Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

where
In the above example, 1 - a/W = 1 – 2 , yt = 0.18
The true reaction variation is shown in Figure 6.5 and it is evident that eqn. (6.17) is
invalid as a result of the axial velocity changes.
The direct problem
The flow angle variation is specified in the direct problem and the radial equilibrium
equation enables the solution of cx and cq to be found. The general radial equilibrium
equation can be written in the form
as cq = csina.
If both dh0/dr and ds/dr are zero, eqn. (6.20) integrated gives
or, if c = cm at r = rm, then
Three-dimensional Flows in Axial Turbomachines 187
If the flow angle a is held constant, eqn. (6.21) simplifies still further,
(6.20)
(6.21)
(6.22)
The vortex distribution represented by eqn. (6.22) is frequently employed in practice
as untwisted blades are relatively simple to manufacture.
The general solution of eqn. (6.20) can be found by introducing a suitable integrating
factor into the equation. Multiplying throughout by exp[2 Úsin 2 adr/r] it follows
that