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 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 1400 kPa. It is intended that the refrigerant will boil at this pressure and be slightly 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 85 % x (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 96 % / (1.02). 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 12 to 23 C. At this condition the saturation temperature of the refrigerant in the condenser will be 32 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 1.8 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 82% / (1.07) and the efficiency of the electric motor driving the boiler feed pump it is 75% x (1.02).

2. Considering the real case, where the turbine and feed pump are not isentropic, and the feed pump electric motor and the electric generator are not 100% efficient (assume no pressure drop in boiler and condenser):

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
d. For the design requirement of 1.8 kW net electrical power output, determine, for the real case
i. the necessary mass flow rate of refrigerant;
ii. the electrical power input to the boiler feed pump motor
iii. the electric output power rating of the turbo generator
iv. the necessary solar collector area
v. the necessary water flow rate through the condenser

Answer 1