Kc. Hall et Cb. Lorence, CALCULATION OF 3-DIMENSIONAL UNSTEADY FLOWS IN TURBOMACHINERY USING THE LINEARIZED HARMONIC EULER EQUATIONS, Journal of turbomachinery, 115(4), 1993, pp. 800-809
An efficient three-dimensional Euler analysis of unsteady flows in tur
bomachinery is presented. The unsteady flow is modeled as the sum of a
steady or mean flow field plus a harmonically varying small perturbat
ion flow. The linearized Euler equations, which describe the small per
turbation unsteady flow, are found to be linear, variable coefficient
differential equations whose coefficients depend on the mean flow. A p
seudo-time time-marching finite-volume Lax- Wendroff scheme is used to
discretize and solve the linearized equations for the unknown perturb
ation flow quantities. Local time stepping and multiple-grid accelerat
ion techniques are used to speed convergence. For unsteady flow proble
ms involving blade motion, a harmonically deforming computational grid
, which conforms to the motion of the vibrating blades, is used to eli
minate large error-producing extrapolation terms that would otherwise
appear in the airfoil surface boundary conditions and in the evaluatio
n of the unsteady surface pressure. Results are presented for both lin
ear and annular cascade geometries, and for the latter, both rotating
and nonrotating blade rows.