RAE M2155 Wing

Application Challenge 1-02 © copyright ERCOFTAC 2004

Overview of CFD Simulations

Numerical simulation of the flow around the wing RAE M2155 have been performed at QINETIQ, for case 1-2-3-4, and at CIRA, only for case 2, with the main aim of validation and assessment of the turbulence models employed.

QINETIQ [3] has used the following turbulence models :

1) A k-ω based variant of the Menter SST scheme

2) A k-ω based EARSM utilising a novel calibration and incorporating explicitly the variable ratio of turbulence production to dissipation rate.

3) A tensorially linear version of the k-ω based EARSM model (only case 3).

while CIRA [4,5,6] has employed the

1) Spalart Allmaras

2) Myong-Kasagi κ-ε

3) Non Linear κ-ε (Myong-Kasagi κ-ε + 2^nd order constitutive relation by Shih)

4) Standard Wilcox κ-ω

5) Kok TNT κ-ω

6) Menter SST κ-ω

turbulence models.

The aerodynamic coefficients, pressure and friction coefficients, and velocity profiles at several locations are available.

Table CFD-A Summary Description of All Test Cases
NAME	GNDPs		PDPs	SPs
	Re	Mach	Incidence (deg)	Detailed Data	DOAPs
CFD 11	4.1x10⁶	0.744	2.5	C_P	C_N
CFD 12	4.1x10⁶	0.806	2.5	C_P	C_N
CFD 13	4.1x10⁶	0.846	1.5	C_P	C_N
CFD 14	4.1x10⁶	0.854	1.5	C_P	C_N
CFD 22	4.1x10⁶	0.806	2.5	C_P, C_f, U	C_L,C_D

Table CFD-B Summary Description of All Available Data Files and Simulated Parameters
	SP1 C_P	SP2 C_f	SP3 U	DOAPs, or other miscellaneous data
CFD 12	✔ac102c12cp02.dat	✔ac102c12cf02.dat	✔ac102c12bla.dat	✔ac102c12doap.dat
	✔ac102c12cp03.dat	✔ac102c12cf03.dat	✔ac102c12blb.dat
	✔ac102c12cp04.dat	✔ac102c12cf04.dat	✔ac102c12blc.dat
	✔ac102c12cp05.dat	✔ac102c12cf05.dat	✔ac102c12bld.dat
	✔ac102c12cp06.dat	✔ac102c12cf06.dat
	✔ac102c12cp07.dat	✔ac102c12cf07.dat
	✔ac102c12cp08.dat	✔ac102c12cf08.dat
	✔ac102c12cp095.dat	✔ac102c12cf095.dat
CFD 14	✔ac102c14cp02.dat	✔ac102c14cf02.dat	✔ac102c14bla.dat	✔ac102c14doap.dat
	✔ac102c14cp03.dat	✔ac102c14cf03.dat	✔ac102c14blb.dat
	✔ac102c14cp04.dat	✔ac102c14cf04.dat	✔ac102c14blc.dat
	✔ac102c14cp05.dat	✔ac102c14cf05.dat	✔ac102c14bld.dat
	✔ac102c14cp06.dat	✔ac102c14cf06.dat
	✔ac102c14cp07.dat	✔ac102c14cf07.dat
	✔ac102c14cp08.dat	✔ac102c14cf08.dat
	✔ac102c14cp095.dat	✔ac102c14cf095.dat
CFD 22	✔ac102c22cp02.dat	✔ac102c22cf02.dat	✔ac102c22bla1.dat	✔ac102c22doap.dat
	✔ac102c22cp03.dat	✔ac102c22cf03.dat	✔ac102c22bla2.dat
	✔ac102c22cp04.dat	✔ac102c22cf04.dat	✔ac102c22bla3.dat
	✔ac102c22cp05.dat	✔ac102c22cf05.dat	✔ac102c22bla4.dat
	✔ac102c22cp06.dat	✔ac102c22cf06.dat	✔ac102c22bla5.dat
	✔ac102c22cp07.dat	✔ac102c22cf07.dat	✔ac102c22bla6.dat
	✔ac102c22cp08.dat	✔ac102c22cf08.dat	✔ac102c22blb1.dat
	✔ac102c22cp095.dat		✔ac102c22blb2.dat
			✔ac102c22blb3.dat
			✔ac102c22blb4.dat
			✔ac102c22blb5.dat
			✔ac102c22blb6.dat
			✔ac102c22bld1.dat
			✔ac102c22bld2.dat
			✔ac102c22bld3.dat
			✔ac102c22bld4.dat
			✔ac102c22bld5.dat
			✔ac102c22bld6.dat

Simulation Case CFD-1

Solution strategy

The code used by QINETIQ for the computations is the BAE SYSTEMS RANSMB. This is a cell centered finite volume code with a central, Jameson type, flux approximation. A multigrid with a four stage Runge-Kutta scheme is used for time stepping.

The turbulence models used in the numerical simulations are :

1) A κ-g based variant of the Menter SST scheme

2) A κ-g based EARSM utilizing a novel calibration and incorporating explicitly the variable ratio of turbulence production to dissipation rate.

3) A tensorially linear version of the κ-g based EARSM model (only case 3).

Computational Domain

The computational domain includes the tunnel walls, and the computations have been performed as internal flow calculations.

The meshes used in the computations were generated at Aircraft Research Association and have approximately 1 million cells. That used by CIRA can be downloaded from ftp://www.cfse.ch/pub/cfse/read/m2155grid.tar.gz

The meshes are of constant cross section. The outflow plane is located at x=12m and the inflow plane is located at x=-12m for case 1 and 2, and at x=-2.5m for case 3 and 4. The wing leading edge at the root section is located at x=0. Therefore the entrance section of the mesh in much longer for case 1 and 2. This is due to problems encountered at ARA during the early computations.

The excessive length of the case 1 and 2 has been partly responsible for some case 2 poor results. The mesh has been recently modified at QINETIQ, so that the length of the entrance section of case 1 and 2 is the same as case 3 and 4.

Boundary Conditions

The following boundary conditions have been used :

• Inflow : Velocity and density prescribed, and pressure extrapolated from interior

• Outflow : Pressure prescribed, and velocity and density extrapolated from interior

• Tunnel walls where the wing is mounted on : No slip

• Tunnel walls not connected to the wing : Slip

• Wing surfaces : No slip

Application of Physical Models

All the turbulence models used in the computations employ a low Reynolds number formulation. The SST Menter requires the use of a blending function in order to switch from a κ-g to a κ-ε formulation.

The value of y+ at the first grid point is assumed to be O(1) and the mesh is thought to be fine enough to resolve the boundary layer.

Numerical Accuracy

• Grid refinement

q Studies were originally conducted at ARA by using a κ-ω model.

q Studies have not performed at QINETIQ due to the high cpu time requirements.

• Convergence

q The solutions show a three to four orders of magnitude reduction of the average density residuals. The typical magnitude of the average density residual at convergence is 10^-5

CFD Results

The data consist of :

• Pressure Coefficients at y/b=0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.95

• Friction Coefficients at y/b= 0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.95

• Boundary layer results at points A,B,C and D

• Lift and drag (pressure and friction) coefficients

CFD12

ac102c12cp02.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c12cp03.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c12cp04.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c12cp05.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c12cp06.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c12cp07.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c12cp08.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c12cp095.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c12cf02.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c12cf03.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c12cf04.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c12cf05.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c12cf06.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c12cf07.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c12cf08.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c12cf095.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c12bla.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: Z/C, U/U_P, P/H)

ac102c12blb.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: Z/C, U/U_P, P/H)

ac102c12blc.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: Z/C, U/U_P, P/H)

ac102c12bld.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: Z/C, U/U_P, P/H)

ac102c12doap.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns:C_L, C_D( pressure), C_D(friction))

CFD14

ac102c14cp02.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c14cp03.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c14cp04.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c14cp05.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c14cp06.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c14cp07.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c14cp08.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c14cp095.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c14cf02.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c14cf03.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c14cf04.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c14cf05.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c14cf06.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c14cf07.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c14cf08.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c14cf095.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c14bla.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: Z/C, U/U_P, P/H)

ac102c14blb.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: Z/C, U/U_P, P/H)

ac102c14blc.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: Z/C, U/U_P, P/H)

ac102c14bld.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: Z/C, U/U_P, P/H)

ac102c14doap.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns:C_L, C_D( pressure), C_D(friction))

References

[3] D.A. Peshkin. Technical Report: DERA/MSS/MSFC1/TR000228. Strictly limited circulation.

Simulation Case CFD-2

Solution strategy

CIRA has used the RANS flow solver ZEN version 6.0

The RANS equations are discretized by means of a cell centered finite volume scheme with blended self adaptive second and fourth order artificial dissipation. The solution procedure is based on a time marching concept. The multigrid scheme is used to accelerate the convergence of the solution, and performs relaxations, by using the Runge Kutta algorithm with local time stepping and residual averaging, on different grid levels. The turbulence equations are uncoupled by the RANS equations and are solved, inside a multigrid cycle, only on the finest grid level.

The turbulence models employed in the numerical simulations are the following :

1) Spalart Allmaras

2) Myong-Kasagi κ-ε

3) Non Linear κ-ε (Myong-Kasagi κ-ε + 2^nd order constitutive relation by Shih)

4) Standard Wilcox κ-ω

5) Kok TNT κ-ω

6) Menter SST κ-ω

Computational Domain

The computational domain includes the wind tunnel walls, and the simulations have been performed as internal flow calculations. Therefore wall tunnel corrections are not necessary.

The inflow plane is located at x=-4m and the outflow plane at x=4.5m. The wing leading edge at the root section is located at x=0.

The mesh used has 36 blocks with 1.2 million point and can be run on 3 different levels.

Boundary Conditions

The following boundary conditions have been used :

1) Inflow : General free-stream with specified enthalpy and momentum, and the pressure extrapolated

2) Outflow : General free-stream with specified pressure and extrapolated velocity and enthalpy

3) Tunnel walls : Slip

4) Wing surfaces : Adiabatic no slip with fixed transition

The tunnel walls boundary layer has shown to have an effect up to 30% wing span.

${{\sqrt {\kappa \over u_{\infty }}}=0.1}$ %, ${\mu \over \mu _{r}}=0.1$

At the inflow the turbulent variables are assumed to be constant, and the free stream values are derived by :

Application of Physical Models

The Wilcox and TNT κ-ω turbulence models do not have a low Reynolds formulation, while the Spalart Allmaras and the κ-ε models employ the use of wall damping functions. The SST Menter κ-ω model, in order to switch from a κ-ω to a κ-ε formulation close to a solid boundary and to take into account the effect of the transport of the principal shear stress (SST formulation), requires the computation of blending functions.

The values of y+ at the first cell center is O(1)

Numerical Accuracy

The computations have been performed on 3 different grid levels.

For the κ-ω SST Menter turbulence model, for example, the following accuracy has been obtained :

• Grid sensitivity

q The lift coefficient changes less than 1% going from the 1st to the 2nd grid level, and less than 0.5% from the 2nd to the finest level.

q The drag coefficient changes of about 15% going from the 1st to the 2nd grid level, and less than 5% from the 2nd to the finest level.

• Convergence on the finest level

q In the last 500 iterations, the lift coefficient changes less than 0.02% and drag coefficient less than 0.03%.

CFD Results

The data consist of :

• Pressure coefficients at y/b=0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.95

• Friction coefficients at y/b= 0.2,0.3,0.4,0.5,0.6,0.7,0.8

• Velocity profiles at the stations A,B, and D

• Lift and drag (pressure and friction) coefficients

CFD22

ac102c22cp02.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c22cp03.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c22cp04.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c22cp05.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c22cp06.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c22cp07.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c22cp08.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c22cp095.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_P)

ac102c22cf02.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c22cf03.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c22cf04.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c22cf05.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c22cf06.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c22cf07.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c22cf08.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns: x/c, C_f)

ac102c22bla1.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22bla2.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22bla3.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22bla4.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22bla5.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22bla6.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22blb1.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22blb2.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22blb3.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22blb4.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22blb5.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22blb6.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22bld1.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22bld2.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22bld3.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22bld4.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22bld5.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22bld6.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence, turbulence model; columns: Z/C, U/U_P)

ac102c22doap.dat (ASCII file; headers: Mach number, Reynolds number, angle of incidence; columns:Turbulence model, C_L, C_D( pressure), C_D(friction))

References

[4] M. Amato, P. Catalano, “An Evaluation of Stress-Strain Relationships for Aeronautical Applications”, XV AIDAA National Congress

[5] M. Amato, P.Catalano, “Non Linear κ-ε Turbulence Modeling for Industrial Applications”, ICAS 2000 Conference

[6] P. Catalano, M. Amato, “Assessment of κ-ω Turbulence modeling in the CIRA Flow Solver ZEN”, ECCOMAS CFD 2001 Conference

Contributors: Pietro Catalano - CIRA; QinetiQ

Site Design and Implementation: Atkins and UniS

CFD Simulations AC1-02

Contents

RAE M2155 Wing

Overview of CFD Simulations

Simulation Case CFD-1

Solution strategy

Computational Domain

Boundary Conditions

Application of Physical Models

Numerical Accuracy

CFD Results

CFD12

CFD14

References

Simulation Case CFD-2

Solution strategy

Computational Domain

Boundary Conditions

Application of Physical Models

Numerical Accuracy

CFD Results

CFD22

References

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CFD Simulations AC1-02

RAE M2155 Wing

Overview of CFD Simulations

Simulation Case CFD-1

Solution strategy

Computational Domain

Boundary Conditions

Application of Physical Models

Numerical Accuracy

CFD Results

CFD12

CFD14

References

Simulation Case CFD-2

Solution strategy

Computational Domain

Boundary Conditions

Application of Physical Models

Numerical Accuracy

CFD Results

CFD22

References

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