Lund university / Energy Sciences / Fluid Mechanics

Computations of cavitating flow on hydrofoils

Aurélia Vallier

Division of Fluid MechanicsDepartment of Energy Sciences

Lund Institute of Technology, Lund Sweden

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Lund university / Energy Sciences / Fluid Mechanics

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OUTLINE

• Introduction

• Modelling

• Problem Setup

• Results

• Conclusions

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

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• Cavitation - what is it? - where does it occur? - different types of cavitation - why do we want to understand it?

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

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Cavitation - what is it?

Boiling

Cavitation

Phase diagram

Definition : Formation of vapor cavities in a liquid due to pressure drop.

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

5

Cavitation – where does it occur?

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

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Cavitation – different types of cavitation

(a) Travelling bubble Attached cavitation - Sheet cavitation (c) -Cloud cavitation (b)(d) Supercavitation

(e) Vortex cavitation

σ=p∞− pv

12

ρu∞2

σ c

σσ c

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

7

Cavitation – different types of cavitation

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

8

Cavitation – different types of cavitation

(a) Travelling bubble Attached cavitation - Sheet cavitation (c) -Cloud cavitation (b)(d) Supercavitation

(e) Vortex cavitation

σ=p∞− pv

12

ρu∞2

σ c

σσ c

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

9

Cavitation – different types of cavitation

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

10

Cavitation – different types of cavitation

(a) Travelling bubble Attached cavitation - Sheet cavitation (c) -Cloud cavitation (b)(d) Supercavitation

(e) Vortex cavitation

σ=p∞− pv

12

ρu∞2

σ c

σσ c

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

11

Cavitation – different types of cavitation

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

12

Cavitation – different types of cavitation

(a) Travelling bubble Attached cavitation - Sheet cavitation (c) -Cloud cavitation (b)(d) Supercavitation

(e) Vortex cavitation

σ=p∞− pv

12

ρu∞2

σ c

σσ c

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

13

Cavitation – different types of cavitation

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

14

Cavitation – different types of cavitation

(a) Travelling bubble Attached cavitation - Sheet cavitation (c) -Cloud cavitation (b)(d) Supercavitation

(e) Vortex cavitation

σ=p∞− pv

12

ρu∞2

σ c

σσ c

Lund university / Energy Sciences / Fluid Mechanics

INTRODUCTION

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Cavitation – why do we want to understand it?

− Negative effects : - noise,

- vibration, - material damages (erosion due to the collapse) - performance reduction

Understand cavitation inception and evolution avoid (at least control and reduce) these effects

− Difficult to predict because it depends on - flow conditions - water nuclei - surface roughness

Lund university / Energy Sciences / Fluid Mechanics

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MODELLING

Inception: - Pressure drop - Nuclei content

Evolution: - Two phase flow - Bubble dynamics - Turbulence -> mixing

Lund university / Energy Sciences / Fluid Mechanics

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MODELLING

Inception: - Pressure drop - Nuclei content

Evolution: - Two phase flow - Turbulence -> mixing - Bubble dynamics

σ=p∞− pv

1/2ρu∞2

Model 1 fluidBarotropic equation of state

Model 2 fluidsVOFInterface trackingTransport equationMass transfert

Rayleght-Plesset equation

ρ R R32

R24νRR=p v− p t −

2SR

2γR0

− pv− p0 R0

R3Γ

Nuclei density n0Nuclei radius R

Turbulence model

Lund university / Energy Sciences / Fluid Mechanics

VOF ---> vapor volume fraction α

MODELLING Sauer Model

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∂

∂ t∇ .u =0

∂u∂ t

u . ∇u =−∇ p∇ 2u−∇

∣∇∣

∂α∂ t

∇ .α u =ml

ρ=ρv αρl 1−α

μ=μv αμl1−α

Mass transfer rate = creation of vapour + destruction of vapour

m0

m−0

Lund university / Energy Sciences / Fluid Mechanics

VOF ---> vapor volume fraction α

MODELLING Sauer Model

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∂

∂ t∇ .u =0

∂u∂ t

u . ∇u =−∇ p∇ 2u−∇

∣∇∣

∂α∂ t

∇ .α u =ml

ρ=ρv αρl 1−α

μ=μv αμl1−α =

n0 .43R3

1n0 . 43R3

d Rd t

= 23

p R −p∞

l

ddt

=1−

n0 .43R2 R

1n0 . 43R3

∇ .u=−1

∂∂t

u ∇ .=−1

∂∂ t

=l−v

∂∂ t

Vapor= small spherical bubbles

Lund university / Energy Sciences / Fluid Mechanics

PROBLEM SETUP

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InletUx=8m/s∇p=0

Outlet∇U=0p=0 Pa

WallU=0 m/s∇p=0

Naca0015 profile (chord length=0.15m , angle of attack=8°)2D geometry (1m*0.5m)Re=1.2 *10⁶

Lund university / Energy Sciences / Fluid Mechanics

RESULTS

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-Spallart Allmaras model

-Wall function (y+= 30)

Lund university / Energy Sciences / Fluid Mechanics

RESULTS

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-Spallart Allmaras model

-Wall function (y+= 30)

Lund university / Energy Sciences / Fluid Mechanics

RESULTS

Lund university / Energy Sciences / Fluid Mechanics

Lund university / Energy Sciences / Fluid Mechanics

PROBLEM SETUP

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InletUx=8m/s∇p=0

Outlet∇U=0p=0 Pa

WallU=0 m/s∇p=0

Injection50 or 500 particles / time step Dp=0.1,1,10 or 50μmUp=0Solution methodLPT one way coupling

Lund university / Energy Sciences / Fluid Mechanics

RESULTS

Statistical average of the nuclei concentration over 40 periods

Dense-at the point of impact(collision)-in the low pressure area(close to the leading edge and above the suction side)

Very dilutedin the boundary layer of the suction side

→Nuclei concentration don't explain cavitation inception

→ Importance of the surface rugosity ?

Lund university / Energy Sciences / Fluid Mechanics

PROBLEM SET UP

Non uniform distribution of the nuclei concentration:-nuclei on the boundary layer (thickness = 6 cells)-nuclei on the first cell close to the surface

Lund university / Energy Sciences / Fluid Mechanics

CONCLUSION

Cavitation is a complex phenomena which- involve multiphase flow, phase transition, no symmetry (need to simulate in 3D), turbulence, instabilities, chock waves, bubbles dynamic, fluid quality, surface rugosity...- and occurs in complex geometry

No empirism free cavitation modelNo comprehensive capabilities to model development of a type of cavitation to an other.

Rather good results for the prediction oh sheet cavitation.Improvement would be achieved if we take account for the influence of the fluid quality, the surface rugosity and the turbulence.

Lund university / Energy Sciences / Fluid Mechanics

Thank you

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Lund university / Energy Sciences / Fluid Mechanics

short about LPT

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Movie LPT ST<<1 and St>>1

d x p

d t= up

m p

d up

d t=FD=−m p

up−u

p

R e p=D p∣up−u∣

Stk=p

fluid time scale