Rankine cycle with reheat and regeneration

The ideal Rankine cycle and how reheat and open or closed feedwater heating raise efficiency and exhaust dryness, with simple-cycle and open-heater worked examples from steam-table data.

Drafted with Aria, reviewed by the AiCanCode.org team. Spotted an error? Use Give Feedback at the bottom of the page.

Why it matters

Most of India's electricity still comes from steam plants — coal, nuclear, solar-thermal and the steam bottoming half of combined-cycle plants — and all of them run on the Rankine cycle. Reheat and regeneration are the two modifications every real plant uses: they let designers raise boiler pressure for efficiency without wrecking the last turbine stages with wet steam, and they cut fuel use by a few percentage points, which is worth crores of rupees a year in a single unit.

Key ideas

Ideal (simple) Rankine cycle, with state numbers used below: 1→2 isentropic compression of saturated liquid in the pump; 2→3 constant-pressure heating to superheated steam in the boiler; 3→4 isentropic expansion in the turbine; 4→1 constant-pressure condensation to saturated liquid.

  • Pump work is small (1–2 % of turbine work) because liquid has a tiny specific volume; this low back-work ratio is the big advantage over gas cycles.
  • Efficiency rises when the mean temperature of heat addition rises (higher boiler pressure, more superheat) or the condenser temperature falls (lower condenser pressure, limited by cooling-water temperature).
  • Raising boiler pressure at a fixed turbine inlet temperature makes the turbine exhaust wetter. Moisture above about 10–12 % erodes blades and lowers stage efficiency.

Reheat. Steam expands in a high-pressure (HP) turbine to an intermediate pressure, returns to the boiler to be reheated (usually to about the original temperature), then expands in a low-pressure (LP) turbine.

  • The main purpose is drier exhaust steam, which allows a higher boiler pressure.
  • It raises net work per kg considerably. Efficiency rises only modestly, and only if the mean temperature of the reheat heat addition exceeds that of the rest of the cycle. The optimum reheat pressure is typically about 20–25 % of boiler pressure: too high gives little benefit in dryness; too low adds heat at a low mean temperature.

Regeneration (feedwater heating). Steam is bled from the turbine at one or more pressures to heat the feedwater before it enters the boiler.

  • It removes the low-temperature part of the heat addition (the feedwater no longer starts at condenser temperature), so the mean temperature of heat addition rises and efficiency increases. Net work per kg of boiler steam falls, because the bled steam does not finish its expansion.
  • Open (direct-contact) FWH: bled steam mixes with feedwater; the outlet is saturated liquid at the heater pressure. Needs a pump after each heater. Also serves as a deaerator.
  • Closed FWH: a shell-and-tube exchanger; streams do not mix, so different pressures are allowed. The condensed bled steam is pumped forward or cascaded (trapped) back to a lower-pressure heater.
  • More heaters give more gain, with diminishing returns. Large plants use 6–8 heaters, one of them open (the deaerator).

Actual cycle. Turbine and pump have isentropic efficiencies below 1; pipes have pressure drops and heat losses. Then w_T = η_T (h₃ − h₄s) and w_P = (h₂s − h₁)/η_P.

Performance indices. Thermal efficiency, specific steam consumption (kg/kWh), heat rate (kJ/kWh = 3600/η) and work ratio.

Formulas

w_P = v₁ (p₂ − p₁) — ideal pump work (kJ/kg). v₁: saturated liquid specific volume (m³/kg), p in kPa. h₂ = h₁ + w_P w_T = h₃ − h₄ — turbine work (kJ/kg). q_in = h₃ − h₂, q_out = h₄ − h₁ (kJ/kg). η = (w_T − w_P) / q_in = 1 − q_out / q_in x₄ = (s₄ − s_f) / s_fg, h₄ = h_f + x₄ h_fg — wet exhaust after isentropic expansion (s₄ = s₃).

Reheat (HP expansion 3→4, reheat 4→5, LP expansion 5→6): w_T = (h₃ − h₄) + (h₅ − h₆), q_in = (h₃ − h₂) + (h₅ − h₄)

Open FWH with bled fraction y per kg of boiler steam (bled state 6, condensate from pump 2, heater outlet 3 as saturated liquid): y = (h₃ − h₂) / (h₆ − h₂) — from y h₆ + (1 − y) h₂ = h₃.

SSC = 3600 / w_net — specific steam consumption (kg/kWh), w_net in kJ/kg. Heat rate = 3600 / η (kJ/kWh). Work ratio = w_net / w_T.

Worked examples

Property values below are from standard steam tables; your data book may differ slightly in the last digit.

Example 1 (standard, simple ideal Rankine cycle). Steam enters the turbine at 10 MPa, 500 °C; condenser pressure is 10 kPa. Find η, the exhaust dryness and SSC. Data: at 10 MPa, 500 °C: h₃ = 3375.1 kJ/kg, s₃ = 6.5995 kJ/kg·K. At 10 kPa: h_f = 191.81, h_fg = 2392.1 kJ/kg, s_f = 0.6492, s_fg = 7.4996 kJ/kg·K, v_f = 0.00101 m³/kg.

  1. Pump: w_P = v₁ (p₂ − p₁) = 0.00101 × (10 000 − 10) = 10.09 kJ/kg; h₂ = 191.81 + 10.09 = 201.90 kJ/kg.
  2. Exhaust: x₄ = (s₃ − s_f)/s_fg = (6.5995 − 0.6492)/7.4996 = 0.7934; h₄ = 191.81 + 0.7934 × 2392.1 = 2089.7 kJ/kg.
  3. w_T = 3375.1 − 2089.7 = 1285.4 kJ/kg; w_net = 1285.4 − 10.1 = 1275.3 kJ/kg.
  4. q_in = 3375.1 − 201.9 = 3173.2 kJ/kg.
  5. η = 1275.3/3173.2 = 0.402; SSC = 3600/1275.3 = 2.82 kg/kWh.

η ≈ 40.2 %, x₄ ≈ 0.79, SSC ≈ 2.82 kg/kWh — the 21 % moisture is why reheat is needed at this pressure.

Example 2 (GATE level, one open feedwater heater). An ideal regenerative cycle: turbine inlet 15 MPa, 600 °C; steam bled at 1.2 MPa to an open FWH; condenser 10 kPa. Find the bled fraction and η. Data: h₅ = 3583.1 kJ/kg, s₅ = 6.6796 kJ/kg·K. Isentropic to 1.2 MPa (superheated): h₆ = 2858.8 kJ/kg. Isentropic to 10 kPa: x₇ = 0.804, h₇ = 2115.2 kJ/kg. At 10 kPa: h₁ = 191.81 kJ/kg, v₁ = 0.00101 m³/kg. At 1.2 MPa: h₃ = h_f = 798.33 kJ/kg, v₃ = 0.001139 m³/kg.

  1. Pump I: w_P1 = 0.00101 × (1200 − 10) = 1.20 kJ/kg; h₂ = 193.01 kJ/kg.
  2. Pump II: w_P2 = 0.001139 × (15 000 − 1200) = 15.72 kJ/kg; h₄ = 798.33 + 15.72 = 814.05 kJ/kg.
  3. FWH balance: y = (h₃ − h₂)/(h₆ − h₂) = (798.33 − 193.01)/(2858.8 − 193.01) = 605.32/2665.79 = 0.2271.
  4. Turbine: w_T = (h₅ − h₆) + (1 − y)(h₆ − h₇) = 724.3 + 0.7729 × 743.6 = 724.3 + 574.7 = 1299.0 kJ/kg.
  5. Pumps: w_P = (1 − y) × 1.20 + 15.72 = 16.65 kJ/kg; w_net = 1282.4 kJ/kg.
  6. q_in = h₅ − h₄ = 3583.1 − 814.05 = 2769.1 kJ/kg; η = 1282.4/2769.1 = 0.463.

y ≈ 0.227, η ≈ 46.3 % (the same cycle without the heater gives about 43.0 %).

For comparison, reheating the same 15 MPa, 600 °C steam at 3 MPa back to 600 °C (no FWH) gives η ≈ 45.1 % with exhaust dryness ≈ 0.915 instead of 0.804.

Common mistakes

  • Forgetting the pump work when finding h₂, or computing it with p in MPa so that it comes out 1000 times too small.
  • Using h₃ − h₄ for q_in in a reheat cycle and leaving out the reheat heat (h₅ − h₄).
  • Multiplying the whole turbine work by (1 − y). Only the expansion after the bleed point carries (1 − y).
  • Taking the open-FWH outlet as anything other than saturated liquid at the heater pressure.
  • Saying regeneration increases work output. It increases efficiency but reduces net work per kg of boiler steam.
  • Reading x from the wrong pressure row or using s_g instead of s_fg in the dryness formula.

For GATE ME

This topic produces long numericals using supplied steam-table data: simple-cycle efficiency, back-work ratio, pump work, exhaust dryness, reheat-cycle efficiency and work, and bled-steam fraction with one open (occasionally closed) heater. Conceptual questions cover the effect of boiler pressure, superheat, condenser pressure and reheat on efficiency and dryness. Practise a clean state table (p, T, h, s, x) before computing anything.

Quick check

  1. Why is the pump work in a Rankine cycle so small compared with the compressor work in a gas turbine?
  2. What is the main purpose of reheat?
  3. Does regeneration increase or decrease the net work per kg of steam generated?
  4. In an open FWH at 1 MPa, what is the state of the water leaving it?
  5. A plant has η = 36 %. What is its heat rate?

Answers: 1. Liquid has a very small specific volume, and w = v Δp. 2. To keep the turbine exhaust drier, allowing higher boiler pressure (with some gain in work and efficiency). 3. Decrease, though efficiency rises. 4. Saturated liquid at 1 MPa. 5. 3600/0.36 = 10 000 kJ/kWh.

Interview questions

All Thermal Engineering interview questions

Try answering each one aloud before you open it.

  1. 1.What is the Rankine cycle with reheat and regeneration?Concept

    The Rankine cycle with reheat and regeneration is an advanced thermodynamic cycle used in power plants to improve efficiency. Reheat involves expanding steam in multiple stages with reheating between stages to increase the average temperature at which heat is added. Regeneration involves preheating the feedwater using steam extracted from the turbine, which reduces the heat input required in the boiler. This combination enhances the thermal efficiency of the cycle.

  2. 2.Explain the purpose of reheating in the Rankine cycle.Concept

    Reheating in the Rankine cycle is used to increase the efficiency of the cycle by reducing the moisture content of the steam at the final stages of expansion. This is achieved by expanding the steam in stages and reheating it between stages, which allows the steam to remain dry and superheated, thus improving the turbine's performance and reducing erosion.

  3. 3.What is regeneration in the Rankine cycle, and why is it used?Concept

    Regeneration bleeds part of the steam from the turbine at intermediate pressures and uses it to heat the feedwater, in open (mixing) or closed (shell-and-tube) feedwater heaters. The boiler then receives water that is already hot, so the low-temperature part of the heat addition is eliminated and the mean temperature of heat addition rises, raising thermal efficiency. Net work per kg of boiler steam falls slightly, because the bled steam does not complete its expansion.

  4. 4.Why is the Rankine cycle with reheat and regeneration more efficient than the basic Rankine cycle?Application

    The Rankine cycle with reheat and regeneration is more efficient than the basic Rankine cycle because it reduces the moisture content of the steam at the turbine's exhaust and increases the average temperature at which heat is added. Reheating keeps the steam dry and superheated, while regeneration preheats the feedwater, both of which contribute to a higher thermal efficiency by reducing irreversibilities and improving the heat addition process.

  5. 5.How does the choice of reheat pressure affect a reheat Rankine cycle?Application

    If the reheat pressure is too close to the boiler pressure, the reheat adds little heat and the LP turbine exhaust stays nearly as wet as without reheat, so the benefit is small. If it is too low, the reheat heat is added at a low mean temperature, which can actually reduce cycle efficiency even though exhaust dryness and work improve. The optimum is usually around 20–25 % of the boiler pressure, chosen to raise the mean temperature of heat addition while keeping exhaust moisture acceptable.

  6. 6.How does regeneration affect the heat rate of a power plant operating on a Rankine cycle?Application

    Regeneration reduces the heat rate of a power plant operating on a Rankine cycle by decreasing the amount of heat required from the boiler. By preheating the feedwater using extracted steam, the cycle requires less fuel to achieve the same power output, thus lowering the heat rate and improving the plant's efficiency.

  7. 7.An ideal reheat Rankine cycle has turbine inlet at 15 MPa and 600 °C, reheat at 3 MPa back to 600 °C, and a condenser at 10 kPa. Estimate its thermal efficiency.Numerical

    From steam tables: h₃ = 3583.1 kJ/kg (s = 6.680), isentropic to 3 MPa gives h₄ ≈ 3075.9 kJ/kg; after reheat h₅ = 3682.8 kJ/kg (s = 7.510), and isentropic expansion to 10 kPa gives x₆ ≈ 0.915, h₆ ≈ 2380.2 kJ/kg. Pump work ≈ 0.00101 × 14 990 ≈ 15.1 kJ/kg, so h₂ ≈ 206.9 kJ/kg. Turbine work = 507.2 + 1302.6 = 1809.8 kJ/kg, net work ≈ 1794.7 kJ/kg, heat input = 3376.2 + 606.9 = 3983.1 kJ/kg, so η ≈ 45 %.

  8. 8.What is the impact of increasing the number of feedwater heaters in a regenerative Rankine cycle?Application

    Increasing the number of feedwater heaters in a regenerative Rankine cycle generally improves the cycle's thermal efficiency. More feedwater heaters allow for better preheating of the feedwater, which increases the average temperature at which heat is added to the cycle. This reduces the fuel consumption and improves the overall efficiency, although the cost and complexity of the system also increase.

  9. 9.Explain how the moisture content of steam affects the performance of a turbine in a Rankine cycle.Concept

    The moisture content of steam affects the performance of a turbine by influencing the efficiency and longevity of the turbine blades. High moisture content can lead to erosion and damage to the blades, reducing the turbine's efficiency and lifespan. Keeping the steam dry and superheated, especially in the final stages of expansion, is crucial for maintaining optimal turbine performance.

Finished this topic? Mark it so your progress, study plan and readiness keep up.

Stuck on something here?

PreviousIdeal gas mixtures and thermodynamic relationsNext Brayton cycle and gas turbines