Computation of Shocked Flows in Compressor Cascades

Abstract

A numerical technique is presented for the calculation of shocked flows in compressor cascades. The problem is posed in the time-dependent form and the asymptotic solution at large times provides the solution of the steady physical problem. The solutions exhibit the formation and movement of shocks as the static pressure ratio across the cascade is varied. The resulting inlet and outlet angles and total pressure loss are also shown.

Three-Dimensional Shock Structures for Transonic/Supersonic Compressor Rotors

“…4 Over a period of years this author has been collecting experience to show that the typical shock wave orientation at the leading edges of supersonic compressor rotor tips, with relative upstream Mach numbers in the range 1.4-1. 8, is not at Presented as Paper 79-0043 at the 17th Aerospace Sciences Meeting, New Orleans, La., Jan. [15][16][17]1979; submitted Feb. 13,1979 40-45 deg from the pressure surface, as would be predicted from conventional two-dimensional supersonic flow analysis, but rather is in the 60-70 deg range, corresponding roughly to maximum theoretical stream deflection and near-sonic downstream Mach number. Apparently, it is coincidental that this wave orientation usually appears to be perpendicular to the line through airfoil leading edges, within measurement resolution.…”

Review—Computational Methods for Internal Flows With Emphasis on Turbomachinery

“…The ease with which this method can be applied has led to many applications in the turbomachinery field. An early application of the MacCormack scheme by Gopalakrishnan and Bozzola [72] was for a transonic compressor cascade with supersonic inlet and subsonic outlet. Kurzrock and Novick [73] have applied this scheme to a rotating blade-to-blade stream surface, with radius change and stream channel convergence.…”

Time-Marching Analysis of Steady Transonic Flow in Turbomachinery Cascades Using the Hopscotch Method

“…However, as Steger( 2 ) and Hindman ( 19 ) note, certain requirements must be met when forming these derivatives in order to minimize geometrically induced errors. The first requirement is to satisfy the grid conservation law which states that the differencing procedure (backward, forward, or centered) used to form the derivatives must be identical to that used to approximate the spatial derivatives in the governing system of equations, equation (6). It is a simple matter to show that if this requirement is not met for the case of uniform flow, the solution algorithm will not reproduce the known uniform conditions.…”