Turbulent eddies in the RANS/LEStransition region

Ugo PiomelliSenthil Radhakrishnan

Giuseppe De Prisco

University of MarylandCollege Park, MD, USA

Research sponsored by the ONR and AFOSR

Outline

• Motivation

• The problem: eddy generation at the RANS/LES interface

• Effects and possible solutions− WMLES

− Zonal RANS

• Conclusions and directions for improvement

Motivation

• Accurate methods are infeasible.

• Feasible methods are (often) inaccurate.

• Hybrid RANS/LES:

− Use (U)RANS in regions in which models are accurate.

− Use LES in non-equilibrium regions (separation, 3D mean flow, high pressure gradients) or where structural information is required (noise emission).

Computational approaches for the simulation of an aircraft(from Spalart, 2000)

DES

• Attached boundary layer URANS, everything else LES.− Detached-eddy simulation (DES)

WMLES

• Wall layer URANS, everything else LES.− Wall-Modeled LES (WMLES)

− Oldest hybrid application (logarithmic law)

LESURANS

Contours of− u 'v '

νT dU / dy

Zonal RANS/LES

• Attached boundary layer URANS, LES includes attached & separated flows.

RANS/LES interface

• Critical issue: RANS/LES interface.− RANS: Reynolds stress supported by the model.

Flow in a compressor and prediffuser.

From Schlüter et al., AIAA Paper 2004-3417

νT dU dy ? − u 'v ' .

RANS/LES interface

• Critical issue: RANS/LES interface.− RANS: Reynolds stress supported by the model

− LES: Reynolds stress supported by the eddies.

νT dU dy ? − u 'v ' .

νT dU dy = − u 'v ' .

Flow in a compressor and prediffuser.

From Schlüter et al., AIAA Paper 2004-3417

RANS/LES interface

• Critical issue: RANS/LES interface.− RANS: Reynolds stress supported by the model

− LES: Reynolds stress supported by the eddies

− Turbulent eddies must be generated at the interface. How?

νT dU dy ? − u 'v ' .

νT dU dy = − u 'v ' .

Flow in a compressor and prediffuser.

From Schlüter et al., AIAA Paper 2004-3417

RANS/LES interface

• Critical issue: RANS/LES interface.− Rapid generation of eddies as the model switches from RANS to LES

behavior can be achieved by: □ Natural amplification of instabilities.

o Shear layers: OK.

Flow in a compressor and prediffuser.

From Schlüter et al., AIAA Paper 2004-3417

RANS/LES interface

• Critical issue: RANS/LES interface.− Rapid generation of eddies as the model switches from RANS to LES

behavior can be achieved by: □ Natural amplification of instabilities.

o Shear layers: OK.o Attached b.l.: less effective. IDDES.

RANS/LES interface

• Critical issue: RANS/LES interface.− Rapid generation of eddies as the model switches from RANS to LES

behavior can be achieved by: □ Natural amplification of instabilities. □ Artificial forcing.

o Synthetic turbulence.o Disturbances from similar calculation.o Controlled forcing.

RANS into LESRANS below LES

Outline

• Motivation

• The problem: eddy generation at the RANS/LES interface

• Effects and possible solutions− WMLES

− Zonal RANS

• Conclusions and directions for improvement

WMLES using hybrid RANS/LES

• Two main methodologies:− Blending function:

□ Compute RANS and SGS eddy viscosity using different models.

□ Blend them using a specified ad hoc function.

□ (Tokyo), Leschziner (Imperial College), Davidson (Chalmers), Edwards (NCSU)...

− Detached eddy simulation:□ Use a single model in the RANS and LES regions.□ Modify the model (length scale) to account for different physics.□ Nikitin et al. (2000), Piomelli et al. (2003), Pasinato et al. (2005), Keating and

Piomelli (2006), Radhakrishnan et al. (2006).

− Main effect of the absence of turbulent eddies at the RANS/LES interface: logarithmic law mismatch (LLM).

WMLES using hybrid RANS/LESLogarithmic law mismatch

RANS log layer

LES log layer

Plane channel flow, Reτ=5,000

Modeled stress

Resolved stress

WMLES using hybrid RANS/LESLogarithmic law mismatch

Plane channel flow, Reτ=5,000

Modeled stress

Resolved stressNominal LES regiony > CDES Δ

Actual LES regionResolved > Modeled

Transition region(DES buffer layer)

WMLES using hybrid RANS/LESLogarithmic law mismatch

Plane channel flow, Reτ=5,000

WMLES of the flow over a ramp

• Experiment: Song & Eaton (2003)

• Calculations

− Reθ= 21,000 at reference location x = −2

− Co-located curvilinear FD code (2nd order in space and time)

− LES with DES-based wall-layer model (668×64×48), RANS.

• Challenging physics:

− Shallow, pressure-driven separation.

− Prediction of the flow after separation depends critically on the accuracy of the mean-velocity prediction.

WMLES of the flow over a ramp

WMLES Experiment

RANS

WMLES of the flow over a ramp

Contours of u’ in a near-wall plane

Isosurfaces of Q = −12

S2 − Ω2( )

WMLES of the flow over a ramp

WMLES

Experiment

Resolved-eddy enhancement

• A transition problem?− Smooth, laminar-like flow in the inner layer.− “Turbulent” flow in the outer layer.− How to accelerate the transition to “turbulence” in the LES region? Diffusion

dominated → advection dominated regime

• A transition problem?− Smooth, laminar-like flow in the inner layer.− “Turbulent” flow in the outer layer− How to accelerate the transition to “turbulence” in the LES region? Diffusion

dominated → advection dominated regime

• Possible solution: add perturbations to stir the flow.• Piomelli et al. (2003)

− Random forcing to generate small-scale fluctuations in the RANS/LES transition region.

− The random fluctuations are “massaged” by the strain field and become eddies.− Forcing amplitude set to match resolved and modelled Reynolds stresses over

the transition region:

Resolved-eddy enhancement

WMLES of the flow over a ramp

Contours of u’ in a near-wall plane

Isosurfaces of Q = −12

S2 − Ω2( )

WMLES of the flow over a ramp

WMLES of the flow over a ramp

WMLES, stochastic force

WMLES Experiment

RANS

WMLES of the flow over a ramp

RANS

WMLESno force

WMLESstochastic force

Experiment

WMLES of the flow over a ramp

WMLES, no forceExperiment

WMLES, stochastic force

Outline

• Motivation

• The problem: eddy generation at the RANS/LES interface

• Effects and possible solutions− WMLES

− Zonal RANS

• Conclusions and directions for improvement

Zonal Hybrid RANS/LES strategies

• Two approaches:− Integrated simulation (DES, Menon, …)

□ Single grid, model changes.

− Separate simulation (CTR, Sagaut, …)□ RANS data used to assign boundary conditions for LES. □ Equivalent to inflow assignment for DNS/LES.

• Generation of eddies by:− Growth of natural disturbances

− Synthetic turbulence

− Synthetic turbulence + controlled forcing

Information transfer between RANS & LES

• RANS gives:− Mean flow− Reynolds stresses

□ Always ⟨u′v′ ⟩□ Sometimes TKE□ Sometimes ⟨u′u′ ⟩, ⟨v′v′ ⟩ and ⟨w′w′ ⟩

• LES requires:− Instantaneous u, v and w.− Spectra and phase relations.

• Synthetic turbulence can be constructed to give− Assigned mean flow and Reynolds stresses− Assigned spectra− No phase relations

Channel flow. Synthetic turbulence at the RANS/LES interface

Controlled

Channel flow. Synthetic turbulence at the RANS/LES interface

• The flow rapidly loses turbulent kinetic energy and begins to relaminarize.

• Eventually, the flow transitions and reaches acceptable turbulence levels 20δ downstream of the inflow.

Reference

Synthetic

Shear stress Mean velocity

x/δ = 10x/δ = 15x/δ = 20

Controlled forcing at the RANS/LES interface

• Philosophy:− Generate reasonably realistic turbulence through inflow conditions or

forcing.□ Spectra□ Stresses□ Selectively amplify bursts to establish the correct shear stress profile.

• Ingredients:− Synthetic turbulence

− Controlled forcing

Synthetic turbulence

• Batten, Goldberg and Chakravarthy AIAA J. 42, 485 (2004)

• Three-dimensional, unsteady velocity field − Mean flow from RANS data

− Fluctuations with □ TKE and ⟨u′v′⟩ from RANS data.□ Length and time scales from the RANS data.

− E(k) ~ k 2 exp(- k 4)

− Possibly�anisotropic

Controlled forcing

• Spille-Kohoff and Kaltenbach. In DNS/LES Progress and Challenges (Liu, Sakell & Beutner eds.) 319 (2001)

• Add forcing term to the v momentum equation at a number of control planes downstream of the interface.

• Use a controller to drive the Reynolds shear stress towards a target Reynolds shear stress.

Channel flow. Controlled forcing at the RANS/LES interface

• The flow adjusts within 10-15δReference

Synthetic

Shear stress Mean velocity

x/δ = 10x/δ = 15

x/δ = 20

Controlledforcing

Channel flow. Controlled forcing at the RANS/LES interface

ControlledSynthetic

Freestream velocity

Decelerating boundary layer

• Calculations of the flow on a flat plate with variable freestream velocity.

• Cartesian staggered code, 2nd order in space and time.

• 384×192×64 points (reference calculation)

• 300×192×64 points (hybrid calculation)

• at the inlet

Decelerating boundary layer

Freestream velocity

Skin-friction coefficient

Synthetic

Controlled

SA-RANS

Decelerating boundary layer

Synthetic

Controlled SA-RANS

SyntheticControlled

SA-RANS

Decelerating boundary layer

Reference

Synthetic turbulence+ controlled

forcing

Conclusions

• The interface between RANS and LES zones may affect critically the accuracy of the flow predictions.

− Separation.

− Turbulent kinetic energy levels

• The need for turbulent eddies in the LES region is recognized.

• Several solutions have been proposed.− Synthetic turbulence

− Forcing (DNS databases, controlled, ….)

− Decreased eddy viscosity

• Partial success so far.− Phase information is crucial.

− Some flows are more forgiving.

Directions for future work

• Improved integration between turbulent physics and model.

• Better understanding of the stability characteristics of the system:

− Smooth, laminar-like flow in the inner layer. Diffusion dominated.

− “Turbulent” flow in the outer layer. Advection dominated.

• Identification of “optimal” disturbances.