Near-wall Reynolds stress modelling for RANS and hybrid RANS/LES methods

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1 Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen Near-wall Reynolds stress modelling for RANS and hybrid RANS/LES methods Axel Probst (now at: C 2 A 2 S 2 E, DLR Göttingen) René Cécora, Rolf Radespiel (Institute of Fluid Mechanics, TU Braunschweig) TAU-User Meeting 2011, , DLR Braunschweig

2 Outline Motivation Near-wall Reynolds-stress (U)RANS modelling model description and implementation validation for subsonic flows validation for transonic flows RSM-based hybrid RANS/LES (DES) modelling Conclusion TAU-User Meeting 2011 Page 2

3 Motivation turbulence modelling is dominant limit to simulation accuracy (esp. at flight boundaries) Goals: 1. avoid known weaknesses of common eddy-viscosity models: isotropy-assumption, no curvature effects, Reynolds stress strain alignment, individual modelling of Reynolds stresses (RSM) 2. extend model validity down to walls: most models (e.g. present TAU models) neglect near-wall effects use of near-wall (i.e. Low-Reynolds) damping and specific length-scale variable 3. combat remaining RANS weakness in separation: use near-wall RSM in hybrid RANS/LES framework Main applications: focus on flight boundaries (stall, shock-induced separation, ) academic subsonic flows in 2D (airfoils) and 3D (engine inlets) in DFG-FOR1066 industrial subsonic and transonic flows (airfoils, wings, full aircrafts) in ComFliTe TAU-User Meeting 2011 Page 3

4 TAU-User Meeting 2011 Page 4 Ф ij : linear or quadratic redistribution + wall reflection DNS-based calibration of low-reynolds damping functions ( term-by-term ): D ij : gradient diffusion model (GGDH) from: Jakirlić (1997) Low-Re ε h -based RSM (Jakirlić et al. 2002, Probst et al. 2008): Near-wall Reynolds-stress model Reynolds-stress equation: l j l i x u x u 2 i j j i x u x u p il j jl i j i l l u u p u u u x ij ij D ij P ij k j i k x u u x

5 Length-scale equation total inhomogeneous Scale-supplying variable: homogeneous part of dissipation h 0. 5 D ε h -equation: homogeneous similar to classical ε-equations, but correct nearwall behaviour additional non-equilibrium terms: length-scale growth limiter sensitize model to pressure-gradients algebraic model to obtain ε h ij = f(εh ) two coefficient sets: original calibration: JHh-v1 RSM reduced dp/dx-sensitivity: JHh-v2 RSM Flat plate Re Θ = 1410 TAU-User Meeting 2011 Page 5

6 Implementation in TAU-Code General: based on present ω-rsm-implementations upwind convection schemes (Roe, Roe2nd) implicit source-term treatment benefits from LU-SGS and Full-Multigrid Special requirements: 2nd (mixed) derivatives of velocity local wall normals in the field (iterative) solution of relation ε h ij = f(εh ) computation of complex damping functions transition trip to induce turbulence onset wct. increase by factor ~1.5 compared to SSG/LRR-ω RSM Convergence history for HGR-01 airfoil, α = 4 TAU-User Meeting 2011 Page 6

7 Basic validation of RANS-RSM various generic flow cases subsonic/transonic, constant/variable pressure, transitional/turbulent, some examples: streamwise velocity Turbulent diffusor Oblique shock-bl interaction Laminar separation bubble TAU-User Meeting 2011 Page 7

8 Subsonic 2D flows single-element HGR-01 airfoil Re = 0,65x10 6, Ma = 0,07 maximum lift (α = 12 ) JHh-v1 RSM TAU-User Meeting 2011 Page 8

9 Subsonic 2D flows single-element HGR-01 airfoil Re = 1,3x10 6, Ma = 0,14 maximum lift (α = 12 ) JHh-v1 RSM TAU-User Meeting 2011 Page 9

10 Subsonic 3D flows engine inlet axisymmetric flow-through nacelle (DFG-FOR1066) Re = 1.3 x 10 6, computed transition (e N ) α = 23.5 separation topology θ = 180 JHh-v2 RSM JHh-v2 RSM α = 24.5 sep. onset and topology well captured by RSMs separation onset far too early with k-ω SST TAU-User Meeting 2011 Page 10

11 Transonic 2D flows RAE2822 airfoil Re = 6.5 x 10 6, α = 2.8 grid-converged results (736 x 176 points, shock refined) Case 9: Ma = 0.73 TAU-User Meeting 2011 Page 11

12 Transonic 2D flows RAE2822 airfoil Re = 6.5 x 10 6, α = 2.8 grid-converged results (736 x 176 points, shock refined) Case 9: Ma = 0.73 Case 10: Ma = 0.75 TAU-User Meeting 2011 Page 12

13 Transonic 3D flows wing flow Onera-M6 wing at Re = x 10 6, Ma = 0.84 α = 4.08 : onset of shock-induced separation Menter SST SSG/LRR-ω-RSM JHh-v2 RSM TAU-User Meeting 2011 Page 13

14 Transonic 3D flows wing flow Onera-M6 wing at Re = x 10 6, Ma = 0.84 α = 4.08 : onset of shock-induced separation TAU-User Meeting 2011 Page 14

15 Transonic 3D flows powered engine inlet industrial engine nacelle LARA with mass suction validation at start conditions with gust: low-ma onflow, large massflow, high incidence transonic flow portions, shock-induced separation disturbance of p tot in fan-plane DC60 JHh-v2 RSM JHh-v2 RSM separation onset just about too early TAU-User Meeting 2011 Page 15

16 Basic ε h -RSM-based DES (ε h -DES) General approach: combine RANS model with LES in separated regime replace length scale in dissipation term with DES scale: calibration / validation with DIT case: central scheme with Matrix-dissipation low-ma preconditioning skew-symmetric flux form (energy-conserving) best results with C DES = 1.1 Decaying isotropic turbulence TAU-User Meeting 2011 Page 16

17 Backward-facing step with ε h -DES Re h = (Driver & Seegmiller, 1985) RANS/LES sensors: DDES, ADDES grid study: 2.6 million 8.8 million points expected and consistent improvement over RANS TAU-User Meeting 2011 Page 17 Q-criterion, colored with spanwise velocity

18 Conclusion overview over Reynolds-stress modelling efforts at ISM, TU Braunschweig ε h -based RSM with DNS-based near-wall modelling and non-equilibrium extensions implemented in TAU and extensively validated JHh-v2 RSM offers best compromise (but loss of accuracy at subsonic airfoil stall) Benefits: (theoretical) advantages by better representation of near-wall physics in 2D/3D and sub-/transonic testcases mostly at least as good as reference models stall prediction in 2D and 3D improved over eddy-viscosity models Drawbacks: transition tripping required (however, solutions are available) increased computational effort (awaiting optimization) moreover, potential as DES-background model demonstrated currently being implemented in central TAU-version ( release 2012) TAU-User Meeting 2011 Page 18