TY - JOUR

T1 - Semianalytical solution of unsteady quasi-one-dimensional cavitating nozzle flows

AU - Delale, Can F.

AU - Pasinlioğlu, Şenay

AU - Başkaya, Zafer

AU - Schnerr, Günter H.

N1 - Funding Information:
Acknowledgments This work was supported in part by TÜB˙TAK under Project 105M035 and in part by Deutsche Forschungs Gemeinschaft (DFG) under Contract SCHN 352/24-1.

PY - 2014/6

Y1 - 2014/6

N2 - Unsteady quasi-one-dimensional bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh-Plesset equation. The model equations are uncoupled by scale separation leading to two evolution equations, one for the flow speed and the other for the bubble radius. The initial-boundary value problem of the evolution equations is then formulated and a semianalytical solution is constructed. The solution for the mixture pressure, the mixture density, and the void fraction are then explicitly related to the solution of the evolution equations. In particular, a relation independent of flow dimensionality is established between the mixture pressure, the void fraction, and the flow dilation for unsteady bubbly cavitating flows in the model considered. The steady-state compressible and incompressible limits of the solution are also discussed. The solution algorithm is first validated against the numerical solution of Preston et al. [Phys Fluids 14:300-311, 2002] for an essentially quasi-one-dimensional nozzle. Results obtained for a two-dimensional nozzle seem to be in good agreement with the mean pressure measurements at the nozzle wall for attached cavitation sheets despite the observed two-dimensional cavitation structures.

AB - Unsteady quasi-one-dimensional bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh-Plesset equation. The model equations are uncoupled by scale separation leading to two evolution equations, one for the flow speed and the other for the bubble radius. The initial-boundary value problem of the evolution equations is then formulated and a semianalytical solution is constructed. The solution for the mixture pressure, the mixture density, and the void fraction are then explicitly related to the solution of the evolution equations. In particular, a relation independent of flow dimensionality is established between the mixture pressure, the void fraction, and the flow dilation for unsteady bubbly cavitating flows in the model considered. The steady-state compressible and incompressible limits of the solution are also discussed. The solution algorithm is first validated against the numerical solution of Preston et al. [Phys Fluids 14:300-311, 2002] for an essentially quasi-one-dimensional nozzle. Results obtained for a two-dimensional nozzle seem to be in good agreement with the mean pressure measurements at the nozzle wall for attached cavitation sheets despite the observed two-dimensional cavitation structures.

KW - Evolution equations

KW - Nonlinear bubble dynamics

KW - Quasi-one-dimensional nozzle flows

KW - Unsteady cavitating flows

UR - http://www.scopus.com/inward/record.url?scp=84899993270&partnerID=8YFLogxK

U2 - 10.1007/s10665-013-9645-6

DO - 10.1007/s10665-013-9645-6

M3 - Article

AN - SCOPUS:84899993270

SN - 0022-0833

VL - 86

SP - 49

EP - 70

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

IS - 1

ER -