Calculation of Three-Dimensional Unsteady Flows in Turbomachinery Using the Linearized Harmonic Euler Equations

[+] Author and Article Information
K. C. Hall, C. B. Lorence

Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708

J. Turbomach 115(4), 800-809 (Oct 01, 1993) (10 pages) doi:10.1115/1.2929318 History: Received February 11, 1992; Online June 09, 2008


An efficient three-dimensional Euler analysis of unsteady flows in turbomachinery is presented. The unsteady flow is modeled as the sum of a steady or mean flow field plus a harmonically varying small perturbation flow. The linearized Euler equations, which describe the small perturbation unsteady flow, are found to be linear, variable coefficient differential equations whose coefficients depend on the mean flow. A pseudo-time time-marching finite-volume Lax-Wendroff scheme is used to discretize and solve the linearized equations for the unknown perturbation flow quantities. Local time stepping and multiple-grid acceleration techniques are used to speed convergence. For unsteady flow problems involving blade motion, a harmonically deforming computational grid, which conforms to the motion of the vibrating blades, is used to eliminate large error-producing extrapolation terms that would otherwise appear in the airfoil surface boundary conditions and in the evaluation of the unsteady surface pressure. Results are presented for both linear and annular cascade geometries, and for the latter, both rotating and nonrotating blade rows.

Copyright © 1993 by The American Society of Mechanical Engineers
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