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 2 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 1600 kPa. It is intended that the refrigerant will boil at this pressure and be slightly superheated, thereby bringing the temperature up to 60° 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 85 % x (1.0X) where X is the last digit of your student number e.g. student number 3087787, thus 1.0X becomes 1.07. 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 93 % / (1.0Y), where Y is the second last digit of your student number. 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 on 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 10 to 30°C. At this condition the saturation temperature of the refrigerant in the condenser will be 35° C. The refrigerant is to enter the boiler feed pump at the 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 1.5 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 95% / (1.0X) and the efficiency of the electric motor driving the boiler feed pump it is 87% x (1.0Y).
1. Sketch a schematic of the system showing each component and the connections between them.
2. For the ideal case where the feed pump and turbine are isentropic and the electric motor on the feed pump and the electric generator are 100% efficient:
a. Determine the specific enthalpy of the refrigerant at the entry and exit of the feed pump, and the entry and exit of the turbine;
b. Sketch and label the process paths of the cycle on a T-s diagram, an h-s diagram and a p-v diagram, also showing the saturated liquid and vapour lines on each diagram.
c. Determine, per kg/sec of refrigerant circulated:
i. the necessary electrical power input for the boiler feed pump motor;
ii. the electric power output of the generator
iii. the net electric output power
iv. the rate of heat delivery to the fluid in the boiler
v. the rate of heat rejection at the condenser
vi. The efficiency of conversion of the heat energy put into the fluid, to net electrical energy.