A Rankine cycle power plant is being developed to operate anirrigation system. In this power plant solar energy will be used toboil a low boiling point fluid within glazed flat plate solarcollectors. The working fluid that has been selected is thecommonly used refrigerant R 134a (1, 1, 1, 2 tetrafluoroethane),tabulated properties of which may be found in Tables A11, A12 andA13 at the rear of the prescribed text.
The plates being used for the solar collector are made of 2layers of aluminium bonded together for much of their area andincorporating tubular passages of oval cross-section in theunbonded areas, within which the refrigerant boils. The workingpressure of this construction is 1400 kPa. It is intended that therefrigerant will boil at this pressure and be slightly superheated,thereby bringing the temperature up to 55 C. The quality of theglazing and insulation on the solar collectors is such that atthese fluid conditions, and with a solar intensity of 1 kW persquare metre onto the glazing, the efficiency of solar energycollection into the fluid is 70%.
The superheated vapour is fed from the boiler to a smallturbine, the isentropic efficiency of which is 85 % x (1.07). Theturbine will drive an electric generator whose output will be usedin part to provide power for the boiler feed pump whose isentropicefficiency is 96 % / (1.02). The remainder of the electricity willbe used to drive an irrigation pump and charge up batteries for usein less sunny periods.
The irrigation pump is responsible for taking cold water from astream, through the condenser of the power plant and on from thatto drip irrigation trickle hoses in the fields nearby. Thecondenser and a water pump are positioned in a concrete lined pitbelow the stream level to ensure the pump is always primed and thecondenser water tubes are free of air locks. The trickle hoses arelaid out in the fields above the stream level. When the power plantis operating at the design condition of 1 kW per square metre solarintensity, the water flow rate through the condenser is to be suchthat it rises in temperature from 12 to 23 C. At this condition thesaturation temperature of the refrigerant in the condenser will be32 C. The refrigerant is to enter the boiler feed pump at thesaturation temperature as a fully condensed liquid.
The various components of the power plant are to be sized suchthat the net electric output available for the water pump andbattery charging is 1.8 kW when the rate of solar energy incidenceon the collector glazing is 1 kW per square metre. The efficiencyof the electric generator is 82% / (1.07) and the efficiency of theelectric motor driving the boiler feed pump it is 75% x (1.02).
2. Considering the real case, where the turbine and feed pumpare not isentropic, and the feed pump electric motor and theelectric generator are not 100% efficient (assume no pressure dropin boiler and condenser):
a. Determine the specific enthalpy of the refrigerant at theentry and exit of the feed pump, and the entry and exit of theturbine;
b. Sketch and label the process paths of the cycle on a T-sdiagram, an h-s diagram and a p-v diagram, also showing thesaturated 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 poweroutput, 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
