Benchmarking rotating flow with free surface deformation Wen Yang, - PowerPoint PPT Presentation

Benchmarking rotating flow with free surface deformation Wen Yang, Guangyang Cui, Jalel Chergui, Yann Fraigneau Ivan Delbende, Laurent Martin Witkowski Universit´ e Pierre et Marie Curie (Paris) & Limsi-Cnrs (Orsay)

Challenge for numerical simulation Air / Water R ∼ 62 . 5 mm , H ∼ 25 . 4 mm , µ ∼ 1 mPa · s , Ω = 638 rpm G = 0 . 4 , Re = 2 . 6 · 10 5 , Fr = 28 . 4

Configuration Parameters : R , Re = Ω R 2 , Fr = Ω 2 R G = H . ν g

Previous studies I : Re ∼ 10 5 , Fr ∼ 1 − 10, H / R ∼ 1 Vatistas, Canada, 1990 → now T. Bohr, Danemark, 2006 → now Iga, Iima, Suzuki, Tasaka, Japan, 2008 → now Theories based on model baseflow : Vatistas, Bohr, Mougel (IMFT).

Configuration II : Two fluids z Fluid 1 R H h Fluid 2 r Fixed cavity Rotating disk Ω Parameters : R , Re = Ω R 2 , Fr = Ω 2 R G = H h = h R , ρ r = ρ 1 , µ r = µ 1 ¯ ν 2 g ρ 2 µ 2 We = ?

Previous studies II : Re ∼ 100 − 10 3 , Fr ∼ 1 − 10, H / R ∼ 1, ¯ h ∼ 0 . 1 − 1, ρ r ∼ 1. Takeda, Japan, 2009 Tsai, Taiwan, 2015 Simulations : ◮ Lopez, USA, 2012, small We ◮ Herrada, Spain, 2015, ρ r << 1, small We

Comparison on ”Mont Fuji” Re=676 Sunfluidh Re = 676, Fr = 1 . 01, H / R = 2 . 2, ¯ h = 1, ρ r = 1 . 03.

Tools for the benchmark ◮ Two experimental setups ◮ First or Old ◮ Second or New ◮ Five different numerical codes : ◮ Rose (Free surface, curvilinear coordinates, Axi, Newton), L. Kahouadji, W. Yang, L. Martin Witkowski ◮ Blue (Finite diff, Front Tracking, 3D cartesian) D. Juric, J. Chergui ◮ Sfemans (Finite element, Level set, 3D cylindrical), J. L. Guermond, C. Nore ◮ SunFluidh (Finite volume, Level set, Axi, soon 3D cylindrical), Y. Fraigneau ◮ Gerris (VOF , AMR, 3D cartesian), S. Popinet

First experimental setup ◮ Set 1 : G = 0.568, Re = 1026, Fr=1.435 ◮ Set 2 : G = 0.248, Re = 1047, Fr=1.496 Radius : R = 6 . 25 cm , Oil : µ = [ 30 − 50 ] mPa · s , ρ = 866 kg / m 3 . Angular Vel. Ω = [ 100 − 200 ] rpm , Height at rest : H = [ 1 . 55 − 6 ] cm .

Comparison of interface and velocity profiles : Set 1 Vitesse azimutale a R/2 : Set 1 1 Hauteur interface : Set 1 Rose 0.65 Sfemans 0.8 Gerris3D 0.6 SunFluidh 0.6 0.55 z h Rose 0.4 0.5 Sfemans Gerris3D 0.45 SunFluidh 0.2 Expe 0.4 0 0 0.5 1 0 0.1 0.2 0.3 0.4 0.5 r Vt Vitesse axiale a R/2 : Set 1 Vitesse radiale a R/2 : Set 1 1 1 Rose Sfemans Gerris3D SunFluidh z 0.5 0.5 z Rose Sfemans Gerris3D SunFluidh 0 0 -0.2 -0.1 0 0.1 0.2 -0.1 -0.05 0 0.05 Vr Vz

Comparison for unsteady flow Spin up from rest (values close to set 2) ◮ Codes : Blue, Gerris, Sunfluidh

Free surface deformation : spin up from rest ◮ Comparison Blue-Gerris-Sunfluidh-experiment height at r = 0 2 Exp Blue 1.5 SunFluidH128 H center (cm) Gerris3D Rose 1 0.5 0 0 2 4 6 Time (s) G = 0 . 248 , Re = 1198 , Fr = 1 . 41

Free surface deformation : spin up from rest Details on the wave : 0 < t < 1 s 1.6 H center (cm) 1.4 Exp Blue SunFluidH128 1.2 Gerris3D 0 0.2 0.4 0.6 0.8 1 Time (s)

New experimental setup ◮ Much better control of rotation rate, accurate geometry : Fast ◮ Measure of free surface height FTP , Pmmh ◮ Velocity measurement LDV : Limsi (soon)

FTP : Fourier Transform Profilometry (Pmmh) L ∆ ϕ h ( x ′ , y ′ ) = ∆ ϕ − ω 0 D ( Takeda et al. )

Newton’s Bucket : Height measurement Too difficult to simulate with water → glycerol (80 %)-water (20 %). h / R = 0 . 444 , Re = 1595 , Fr = 1 . 52 , We = 1361 3 0 Sunfluidh t=3 s Sunfluidh 128x128 FTP Measure t=3s 2 FTP Measure -0.5 Sunfluidh t=5 s FTP Measure t=5 s 1 -1 h(cm) h(cm) 0 -1.5 -1 -2 -2 -2.5 -3 0 2 4 6 0 5 10 15 20 t(s) x(cm) h ( r = 0 , t ) h ( r , t = 3 s ) et h ( r , t = 5 s )

Newton’s Bucket : comparison at steady state 3 ROSE Needle Measure 2 Sunfluidh 128x128 FTP Measure 1 Theoritical parabola h(cm) 0 -1 -2 -5 0 5 x(cm) ◮ Weak deformation : good agreement ( t = 3 s et t = 5 s ) ◮ Larger deformation : 10% error at the axis.

Conclusion, Next steps ◮ Good predictions for large deformation, small density ratio, 2D axi, moderate Re < Re c ◮ Need to check velocity in experiment : all effect included ? ◮ Improve height measurement → validate temporal evolution. Welcome : ◮ Any suggestions to prevent problems we will face : expe/num ◮ Other code that could simulate such flow.