10.2 Corrected Flow Per Unit Area

Appreciation for the overall response of a compressible flow to alterations in area, and addition of mass, momentum, and energy can be gained through consideration of the corrected flow per unit area introduced in Section 2.5. For a perfect gas with constant specific heats it was shown that the quantity is a function of Mach number only, denoted as D( M):

The functional dependence is depicted in Figure 2.6, with D( M) increasing from zero at M = 0 to a maximum at M = 1 and then decreasing at higher Mach numbers. For a specified fluid, with constant values of R and ?, the Mach number in a channel is a function of , where T _t and p _t are the local values of the stagnation temperature and pressure. ^[1]

We describe compressible flow behavior in two steps: (i) computation of the change in corrected flow per unit area, and hence Mach number, resulting from geometry variation and addition of mass, momentum, and energy, and then (ii) linkage of the changes to specific physical processes. We thus consider the corrected flow per unit area in a channel with Mach number, M _i, at an initial station i, and determine the changes between this and a downstream station if the area, mass flow, stagnation temperature, and stagnation pressure are altered from A, , T _t , p _t to (