Computation of unsteady flow in turbomachinery

Abstract

Unsteady flow analysis has been gradually introduced in turbomachinery design systems to improve machine performance and structural integrity. A project on computation of unsteady flows in turbomachinery has been carried out. A quasi 3-D time-linearized Euler/Navier-Stokes method has been developed for unsteady flows induced by the blade oscillation and unsteady incoming wakes, hi this method, the unsteady flow is decomposed into a steady flow plus a harmonically varying unsteady perturbation. The coefficients of the linear perturbation equation are formed from steady flow solutions. A pseudo-time is introduced to make both the steady flow equation and the linear unsteady perturbation equation time-independent. The 4-stage Runge-Kutta time-marching scheme is implemented for the temporal integration and a cell-vertex scheme is used for the spatial discretization. A 1-D/2-D nonreflecting boundary condition is applied to prevent spurious reflections of outgoing waves when solving the perturbation equations. The viscosity in the unsteady Navier- Stokes perturbation equation is frozen to its steady value. The present time-linearized Euler/Navier-Stokes method has been extensively validated against other well- developed linear methods, nonlinear time-marching methods and experimental data. Based upon the time-linearized method, a novel quasi 3-D nonlinear harmonic Euler/Navier-Stokes method has been developed. In this method, the unsteady flow is divided into a time-averaged flow plus an unsteady perturbation. Time-averaging produces extra nonlinear "unsteady stress" terras in the time-averaged equations and these extra terras are evaluated from unsteady perturbations. Unsteady perturbations are obtained by solving a first order harraonic perturbation equation, while the coefficients of the perturbation equation are forraed from time-averaged solutions. A strong coupling procedure is applied to solve the time-averaged equation and the unsteady perturbation equation simultaneously in a pseudo-time domain. An approximate approach is used to linearize the pressure sensors in artificial smoothing