Page 293 - Fluid Mechanics and Thermodynamics of Turbomachinery

274 Fluid Mechanics, Thermodynamics of Turbomachinery
2. The mass flow rate of gas through the turbine given in Problem No. 1 is 3.1 kg/s, the
ratio of the rotor axial width/rotor tip radius (b 2 /r 2 ) is 0.1 and the nozzle isentropic velocity
ratio ( 2 ) is 0.96. Assuming that the space between nozzle exit and rotor entry is negligible
and ignoring the effects of blade blockage, determine:

(i) the static pressure and static temperature at nozzle exit;
(ii) the rotor tip diameter and rotational speed;
(iii) the power transmitted assuming a mechanical efficiency of 93.5%.
3. A radial turbine is proposed as the gas expansion element of a nuclear powered Brayton
cycle space power system. The pressure and temperature conditions through the stage at the
design point are to be as follows:
Upstream of nozzles, p 01 D 699 kPa,T 01 D 1, 145 K;
Nozzle exit, p 2 D 527.2 kPa,T 2 D 1, 029 K;
Rotor exit, p 3 D 384.7 kPa,T 3 D 914.5K,T 03 D 924.7K.

The ratio of rotor exit mean diameter to rotor inlet tip diameter is chosen as 0.49 and the
required rotational speed as 24,000 rev/min. Assuming the relative flow at rotor inlet is radial
and the absolute flow at rotor exit is axial, determine:

(i) the total-to-static efficiency of the turbine;
(ii) the rotor diameter;
(iii) the implied enthalpy loss coefficients for the nozzles and rotor row.
The gas employed in this cycle is a mixture of helium and xenon with a molecular
weight of 39.94 and a ratio of specific heats of 5/3. The universal gas constant is, R 0 D
8.314 kJ/(kg-mol K).
4. A film-cooled radial inflow turbine is to be used in a high performance open Brayton
cycle gas turbine. The rotor is made of a material able to withstand a temperature of 1145 K at
a tip speed of 600 m/s for short periods of operation. Cooling air is supplied by the compressor
which operates at a stagnation pressure ratio of 4 to 1, with an isentropic efficiency of 80%,
when air is admitted to the compressor at a stagnation temperature of 288 K. Assuming that
the effectiveness of the film cooling is 0.30 and the cooling air temperature at turbine entry
is the same as that at compressor exit, determine the maximum permissible gas temperature
at entry to the turbine.
Take
D 1.4 for the air. Take
D 1.333 for the gas entering the turbine. Assume R D
287 J/(kg K) in both cases.
5. The radial inflow turbine in Problem 8.3 is designed for a specific speed  s of 0.55
(rad). Determine:

(1) the volume flow rate and the turbine power output;
(2) the rotor exit hub and tip diameters;
(3) the nozzle exit flow angle and the rotor inlet passage width/diameter ratio, b 2 /D 2 .
6. An inward flow radial gas turbine with a rotor diameter of 23.76 cm is designed to
operate with a gas mass flow of 1.0 kg/s at a rotational speed of 38 140 rev/min. At the
design condition the inlet stagnation pressure and temperature are to be 300 kPa and 727 ° C.
The turbine is to be “cold” tested in a laboratory where an air supply is available only at the
stagnation conditions of 200 kPa and 102 ° C.
(a) Assuming dynamically similar conditions between those of the laboratory and the
projected design determine, for the “cold” test, the equivalent mass flow rate and the speed
of rotation. Assume the gas properties are the same as for air.