Question 5.7: A dual-pressure steam turbine of a combined-cycle power plan......
A dual-pressure steam turbine of a combined-cycle power plant is operating under the following conditions (refer to Figures 5.8, 5.9, and 5.11):
• Gas turbine exhaust gas mass flow is m_{g} = 590 kg/s and exhaust gas temperature is t_{exh} = 630°C
• Live (HP) steam condition is p_{1} = 100 bar, t_{1} = 500°C, and enthalpy is h_{1} = 3500 kJ/kg
• LP steam condition is p_{2} = 5 bar and h_{2s} = 2625 kJ/kg (from h–s diagram, Appendix 11
• Condenser pressure is p_{3} = 0.05 bar
• Rate of steam generation in the HP section of the HRSG is m_\mathrm{HP} = 81.5 kg/s
• Rate of steam generation in the LP section of the HRSG is m_\mathrm{LP} = 9.5 kg/s
• Isentropic efficiency of steam turbine is \eta_\mathrm{it} = 0.9
• Specific heat of exhaust gas is c_\mathrm{pg} = 1.05 kJ/(kg K)
Calculate (i) the power output of the steam turbine P_\mathrm{ST} and (ii) the thermal efficiency of the steam turbine \eta_\mathrm{ST}.
1. After isentropic expansion in the HP and LP turbine sections, the enthalpy of steam is found from the h–s diagram, Appendix 11 as
h_{2s}=2625\, \mathrm{kJ/kg}\ \ \ h_{3s}=2075\, \mathrm{kJ/kg}2. Actual steam enthalpies at states 2 and 3:
h_{2}\,=\,h_{1}\,-\,(h_{1}-h_{2s})\mathbf{h}_{\mathrm{it}}\,=\,3500-(3500-2625)\times0.9\,=\,2712\,\mathrm{kJ}/\mathrm{kg}h_{3}\,=\,h_{2}\,-\,(h_{2}\,-\,h_{3s})\mathbf{h}_{\mathrm{it}}\,=\,2712-\,(2712-\,2075)\times0.9\,=\,2139\;{\mathrm{kJ}}/{\mathrm{kg}}
3. Actual specific work of the HP and LP turbine sections, respectively
w_{\mathrm{{HP}}}=h_{1}-h_{2}\,=\,3500-2712\,=788\,\mathrm{kJ}/\mathrm{kg}w_{\mathrm{{LP}}}=h_{2}-h_{3}\,=\,2712-2139\,=573\,\mathrm{kJ}/\mathrm{kg}
4. Steam mass flow rate in the HP and LP turbine sections, respectively
m_\mathrm{HP}\,=\,81.5\,\mathrm{kg}/sm_{\mathrm{LP}}^{\prime}\,=\,m_{\mathrm{H } \mathrm{P}}\,+\,m_{\mathrm{LP}}\,=\,8 1.5\,+\,1 0.5\,=\,92\,\,\mathrm{kg}/s
5. Power output of the steam turbine
P_{\mathrm{ST}}\,=\,m_{\mathrm{HP}}w_{\mathrm{HP}}\,+\,m_{\mathrm{LP}}^{\prime}w_{\mathrm{LP}}\,=\,81.5\times788\,+\,92\times573\,=\,116,938\,\,\mathrm{kW}6. Plant heat input rate is
\mathrm{Q_{\mathrm{in}}}=m_{\mathrm{g}}c_{\mathrm{pg}}t_{\mathrm{exh}}\,=\,590\times1.05\times630\,=\,390,285\, \mathrm{kJ/s}Efficiency of steam turbine plant is
{\bf h}_\mathrm{ST}\,=\,P_\mathrm{ST}/Q_{\mathrm{in}}\,=\,116,938\,\mathrm{ k}{\mathrm{W/390}},285\,\,\mathrm{kJ/s}\,=\,0.3The performance parameters of a triple-pressure combined-cycle are cal-culated in Example 5.8.