VIRTUE / WP4 Delft Twisted Foil in steady flow Simulation with EOLE

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Alyson Wilson
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1 6 th Framework Programme "Sustainable development, global change and ecosystems" Project No / WP4 Delft Twisted Foil in steady flow Simulation with EOLE Workshop Oct , 2007 R. Marcer Principia

2 Main features of EOLE Multi-blocks structured curvilinear grids, Moving grids : rigid grid or spring method Finite volume scheme, fully conservative Monophase or multiphase flow VOF implicit free surface method Interface cavitation model Turbulence modeling : k-ε model coupled with a Gorski model for the boundary layer Coupling with a mechanical model

3 VOF interface tracking method liquid F=1 : liquid cells F=0 : vapour cells vapour Liquid vapour interface 0<F<1 : cells containing an interface F=0.6 F=1 F=0.4 VOF model

4 F = F t = Interface VOF-cavitation mass transfer model F t + div [ ρ( U W )] F = Ft kinematic VOF (by SLVOF) thermodynamic VOF (source term) W r = possible grid velocity ρ = VOF ρ + ( 1 VOF) l Calculation of the mass transfer term F t Using the total enthalpy of the liquid mixture de F df ( p, dp t = = f, C ) dt t dt dt ρ vap r r

5 Algorithm of the multiphase flowmechanic models At each time step pseudo-time τ iteration loop : mass momentum VOF mechanic ~ ρ r n+ 1 + C ρ = div n τ ~ r n 1 r n+ 1 r r r ρu + C0 ρu = div ρu U W τ r n 1 [ ρ( U W )] D ρ + r n 1 r r ( ) ( ) [ ( ) + pi τ ] + ρg + D ( ρu ) + r r n r n+ 1 n+ 1 1 ( ρf ) + C ( ρf ) = div[ ρ( U W ) F ] + D ( ρu ) + ( ρ ) n + 0 τ &r X τ r X τ n+ 1 &r n+ 1 { + C X = + 0 ψ n+ 1 r n+ 1 &r n + C X = X Dn and turbulence equations r r n+ 1 &r n 1 &r ( X, X, U ) + Dn ( X ) r ( X ) ρ W r = VOF ρl + ( 1 VOF) ρ = the grid velocity n F t Mass transfer term vap n

6 Twist 11 hydrofoil Incidence = -2 σ=1.04 V=6.97m/s t=1ms Meshes : Mesh 1 : coarse - full geo cells TE : 3L Mesh 2 : refined - full geo 1M cells TE : 6L Mesh 3 : refined - half geo cells TE : 3L

7 Twist 11 hydrofoil mesh 1 Mesh 1: 2 blocks cells full geometry behind TE : 3L X Y Z 0.2 3L Z 0.2 X L Y

8 Twist 11 hydrofoil mesh 2 Mesh 2 : 2 blocks cells full geometry behind TE : 6L 1 6L 0.5 X 0 2L Y Z

9 Twist 11 hydrofoil mesh 3 Mesh 3 : 2 blocks cells half geometry behind TE : 3L X Y Z L 0.2 X 0 2L Y Z

10 Twist 11 hydrofoil - meshes Z X 2mm Y 1mm Mesh 1 Meshes 2 and 3

11 Shedding cycle mesh 1 (coarse) symmetry plane X Z Y X Z Y X Z Y liquid WP vapour t=1.52s liquid vapour t=1.53s liquid vapour t=1.55s Z Z Z X Y X Y X Y liquid vapour t=1.57s liquid vapour t=1.59s liquid vapour t=1.60s

12 Shedding cycle mesh Periodic cavitation on 1 period (T=0.05s)

13 Comparison EOLE/experience mesh 2 symmetry plane

14 Comparison EOLE/experience mesh 2 symmetry plane

15 Comparison EOLE/experience mesh 2 symmetry plane

16 Comparison EOLE/experience mesh 2 symmetry plane

17 Shedding cycle mesh 2 Pressure field jet impact Implosion of vapour cavities shedding cycle and re-entrant jet process

18 Twist 11 hydrofoil mesh 2 full geometry

19 Comparison EOLE/experience mesh 2

20 Comparison EOLE/experience mesh 2

21 Comparison EOLE/experience mesh 2

22 Comparison EOLE/experience mesh 2

23 Shedding frequency mesh 2 Fz (N) 550 measurements : f=21 Hz --- T=0.048s EOLE : f=18 Hz --- T=0.055s T Spectral analysis of the lift force 35 main frequency EOLE = 18 Hz measurements = 21 Hz t (s) Lift force PRINCIPIA Hz PRINCIPIA Shedding frequency

24 Twist 11 hydrofoil mesh 3 (half geometry)

25 Comparison EOLE/experience mesh 3

26 Comparison EOLE/experience mesh 3

27 Shedding frequency mesh 3 Fz (N) t(s) Lift force Shedding frequency

28 Re-entrant jet mechanism mesh 3 Foeth, Terwisga, 2006

29 Re-entrant jet mechanism Periodic tranversal oscillations Half geometry Full geometry

30 Full geometry periodic transversal oscillations Fy (N) t (s) Transversal load Fy PRINCIPIA

31 Shedding frequency conclusion Experiment mesh 1 : coarse 3L mesh 2 : refined, full geometry 6L mesh 3 : refined, half geometry 3L Shedding frequency 21 Hz 12 Hz 18 Hz 17.5 Hz

32 Conclusions (1) : ability of EOLE 3D re-entrant jet mechanism Cavitation shape cavitation extension and volume (versus σ) shedded cavities process wavy character of the interface Periodic shedding cycle Quite realistic values of : Natural shedding frequency Lift load Jet impact on the wall (erosion) Implosion of shedded vapour cavities

33 Possible improvements Mesh refinement t=0.5ms (instead of 1ms) 100 t for a shedding period Turbulence (SST?)

Computations of unsteady cavitating flow on wing profiles using a volume fraction method and mass transfer models

$Computations of unsteady cavitating flow on wing profiles using a volume fraction method and mass transfer models$ Computations of unsteady cavitating flow on wing profiles using a volume fraction method and mass transfer models Tobias Huuva *, Aurelia Cure, Göran Bark * and Håkan Nilsson * Chalmers University of Technology,