14 Time-Marching Analysis of the Blade-to-Blade Plane Flow

Chapters 12 and 13 have reviewed methods, to predict flow in the blade-to-blade plane, that are suitable for subsonic and slightly supersonic flows. While this covers many centrifugal compressor analysis problems, the design of high pressure ratio compressors can involve a substantial supersonic flow character, beyond the capability of those potential flow methods. A modern design and analysis system should include an analysis capable of considering any Mach number level. The potential flow methods presented in Chapters 12 and 13 are suitable for solving subsonic flow problems where the governing equations are elliptic in mathematical form. There, the flow analysis involves solving a classical boundary value problem. For supersonic flow, the time-steady equations of fluid dynamics become hyperbolic in form. In this case, the solution procedure required is some type of marching solution, such as the method of characteristics. With mixed subsonic-supersonic flow, the problem is highly complex, requiring two types of solution procedures to be matched to each other in some fashion.