One-equation RG Hybrid RANS/LES...

Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University – UGent

FACULTY OF ENGINEERING

One-equation RG Hybrid RANS/LES modelling

C. De Langhe1, J. Bigda2, K. Lodefier1 and E. Dick1

1Ghent University, Belgium2Silesian University of Technology, Poland


Introduction

• The original two-equation RG hybrid RANS/LES model is reduced to a one-equation model -> transport equation for the mean dissipation rate ε -> prescribed length scale

• Motivation: in hybrid RANS/LES RANS is generally only performed close to walls -> simple length scale prescription possible. Most of the flow complexity is captured by the LES part of the simulation -> there the length scale is determined by the filter width.


Advantages

‣ computationally simple and robust‣ the near-wall modelling is significantly simplified‣ the RANS limit of the subgrid model is better defined‣ we avoid the (somewhat ad-hoc) modelling of a transport equation

for the turbulent kinetic energy

• The resulting model is about the simplest one can obtain which still includes history and non-equilibrium effects, and has a RANS limit (low quality far from walls) and DNS limit .

• Only one constant had to be calibrated against channel flow.


The model

20 0 0

4( ) min( , ) ( 2 ) ( 1.39( ( ) ) )3

∂ ∂= Λ Λ Λ − + + Λ −

∂ ∂c c k ci i

D PDt x x

ε εν ε ν ν ν

1 34 4

0 030

0 1( ) 1c cRν νν

/⎛ ⎞⎜ ⎟− −⎛ ⎞⎜ ⎟⎜ ⎟

⎝ ⎠⎜ ⎟⎜ ⎟⎝ ⎠

. εΛ = + Λ − Λ

400.22 /w uτε ν=

Λc = max( π/Δ , π/L) with Δ the filter width

( )1 430 00.215 /ε ν

/Λ =

3/ 4−= ∼ 2.20L C y yμ κ


Channel flow calibration

RANS velocity and ε profiles for = 395, 640 and 1020 Reτ


Impinging jet

• differs substantially from a wall-parallel flow; RANS models with simple prescriptions for the length scale typically fail.

• Nozzle-plate distance 2D (Baughn and Shimizu, 1989)• Re = 23000• 1.6 million grid points, performed with Fluent.• Comparison of one-equation RG hybrid RANS/LES model,

DES (Spalart-Allmaras) and dynamic Smagorinsky• Stochastic perturbations on the inlet velocity profile for the

LES and RG hybrid RANS/LES (using the vortex method as implemented in Fluent)


Impinging jet

• In the DES computation, the CDES -constant had to be lowered from the standard value of 0.65 to 0.25, in order for the flow to develop turbulent structures and LES-like behaviour.

• Investigation of the ratio of resolved over the total turbulent kinetic energy showed that in most of the active flow domain, about 50 to 70% of the turbulent kinetic energy is resolved. These computations should therefore be seen as a VLES rather than as a genuine LES in the LES part.


Impinging jet

D

D

H=2

D (6

D)

12D

z

r


Impinging jet

Contour plots of vorticity magnitude (left) and turbulent viscosity ratio (right) for the RG hybrid RANS/LES


Impinging jet

Iso-pressure contours RG model


Impinging jet

Ratio of resolved over total turbulent kinetic energy


Impinging jet

Mean velocity profiles: comparison of RG (line), DES(---), LES (…) with exp. (o)

r/D=0.5

0

0.5

1

1.5

0 0.1 0.2 0.3z/D

U/Wb

r/D=1.0

0

0.5

1

1.5

0 0.1 0.2 0.3z/D

U/Wb

r/D=2.5

0

0.5

1

1.5

0 0.1 0.2 0.3z/D

U/Wb

r/D=3.0

0

0.5

1

1.5

0 0.1 0.2 0.3z/D

U/Wb


Impinging jet

Nusselt number profiles obtained with LES ▲, DES □, and RG hybrid RANS/LES (line), compared with experiments of Baughn and Shimizu (○).

0

40

80

120

160

200

0 1 2 3 4 5 6r/D

Nu


Impinging jet

Shear stress profiles for the RG model: resolved (---), modeled (…) and total (line)

r/D=1

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 0.1 0.2 0.3z/D

<u'w

'>/W

b2

r/D=2.5

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 0.1 0.2 0.3z/D

<u'w

'>/W

b2

r/D=3

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 0.1 0.2 0.3z/D

<u'w

'>/W

b2

r/D=0.5

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 0.1 0.2 0.3z/D

-<u'

v'>/

Wb2


Impinging jet H/D=6

Contour plots of vorticity magnitude (left) and turbulent viscosity ratio (right)


Impinging jet H/D=6

Nusselt number profile for RG hybrid RANS/LES (line) and DES (squares) for H/D=6, compared with experiments of Baughn et al. (Δ) and Colucci and Viskanta (○)

0

50

100

150

200

0 1 2 3 4 5 6r/D

Nu


Plane asymmetric diffuser

• RG hybrid RANS/LES simulation of a plane asymmetric diffuser, as measured by Obi et al. (Obi et al., 1993) and Buice and Eaton (Buice and Eaton, 2000)

• Re=9000, based on the bulk velocity at the inlet and half channel width

• Very coarse grid of only 262000 points=> LES part is a coarse VLES

• Especially in the channel behind the expansion section, the resolution is very coarse (the LES in that region has most of the stresses modelled)



Contours (clipped) of vorticity magnitude near the expansion corner (red for higher magnitude) -> VLES



RANS (red) and LES zone (blue) near the expansion corner



Skin friction and pressure coeff. on upper and lower wall (blue dots), compared with exp. of Buice et al. (crosses)

−5 0 5 10 15 20 25 30 35 40 45−2

0

2

4

6

8

10x 10

−3

x/h

Cf

−5 0 5 10 15 20 25 30 35 40 45−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

x/h

Cp



Mean velocity and shear stress profiles at different locations. Line: RG hybrid RANS/LES, symbols: experiment.

−1 0 10

1

2

3

4

5y/

h

U/Ub

x/h=6

−0.01 0 0.010

1

2

3

4

5

y/h

<uv>/Ub2

x/h=14 x/h=20 x/h=24 x/h=30


Conclusions(1)

• Formulation of a one-equation variant of the RG hybrid RANS/LES model was presented. Motivation is that modelling of the length scale in hybrid RANS/LES is generally simpler than in RANS.

• The absence of damping functions in the near-wall modelling makes the model robust, and widely applicable.Only one constant had to be calibrated.


Conclusions(2)

• The model can successfully handle an impinging jet flow, where usually, in RANS, simple length scale prescriptions fail.

• The simulation of the asymmetric diffuser showed that the position, length and shape of the recirculation zone were in good agreement with the experiments.The simulation was performed on a very coarse gridaccording to LES standards, and the non-RANS part of the simulation is actually VLES in this case.

One-equation RG Hybrid RANS/LES...

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