cavitation modelling based on eulerian-eulerian multiphase ... · objectives increase the...

Cavitation modelling based onEulerian-Eulerian multiphase flowCavitation modelling based on

Eulerian multiphase flow

M. PageS. Cupillard

A-M. GirouxP. Proulx

R. Bannari

OutlinesOutlines

Introduction

Multiphase solver and Cavitation Models

Test Cases:

• Rouse and McNown

•Naca66 MOD (4-6⁰)

•Venturi

Results

Coupled DQMOM-Cavitation

Conclusion and future work

Multiphase solver and Cavitation Models

Cavitation


2

Introduction

3

Consequences

Introduction

4

Objectives

Increase the efficiency of turbo machinery.

Better understanding of the complex relationship betweenthe cavitation and the associated drop in performance.

The accurate prediction of thisphenomenon is essential for:

Increase the efficiency of turbo machinery.

Better understanding of the complex relationship betweenthe cavitation and the associated drop in performance.

The accurate prediction of thisphenomenon is essential for:

5

Multiphase Flow Models

Multiphase flow models:

VOF Model

The Mixture Model

Euler

Euler-

Multiphase Flow Models

VOF Model

The Mixture Model

Euler-Euler Approach

-Lagrange Approach

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VOF Approach

Other models are implemented :Zwart and Singhal

Multiphase Flow Models:VOF Approach

VOF Approach

Other models are implemented :Zwart and Singhal

Multiphase Flow Models:VOF Approach

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twoPhaseEulerFoam

s

• no cavitation• Two phase flow (with two vector equation)• interphase forces• only dispersed k-epsilon model• solved equations :

Must use the good correlations!!

Multiphase Flow Models:Eulerian-Eulerian Approach

twoPhaseEulerFoam

Two phase flow (with two vector equation)

epsilon model

Multiphase Flow Models:Eulerian Approach

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• Implementation of cavitation modelsSchnerrSauer, Merkle and Kunz)• wall function and turbulent viscosity adapted• New coefficients for interphase forces correlations• Rearrangement of forces: Drag force is implemented asimplicit form (from p equation to momentum matrix)

twoPhaseEulerFoam

no cavitation Two phase flow (with two vector equation) interphase forces only dispersed k-epsilon model solved equations :


twoPhaseEulerCavFoam

cavitation models : (Singhal, Zwart,SchnerrSauer, Merkle and Kunz)

and turbulent viscosity adaptedNew coefficients for interphase forces correlationsRearrangement of forces: Drag force is implemented as

implicit form (from p equation to momentum matrix)

twoPhaseEulerFoam

Two phase flow (with two vector equation)

epsilon model



9

• Implementation of cavitation modelsSchnerrSauer, Merkle and Kunz)• wall function and turbulent viscosity adapted• New coefficients for interphase forces correlations• Rearrangement of forces: Drag force is implemented asimplicit form (from p equation to momentum matrix)



Implementation of cavitation models : (Singhal, Zwart,SchnerrSauer, Merkle and Kunz)

wall function and turbulent viscosity adaptedNew coefficients for interphase forces correlationsRearrangement of forces: Drag force is implemented as

implicit form (from p equation to momentum matrix)



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Sauer Singhal

Cavitation Models:

Kunz Zwart

1e 7 / 1e 8

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SinghalSauer

Cavitation Models:

Singhal argues that a linear rather than a quadratic velocity dependence is morerelevant, and the relative velocity is of the same order

Kunz Zwart

Singhal argues that a linear rather than a quadratic velocity dependence is morerelative velocity is of the same order than :

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Cavitation Models:

Saeur Singhal

•Re is modeled proportional to the amount by which thepressure is below the vapor pressure.

•Rc modeled using a third order of volume fraction.

Kunz Zwart

is modeled proportional to the amount by which the

modeled using a third order of volume fraction.13

Sauer Singhal

Cavitation Models:

ZwartKunz

rnuc= 5.e-4

Fvap =50Fcond =0.01RB= 1.e-6

Kunz

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Test Cases: Used parameters

Models Schnerr &Sauer Singhal

Cc - 0.01

Ce -0.02

Radius/bubblenumber density n0=1.e8 -

Cavitation number

Two phase flow

Turbulence

Used parameters

Singhal Kunz Zwart

0.01 1000 50

0.021000 0.01

- - R=1.e-6

VOF/E-E

RAS k-ε

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Test Cases: Hemispherical Body (Rouse and McNown)

Mesh 0 Mesh 1

5.17<Y+<38.8 5.63<Y+<31.8

Hemispherical Body (Rouse and McNown)

Mesh 1 Mesh2

5.63<Y+<31.8 1.45<Y+<19.61

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Effect of the wall function and Y+ on the numerical result usinginterPhaseChangeFoam with and without cavitation.


Effect of the wall function and Y+ on the numerical result usinginterPhaseChangeFoam with and without cavitation. 17


Validation of twoPhaseEulerCavFoammodel (σ=0.2) and the comparison with commercial code andinterPhaseChangeFoam solver.


Validation of twoPhaseEulerCavFoam with Zwart cavitation) and the comparison with commercial code and

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Validation of twoPhaseEulerCavFoam and the thethe Singhal cavitation model. (σ=0.2)


Validation of twoPhaseEulerCavFoam and the the assumption proposed by

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Validation of twoPhaseEulerCavFoamwith Kunz cavitation model (σ=0.2)


Validation of twoPhaseEulerCavFoamwith Zwart cavitation model (σ=0.5)

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Test Cases: Naca66-MOD (Shen 1989

σ= 0.98α= 6⁰

Shen 1989), 4 and 6 degree

σ= 1α= 4⁰ 21

Test Cases: Venturi (Stutz & Reboud (2000))Venturi (Stutz & Reboud (2000))

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Test Cases: Venturi

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Test Cases: Venturi (σ=2.4)

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Turbulence can be modified by reducing theturbulent viscosity in the cavity region(Coutier et al. 2003) as :


n=1

n=10

Turbulence can be modified by reducing theturbulent viscosity in the cavity region

n=1

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•The result with the correction of turbulent viscosity increasethe accuracy using the interPhaseChangeFoam solver.

•The Kunz, Singhal and Sauer cavitations model are lessaccurate than Zwart model for this case (empirical constant).

The result with the correction of turbulent viscosity increasethe accuracy using the interPhaseChangeFoam solver.

The Kunz, Singhal and Sauer cavitations model are lessaccurate than Zwart model for this case (using the same

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•The result with the correction of turbulent viscosity increase theaccuracy using the interphaseChangeFoam solver.

•The Kunz, Singhal and Sauer cavitations model are less accuratethan Zwart model for this case.

•The E-E multiphase flow (twoPhaseEulerCavFoamcavitation good than interphaseChangeFoam.

The result with the correction of turbulent viscosity increase theaccuracy using the interphaseChangeFoam solver.

The Kunz, Singhal and Sauer cavitations model are less accurate

twoPhaseEulerCavFoam) predictinterphaseChangeFoam.

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Sauer Singhal

Cavitation Models:

Use a distribution ofradius bubble.

ZwartKunz

rnuc= 5.e-4

Fvap =50Fcond =0.01RB= 1.e-6

Kunz

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Use a distribution ofradius bubble.


KolmogorovEnergy scale

breakup

d1

d2

coalescence

Cavitation

large surface Energy

(uniform)

H0d12

Small surface energy

(non-uniform)

d12

[Bannari et al., 2008; 2009- Selma et al., 2010].


Selma et al., 2010].

Cavitation

32




Cavitation

33


Zwart

Sauer



Cavitation

34

Coupled DQMOM-Cavitation: Venturi

Coupled PBE-cavitations

Cavitation: Venturi

DQMOM+ E-E (Zwart model)

Commercial code

E-E Zwart model

35


(1)

(2)

The shedding cycle for cavity

Cavitation: Venturi

(3)

(4)

36


Coupled DQMOM andcavitation

(1)

(2)

Cavitation: VenturiEulerian-Eulerainmodel using Zwart

(3)

(4)

37

The coalescence is less dominant thanthe break-up (the weight of this rangeis less than 10%)

Initilaisation of weightw0=w1=w2=33.33%

Initilaisation of sizesL0=8.e -7L1=1.e-6L2=1.e-5

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•The result with the correction of turbulent viscosityincrease the accuracy using the interPhaseChangeFoamsolver.• The E-E multiphase flow solver (was validated on three different test cases.•The Kunz, Singhal and Sauer cavitation models are lessaccurate than Zwart model.•The E-E multiphase flow predict cavitation better than theinterPhaseChangeFoam solver.• Use of the cavitation model on hydraulic turbine, andstudy the effect on the efficiency.


The result with the correction of turbulent viscosityincrease the accuracy using the interPhaseChangeFoam

E multiphase flow solver (twoPhaseEulerCavFoam)was validated on three different test cases.The Kunz, Singhal and Sauer cavitation models are less

E multiphase flow predict cavitation better than thesolver.

Use of the cavitation model on hydraulic turbine, andstudy the effect on the efficiency. 39

Thanks

The authors wish to acknowledge the financial support ofthe FQRNT and Hydro-Québec.

The authors also wish to thank thepackage for their hard work and gracious collaboration.

Thanks

The authors wish to acknowledge the financial support of

The authors also wish to thank the developers of the OpenFOAMpackage for their hard work and gracious collaboration.

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cavitation modelling based on eulerian-eulerian multiphase ... · objectives increase the...

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