Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

218 Fluid Mechanics, Thermodynamics of Turbomachinery
Thus,
where
The absolute Mach number M1 and the relative Mach number M r1 are defined as
Using these relations together with eqn. (7.10)
Since and a01 = (gRT01) 1/2 1
2
12
a01 a1= 1+ ( g -1)
M
2
1 the above equation is rearranged
to give
(7.11)
This equation is extremely useful and can be used in a number of different ways. For
a particular gas and known inlet conditions one can specify values of g, R, p01 and T 01
and obtain m . W 2 /k as a function of Mr1 and bs1. By specifying a particular value of Mr1
as a limit, the optimum value of bs1 for maximum mass flow can be found. A graphical
procedure is the simplest method of optimising bs1 as illustrated below.
Taking as an example air, with g = 1.4, eqn. (7.11) becomes
(7.11a)
The right-hand side of eqn. (7.11a) is plotted in Figure 7.4 as a function of bs1 for
Mr1 = 0.8 and 0.9. These curves are a maximum at b s1 = 60deg (approximately).
Shepherd (1956) considered a more general approach to the design of the compressor
inlet which included the effect of a free-vortex prewhirl or prerotation. The effect
of prewhirl on the mass flow function is easily determined as follows. From the velocity
triangles in Figure 7.5,
Also,
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