TY - CHAP

T1 - Shocks in quasi-one-dimensional bubbly cavitating nozzle flows

AU - Delale, Can F.

AU - Schnerr, Günter H.

AU - Pasinlioğlu, Şenay

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2013.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Stationary and propagating shock waves in bubbly cavitating flows through quasi-one-dimensional converging-diverging nozzles 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 semi-analytical 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. The steady-state compressible limit of the solution with stationary shocks is obtained and the stability of such shocks are examined. Finally, results obtained using the semi-analytical constructed algorithm for propagating shock waves in bubbly cavitating flows through converging-diverging nozzles, which agree with those of previous numerical investigations, are presented.

AB - Stationary and propagating shock waves in bubbly cavitating flows through quasi-one-dimensional converging-diverging nozzles 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 semi-analytical 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. The steady-state compressible limit of the solution with stationary shocks is obtained and the stability of such shocks are examined. Finally, results obtained using the semi-analytical constructed algorithm for propagating shock waves in bubbly cavitating flows through converging-diverging nozzles, which agree with those of previous numerical investigations, are presented.

UR - http://www.scopus.com/inward/record.url?scp=85031020067&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-34297-4_7

DO - 10.1007/978-3-642-34297-4_7

M3 - Chapter

AN - SCOPUS:85031020067

SN - 9783642342967

SP - 205

EP - 234

BT - Bubble Dynamics and Shock Waves

PB - Springer Berlin Heidelberg

ER -