### Abstract

Original language | English |
---|---|

Pages (from-to) | 230-249 |

Journal | IMA journal of applied mathematics |

Volume | 74 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 |

### Fingerprint

### Keywords

- IR-86553
- temporal stability
- steady-state solutions
- Bubbly cavitating flows
- METIS-245248

### Cite this

*IMA journal of applied mathematics*,

*74*(2), 230-249. https://doi.org/10.1093/imamat/hxn036

}

*IMA journal of applied mathematics*, vol. 74, no. 2, pp. 230-249. https://doi.org/10.1093/imamat/hxn036

**On the temporal stability of steady-state quasi-1D bubbly cavitating nozzle flow solutions.** / Pasinlioglu, S.; Delale, C.F.; Schnerr, Günter.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - On the temporal stability of steady-state quasi-1D bubbly cavitating nozzle flow solutions

AU - Pasinlioglu, S.

AU - Delale, C.F.

AU - Schnerr, Günter

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - IR-86553

KW - temporal stability

KW - steady-state solutions

KW - Bubbly cavitating flows

KW - METIS-245248

U2 - 10.1093/imamat/hxn036

DO - 10.1093/imamat/hxn036

M3 - Article

VL - 74

SP - 230

EP - 249

JO - IMA journal of applied mathematics

JF - IMA journal of applied mathematics

SN - 0272-4960

IS - 2

ER -