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A Numerical Method for 3D Barotropic Flows in Turbomachinery

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'Compressible' method suitably preconditioned to deal with the liquid, nearly ... The preconditioned scheme requires a smaller time-step to remain stable: the ... – PowerPoint PPT presentation

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Title: A Numerical Method for 3D Barotropic Flows in Turbomachinery


1
A Numerical Method for 3D Barotropic Flows in
Turbomachinery
Multiphase05, Porquerolles, April 2005
  • Towards Simulation of Cavitation

Edoardo Sinibaldi Scuola Normale Superiore di Pisa
François Beux Scuola Normale Superiore di Pisa
Maria Vittoria Salvetti Dip. Ing. Aerospaziale,
Università di Pisa
2
Research Framework (1)
3
Research Framework (2)
Development
4
Constitutive Law (1)
5
Constitutive Law (2)
EXAMPLE MIXTURE SOUND-SPEED CURVE FOR
WATER-VAPOUR AT T20C
6
Constitutive Law (3)
EXAMPLE BAROTROPIC CURVE FOR WATER-VAPOUR
MIXTURE AT T20C
7
Constitutive Law (detail)
8
Governing Equations (1)
9
Governing Equations (2)
10
Numerical Discretisation
OLD
NEW
11
Space Discretisation (1)
1D for simplicity
FINITE VOLUMES
12
Space Discretisation (2)
13
Space Discretisation (3)
LOW-MACH NUMBER ASYMPTOTIC STUDY (Guillard
Viozat, 1999 perfect gas state law)
same kind of result as for perfect gas!
14
Space Discretisation (4)
PRECONDITIONING for LOW-MACH NUMBERS
In conservative variables, for a generic
BAROTROPIC state law
15
Space Discretisation (5)
PRECONDITIONING for LOW-MACH NUMBERS
same kind of result as for perfect gas!
16
1D Validation (1)
17
1D Validation (2)
18
1D Validation (3)
19
1D Validation (4)
20
Time Discretisation (1)
21
Time Discretisation (2)
ON THE NUMERICAL FLUX LINEARISATION
22
1D Validation (5)
COMPLETE RESULTS
23
3D Numerical Discretisation (1)
24
3D Numerical Discretisation (2)
25
3D Numerical Discretisation (3)
26
3D Validation (1)
27
3D Validation (2)
3 SYMMETRICAL GRIDS
28
3D Validation (3)
29
3D Validation (4)
30
3D Validation (5)
TEMPORARY ACHIEVEMENTS
The PRECONDITIONING strategy effectively
counteracts the accuracy problem at low Mach
numbers. Preliminary numerical experiments
suggested the value k 1 for the calibration
parameter involved in the local preconditioning
ß2 k M2, thus confirming the theoretical
result. The LINEARISED IMPLICIT strategy well
extends to 3D indeed, for the non-cavitating
test-cases a CFL coefficient as high as 400 has
been exploited. When cavitation occurs, however,
a significant time-step reduction must be
accepted, as already suggested by the 1D
validation (efficiency problem)
31
3D Numerical Discretisation (4)
WELCOME TO THE ROTATING WORLD!
32
3D Validation (6)
33
3D Validation (7)
Details of the inducer geometry
34
3D Validation (8)
NUMERICAL RESULTS vs EXPERIMENTS
A cavitating simulation has been performed but,
due to the efficiency problem, it does not seem
to converge within reasonable cpu times (unless
very powerful supercomputing resources are
available)
35
3D Validation (9)
NUMERICAL RESULTS
36
Conclusions and Perspectives
Method robust and quite accurate (1st order) for
non-cavitating flows. The accuracy has been
increased to second order (MUSCL Defect
Correction) for the 1D scheme application to the
1D shallow-water eqns (Sinibaldi Beux, SIMAI,
Venezia, 2004)
  • For cavitating flows the efficiency problem must
    be addressed. To the purpose
  • investigation of smoother barotropic laws the
    one used is significantly stiffer than other
    common models! (ongoing)
  • investigation of the entropic character of the
    scheme (state law) at phase transition
    comparison with the exact solution to a 1D
    Riemann problem for generic barotropic state laws
    (ongoing)
  • mixture fractions transport, relaxation of the
    density?

As for physical modelling inclusion of the
effects of viscosity and turbulence
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