Page 74 - Advanced thermodynamics for engineers

58 CHAPTER 3 ENGINE CYCLES AND THEIR EFFICIENCIES

P3.8 Yet another cycle is proposed in which energy is added at constant volume until the fluid
achieves state 2, the gas is then expanded to its initial pressure (state 3) before being
compressed isobarically back to its initial conditions (state 1). Show that the thermal efficiency
of this cycle is

kðT 3 T 1 Þ
h ¼ 1
th
ðT 2 T 1 Þ
If the initial conditions are 27 C and 1.0 bar, and the energy added is 2000 kJ/kg, calculate

the thermal efficiency of the cycle. What is the specific work output of the cycle?
[35.4%; 708 kJ/kg]

Examples P3.2 and P3.9–P3.13 follow the development of a basic Rankine cycle to demon-
strate how the efficiency of such cycles can be improved.
P3.9 The condenser pressure of the turbine in P3.2 is reduced to 0.15 bar. Calculate the same para-
meters for this cycle as in the previous example. Why have the parameters improved so much?
[28.97%; 32.65%; 744.8 kW/(kg/s)]
P3.10 Both cycles in P3.2 and P3.9 resulted in extremely ‘wet’ steam (low quality) at the exit to the
turbine. This would cause erosion of the blades, and should be avoided. One way of achieving
this is to superheat the steam before it leaves the boiler: assuming that the temperature of the
steam leaving the superheater is 400 C, calculate the same parameters for this cycle using

the basic data in P3.9. What is the quality of the steam leaving the turbine?
Also calculate the mean temperatures of energy addition and rejection, and show that a
Carnot cycle with these temperatures would have the same efficiency as this Rankine cycle.
[31.02%; 51.40%; 937 kW/(kg/s); 0.878; 474 K; 326.9 K]
P3.11 Problems P3.2, P3.9 and P3.10 have shown how the efficiency of a basic Rankine cycle can be
improved, but even after superheating the steam leaving the turbine is still wet. This situation
could be alleviated by using two turbine stages and reheating the steam between them.
Calculate the basic parameters for the cycle if the steam is withdrawn from the HP turbine at
10 bar and reheated to 400 C.

What are the specific power outputs of each turbine?
[32.14%; 51.40%; 1039 kW/(kg/s); 0.925; 845 kW; 196 kW]
P3.12 Recalculate P3.11 with the pressure at which steam is reheated and reduced to 5 bar. What
have been the benefits of using this lower pressure?
[32.36%; 51.40%; 1101 kW/(kg/s); 0.970; 745 kW; 358 kW]
P3.13 Problem P3.12 seems to demonstrate that the efficiency of the reheated Rankine cycle gets
better as the work distribution between the high pressure (HP) and low pressure (LP) turbines
becomes more equal. Do some calculations to see if this proposition is true. At what reheat
pressure are the turbine power outputs approximately equal, and what are the salient
parameters of the cycle?
[1.5 bar; 32.69%; 51.40%; 1180 kW/(kg/s); 0.983; 590 kW; 592 kW]
P3.14 What has the development of the basic Rankine cycle carried out in Problems P3.9–P3.14
shown you about the effect of the salient parameters on the efficiency of the cycle? Evaluate
the mean temperature of energy addition and rejection for the cycles.