The Ideal Reheat Rankine Cycle Consider a steam power plant operating on the ideal reheat Rankine cycle. Steam enters the high-pressure turbine at 15 MPa and 600°C and is condensed in the condenser at a pressure of 10 kPa. If the moisture content of the steam at the exit of the low-pressure turbine

Question

The Ideal Reheat Rankine Cycle Consider a steam power plant operating on the ideal reheat Rankine cycle. Steam enters the high-pressure turbine at 15 MPa and 600°C and is condensed in the condenser at a pressure of 10 kPa. If the moisture content of the steam at the exit of the low-pressure turbine is not to exceed 10.4 percent, determine (a) the pressure at which the steam should be reheated and (b) the thermal efficiency of the cycle. Assume the steam is reheated to the inlet temperature of the high-pressure turbine.

Accepted Answer

A steam power plant operating on the ideal reheat Rankine cycle is considered. For a specified moisture content at the turbine exit, the reheat pressure and the thermal efficiency are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible.
Analysis The schematic of the power plant and the T-s diagram of the cycle are shown in Fig. 10–13. We note that the power plant operates on the ideal reheat Rankine cycle. Therefore, the pump and the turbines are isentropic, there are no pressure drops in the boiler and condenser, and steam leaves the condenser and enters the pump as saturated liquid at the condenser pressure.
(a) The reheat pressure is determined from the requirement that the entropies at states 5 and 6 be the same:

State 6: [latex]\begin{aligned}&P_{6}=10 kPa \&x_{6}=0.896 \quad ext { (sat. mixture) } \&s_{6}=s_{f}+x_{6} s_{f g}=0.6492+0.896(7.4996)=7.3688 kJ / kg \cdot K\end{aligned}[/latex]

Also,

[latex] h_{6}=h_{f}+x_{6} h_{f g}=191.81+0.896(2392.1)=2335.1 kJ / kg [/latex]

Thus,

State 5: [latex] \left.\begin{array}{l}T_{5}=600^{\circ} C \s_{5}=s_{6}\end{array} ight\} \quad \begin{aligned}&P_{5}= 4 . 0 M P a \&h_{5}=3674.9 kJ / kg\end{aligned}[/latex]

Therefore, steam should be reheated at a pressure of 4 MPa or lower to prevent a moisture content above 10.4 percent.

(b) To determine the thermal efficiency, we need to know the enthalpies at all other states:

State 1: [latex]\left.\begin{array}{l}\begin{array}{l}P_{1}=10 kPa \ ext { Sat. liquid }\end{array}\end{array} ight\} \quad \begin{aligned}&h_{1}=h_{f @ 10 kPa }=191.81 kJ / kg \&v_{1}=v_{f @ 10 kPa }=0.00101 m ^{3} / kg\end{aligned}[/latex]

State 2: [latex]\begin{aligned}P_{2}=& 15 MPa \s_{2}=& s_{1} \w_{ ext {pump,in }}=& v_{1}\left(P_{2}-P_{1} ight)=\left(0.00101 m ^{3} / kg ight) \& imes[(15,000-10) kPa ]\left(\frac{1 kJ }{1 kPa \cdot m ^{3}} ight) \=& 15.14 kJ / kg \h_{2}=& h_{1}+w_{ ext {pump,in }}=(191.81+15.14) kJ / kg =206.95 kJ / kg\end{aligned}[/latex]

State 3: [latex]\left.\begin{array}{l}\begin{array}{l}P_{3}=15 MPa \T_{3}=600{ }^{\circ} C\end{array}\end{array} ight\} \begin{aligned}&h_{3}=3583.1 kJ / kg \&s_{3}=6.6796 kJ / kg \cdot K\end{aligned}[/latex]

State 4: [latex]\left.\begin{array}{l}P_{4}=4 MPa \s_{4}=s_{3}\end{array} ight\} \begin{aligned}&h_{4}=3155.0 kJ / kg \&\left(T_{4}=375.5^{\circ} C ight)\end{aligned}[/latex]

Thus

[latex]\begin{aligned}q_{ ext {in }} &=\left(h_{3}-h_{2} ight)+\left(h_{5}-h_{4} ight) \&=(3583.1-206.95) kJ / kg +(3674.9-3155.0) kJ / kg \&=3896.1 kJ / kg \q_{ ext {out }} &=h_{6}-h_{1}=(2335.1-191.81) kJ / kg \&=2143.3 kJ / kg\end{aligned}[/latex]

and

[latex] \eta_{ ext {th }}=1-\frac{q_{ ext {out }}}{q_{ ext {in }}}=1-\frac{2143.3 kJ / kg }{3896.1 kJ / kg }=0.450 ext { or } 45.0 \% [/latex]

Discussion This problem was solved in Example 10–3c for the same pressure and temperature limits but without the reheat process. A comparison of the two results reveals that reheating reduces the moisture content from 19.6 to 10.4 percent while increasing the thermal efficiency from 43.0 to 45.0 percent.

Question 10.4: The Ideal Reheat Rankine Cycle Consider a steam power plant ...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions