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)
WMLES
• Wall layer URANS, everything else LES.− Wall-Modeled LES (WMLES)
− Oldest hybrid application (logarithmic law)
LESURANS
Contours of− u 'v '
νT dU / dy
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.
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
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
• 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
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
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.