TABLE OF CONTENTS To determine the temperature rise of an existing compressor stage, one must relate the flow Mach numbers and angles contained in equation 5.10 to the geometry, the rotative speed, and any other relevant characteristics of the machine. The problem of turbomachine fluid mechanics posed in this way is called the direct problem. It can also be posed in the opposite sense: Given the desired flow angles and Mach numbers, determine the required geometry. This is called the inverse problem, and it is the problem faced in design. In this discussion the inverse problem will be considered in the main, because it is the most convenient vehicle for exhibiting the limitations and design compromises that lead to the prominent characteristics of turbomachinery. The direct problem will be discussed in a qualitative way to bring out the main features of off-design behavior.
The inverse problem (also called the design problem) is conventionally divided into two parts. One imagines first an axisymmetric (no variation in the tangential direction) "throughflow" with axial, tangential, and radial components of velocity; all of these can change discontinuously (or, in more refined analyses, gradually) at axial locations corresponding to the blade rows. In the limit of sudden changes, the blade rows are considered thin "actuator discs" which change the momentum and energy of the fluid, but the variations from blade to blade in the tangential direction are neglected. The throughflow is, to a certain approximation, determined by the...
