Prediction of unsteady flows in turbomachinery using the linearized Euler equations on deforming grids
Abstract
A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. The model accounts for blade loading, blade geometry, shock motion, and wake motion. Assuming that the unsteadiness in the flow is small relative to the nonlinear mean solution, the unsteady Euler equations can be linearized about the mean flow. This yields a set of linear variable coefficient equations that describe the small amplitude harmonic motion of the fluid. These linear equations are then discretized on a computational grid and solved using standard numerical techniques. For transonic flows, however, one must use a linear discretization which is a conservative linearization of the nonlinear discretized Euler equations to ensure that shock impulse loads are accurately captured. Other important features of this analysis include a continuously deforming grid which eliminates extrapolation errors and hence, increases accuracy, and a new numerically exact, nonreflecting farfield boundary condition treatment based on an eigenanalysis of the discretized equations. Computational results are presented which demonstrate the computational accuracy and efficiency of the method and demonstrate the effectiveness of the deforming grid, farfield nonreflecting boundary conditions, and shock capturing techniques. A comparison of the present unsteady flow predictions to other numerical, semianalytical, and experimental methods shows excellent agreement. In addition, the linearized Euler method presented requires one to two ordersofmagnitude less computational time than traditional timemarching techniques making the present method a viable design tool for aeroelastic analyses.
 Publication:

Final Technical Report Duke Univ
 Pub Date:
 April 1993
 Bibcode:
 1993duke.reptR....C
 Keywords:

 Computational Fluid Dynamics;
 Computational Grids;
 Linearization;
 Transonic Flow;
 Turbomachine Blades;
 Unsteady Flow;
 Aeroelasticity;
 Boundary Conditions;
 Euler Equations Of Motion;
 Far Fields;
 Flow Distribution;
 Nonlinear Equations;
 Fluid Mechanics and Heat Transfer