1

A combined RANS-LES strategy with arbitrary interface location for near-wall

flows

Michael Leschziner and Lionel Temmerman

Imperial College London

2

Overview

1. Motivation

2. Method Description

3. Observation from Past Work

4. Modelling practice and Methodology

5. Results for Channel Flow

6. Results for Hill Flow

7. Concluding Remarks

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Motivation

Grid requirements for LES of wall-bounded flows:

Number of nodes rises as (Chapman (1979)) High Reynolds LES is prohibitively expensive Cost reducing strategies:

• Wall functions (Schumann (1975); Werner and Wengle (1993));

• Zonal approach (Balaras et al (1996));

• Hybrid RANS-LES methods (DES - Spalart et al (1997); Hamba (2001)).

50 2 20x y z 1.8ReL

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Alternative Approaches

Wall functions:• Mostly based on log-law approximations;

• Tends to be ‘adequate’ in simple shear flows;

• Inadequate for separated flows (no universal behaviour).

Zonal approach:• Simplified set of equations resolved near the wall (TBL

equations);

• Saving results from the removal of the Poisson problem;

• Not adequate for all flows.

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Alternative Approaches

Hybrid RANS-LES strategies:• Part of the turbulence is modelled in the ‘RANS’ layer;

• Allow to use large aspect ratio cells – we hope!

• Location of the interface: either decided by user; or controlled by cell dimensions – compare y and =

f(x,y,z) as in DES; Interface shift done via modifications of the grid: shift away from

the wall higher x and z; High streamwise/spanwise resolution required in some flows

(separated) even with RANS methods interface may be too close to the wall.

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Method Description

RANS layer prescribed by reference to the wall distance.

 

RANS Layer

LES Domain

Imposed LES conditionsat interface

Imposed RANS conditionsat interface

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Observations from Previous Work

In the URANS region, the resolved and the modelled contributions to the motion are of equal importance.

Total is too high need of an ad hoc modification to reduce the total motion.

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Modelling Practice

RANS model: one-equation transport model for turbulence energy (Wolfshtein (1969));

SGS model: One-equation transport model for SGS energy (Yoshizawa and Horiuti (1985))

Assumption: RANS and LES grids are identical at the interface;

Target:• Velocity: ;

• Viscosity: ;

• Modelled energy: .

LESRANS UU intint LESt

RANSt int,int,

LESRANS kk intmod,intmod,

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Methodology

mod modRANS LES with

5.0mod klCRANS

hencemod,int

,int 0.5,int

LES

RANS

Cl k

< . > : spatial average in the homogeneous directions.

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Methodology

,int

int int

0.09

1 exp0.09

1 exp

C

yC

y

,int

int int

0.09 for 2727

0.09 1 exp( ( ( 34)) / )0.09

1 exp( ( 34) /

for 27)

y

yC y

C y y yC

y y y

Function 1

Function 2

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Channel Flow – Case Description

Periodic channel flow;

;

RANS-LES and coarse LES:• Computational domain: ;

• Grid: 64 x 64 x 32 cells with and ;

Dense LES:• Computational domain: ;

• Grid: 512 x 128 x 128 cells with .

42200Re b

hhh 224.0)1(

cy

hhh 5.022 75.0)1(

cy

zx

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Channel Flow - Results

Time-averaged velocity and shear stressprofiles for the LES computations.

64 x 64 x 32 cells

512 x 128 x 128 cells

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Channel Flow - Results

Time-averaged C profiles across the RANS layer (64 x 64 x 32 cells).

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Channel Flow - Results

Time-averaged velocity profiles for the hybrid RANS-LES computations (64 x 64 x 32 cells).

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Channel Flow - Results

Time-averaged shear stressand turbulent energy profiles for the hybrid RANS-LES computations (64 x 64 x 32 cells).

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Channel Flow - Observations

Encouraging results.

The response to the parameters change is small.

Response to the change of location of the

interface:• Change in the proportion of modelled motion;

• Variation in the width of near-wall total turbulence

energy peak.

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Hill Flow – Case Description

Periodic channel flow with constrictions at both ends

Reynolds number based on channel height and bulk

velocity is 21560

Data from highly resolved LES computations (5 x 106 cells)

by Temmerman et al (2003) Domain size: 9h x 3.036 h x 4.5 h (h=hill height) Grid details:

• Discretisation: 112 x 64 x 56 cells (4 x 105 cells);

• Near-wall resolution: y+c(1)1;

• Spanwise and streamwise resolution: x = z.

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Hill Flow - Results

Left: location of the RANS-LES near-wall interface.

Right: Distribution of C along the interface

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Hill Flow - Results

Averaged streamlines for the reference simulation, LES, DES and RANS-LES cases.

(x/h)sep. = 0.22

(x/h)reat. = 4.72

(x/h)sep. = 0.21

(x/h)reat. = 5.30

(x/h)sep. = 0.23

(x/h)reat. = 4.64

(x/h)sep. = 0.23

(x/h)reat. = 5.76

196 x 128 x 186 cells 112 x 64 x 56 cells

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Hill Flow - Results

Left: Distribution of C across the lower RANS layer (right).

Right: Streamwise velocity profiles in wall units at x/h = 2.0.

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Hill Flow - Results

Streamwise velocity profiles at x/h = 2.0.

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Hill Flow - Results

Turbulent viscosity profiles at two streamwise positions.

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Hill Flow - Observations

The location of reattachment is overestimated by the hybrid RANS-LES and DES probably because of the wrong prediction of the wall shear stress.

Compared to the channel case, C has a similar behaviour.

Overall, good agreement with the reference data. Difficult to draw definitive conclusions; too low Reynolds

number.

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Concluding Remarks

New hybrid RANS-LES method allowing:• Freedom in locating the interface;

• Dynamic adjustment of the RANS model to ensure continuity across the interface.

For identical grids, the results obtained with the RANS-LES approach were significantly better than those obtained with LES.

Application to a recirculating flow:• Results are non-conclusive due to low Reynolds number new test

case (separated hydrofoil at Rec = 2.15 x 106);

• The hybrid RANS-LES approach overestimates the recirculation zone length.