13

Ideal gas power cyclesGenera] introductionIf a substance passes through a series of processes such that it is eventually returned to its original state then the substance is said to have been taken through a cycle (see section 1.13).

During a cycle there will be some heat transfer and some work transfer to and from the substance.Since after performing a cycle, the substance is returned to its original state, then, by the first law of thermodynamics, f()Q = oW (see section 3.3)(1)Thus, for a cycle, the net work transfer can be determined by an analysis of the net heat transfer, or, t .Net work done = Net heat received Net heat rejected(2)Net work doneThe ratio, :-Net heat receivedis called the thermal efficiency (see section 1.30), or,iWThermal q =(3)where | W Net work done, jQ = Net heat received.Note also that, because the area under a process illustrated on a pressure-volume graph is equal to the work done, then, the net area of a pressu re-volume diagram of a cycle is equal to the net work of the cycle.This, therefore, gives another method by which the net work of a cycle can be determined.The equation,& WThermal rj = -y-iQgives the theoretical or ideal thermal efficiency. The actual thermal efficiency of a practical cycle is given by the equation,, ,,Actual work doneActual thermal n = (4)Thermal energy from fuelThis is always less than the theoretical thermal efficiency.A practical cycle is carried out in an engine or turbine and will incur many losses which will include heat transfer loss, fuel combustion loss, non- uniform energy distribution in the working substance, friction, leakage, the need to keep temperatures within practical working limits, the running of auxiliary equipment such as pumps, alternators, valve gear and cooling equipment.The ratio of the actual thermal efficiency and the ideal thermal efficiency is called the relative efficiency or efficiency ratio, thus, Actual thermal efficiencyRelative efficiency = - (5)Ideal thermal efficiencyAnother useful concept is the consideration of a cycle is that of the work ratio. This is defined as:Network done|WWork ratio = = - (6)Positive work done Positive work doneWhere, net work done = positive work done negative work done = | W.Note that, from equation (6), if the negative work is reduced then the work ratio > 1.A cycle with good ideal thermal efficiency together with a good work ratio suggests good overall efficiency potential in a practical power producing plant using the cycle.Work ratio can give comparative indication of plant size. A plant with a low work ratio would suggest that the work components of the plant are larger when compared with a plant which has a higher work ratio and similar power output.Work ratio is most commonly applied to such cycles as arranged in steam plant and gas turbines. Such plants are composed of separate units each performing a particular function. In a steam plant there is the boiler, the engine or turbine, the condenser and the feed pump (see Chapter 8). In a gas turbine there is the compressor, the combustion chamber (or chambers) and the turbine (see Chapter 14).Another form of comparison between cycles is by means of the specific steam or fuel consumption.In the case of steam plant,Mass flow of steam in kg/hSpecific steam consumption = .-,--.7(7)Power output in kwThis gives the mass of steam used per unit power output in kg/kW h.In the case of internal combustion engines such as the gas turbine and the petrol or diesel engine the specific fuel consumption is used where,Mass of fuel used in kg/hSpecific fuel consumption = (8)^PoweroutputinkWThis gives the mass of fuel used per unit power output in kg/kW h.Thus a cycle which has a lower specific steam or fuel consumption indicates that it has better energy conversion performance than a cycle with a higher specific steam or fuel consumption.The specific steam or fuel consumption can also be determined from a knowledge of the specific work output.IfkJSpecific work output = w - -kg (steam or fuel)then,1 kg _ 1 kg _ 3 600 kg w kJ w kW s w kW h= specific steam or fuel consumption(9)(Note that 1 kW = 1 kJ/s. 1 kJ = 1 kW s.)In the case of reciprocating engines such as steam, petrol and diesel engines which use a piston-crank mechanism,ameansof comparisonbetween cycles can be made by means of themeaneffective pressure.This isthat theoretical pressure which, if it was maintained constant throughout the volume change of the cycle (engine stroke of a practical cycle), would give the same work output as that obtained from the cycle.Figure 13.1 illustrates a cycle plotted on a P-V diagram and operating between the volume limits of K, and V2.The area of the cycle diagram will determine the work done = | W. This is called the indicated work done.The stroke volume of the diagram - Vi V2.

The mean effective pressure is determined by the equation,iwPM'= i, where PM = mean effective pressure (10)VI ~ '2Note that W/(Vl V2) is also the work done/unit swept volume.Thus a cycle with a higher mean effective pressure will indicate that it has better work characteristics than a cycle with a lower mean effective pressure.A further note concerning the cycles used in internal combustion engines is that, if the effects of the fuel used is neglected, the gas can be considered to closely approximate to that of air alone. Thus, the theoretical cycles such as the constant volume, constant pressure and the Diesel cycles are sometimes referred to as the air standard cycles and the related efficiencies are referred to as air standard efficiencies.