LES calibration that a different Smagorinsky constant is required for this case

than for most shear flow cases. Nevertheless, the results give an indication of the behavior of the model for resolved

flow conditions. The figure also shows that the model reacts as expected to changes in FSAS. The lower the value, the

stronger the diffusive character of the model (Note that FSAS=0 corresponds to the standard SST model.

Figure 1: Decay of turbulence for the DHIT case. Comparison of experimental data, LES and SAS

simulations with different constants FSAS

Figure 2: Resolved structures in DHIT case for SST-SAS model with FSAS=1.25. Color gives ratio of turbulent

length-scale to grid spacing


7

Figure 2 shows the flow structures of the testcase also at t=0.87 (isosurface of S2-Ω2

). The color of the structures is

the turbulent length-scale, L, divided by the grid spacing 32/2π=∆ . The ratio is of the order of 0.15. The model is

therefore returning a length-scale much smaller than the domain size.

2) Cylinder in Crossflow

The grid consisting of 3.18x106 hexahedral elements is shown in Figure 3. It includes two non-matched domains,

connected using the general grid interface of CFX-5. The near-wall resolution corresponds to the average y+ value

between 1.5 and 2. The size of the domain in the transversal direction is equal to two cylinder diameters. Periodicity

is specified at the side planes. The inlet velocity corresponds to a Reynolds number of 3.6⋅106. The time step size is

selected to be 1/30th of the hydrodynamic time scale, based on the cylinder diameter and the inlet velocity.

Figure 3: Numerical grid for flow around cylinder

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

0 30 60 90 120 150 180α

Cp van Nunen, Re=2.79E6

van Nunenn, Re=4.78E+6

SAS SST, Fsas=1.25, Re=3.6E+6

Figure 4: Time averaged wall pressure distribution on surface of cylinder in comparison with experimental

data


8

Figure 4 shows the wall pressure coefficient, Cp, in comparison with experimental data from van Nunen (1974). The

two experiments envelope the numerical results in terms of the Re number. This is also reflected in the Cp-

distribution, where the numerical curve lies between the two experiments.

Figure 5 shows iso-surfaces of S2-Ω2

=105[1/s

2]. For different constants FSAS the resolved turbulent structures change

from classical URANS for FSAS=0 to a resolution down to the grid limit for FSAS=1.25 and FSAS=1.5.

Figure 5: Resolved structures for cylinder in crossflow using different constants FSAS. Note the different scales

on the color bar

3) Film Cooling for a Turbine Blade

One of the limiting factors in the design of high-pressure turbine blades is the maximum temperature on the blade

surface. In order to increase the overall efficiency, the first blades behind the combustion chamber are equipped with

active cooling devices. The current application is for the film cooling of the trailing edge of a turbine blade. Due to

the decreasing thickness of the blade near the trailing edge, the cooling is achieved by a cooling film injected

parallel to the blade surface. Figure 6 shows the geometry of the blade and the surface grid for the AITEB testcase

of Martini et al. (2003). There are two inlet regions for this simulation. On the upper inlet, the hot gas enters the

FSAS=0.00 (URANS) FSAS=1.00

FSAS=1.25 FSAS=1.50


9

domain and at the inlet to the cooling channel, cold gas is injected. The cold gas does however pass over a hot wall

before it reaches the mixing zone. It does therefore not stay at the inlet temperature. The reference temperature for

the cold gas is taken downstream of the cold gas inlet. It is therefore not the value of the cold gas at the inlet. In the

simulations, the reference temperature was taken at the same location as in the experiment. The upper boundary of

the domain is a free slip adiabatic wall. Periodicity is applied at the side planes. This testcase is courtesey of Dr.

Lutum of MTU Aero Engines and has been investigated within the EU-project AITEB, G4RD-CT-1999-00055

Figure 6: Schematic of the computational domain and the location of reference point for the cooling

temperature

The finite-volume grid consists of 6.48⋅10

5 hexahedral elements. Most the walls are resolved with the y+

values

below 1. A time step of ∆t=1.x10-5

s was used. (Typical velocity 50 m/s and dimension L~0.1m)

The main parameter for the evaluation of the device is the cooling efficiency. It is defined as follows:

cold

ref

hot

in

w

hot

in

TT

TT

−

−=η

(14)

hot

inT is the temperature of the hot gas at the inlet. wT is the computed wall temperature at the adiabatic wall section.

cold

refT is the reference temperature taken at the reference point shown in Figure 6.

Figure 7 shows the cooling efficiency (averaged in time and spanwise direction) for three different simulations

against the experimental data. Clearly, both steady RANS and URANS do not provide sufficient mixing to

H

Measurement point for

cooling gas ref.

temperature

Hot inlet

Cooling inlet

Hot surface Adiabatic surface

H


10

reproduce the experimental results. The cooling efficiency is therefore computed too optimistic, as the trailing edge

surface is shielded from the hot gas. The SAS model produces a significantly stronger mixing of the two streams and

results in a much better agreement of the cooling efficiency with the experiments.

0

0.5

1

0 5 10 15x/h

η

SAS SST

RANS SST

URANS SST

Experiment

Figure 7: Cooling efficiency for different version of the SST model compared to experimental data

Figure 7 shows deviations between all three simulations and the experiments at the start of the adiabatic wall. This

might not be so much a deficiency in the simulations in the mixing zone, but a systematic mismatch with the

reference conditions of the experiment. The most likely reason is a difference in the reference temperature cold

refT due

to different inlet conditions of the cold stream, or an incorrect prediction of the mixing upstream of the reference

point. Nevertheless, the results demonstrate the improved performance of the SAS model vs. standard URANS or

RANS simulations. In order to resolve the differences in the reference temperature, a further refinement in the

cooling channel is required.

Figure 8 shows the turbulent structures computed by the SAS model. They represent an iso-surface of Ω2-

S2=10

5[1/s

2]. The color represent the turbulent length-scale vs. the height of the base, H (see Figure 6).

Figure 8: Turbulent structures computed by the SST-SAS model for film cooling test case


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4) Cavity Flow

The final testcase is work in progress and not yet statistically converged. Nevertheless, first results are presented to

demonstrate the applicability of the method to this flow type. Air flow past a 3-D rectangular shallow cavity is

calculated in this test, with the cavity geometry and flow conditions corresponding to the M219 experimental test

case of Henshaw (2000). The geometry dimensions of the M219 cavity are L×W×D = 5×1×1 (length, width, and

depth), with a depth D of 4 inches. The side boundaries are treated as symmetry planes, the top boundary is a far-

field boundary, and all the solid surfaces as adiabatic non-slip walls. The ambient space, included into the

computational domain, is characterised by the following dimensions:

• The inlet is located 31 inches upstream of the cavity leading edge;

• The outlet is located 21 inches downstream of the cavity trailing edge;

• The top boundary is 68 inches above the cavity opening level;

• Space equal to the cavity width is left on each of the side boundaries and the correspondent side edge of the

cavity.

The grid consists of 1.05x6⋅106 hexahedral elements. The time step for the simulation is 2⋅10

-5 s, which is 18 times

less than the hydrodynamic time scale based on the inlet velocity and cavity depth. The inlet Mach number is

Ma=0.85.

Figure 9 shows the geometry and the turbulent structures (Ω2-S2=105[1/s

2]) produced by the SST-SAS model.

Figure 9: Geometry and turbulent structures for flow over cavity.

Figure 10 shows unsteady pressure fluctuations vs time. Albeit not at a statistically converged level, the pressure

fluctuations in the simulation are of the same magnitude (though somewhat larger) as observed in the experiments.

The simulations are currently continued and will be repeated on a finer grid for a one-to-one comparison of the

turbulent spectrum with the experimental data.


12

Figure 10: Pressure fluctuations inside cavity compared to experimental data.

V. Summary

A transformation of the Scale-Adaptive Simulation (SAS) term from the k-νt model to the SST turbulence model has

been presented. The transformation results in an additional term in the SST model, which has little effect on the

RANS region of the SST model, but allows the extension of the SAS modus into the SST environment. The

additional term contains the second derivative of the resolved flow field, resulting in a length-scale, which reacts to

the von Karman length-scale in unsteady regimes. As a result, the SST-SAS model shows a behavior similar to the

DES approach, but avoids some of the issues related to grid sensitivities of that methodology. The SST-SAS

formulation also greatly increases the applicability of the model compared to standard URANS formulations, which

produces unphysical results for most unsteady flows.

The SST-SAS model was applied/calibrated to the Decaying Homogenous Isotropic Turbulence (DHIT) testcase. It

was shown that with a proper calibration of the constants, the model can operate in a way much similar to standard

LES/DES methods.

The flow around a cylinder in crossflow demonstrated that the model can gradually be shifted from a URANS to a

scale-resolving model by changing the main calibration constant. Good agreement with experimental data for similar

Reynolds numbers was achieved for the time-averaged wall pressure distribution.

The simulation of the mixing zone in the trailing edge region of a turbine blade with film cooling demonstrated the

technical applicability of the method. Significantly improved results could be obtained for the cooling efficiency as

compared to steady or URANS simulations.

In a final demonstration, the flow in a 3D cavity was computed. The simulations could not be fully completed for

the present paper, but a first comparison shows an encouraging agreement with the unsteady experimental pressure

fluctuations inside the cavity.

VI. Acknowledgment

The current work was partially supported by the EU within the research project DESIDER (Detached Eddy

Simulation for Industrial Aerodynamics) under contract No. AST3-CT-200-502842

(http://cfd.me.umist.ac.uk/desider).


13

VII. References

Compte-Bellot, G and Corrsin, S., 1971, “Simple Eulerian time correlation of full – and narrow band velocity

signals in grid-generated, “isotropic” turbulence.”. J. Fluid Mech. 48., pp. 273-337.

Davidson L. and Dahlström, S., 2005, “Hybrid LES-RANS: Computation of the flow around a three-dimensional

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