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