Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

256 Fluid Mechanics, Thermodynamics of Turbomachinery
It is worth commenting that higher total-to-static efficiencies have been obtained
in other small radial turbines operating at higher pressure ratios. Rodgers (1969) has
suggested that total-to-static efficiencies in excess of 90% for pressure ratios up to
five to one can be attained. Nusbaum and Kofskey (1969) reported an experimental
value of 88.8% for a small radial turbine (fitted with an outlet diffuser, admittedly!)
at a pressure ratio p01/p4 of 1.763. In the design point exercise given above the high
rotor enthalpy loss coefficient and the corresponding relatively low total-to-static efficiency
may well be related to the low relative velocity ratio determined on the hub.
Matters are probably worse than this as the calculation is based only on a simple onedimensional
treatment. In determining velocity ratios across the rotor, account should
also be taken of the effect of blade to blade velocity variation (outlined in this chapter)
as well as viscous effects. The number of vanes in the rotor (ten) may be insufficient
on the basis of Jamieson’s theory* (1955) which suggests 18 vanes (i.e. Zmin = 2ptan
a2). For this turbine, at lower nozzle exit angles, eqn. (8.13) suggests that the relative
velocity ratio becomes even less favourable despite the fact that the Jamieson blade
spacing criterion is being approached. (For Z = 10, the optimum value of a2 is about
58deg.)
Mach number relations
Assuming the fluid is a perfect gas, expressions can be deduced for the important
Mach numbers in the turbine. At nozzle outlet the absolute Mach number at the nominal
design point is
1
Now, T = T - c ( 2C
)= T - U cosec C .
2 a
2 01 2 2
where a2 = a 01(T 2/T 01) 1/2 . Hence,
p 01 2 2 p
2
2
At rotor outlet the relative Mach number at the design point is defined by
*Included in a later part of this chapter.
(8.14)