Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

236 Fluid Mechanics, Thermodynamics of Turbomachinery
at 15,000rev/min. The stagnation pressure ratio between diffuser outlet and impeller
inlet is 4.2 and the overall efficiency (total-to-total) is 83%. Determine the impeller tip
radius and power required to drive the compressor when the mass flow rate is 2kg/s
and the mechanical efficiency is 97%. Given that the air density at impeller outlet is
2kg/m 3 and the axial width at entrance to the diffuser is 11mm, determine the absolute
Mach number at that point. Assume that the slip factor ss = 1 - 2/Z, where Z is the
number of vanes.
(For air take g = 1.4 and R = 0.287kJ/(kg K).)
Solution. From eqn. (7.3a) the specific work is
since cq1 = 0. Combining eqns. (7.20) and (7.21) with the above and rearranging gives
where r = p03/p01 = 4.2; Cp = gR/(g - 1) = 1.005kJ/kg K,ss = 1 - 2/17 = 0.8824.
0. 286
2 1005 ¥ 295 4. 2 -1
Therefore U2 =
0. 8824 ¥ 0. 83
Therefore U2 = 452m/s.
The rotational speed is
Thus, the impeller tip radius is
The actual shaft power is obtained from
Although the absolute Mach number at the impeller tip can be obtained almost directly
from eqn. (7.28) it may be instructive to find it from
where
Therefore
Since
( )
= 20 5 ¥ 10
4
. .