1 ds-pc/eip5, friedrich | 13-16/08/2012 | © robert bosch gmbh 2012. all rights reserved, also...

1 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights.

3D-1D coupling of

compressible density-based CFD solvers

for cavitating flows

Martina Friedrich, Uwe Iben, Henning Kreschel (Robert Bosch GmbH), Romuald Skoda (Ruhr University Bochum), Claus-Dieter Munz (University of Stuttgart)

August 13th-16th 2012: 8th International Symposium on CavitationAbstract No. 28


3D-1D coupling of CFD solvers for cavitating flowsContent

1. Introduction

2. 3D-1D coupling interface models

3. Numerical results

4. Summary and Outlook


1. Introduction: 3D-1D coupling (compressible code)

3D-1D coupling of CFD solvers

Example: cavitating hydraulic systemcut for 3D simulation:

Which boundary condition?

m

cavitation

3D simulation computing time

:

3D-Simulation only of interesting part of the system with suitable boundary conditions.

4

p=const. or p(t)p=const. or p(t)

DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights.



Simulation of cavitating hydraulic system

BC 1 BC 2 =const. or m

)t(m

collapsed cavitation bubble

cavitation bubble

omitted pressure wave

reflection at outlet

reflection at wall

compressible, explicit 3D CFD solver:Euler equations with barotropic equation of state )(p

reflections also at inlet (not focused here)

artificial influence on cavitation bubbles possible

incompressible 3D CFD solver

5

compressible, explicit 3D CFD solver:Euler equations with barotropic equation of state

compressible, explicit 3D and 1D CFD solver:Euler equations with barotropic equation of state

p=const. or p(t)

BC 2p=const. or p(t)




Simulation: cavitating hydraulic system


)t(m3D solver

1D solver

no reflection at coupling interface

Aim: 3D-1D coupling interface models for compressible CFD solvers

3D-1D coupling interface

)(p


2. Interface models 3D-1D coupling of CFD solvers

Simulation: cavitating hydraulic system

3D-1D coupling interface models (exchange at each timestep):

PVar: primitive variables (commonly used for incompressible codes)

Flux: numerical fluxes calculated using cross-section averaged primitive variables

p=const. or p(t)


)t(m1D solver

3D-1D coupling interface

3D solver

2D

Aim: mass and streamwise momentum conserving coupling algorithm!


2. Interface models 3D-1D coupling of CFD solvers

Aim: Simulation of complete cavitating hydraulic systems 3D

simulation

m

cavitation

1D simulation

3D-1D simulation

Improve: 1) prediction of system behaviour, 2) boundary condition for CFD simulations

8

0

1

2

3

4

5

6

0 0 0 0 0

0

1

2

3

4

5

6

0 0 0 0 0

0

1

2

3

4

5

6

0 0 0 0 0

0

1

2

3

4

5

6

0 0 0 0 0


3. Numerical results 3D-1D coupling of CFD solvers

a) Reference solution: 1D pressure wave (Riemann Problem)

1D solver

1D solverp1= const., u=0 m/s p2<< p1, u=0 m/s

1D solver

u

x0

t1t2t3t4

timetravelling 1D pressure waves

9

0

1

2

3

4

5

6

0 0 0 0 0

0

1

2

3

4

5

6

0 0 0 0 0

0

1

2

3

4

5

6

0 0 0 0 0

0

1

2

3

4

5

6

0 0 0 0 0

0

1

2

3

4

5

6

7

0 0 0 0 0



a) PVar: 1D pressure wave (Riemann Problem)

1D solver

2D solver

2D-1D coupling interface: apply interface model PVar

p1= const., u=0 m/s p2<< p1, u=0 m/s

1D solver

u

x0

t1t2t3t4

time u

x

1D solver 2D solver

2D-1D coupling interface: PVar



b) 2D reference solution: 2D pressure wave ( )0v

t1t2t3t4

pressure velocity x-direction

velocity y-direction

xt5

2D simulation

y

1D

so

lver

1D

so

lver

1D

so

lver



b) PVar: 2D pressure wave ( )

2D-1D interface 2D-1D interface 2D-1D interface



2D-1D coupling: interface model “PVar”

t5

y

x

1D

so

lver

1D

so

lver

1D

so

lver

0v

12

p=const. or p(t)



PVar: cavitating hydraulic system (2D)

BC 1 =const. or m

)t(m

BC 2

reflection at outlet

2D-1D coupling: PVar

1D solver

2D-1D coupling: interface model “PVar”

13

0

1

2

3

4

5

6

0 0 0 0 0

0

1

2

3

4

5

6

0 0 0 0 0



a) Flux: 1D pressure wave (Riemann Problem)

1D solver

2D solver

2D-1D coupling interface: apply interface model

p1= const., u=0 m/s p2<< p1, u=0 m/s

1D solver

u

x0

t1t2t3t4

timetravelling 1D pressure waves u

x

1D solver 2D solver

2D-1D coupling interface: Flux



b) 2D reference solution: 2D pressure wave ( )

t5



y

x

2D simulation

1D

so

lver

1D

so

lver

1D

so

lver

0v



b) Flux: 2D pressure wave ( )

2D-1D interface 2D-1D interface 2D-1D interface



2D-1D coupling: interface model “Flux”

t5

y

x

1D

so

lver

1D

so

lver

1D

so

lver

0v



b) Flux: 2D pressure wave ( )

<6%

<1.5%

mass error

2D – 2D-1D Flux:

< 3.5e-6 %

* %-error: cross-section area average related to max. value

*

0v

2D-1D coupling: interface model “Flux”


3D-1D coupling of CFD solvers for cavitating flows


b) 2D reference solution: 2D pressure wave ( )0v


area average



c) 2D reference solution: 2D pressure waves ( )0v

t1



2D simulation

t2t3t4x

y

1D

so

lver

1D

so

lver

1D

so

lver



c) Flux: 2D pressure waves ( )t4

>0

mass error2D – 2D-1D Flux:

<1.0e-4 %

%-error: cross-section area average related to max. value

<4.5%

<2.5%

0v

20

p=const. or p(t)



Flux: cavitating hydraulic system (2D)

BC 1 =const. or m

)t(m

BC 2

no reflection at coupling interface

2D-1D coupling: Flux

2D simulation (longer channel)

1D solver

2D solver


4. Summary and Outlook 3D-1D coupling of CFD solvers

Aim: 3D-1D coupling interface models for compressible CFD solvers

Result: Interface models to couple compressible 2D and 1D CFD solvers:

PVar Flux

Summary

2D-1D interface

y

x

1D

so

lver

pre

ssur

e

y

x

1D

so

lver

2D-1D interface

22

computing time



Summary: 3D-1D simulation for hydraulic systems

3D simulation

m

cavitation

1D simulation3D-1D

simulationBC 1 BC 2

23

computing time



Outlook: 3D-1D simulation for complete hydraulic systems

3D simulation

m

cavitation

1D simulation

3D-1D simulation


3D-1D coupling of

compressible density-based CFD solvers

for cavitating flows

Martina Friedrich, Uwe Iben, Henning Kreschel (Robert Bosch GmbH), Romuald Skoda (Ruhr University Bochum), Claus-Dieter Munz (University of Stuttgart)

August 13th-16th 2012: 8th International Symposium on CavitationAbstract No. 28

1 ds-pc/eip5, friedrich | 13-16/08/2012 | © robert bosch gmbh 2012. all rights reserved, also...

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