朗肯循环：把极限花掉

Four components, two dome crossings

• The Rankine cycle 朗肯循环 is the power plant: pump to boiler 锅炉 to turbine to condenser 冷凝器, and back. The working fluid changes phase twice per lap, which is exactly why the cycle hugs the saturation dome on both diagrams.
• Heat enters at the high-pressure isobar, work leaves at the isentropic expansion, heat leaves at the condenser pressure, and the pump pays a tiny $v\,\Delta p$ to close the loop - liquid $v$ is small, so the pump is nearly free.

The ideal baseline

• Boiler at $4\ \mathrm{MPa}$, saturated vapour ($h_3 = 2801.4$, $s_3 = 6.0700\ \mathrm{kJ/(kg\,K)}$); condenser at $10\ \mathrm{kPa}$. The turbine leg: $s_4 = s_3$ gives $x_4 = (6.0700 - 0.6492)/7.5009 = \mathbf{0.7227}$, $h_4 = 191.81 + 0.7227 \times 2392.8 = \mathbf{1921.1}\ \mathrm{kJ/kg}$.
• The pump leg: $h_2 = 191.81 + 0.001010 \times 3990 = \mathbf{195.8}$. So work out $2801.4 - 1921.1 = \mathbf{880.3}$, work in $\mathbf{4.0}$, heat in $2801.4 - 195.8 = \mathbf{2605.6}$, and $\eta = 876.3/2605.6 = \mathbf{33.6\%}$ - every number one dome walk or one $v\,\Delta p$.

Two upgrades, priced

• Superheat 过热 to $4\ \mathrm{MPa}$, $480^\circ\mathrm{C}$ ($h_3 = 3398.3$, $s_3 = 6.7677$): $x_4 = \mathbf{0.8157}$, $h_4 = \mathbf{2143.6}$, and $\eta$ rises to $\mathbf{39.1\%}$ - the exhaust quality 排气干度 climbs from 0.72 toward 0.82, still wet.
• Reheat 再热 expands from an intermediate $800\ \mathrm{kPa}$ back up to $480^\circ\mathrm{C}$ before the final expansion: work rises again and the exhaust crosses above 0.9, clearing the 0.88 blade-erosion line. Raising boiler pressure does the same to efficiency - the same cycle at $1$ versus $4\ \mathrm{MPa}$ moves $\eta$ from $25.3\%$ to $32.3\%$ - because the average heat-in temperature rises while the pump cost barely moves.

Three cycle slips

Recap