On the temporal stability of steady-state quasi-1D bubbly cavitating nozzle flow solutions

Quasi-1D unsteady bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the non-linear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation. The various damping mechanisms are considered by a single damping coefficient...

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Bibliographic Details
Published in:IMA journal of applied mathematics 2009-04, Vol.74 (2), p.230-249
Main Authors: Pasinlio lu, enay, Delale, Can F., Schnerr, Günter H.
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
bubbly cavitating flows
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations
Sciences and techniques of general use
steady-state solutions
temporal stability
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:Quasi-1D unsteady bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the non-linear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation. The various damping mechanisms are considered by a single damping coefficient lumping them together in the form of viscous dissipation and by assuming a polytropic law for the expansion and compression of the gas. The complete system of equations, by appropriate uncoupling, are then reduced to two evolution equations, one for the flow speed and the other for the bubble radius when all damping mechanisms are considered by a single damping coefficient. The evolution equations for the bubble radius and flow speed are then perturbed with respect to flow unsteadiness resulting in a coupled system of linear partial differential equations (PDEs) for the radius and flow speed perturbations. This system of coupled linear PDEs is then cast into an eigenvalue problem and the exact solution of the eigenvalue problem is found by normal mode analysis in the inlet region of the nozzle. Results show that the steady-state cavitating nozzle flow solutions are stable only for perturbations with very small wave numbers. The stable regions of the stability diagram for the inlet region of the nozzle are seen to be broadened by the effect of turbulent wall shear stress.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxn036