Consider an ideal combined cycle with compression ratio of 7:1 in which air enters the compressor at 295 K, enters the turbine at 1200 K, and exits the heat exchanger at 400 K. In the steam cycle, steam is compressed to 8 MPa, heated to 400°C in the heat exchanger, and then condensed at a pressure

Question

Consider an ideal combined cycle with compression ratio of 7:1 in which air enters the compressor at 295 K, enters the turbine at 1200 K, and exits the heat exchanger at 400 K. In the steam cycle, steam is compressed to 8 MPa, heated to 400°C in the heat exchanger, and then condensed at a pressure of 10 kPa. Calculate the theoretical efficiency of this cycle, and compare to the efficiencies of the two cycles separately.

Accepted Answer

Refer to the accompanying T-s diagram in Fig. 6-8. Note that the gas cycle enthalpy values in the table below are numbered 5 through 9, as in Fig. 6-7. First solve for the enthalpy values for the two cycles separately. These calculations are carried out similarly to Examples 6-3 and 6-5. For the gas cycle, we obtain the following values:

State	p[latex]_r[/latex]	h′
5	1.3068	295.2
6	9.1476	515.1
7	238	1277.8
8	34	747.3

Let us call the enthalpy of the gas leaving the heat exchanger h[latex]_9[/latex]. From the air tables, for 400 K we obtain h[latex]_9[/latex] = 400.1 kJ/kg. On the steam side, we calculate the following table of values:

State	h	s
1	191.8	not used
2	199.9	not used
3	3139.4	6.3658
4	2015.2	6.3658

It is now possible to evaluate y for the exchanger from Eq. (6-7):

[latex]y=\frac{m_{s}}{m_{g}}=\frac{h_{ ext {in }}-h_{ ext {out }}}{h_{ ext {out }}-h_{ ext {in }}} [/latex] (6-7)

[latex]y=\frac{h_{8}^{\prime}-h_{9}^{\prime}}{h_{2}-h_{3}}=\frac{(747.3-400.1)}{(3139.4-199.9)}=0.118[/latex]

In order to calculate net work and efficiency, we first need the net work for the gas and steam cycles, ω[latex]_{g.net}[/latex] and ω[latex]_{s.net}[/latex], respectively. From the above data, we obtain ω[latex]_{g.net}[/latex] = 310.6 kJ/kg and ω[latex]_{s.net} [/latex] = 1116.1 kJ/kg, and also q[latex]_{in}[/latex] = 762.7 kJ/kg for the gas cycle. Total net work and overall efficiency are as follows:

[latex]\begin{aligned} w_{ ext {tot }} &=310.6+(0.118) 1116.1=442.4 \mathrm{~kJ} / \mathrm{kg} \ \eta_{ ext {overall }} &=\frac{w_{ ext {tot }}}{q_{\mathrm{m}}}=\frac{442.4}{762.7}=58.0 \% \end{aligned}[/latex]

This value compares very favorably to the efficiencies of each cycle separately. For the steam cycle, q[latex]_{s.in}[/latex] = 2938.3 kJ/kg. Thus h[latex]_s[/latex] = 1116.1/2939.5 = 38.0%, and h[latex]_g[/latex] = 310.6/762.7 = 40.7%.

Question 6.8: Consider an ideal combined cycle with compression ratio of 7...

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