Hybrid RANS/LES simulations of a cavitating flow in Venturi

Transcription

1 Hybrid RANS/LES simulations of a cavitating flow in Venturi TSFP-8, August Poitiers - France Jean Decaix jean.decaix@hevs.ch University of Applied Sciences, Western Switzerland Eric Goncalves eric.goncalves@legi.grenoble-inp.fr Laboratoire des Ecoulements Géophysiques et Industrielles

2 1 Introduction 2 Cavitating flow modelling 3 Solver and test case 4 Results 5 Conclusion

3 Study overview Objectives To compute a 3D cavitation sheet on a Venturi geometry by application of Hybrid RANS/LES turbulence models Detached Eddy Simulation and Scale Adaptive Simulation based on the Spalart-Allamras model Motivations Some studies put in evidence 3D mecanisms for the cavitation cloud sheddings Cavitation sheet on a Venturi geometry

4 Cavitating flow features Main characteristics : liquid/vapour mixtureρ liq = 1000 kg/m 3 ; ρ vap = 0.02 kg/m 3 unsteady cavity closure large range of Mach number compressibility effects on turbulence? u k,i x i = 1 α k u k n kδ I Pressure/temperature diagram Mixture speed of sound (Wallis 1967)

5 Flow modelling Homogeneous compressible RANS approach One fluid compressible RANS modelling : ρ ũ i t ρẽ t ρ t + ρ ũ l x l = 0 + ρ ũ lũ i x l + ρ ũ i H x i = p + σ il τ il x i x l x l = σ ilũ l x i q i x i Qt i x i Turbulence model Hybrid RANS/LES models with an eddy-viscosity assumption Cavitation modelled barotropic equation of state (Delannoy & Kueny 1990)

6 Turbulence modelling : DES model DES97 formulation ρ ν t + [ ρ u l ν 1 ] ν (µ+ρ ν) = c b1 (1 f t2 ) Sρ ν x l σ x l + c b2 σ ρ ν x l ν x l ( c ω1 f ω c ) b1 ν 2 κ 2 f t2 d 2 with : d = min(d, C DES ) the new distance d is the distance from the nearest wall, = max( x, y, z)

7 Turbulence modelling : a SAS formulation of the Spalart and Allmaras model The modify ν transport equation Substitution of the distance d by The von Karman length scale L vκ ρ ν + [ ρ ũ l ν 1 ] ν (µ+ρ ν) = c b1(1 f t2) Sρ ν t x l σ x l + cb2 ρ ν ν σ x l x l ν 2 c ω1 f ωρξ sas cb1 ν2 ft2ρ κ2 d 2 with a tunable parameter ξ SAS = 3 (for cavitating flows). L 2 vk

8 Main feature of the hybrid RANS/LES model To Provide an adaptive turbulence length scale For the Spalart and Allmaras SAS model, equilibrium assumption gives : ν = L 2 vk S For the DES model : ν = (C DES ) 2 S The von Karman length scale L vκ gives an information on the heterogeneity of the flow. L vκ = κ U U ; U U 2 U i 2 U i = S ; = xk 2 xj 2

9 Numerical code Main features An in house unsteady compressible RANS code Cell-center finite-volume formulation for structured meshes Spatial discretisation : Space-centered Jameson scheme for convective flux of the mean flow Upwind Roe scheme for the convective flux of the turbulent flow Temporal discretisation : Time integration perfomed with a low storage method coupled with a dual time stepping approach A pre-conditionning strategy is applied in incompressible regions

10 Experimental conditions Operating point U inlet = 10.8 m/s σ inlet = P inlet P vap 0.5ρU inlet Observations A quasi stable cavitation sheet of 0.70 to 0.85 m lenght An unsteady closure region with vapour cloud shedding and a liquid re-entrant jet Available quantities Five stations of measurement equipped with double optical probes provide longitudinal velocity void fraction Pressure and p rms profiles at the wall

11 Introduction Cavitating flow modelling Solver and test case Results Conclusion Numerical conditions Meshes 3D numerical computation with a mesh composed of nodes Boundary conditions inlet velocity outlet non-reflective condition no slip condition at the wall farfield value of turbulence quantities Time integration dual time approach with 100 sub-iterations dimensional time step : t = s Y X Left wall Z Inlet Outlet Righ wall

12 Computations 2 computations performed Model cavitation number comments SA SAS σ inlet = 0.6 Unsteady cavitation sheet with a liquid re-entrant jet ; low frequency around 6 Hz SA DES σ inlet = 0.6 U-shape cavitation sheet with a liquid re-entrant jet ; low frequency around 6 Hz Experiment σ inlet = 0.55 Unsteady cavitation sheet with a liquid re-entrant jet ; No 3D visualisation ; No particular frequency

13 Station 3 and 4 : void fraction and longitudinal velocity Comments Satisfactory agreement between experiment and models Models overestimate void fraction at the wall and the re-circulation thickness 0.01 EXPE SA-SAS SA-DES EXPE SA-SAS SA-DES y (m) y (m) alpha u (m/s) 0.01 EXPE SA-SAS SA-DES EXPE SA-SAS SA-DES y (m) y (m) alpha u (m/s)

14 Mean pression and RMS pressure fluctuations at the bottom wall Comments DES underestimates pressure dowstream the cavity 3D computations overestimates the p rms dowstream the cavity EXP SA-SAS SA-DES 0.8 EXP SA-SAS 0.7 SA-DES 0.6 (P-Pv)/Pv P rms / P mean x-x i (m) x-x inlet (m)

15 Dynamic behaviour of cavitation sheet : SA-SAS computation Gradrho: Y Z X Density gradient visualization

16 Transversal instability : SA-SAS computation Void fraction contour and velocity vector alpha: z 0.03 z x x

17 Fourier transform analysis Cavitation sheet frequency Amplitude Fréquence (Hz) y (m) k=5 <=> z = 1,38 mm k=57 <=> z=48,4 mm t (s) FFT of the vapour volume low frequency 6Hz. Time evolution of the re-entrant jet thickness on each side

18 Experiment 1 vs Computation Bifurcation For σ 2 i < 4, shedding is conducted by a shock spanwise structures and low frequency 8 Hz For σ 2 i > 4, shedding is conducted by a re-entrant jet no low frequency, no spanwise structures Present test case : σ 2 i 4.3 i 1. S. Prothin et al. Image processing using POD and DMD for the study of cavitation development on a NACA0015, in : 13th Journées de l Hydrodynamique, Laboratoire Saint Venant, Chatou, France, 2012

19 Conclusion Main results Velocity and void fraction profiles agree well with the experiment in the mid-span p rms overestimated downstream the cavity in the mid-span A transversal instability characterized by a re-entrant jet oscillation (6 Hz) and a transversal flow Limitations Results have to be analysed with caution as : No measurements are available in the transversal direction to validate the computation, Only one experiment put in evidence the existence of a transversal mode