Abstract
The present paper describes the starting efforts made for constructing a numerical frame aimed at simulating propellant flows occurring in the feed turbopumps of modern liquid propellant rocket engines. A homogeneous-flow cavitation model, accounting for thermal effects and active nuclei concentration, is considered, which leads to a barotropic state law. The 3D continuity and momentum equations for compressible inviscid flows are discretized by a finite-volume approach, applicable to unstructured grids. The numerical fluxes are computed through a shock-capturing Roe-type upwind scheme, defined for barotropic flows. The accuracy of the proposed method at low Mach numbers is ensured by ad-hoc preconditioning, which only modifies the upwind part of the numerical flux; thus, the time consistency is maintained and the proposed method can also be used for unsteady problems. Time advancing is carried out by an implicit linearized scheme, in which the linearization only exploits the properties of the Roe matrix. Examples of applications are provided for flow configurations of increasing geometric complexity, viz. some 1D validation benchmarks, the flow around a hydrofoil mounted in a tunnel and the flow in a turbo-pump inducer.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
T. Barberon and P. Helluy. Finite volume simulation of cavitating flows. Computers & Fluids, 34:832–858, 2005.
F. Beux, M.-V. Salvetti, A. Ignatyev, D. Li, C. Merkle, and E. Sinibaldi. A numerical study of non-cavitating and cavitating liquid flow around a hydrofoil. Mathematical Modelling and Numerical Analysis, 39(3):577–590, 2005.
M. Bilanceri. Studio dell’effetto della legge di stato nella simulazione di un flusso cavitante barotropico. Bsc Thesis in Aerospace Engineering, University of Pisa, Pisa (Italy), a.a. 2005, 2005.
C. E. Brennen. Hydrodynamics of Pumps. Concepts ETI Inc. and Oxford University Press, 1994.
A. Cervone, L. Torre, C. Bramanti, E. Rapposelli, and L. d’Agostino. Experimental characterization of the cavitation instabilities in the AVIO FAST2 inducer. In Proc. 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Tucson (Arizona, USA), July 2005.
A. Cervone, C. Bramanti, E. Rapposelli, and L. d’Agostino. Thermal cavitation experiments on a naca 0015 hydrofoil. Journal of Fluids Engineering, Transactions of the ASME, 128(2):326–331, 2006.
C.H. Choi, S.-S. Hong, B.J. Cha, and S. Yang. Study on the hydraulic performance of a turbopump inducer. In Proc. ASME FEDSM’03-4th ASME/JSME Joint Fluids Engineering Conference, Honolulu (Hawaii, USA), July 2003.
O. Coutier-Delgosha and J.A. Astolfi. Numerical prediction of the cavitating flow on a two-dimensional symmetrical hydrofoil with a single fluid model. In Proc. CAV2003-Fifth International Symposium on Cavitation, Osaka (Japan), November 2003.
O. Coutier-Delgosha, J-L. Reboud, and R. Fortes-Patella. Numerical study of the effect of the leading edge shape on cavitation around inducer blade sections. In Proc. CAV2001-Fourth International Symposium on Cavitation, Pasadena (California, USA), June 2001.
O. Coutier-Delgosha, R. Fortes-Patella, J-L. Reboud, N. Hakimi, and C. Hirsch. Stability of preconditioned Navier-Stokes equations associated with a cavitation model. Computers & Fluids, 34:319–349, 2005a.
O. Coutier-Delgosha, R. Fortes-Patella, J. L. Reboud, N. Hakimi, and C. Hirsch. Numerical simulation of cavitating flow in 2D and 3D inducer geometries. International Journal for Numerical Methods in Fluids, 48:135–167, 2005b.
O. Coutier-Delgosha, P. Morel, R. Fortes-Patella, and J. L. Reboud. Numerical simulation of turbopump inducer cavitating behavior. International Journal of Rotating Machinery, 2:135–142, 2005c.
L. d’Agostino and E. Rapposelli. A modified bubbly isenthalpic model for numerical simulation of cavitating flows. AIAA paper 2001-3402, 2001.
C. Farhat, B. Koobus, and H. Tran. Simulation of vortex shedding dominated flows past rigid and flexible structures. In Computational Methods for Fluid-Structure Interaction, pages 1–30. Tapir, 1999.
L. Fezoui and B. Stoufflet. A class of implicit upwind schemes for Euler simulations with unstructured meshes. Journal of Computational Physics, 84:174–206, 1989.
H. Guillard and C. Viozat. On the behaviour of upwind schemes in the low Mach number limit. Computers & Fluids, 28:63–86, 1999.
H.W.M. Hoeijmakers, M.E. Janssens, and W. Kwan. Numerical simulation of sheet cavitation. In Proc. Third International Symposium on Cavitation, Grenoble (France), April 1998.
A. Hosangadi, V. Ahuja, and R.J. Ungewitter. Simulations of cavitating flows in turbopumps. AIAA paper 2003-1261, 2003.
A. Hosangadi, V. Ahuja, and R.J. Ungewitter. Simulations of cavitating cryogenic inducers. AIAA paper 2004-4023, 2004.
M. Ishii. Thermo-fluid Dynamic Theory of Two-Phase Flow. Eyrolles, 1975.
M.E. Janssens, S.J. Hulshoff, and H.W.M. Hoeijmakers. Calculation of unsteady attached cavitation. AIAA paper 97-1936, 1997.
K.C. Karki and S.V. Patankar. Pressure based calculation procedure for viscous flows at all speed in arbitrary configurations. AIAA Journal, 27(9):1167–1174, 1989.
R. F. Kunz, D. A. Boger, D. R. Stinebring, T. S. Chyczewski, J. W. Lindau, H. J. Gibeling, S. Venkateswaran, and T. R. Govindan. A preconditioned Navier-Stokes method for two-phase flows application to cavitation prediction. Computers & Fluids, 29:849–875, 2000.
J.J. Mc-Guirck and Page G.J. Shock-capturing using a pressure correction method. AIAA Journal, 28(10):1751–1757, 1990.
C. L. Merkle, J. Feng, and P. E. O. Buelow. Computational modeling of the dynamics of sheet cavitation. In Proc. Third International Symposium on Cavitation, Grenoble (France), April 1998.
B. Pouffary, R. Fortes-Patella, and J-L Reboud. Numerical simulation of cavitating flow around a 2D hydrofoil: a barotropic approach. In Proc. CAV2003-Fifth International Symposium on Cavitation, Osaka (Japan), November 2003.
Q. Qin, C. C. S. Song, and R.E.A. Arndt. A virtual single-phase natural cavitation model and its application to CAV2003 hydrofoil. In Proc. CAV2003-Fifth International Symposium on Cavitation, Osaka (Japan), November 2003.
J-L. Reboud, B. Stutz, and O. Coutier. Two-phase flow structure of cavitation: experiment and modelling of unsteady effects. In Proc. Third International Symposium on Cavitation, Grenoble (France), April 1998.
P. L. Roe. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics, 43:357–372, 1981.
Y. Saito, I. Nakamori, and T. Ikohagi. Numerical analysis of unsteady vaporous cavitating flow around a hydrofoil. In Proc. CAV2003-Fifth International Symposium on Cavitation, Osaka (Japan), November 2003.
I. Senocak and W. Shyy. A pressure-based method for turbolent cavitating flow computations. Journal of Computational Physics, 176:363–383, 2002.
W. Shyy, J. Wu, and Y. Utturkar. Computational modeling of cavitation for liquid rocket applications. AIAA paper 2004-3985, 2004.
E Sinibaldi. Implicit preconditioned numerical schemes for the simulation of three-dimensional barotropic flows. Edizioni della Normale, 2007. In Press.
E. Sinibaldi, F. Beux, and M.V. Salvetti. A preconditioned implicit Roe scheme for barotropic flows: towards simulation of cavitation phenomena. Rapport de recherche 4891, INRIA, 2003.
E. Sinibaldi, F. Beux, and M.V. Salvetti. A preconditioned compressible flow solver for numerical simulation of 3D cavitation phenomena. In Proc. ECCOMAS2004, Jyväskylä (Finland), July 2004.
C. C. S. Song and J. He. Numerical simulation of cavitating flows by single-phase flow approach. In Proc. Third International Symposium on Cavitation, Grenoble (France), April 1998.
E. F. Toro. Riemann solvers and numerical methods for fluid dynamics. Springer, 1997.
E. Turkel. Preconditioned methods for solving the incompressible and low speed compressible equations. Journal of Computational Physics, 72:277–298, 1987.
E. Turkel, A. Fiterman, and B. van Leer. Frontiers of Computational Fluid Dynamics, chapter Preconditioning and the limit of the compressible to the incompressible flow equations for finite difference schemes., pages 215–234. Chichester, Wiley, 1994.
D. R. van der Heul, C. Vuik, and P. Wesseling. A staggered scheme for hyperbolic conservation laws applied to unsteady sheet cavitation. Computing and Visualization in Science, 2:63–68, 1999.
D. R. van der Heul, C. Vuik, and P. Wesseling. Efficient computation of flow with cavitation by compressible pressure correction. In Proc. ECCOMAS 2000, Barcelona (Spain), September 2000.
C. Viozat. Implicit upwind schemes for low mach number compressible flows. Technical Report RR-3084, INRIA, 1997.
J. Wu, Y. Utturkar, and W. Shyy. Assessment of modeling strategies for cavitating flow around a hydrofoil. In Proc. CAV2003-Fifth International Symposium on Cavitation, Osaka (Japan), November 2003.
T. Y. Wu. Cavity and wake flows. Annual Review of Fluid Mechanics, 3:243–284, 1972.
H. Yamada, S. Hasegawa, M. Watanabe, T. Hashimoto, T. Kimura, J. Takita, and I. Kubota. Observation of the inner flow in the inducer. In Proc. 9th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu (Hawaii, USA), February 2002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 CISM, Udine
About this chapter
Cite this chapter
Salvetti, MV., Sinibaldi, E., Beux, F. (2007). Towards the simulation of cavitating flows in inducers through a homogeneous barotropic flow model. In: d’Agostino, L., Salvetti, M.V. (eds) Fluid Dynamics of Cavitation and Cavitating Turbopumps. CISM International Centre for Mechanical Sciences, vol 496. Springer, Vienna. https://doi.org/10.1007/978-3-211-76669-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-211-76669-9_9
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-76668-2
Online ISBN: 978-3-211-76669-9
eBook Packages: EngineeringEngineering (R0)