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 ∼ 62.5mm, H ∼ 25.4mm, µ ∼ 1 mPa · s, Ω = 638 rpm G = 0.4, Re = 2.6 · 105, Fr = 28.4

Configuration

Parameters : G = H R , Re = ΩR2 ν , Fr = Ω2R g .

Previous studies I : Re ∼ 105 , 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

Fluid 2 Ω r Fixed cavity Rotating disk h H R z Fluid 1

Parameters : G = H R , Re = ΩR2 ν2 , Fr = Ω2R g ¯ h = h R , ρr = ρ1 ρ2 , µr = µ1 µ2 We = ?

Previous studies II : Re ∼ 100 − 103, Fr ∼ 1 − 10, H/R ∼ 1, ¯ h ∼ 0.1 − 1, ρr ∼ 1.

Takeda, Japan, 2009 Tsai, Taiwan, 2015 Simulations :

◮ Lopez, USA, 2012, small We ◮ Herrada, Spain, 2015, ρr << 1, small We

Comparison on ”Mont Fuji”

Re=676 Sunfluidh

Re = 676, Fr = 1.01, H/R = 2.2, ¯ h = 1, ρr = 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/m3. Angular Vel. Ω = [100 − 200] rpm, Height at rest : H = [1.55 − 6] cm.

Comparison of interface and velocity profiles : Set 1

0.5 1

r

0.4 0.45 0.5 0.55 0.6 0.65

h Hauteur interface : Set 1

Rose Sfemans Gerris3D SunFluidh Expe 0.1 0.2 0.3 0.4 0.5 Vt 0.2 0.4 0.6 0.8 1 z Vitesse azimutale a R/2 : Set 1

Rose Sfemans Gerris3D SunFluidh

• 0.2
• 0.1

0.1 0.2

Vr

0.5 1

z Vitesse radiale a R/2 : Set 1

Rose Sfemans Gerris3D SunFluidh

• 0.1
• 0.05

0.05

Vz

0.5 1

z Vitesse axiale a R/2 : Set 1

Rose Sfemans Gerris3D SunFluidh

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 4 6

Time (s)

0.5 1 1.5 2

H center (cm)

Exp Blue SunFluidH128 Gerris3D Rose

G = 0.248, Re = 1198, Fr = 1.41

Free surface deformation : spin up from rest

Details on the wave : 0 < t < 1s

0.2 0.4 0.6 0.8 1

Time (s)

1.2 1.4 1.6

H center (cm)

Exp Blue SunFluidH128 Gerris3D

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)

h(x′, y′) =

L∆ϕ ∆ϕ−ω0D( 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

5 10 15 20

t(s)

• 2.5
• 2
• 1.5
• 1
• 0.5

h(cm)

Sunfluidh 128x128 FTP Measure 2 4 6

x(cm)

• 3
• 2
• 1

1 2 3

h(cm)

Sunfluidh t=3 s FTP Measure t=3s Sunfluidh t=5 s FTP Measure t=5 s

h(r = 0, t) h(r, t = 3s) et h(r, t = 5s)

Newton’s Bucket : comparison at steady state

• 5

5

x(cm)

• 2
• 1

1 2 3

h(cm)

ROSE Needle Measure Sunfluidh 128x128 FTP Measure Theoritical parabola

◮ Weak deformation : good agreement (t = 3s et t = 5s ) ◮ Larger deformation : 10% error at the axis.

Conclusion, Next steps

◮ Good predictions for large deformation, small density ratio, 2D

axi, moderate Re < Rec

◮ 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.