One of the early space power systems built and tested for NASA was based on the Brayton cycle and incorporated an IFR turbine as the gas expander. Some of the data available concerning the turbine are as follows: Total-to-total pressure ratio (turbine inlet to turbine exit), p01/p03 ¼1.560; Total-to-static pressure ratio, p01/p3 ¼1.613; Total temperature at turbine entry, T01 ¼1083K; Total pressure at inlet to turbine, T01 ¼91kPa; Shaft power output (measured on a dynamometer), Pnet ¼22.03kW; Bearing and seal friction torque (a separate test), tf ¼0.0794Nm;300 CHAPTER 8 Radial Flow Gas TurbinesRotor diameter, D2 ¼15.29cm; Absolute flow angle at rotor inlet, a2 ¼72°; Absolute flow angle at rotor exit, a3 ¼0°; The hub to shroud radius ratio at rotor exit, r3h/r3s ¼ 0.35; Ratio of blade speed to jet speed, ?¼U2/c0 ¼0.6958; (c0 based on total-to-static pressure ratio.) For reasons of crew safety, an inert gas argon (R ¼208.2 J/(kgK), ratio of specific heats, ?¼1.667) was used in the cycle. The turbine design scheme was based on the concept of optimum efficiency.

Determine, for the design point

(i) the rotor vane tip speed;

(ii) the static pressure and temperature at rotor exit;

(iii) the gas exit velocity and mass flow rate;

(iv) the shroud radius at rotor exit;

(v) the relative flow angle at rotor inlet;

(vi) the specific speed. Note: The volume flow rate to be used in the definition of the specific speed is based on the rotor exit conditions.