Turbulent eddies in the RANS/LES transition region

Turbulent eddies in the RANS/LES transition region Ugo Piomelli Senthil Radhakrishnan Giuseppe De Prisco University of Maryland College 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 Computational approaches for the simulation of an aircraft (from Spalart, 2000) 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).

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

WMLES Contours of u'v' ν T du / dy LES URANS Wall layer URANS, everything else LES. Wall-Modeled LES (WMLES) Oldest hybrid application (logarithmic law)

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. ν T 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. ν T du dy? u'v'. ν T 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 ν T du dy? u'v'. LES: Reynolds stress supported by the eddies ν T du dy = u 'v'. Turbulent eddies must be generated at the interface. How? 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 below LES RANS into 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/LES Logarithmic law mismatch RANS log layer LES log layer Plane channel flow, Re τ =5,000

WMLES using hybrid RANS/LES Logarithmic law mismatch Resolved stress Modeled stress Plane channel flow, Re τ =5,000

WMLES using hybrid RANS/LES Logarithmic law mismatch Nominal LES region y > C DES Δ Resolved stress Actual LES region Resolved > Modeled Modeled stress Transition region (DES buffer layer) Plane channel flow, Re τ =5,000

WMLES of the flow over a ramp Experiment: Song & Eaton (2003) Calculations Re θ = 21,000 at reference location x = 2 Co-located curvilinear FD code (2 nd 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 RANS WMLES Experiment

WMLES of the flow over a ramp Isosurfaces of Q = 1 ( 2 S2 Ω 2 ) Contours of u in a near-wall plane

WMLES of the flow over a ramp Experiment WMLES

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

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 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:

WMLES of the flow over a ramp Isosurfaces of Q = 1 ( 2 S2 Ω 2 ) Contours of u in a near-wall plane

WMLES of the flow over a ramp

WMLES of the flow over a ramp RANS WMLES Experiment WMLES, stochastic force

WMLES of the flow over a ramp Experiment WMLES stochastic force WMLES no force RANS

WMLES of the flow over a ramp Experiment WMLES, no force 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. Reference Eventually, the flow transitions and reaches acceptable turbulence levels 20δ downstream of the inflow. Synthetic Shear stress Mean velocity x/δ = 10 x/δ = 15 x/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 ) Possiblyanisotropic

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 10-15δ Reference Controlled forcing Synthetic Shear stress Mean velocity x/δ = 10 x/δ = 15 x/δ = 20

Channel flow. Controlled forcing at the RANS/LES interface Synthetic Controlled

Decelerating boundary layer Calculations of the flow on a flat plate with variable freestream velocity. Cartesian staggered code, 2 nd order in space and time. Freestream velocity 384 192 64 points (reference calculation) 300 192 64 points (hybrid calculation) at the inlet

Decelerating boundary layer Freestream velocity Skin-friction coefficient SA-RANS Controlled Synthetic

Decelerating boundary layer SA-RANS Synthetic Controlled Synthetic Controlled 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.