Figure 3 . Rankine-Hirn cycle
It is assumed that the water feed pump outlet pressure is equal toPFP = 93 bars [30]. The input data are
summarized in Table 10.
The first value of steam mass flow is assumed:
Super heater level
Assume \(T_{s9}\)
then calculate\(Q_{a}={\dot{m}}_{s}\left(h_{s9}-h_{\text{sat}}\right)\ \)\(\text{and\ \ \ }T_{g4^{\prime}}=T_{g4}-\frac{Q_{a}}{{\dot{m}}_{g}C_{\text{pg}}}\)
Calculate \(Q_{t}=\left(\text{UA}\right)F\text{TLM}\) and\(TLM=\frac{\left(T_{g4^{{}^{\prime}}}-T_{\text{sat}}\right)-\left(T_{g4}-T_{s9}\right)}{\ln\frac{\left(T_{g4^{\prime}}-T_{\text{sat}}\right)}{\left(T_{g4}-T_{s9}\right)}}\)
Estimate\({\left(\text{UA}\right)=\left(\text{UA}\right)}_{d}\left(\frac{{\dot{m}}_{g}}{{\dot{m}}_{g}}\right)^{0.65}\left(\frac{F_{g}}{F_{\text{gd}}}\right)\left(\frac{{\dot{m}}_{s}}{{\dot{m}}_{\text{sd}}}\right)^{0.15}\)
Check: \(\frac{\left(Q_{a}-Q_{t}\right)}{Q_{a}}<\varepsilon\)
Then put \(Q_{t}=Q_{1}\) and pass to the second step which is the
evaporator level. If the assumed duty does not match the exhaust gases
to the steam at the superheater level, the case\(\frac{\left(Q_{a}-Q_{t}\right)}{Q_{a}}\geq\varepsilon\), another
value of Ts9 is assumed and the superheater
calculations are repeated.
Evaporator level
\(\ln{\frac{\left(T_{g4^{\prime}}-T_{\text{sat}}\right)}{\left(T_{g5^{\prime}}-T_{\text{sat}}\right)}=\frac{\text{UA}}{{\dot{m}}_{g}C_{\text{pg}}}\text{\ \ \ \ \ \ \ \ \ \ }}\)
and\(\ln{\frac{\left(T_{g4^{\prime}}-T_{\text{sat}}\right)}{\left(T_{g5^{\prime}}-T_{\text{sat}}\right)}=K\left({\dot{m}}_{g}\right)_{d}^{-0.4}}\)
with \(K=f(A/C_{\text{pg}})\)\(K\mathbf{=}\left({\dot{m}}_{g}\right)_{d}^{0.4}\ln\frac{\left(T_{g4^{\prime}}-T_{\text{sat}}\right)}{\left(T_{g5^{\prime}}-T_{\text{sat}}\right)}\)
Then calculate \(T_{g5^{\prime}}\) from:
\begin{equation}
\ln{\frac{\left(T_{g4^{\prime}}-T_{\text{sat}}\right)}{\left(T_{g5^{\prime}}-T_{\text{sat}}\right)}=K\left({\dot{m}}_{g}\right)^{-0.4}\text{\ \ \ \ \ \ \ }}\nonumber \\
\end{equation}then\(\text{\ \ \ \ \ \ \ \ }Q={\dot{m}}_{g}C_{\text{pg}}\left(T_{g4^{\prime}}-T_{g5^{\prime}}\right)\)
\(Q_{2}=Q+\frac{Q_{\text{SF}}}{2}\) and\(\text{\ Q}_{2}={\dot{m}}_{s}(h_{\text{sat}}-h_{w7})\)
\(\frac{Q_{\text{SF}}}{2}\) is the solar energy carried by HTF and
released to HSSG.
Economizer level
Assume \(T_{w7}\):
\(Q_{a}={\dot{m}}_{s}\left(h_{w7}-h_{w6}\right)\)
and \(T_{g5}=T_{g5^{\prime}}-\frac{Q_{a}}{{\dot{m}}_{g}C_{\text{pg}}}\)
\begin{equation}
Q_{t}=\left(\text{UA}\right)F\text{TLM}\nonumber \\
\end{equation}With:\({\left(\text{UA}\right)=\left(\text{UA}\right)}_{d}\left(\frac{{\dot{m}}_{g}}{{\dot{m}}_{\text{gd}}}\right)^{0.65}\left(\frac{F}{F_{d}}\right)\)
and\(TLM=\frac{\left(T_{g5^{\prime}}-T_{w7}\right)-\left(T_{g5}-T_{w6}\right)}{\ln\frac{\left(T_{g5^{\prime}}-T_{w7}\right)}{\left(T_{g5}-T_{w6}\right)}}\)
If the assumed duty does not match the exhaust gases to steam at
economizer level, case\(\frac{\left(Q_{a}-Q_{t}\right)}{Q_{a}}\geq\varepsilon\) assume
another value of \(T_{w7}\) and repeat the economizer calculations
by\(\text{\ Q}_{3}=Q_{t}\)
Calculation of the steam mass\({\dot{m}}_{s}=\frac{\left(Q_{1}+Q_{2}+Q_{3}\right)}{\left(h_{s9}-h_{w6}\right)}\), and then
check:\(\ \frac{\left({\dot{m}}_{s}-{\dot{m}}_{s}\right)}{{\dot{m}}_{s}}<\varepsilon\).
If the assumed steam mass flow value \({\dot{m}}_{s}\) does not match,
the case\(\frac{\left({\dot{m}}_{s}-{\dot{m}}_{s}\right)}{{\dot{m}}_{s}}\geq\varepsilon\),
the calculated steam mass flow rate is reassigned as a value and
computations starts from the first step which is the superheater and the
whole calculation procedure is repeated.
Table 10. Data to steam cycle