Design Method for Subsonic and Transonic Cascade With Prescribed Mach Number Distribution

Abstract

An iterative procedure for blade design, using a Time Marching procedure to solve the unsteady Euler equations in the blade-to-blade plane is presented. A flow solver, which performs the analysis of the flow field for a given geometry, is transformed into a design method. This is done by replacing the classical slip condition (no normal velocity component) by other boundary conditions, in such a way that the required pressure or Mach number distribution may be imposed directly on the blade. The unknowns are calculated on the blade wall using the so-called compatibility relations. Since the blade shape is not compatible with the required pressure distribution, a non-zero velocity component normal to the blade wall evolves from the new flow calculation. The blade geometry is then modified by resetting the wall parallel to the new flow field, using a transpiration technique, and the procedure is repeated until the calculated pressure distribution has converged to the required one. Examples for both subsonic and transonic flows are presented and show a rapid convergence to the geometry required for the desired Mach number distribution. An important advantage of the present method is the possibility to use the same code for the design and the analysis of a blade.