RANS/LES interface

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
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•
•
•
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)
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•
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Accurate methods are infeasible.
Feasible methods are (often) inaccurate.
Hybrid RANS/LES:
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Use (U)RANS in regions in which models are accurate.
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Use LES in non-equilibrium regions (separation, 3D mean flow, high pressure
gradients) or where structural information is required (noise emission).
DES
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Attached boundary layer URANS, everything else LES.
−
Detached-eddy simulation (DES)
WMLES
Contours of
− u 'v'
ν T dU / dy
LES
•
Wall layer URANS, everything else LES.
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Wall-Modeled LES (WMLES)
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Oldest hybrid application (logarithmic law)
URANS
Zonal RANS/LES
•
Attached boundary layer URANS, LES includes attached &
separated flows.
RANS/LES interface
•
Critical issue: RANS/LES interface.
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RANS: Reynolds stress supported by the model.
Flow in a compressor
and prediffuser.
From Schlüter et al.,
AIAA Paper 20043417
ν T dU dy ? − u 'v' .
RANS/LES interface
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Critical issue: RANS/LES interface.
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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' .
Flow in a compressor
and prediffuser.
From Schlüter et al.,
AIAA Paper 20043417
RANS/LES interface
•
Critical issue: RANS/LES interface.
−
RANS: Reynolds stress supported by the model
ν T dU dy ? − u 'v' .
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LES: Reynolds stress supported by the eddies
ν T dU dy = − u 'v' .
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Turbulent eddies must be generated at the interface. How?
Flow in a compressor
and prediffuser.
From Schlüter et al.,
AIAA Paper 20043417
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 20043417
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
o
Shear layers: OK.
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.
Disturbances from similar calculation.
o
Controlled forcing.
o
RANS into LES
RANS 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
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Two main methodologies:
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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)...
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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).
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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, Reτ=5,000
WMLES using hybrid RANS/LES
Logarithmic law mismatch
Resolved stress
Modeled stress
Plane channel flow, Reτ=5,000
WMLES using hybrid RANS/LES
Logarithmic law mismatch
Nominal LES region
y > CDES Δ
Resolved stress
Actual LES region
Resolved > Modeled
Modeled stress
Transition region
(DES buffer layer)
Plane channel flow, Reτ=5,000
WMLES of the flow over a ramp
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Experiment: Song & Eaton (2003)
Calculations
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Reθ= 21,000 at reference location x = −2
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Co-located curvilinear FD code (2nd order in space and time)
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LES with DES-based wall-layer model (668×64×48), RANS.
Challenging physics:
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Shallow, pressure-driven separation.
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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
(
1 2
Q = − S − Ω2
2
Contours of u’ in a near-wall plane
)
WMLES of the flow over a ramp
Experiment
WMLES
Resolved-eddy enhancement
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A transition problem?
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−
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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
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A transition problem?
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−
−
•
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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)
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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
(
1 2
Q = − S − Ω2
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:
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Integrated simulation (DES, Menon, …)
□ Single grid, model changes.
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Separate simulation (CTR, Sagaut, …)
□ RANS data used to assign boundary conditions for LES.
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□ Equivalent to inflow assignment for DNS/LES.
Generation of eddies by:
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Growth of natural disturbances
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Synthetic turbulence
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Synthetic turbulence
+ controlled forcing
Information transfer between RANS & LES
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RANS gives:
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Mean flow
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Reynolds stresses
□ Always 〈 u′v′ 〉
□ Sometimes TKE
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□ Sometimes 〈 u′u′ 〉, 〈 v′v′ 〉 and 〈 w′w′ 〉
LES requires:
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Instantaneous u, v and w.
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Spectra and phase relations.
Synthetic turbulence can be constructed to give
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Assigned mean flow and Reynolds stresses
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Assigned spectra
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No phase relations
Channel flow. Synthetic turbulence at the
RANS/LES interface
Controlled
Channel flow. Synthetic turbulence at the
RANS/LES interface
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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.
Shear stress
Reference
Synthetic
Mean velocity
x/δ = 10
x/δ = 15
x/δ = 20
Controlled forcing at the RANS/LES interface
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Philosophy:
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Generate reasonably realistic turbulence through inflow conditions or
forcing.
□ Spectra
□ Stresses
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□ Selectively amplify bursts to establish the correct shear stress profile.
Ingredients:
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Synthetic turbulence
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Controlled forcing
Synthetic turbulence
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Batten, Goldberg and Chakravarthy AIAA J. 42, 485 (2004)
Three-dimensional, unsteady velocity field
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Mean flow from RANS data
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Fluctuations with
□ TKE and 〈u′v′〉 from RANS data.
□ Length and time scales from the RANS data.
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E(k) ~ k 2 exp(- k 4)
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Possibly anisotropic
Controlled forcing
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Spille-Kohoff and Kaltenbach. In DNS/LES Progress and
Challenges (Liu, Sakell & Beutner eds.) 319 (2001)
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Add forcing term to the v momentum equation at a number of
control planes downstream of the interface.
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Use a controller to drive the Reynolds shear stress towards a
target Reynolds shear stress.
Channel flow. Controlled forcing at the
RANS/LES interface
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The flow adjusts within 10-15δ
Reference
Controlled
forcing
Synthetic
Shear stress
Mean velocity
x/δ = 15
x/δ = 10
x/δ = 20
Channel flow. Controlled forcing at the
RANS/LES interface
Synthetic
Controlled
Decelerating boundary layer
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Calculations of the flow on a
flat plate with variable
freestream velocity.
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Cartesian staggered code,
2nd order in space and time.
Freestream velocity
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384×192×64 points
(reference calculation)
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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
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The interface between RANS and LES zones may affect
critically the accuracy of the flow predictions.
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Separation.
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Turbulent kinetic energy levels
The need for turbulent eddies in the LES region is recognized.
Several solutions have been proposed.
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Synthetic turbulence
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Forcing (DNS databases, controlled, ….)
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Decreased eddy viscosity
Partial success so far.
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Phase information is crucial.
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Some flows are more forgiving.
Directions for future work
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Improved integration between turbulent physics and model.
Better understanding of the stability characteristics of the
system:
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Smooth, laminar-like flow in the inner layer. Diffusion dominated.
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“Turbulent” flow in the outer layer. Advection dominated.
Identification of “optimal” disturbances.