Question

A Rankine cycle power plant is being developed to operate an irrigation system. In this power
plant solar energy will be used to boil a low boiling point fluid within glazed flat plate solar
collectors. The working fluid that has been selected is the commonly used refrigerant R 134a
(1, 1, 1, 2 tetrafluoroethane), tabulated properties of which may be found in Tables A11, A12
and A13 at the rear of the prescribed text.
The plates being used for the solar collector are made of top and bottom layers of
aluminium bonded together for much of their area and incorporating tubular passages of oval
cross-section in the unbonded areas, within which the refrigerant boils. The working pressure
of this construction is 1400 kPa (absolute). It is intended that the refrigerant will boil at this
pressure and be superheated, thereby bringing the temperature up to 55° C. The quality of
the glazing and insulation on the solar collectors is such that at these fluid conditions, and
with a solar intensity of 1 kW per square metre onto the glazing, the efficiency of solar energy
collection into the fluid is 70%.
The superheated vapour is fed from the boiler to a small turbine, the isentropic
efficiency of which is 83 % x (1.01) .The turbine will drive an electric
generator whose output will be used in part to provide power for the boiler feed pump whose
isentropic efficiency is 91 % / (1.08).
The remainder of the electricity will be used to drive an irrigation pump and charge up
batteries for use in less sunny periods.
The irrigation pump is responsible for taking cold water from a stream, through the
condenser of the power plant and from that to drip irrigation trickle hoses in the fields nearby.
The condenser and a water pump are positioned in a concrete lined pit below the stream
level to ensure the pump is always primed and the condenser water tubes are free of air
locks. The trickle hoses are laid out in the fields above the stream level. When the power
plant is operating at the design condition of 1 kW per square metre solar intensity, the water
flow rate through the condenser is to be such that it rises in temperature from 14°C to 21°C.
At this condition the saturation temperature of the refrigerant in the condenser will be 34° C.
The refrigerant is to enter the boiler feed pump at this saturation temperature as a fully
condensed liquid.
The various components of the power plant are to be sized such that the net electric
output available for the water pump and battery charging is 1.7 kW when the rate of solar
energy incidence on the collector glazing is 1 kW per square metre. The efficiency of the
electric generator is 92% / (1.0X) and the efficiency of the electric motor driving the boiler
feed pump it is 85% x (1.0Y).

4. For the design requirement of 1.7 kW net electrical power output, determine, for the real
case:
a. the necessary mass flow rate of refrigerant;
b. the electrical power input to the boiler feed pump motor;
c. the electrical output power rating of the turbo generator;
d. the necessary solar collector area;
e. the necessary water flow rate through the condenser.

Answer 1