A priori analysis of an anisotropic subfilter model for heavy particle dispersion

Transcription

1 Workshop Particles in Turbulence, COST Action MP0806 Leiden, May 14-16, 2012 A priori analysis of an anisotropic subfilter model for heavy particle dispersion Maria Knorps & Jacek Pozorski Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Gdańsk, Poland 1

2 LES of particle-laden flows: double meaning of filtering * single-phase turbulent flow computations: subfilter fluctuations are neglected from definition * two-phase flows with the dispersed phase: subfilter fluctuations may be of importance (need for modelling?) in Large-Eddy Simulation (LES), particles filter out some flow scales (shorter than their momentum relaxation time) and move in a filtered velocity field (of larger flow scales) Particle-laden HIT: preferential concentration patterns: a) DNS, b) a priori LES [Pozorski & Apte, JMF 2009] 2

3 LES of particle-laden flows: impact of filtering [Fede & Simonin, PoF 2006] 3

4 LES for fluid: governing equations Dynamics of large-eddy motion (filtered N-S eq.): Closure of the SGS stress tensor: dynamic model of Germano & Lilly (double filtering) Closure of the subfilter turbulent energy: developed for compressible flows (Yoshizawa 1982; Moin et al. 1991) 4

5 Dynamics of heavy particles in turbulent flow (point particles, drag only) Variants considered for velocity: DNS (just interpolation) a priori LES (filtering+interpolation) a priori LES with a model for reconstruction of SGS f@p velocity Structural approaches (reconstruction of SGS field): 1) approximate deconvolution (Kleiser etal. 2001, Kuerten PoF 2006), 2) fractal reconstruction (Scotti & Meneveau 1999; Salvetti & Soldati 2006) 3) linear-eddy model (Kerstein 1990s): triplet map, 4) kinematic simulation 5 (Flohr & Vassilicos, JFM 2000; Kahn etal., IJNMBE 2010)

6 SGS particle dispersion model: isotropic formulation Langevin eq. for SGS fluid velocity along particle trajectories estimation of the SGS fluid time scale (here: direction-independent): Remarks: _ * L Csg sg 2 3 sg k r - model formulation akin to existing RANS proposals, - in non-homogeneous RANS, additional terms needed to prevent from spurious drifts - alternative formulation for instantaneous f@p velocity (Minier & Peirano, 2001) - in LES, initially proposed for homogeneous isotropic turbulence, - channel flow results (incl.deposition) not satisfactory: i) non-homogeneous extra terms needed? (or full instant. velocity form?), ii) anisotropy of small scales in LES? 6

7 Digression: PDF method (statistical approach) The Generalized Langevin model for fluid velocity: (*) common assumption (Pope 1985), based on consistency with Kolmogorov hypotheses: identification of G and B tensors based on DNS results for TCF at Re=180; anisotropic model (*) used with success in a stand-alone PDF computation [Taniere et al., PoF 2010] 7

8 Anisotropic SGS particle dispersion: idea of the new model proposal the Bardina model: proposed estimation of SGS velocity fluctuations: (based on the component decomposition of residual energy) anisotropic variant of SGS particle dispersion model (no gradient terms here): 8

9 DNS of particle-laden turbulent channel flow: geometry Channel flow at Re 150with the domain size of 4 h 2h 2 h : benchmark, several data sets available [Marchioli, Soldati, Kuerten et al., IJMF 2008] present DNS: 128 x 128 x 128 mesh x 14.7 y z 7.4 filtered DNS (a priori LES): 32 x 64 x 32 mesh considered particle classes: St 1, 5, 25, r ( St 5) p 9

10 flow and particle solvers; idea of a priori LES Solver: academic DNS/LES spectral code (J.G.M. Kuerten,TU/e, NL) + particle tracking (2 nd order R-K in time, 2 nd order Lagrange interpolation for f@p) A priori LES: * fluid (DNS) and particle fields known at t^n * filtering applied to fluid velocity * residual f@p velocity updated (if SGS particle dispersion model) * fluid DNS and particles (all variants) advanced by a time step * detailed information available statistics computed at t^(n+1)

11 SGS fluid turbulent energy: a priori LES of channel flow the Bardina model: estimate of Miller & Bellan (PoF 2000): Assessment of residual turbulent energy: dynamic model (Yoshizawa formula) vs. the Bardina estimation (earlier results from a FV code). 11

12 Bardina model vs. a priori LES for fluid Bardina model: Estimated SGS fluid turbulence intensities across the channel (Cm=0.3) 12

13 Particle concentration profile St=5 Normalised particle number density across the channel. 13

14 Mean particle velocity St=1 St=5 streamwise component (upper plots); wall-normal component (lower plot). St=5 14

15 Intensity of particle velocity fluctuations: streamwise and spanwise, St=5 Particle rms fluctuating velocity: streamwise (left plot), b) spanwise (right plot). DNS; a priori LES; apriori LES with two variants of SGS dispersion model with C_sg=

16 Intensity of particle velocity fluctuations: wall-normal, St=1 and St=5 St=1 St=5 Particle rms wall-normal velocity. DNS, a priori LES and a priori LES with stochastic SGS dispersion models (isotropic and anisotropic). [Pozorski et al., ETMM9, 2012, in preparation] 16

17 Channel flow: particle velocity cross-correlation St=1 St=5 Particle shear stress (correlation of streamwise and wall-normal particle velocity components). Proposal for subfilter dispersion model with cross-correlation: for i k 17

18 Conclusion importance of SGS particle dispersion in LES: - preferential concentration, particle dispersion and deposition may be affected, - anisotropy effects commonly modelled in RANS, less clear in LES, - here: anisotropy included in stochastic Langevin model results of a priori LES, next-term work: - considerable improvement noticed in near-wall r.m.s. fluctuating velocity, - room for improvements through account for cross-correlation terms - definitive answers expected from true, or a posteriori, LES (underway) - formulation in terms of instantaneous, not residual, f@p velocity promising - hints from ideal stochastic forcing (Bianco et al. 2011, Kuerten & Guerts 2012) 18

19 Acknowledgements: - J.G.M. Kuerten (TU Eindhoven, NL) for spectral DNS code - J.P. Minier (EDF R & D, Chatou, FR) for fruitful discussions - Computing Centre TASK (Gdańsk, PL) for CPU time granted - COST Action MP0806 Particles in Turbulence for STSM with F. Toschi and J.G.M. Kuerten at TU/e 19