Rankine cycle with reheat and regeneration

The ideal Rankine cycle and how reheat and open or closed feedwater heating change exhaust quality, work and efficiency, with steam-table numericals.

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Why it matters

Most of the electricity used to make and charge vehicles still comes from steam power plants running on the Rankine cycle, and the same cycle is the basis of organic Rankine systems proposed for recovering heat from truck exhaust. Reheat and regeneration are the two standard modifications that raise efficiency and protect the turbine, and GATE regularly tests state-point calculations on them.

Key ideas

Ideal (simple) Rankine cycle. Four steady-flow processes with water as the working fluid: 1→2 isentropic compression of saturated liquid in the pump (condenser to boiler pressure); 2→3 constant-pressure heat addition in the boiler (subcooled liquid → superheated steam); 3→4 isentropic expansion in the turbine; 4→1 constant-pressure heat rejection in the condenser to saturated liquid. The pump handles liquid, so its work is tiny (about 1% of turbine work); this high work ratio is the main advantage over a Carnot vapour cycle.

Ways to raise efficiency. The cycle efficiency rises when the mean temperature of heat addition rises or the mean temperature of heat rejection falls:

  • Lower condenser pressure (limited by cooling-water temperature; increases exhaust moisture).
  • Higher superheat temperature (limited by metallurgy, around 600 °C).
  • Higher boiler pressure (raises efficiency but increases exhaust moisture at a fixed turbine inlet temperature).

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. Its main purpose is to keep the exhaust dryness fraction acceptable (about 0.88–0.9 or more) while using high boiler pressure. Efficiency improves only modestly and only if the mean temperature of the extra heat addition is above that of the basic cycle; very low reheat pressures can lower efficiency. A rule of thumb places reheat at about one-fifth to one-quarter of boiler pressure.

Regeneration (feedwater heating). Steam is bled (extracted) from the turbine to heat the feedwater before it enters the boiler. The low-temperature part of heat addition is replaced by internal heat exchange, so the mean temperature of heat addition rises and efficiency increases. Turbine work per kg of boiler steam falls, so more steam must be raised for the same power, but heat input falls even more.

  • Open (direct-contact) heater: bled steam mixes with feedwater; the exit is saturated liquid at the heater pressure. Each open heater needs its own pump downstream. It also serves as a deaerator.
  • Closed heater: a shell-and-tube exchanger; streams do not mix and can be at different pressures. Drains are pumped forward or cascaded backward through a trap.
  • More heaters raise efficiency with diminishing returns; large plants use 5–8.

Ideal regenerative limit. With infinitely many heaters the cycle approaches Carnot efficiency between the boiler and condenser saturation temperatures (for a saturated cycle).

Real cycles. Turbine and pump isentropic efficiencies, pressure drops and heat losses all reduce the efficiency. η_T = (h₃ − h₄)/(h₃ − h₄s); η_P = (h₂s − h₁)/(h₂ − h₁).

Formulas

w_P = v_f (P₂ − P₁) — ideal pump work, kJ/kg; v_f in m³/kg at condenser pressure; P in kPa.

w_T = h₃ − h₄ (simple); w_T = (h₃ − h₄) + (h₅ − h₆) (with reheat; 3→4 HP turbine, 4→5 reheater, 5→6 LP turbine) — kJ/kg.

q_in = (h₃ − h₂) (simple); q_in = (h₃ − h₂) + (h₅ − h₄) (reheat) — kJ/kg.

η = (w_T − w_P) / q_in = 1 − q_out / q_in

x = (s − s_f) / s_fg — quality after isentropic expansion into the wet region.

y = (h_f,heater − h_in,fw) / (h_bleed − h_in,fw) — fraction of steam bled to an open feedwater heater (energy balance: y h_bleed + (1 − y) h_in,fw = h_f,heater).

Work ratio = (w_T − w_P) / w_T; SSC = 3600 / w_net — specific steam consumption, kg/kWh, with w_net in kJ/kg.

Worked examples

Example 1 (standard, simple cycle). Steam enters the turbine at 10 MPa, 500 °C; the condenser is at 10 kPa. Find the ideal cycle efficiency. 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 = v_f ΔP = 0.00101 × (10 000 − 10) = 10.1 kJ/kg; h₂ = 191.81 + 10.1 = 201.9 kJ/kg.
  2. Turbine exit: x₄ = (s₃ − s_f)/s_fg = (6.5995 − 0.6492)/7.4996 = 0.793; h₄ = 191.81 + 0.793 × 2392.1 = 2089.7 kJ/kg.
  3. w_T = 3375.1 − 2089.7 = 1285.4 kJ/kg; q_in = 3375.1 − 201.9 = 3173.2 kJ/kg.
  4. η = (w_T − w_P)/q_in = (1285.4 − 10.1)/3173.2 = 0.402 (40.2%).

The exhaust is 21% moisture, which is too wet for a real turbine; this is what reheat fixes.

Example 2 (GATE level, reheat). Steam at 15 MPa, 550 °C expands isentropically to 3 MPa, is reheated to 550 °C and expands isentropically to 10 kPa. Data: h₃ = 3450.5 kJ/kg (15 MPa, 550 °C); h₄ = 2984.0 kJ/kg (3 MPa, s = s₃); h₅ = 3569.6 kJ/kg, s₅ = 7.3767 kJ/kg·K (3 MPa, 550 °C). Condenser data as in Example 1. Find the exhaust quality and the efficiency.

  1. Pump: w_P = 0.00101 × (15 000 − 10) = 15.1 kJ/kg; h₂ = 191.81 + 15.1 = 206.9 kJ/kg.
  2. LP exit: x₆ = (s₅ − s_f)/s_fg = (7.3767 − 0.6492)/7.4996 = 0.897; h₆ = 191.81 + 0.897 × 2392.1 = 2337.6 kJ/kg.
  3. Turbine work: w_T = (h₃ − h₄) + (h₅ − h₆) = 466.5 + 1232.0 = 1698.5 kJ/kg.
  4. Heat input: q_in = (h₃ − h₂) + (h₅ − h₄) = 3243.6 + 585.6 = 3829.2 kJ/kg.
  5. η = (1698.5 − 15.1)/3829.2 = 0.440 (44.0%).

Without reheat, the same boiler conditions give x ≈ 0.783 and η ≈ 42.2%. Reheat raised the exhaust quality from 0.78 to 0.90, and the efficiency by about 1.7 percentage points.

Example 3 (regeneration, short). For the cycle of Example 1, add one open feedwater heater supplied with steam bled at 1 MPa (h = 2783.6 kJ/kg, h_f at 1 MPa = 762.7 kJ/kg). The condensate pump raises h to 192.8 kJ/kg. Bled fraction y = (762.7 − 192.8)/(2783.6 − 192.8) = 0.220. Working through turbine work (1132.8 kJ/kg), total pump work (10.9 kJ/kg) and heat input (3375.1 − 772.8 = 2602.3 kJ/kg) gives η ≈ 43.1%, up from 40.2%.

Common mistakes

  • Using h_g instead of h_f + x h_fg for wet turbine exhaust.
  • Forgetting the reheater heat in q_in, or forgetting the second turbine in w_T.
  • Using the boiler-pressure v_f in the pump-work formula; use the liquid entering the pump.
  • In regeneration, multiplying the whole turbine work by the full mass flow; after the bleed point only (1 − y) continues.
  • Expecting reheat to raise efficiency a lot; its main job is exhaust dryness.
  • Mixing pressure units in v ΔP (kPa gives kJ/kg directly).

For GATE ME

Expect complete cycle numericals with steam-table data given in the question: pump work, quality at turbine exit, net work, efficiency, steam rate, and the effect of reheat or one open feedwater heater (find the bled fraction). Conceptual MCQs test what happens to efficiency, moisture and work ratio when boiler pressure, superheat or condenser pressure change. Practise drawing the T–s diagram and labelling state points before any arithmetic.

Quick check

  1. Why is the pump work in a Rankine cycle so small?
  2. What is the main purpose of reheat?
  3. Does turbine work per kg of boiler steam rise or fall with regeneration?
  4. A turbine produces 1200 kJ/kg and the pump takes 12 kJ/kg; heat input is 3000 kJ/kg. What is the efficiency?

Answers: 1. It compresses liquid, whose specific volume is about a thousandth of steam's. 2. To keep the turbine exhaust dryness fraction acceptable at high boiler pressure. 3. It falls, but heat input falls proportionally more. 4. (1200 − 12)/3000 = 0.396 (39.6%).

Interview questions

All Thermodynamics and Heat Transfer 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, while regeneration involves preheating the feedwater using steam extracted from the turbine. This reduces the moisture content at the turbine exhaust and increases the average temperature at which heat is added to the cycle.

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

    The main purpose of reheat is to keep the turbine exhaust dry enough, roughly 0.88–0.9 quality or better, so that high boiler pressures can be used without the last stages eroding. Steam is expanded in the HP turbine to an intermediate pressure, returned to the boiler and reheated to about the original temperature, then expanded in the LP turbine. Efficiency rises only modestly, by a percentage point or two, and only if the reheat pressure is high enough that the extra heat is added at a high mean temperature; a typical choice is about one-fifth to one-quarter of the boiler pressure.

  3. 3.Why is regeneration used in the Rankine cycle?Concept

    Regeneration is used in the Rankine cycle to improve thermal efficiency by preheating the feedwater before it enters the boiler. This is done by extracting steam from the turbine and using it to heat the feedwater in feedwater heaters. This process increases the average temperature at which heat is added to the cycle, thereby reducing fuel consumption.

  4. 4.How does the Rankine cycle with reheat and regeneration differ from the basic Rankine cycle?Concept

    The basic Rankine cycle consists of four processes: isentropic compression, constant pressure heat addition, isentropic expansion, and constant pressure heat rejection. The Rankine cycle with reheat and regeneration adds complexity by including reheating and feedwater heating processes. Reheating involves expanding steam in multiple stages with reheating between stages, while regeneration involves using extracted steam to preheat the feedwater, both of which improve efficiency.

  5. 5.What happens if the reheat temperature is too high in the Rankine cycle?Application

    If the reheat temperature is too high, it can lead to material stress and potential damage to the turbine and other components due to excessive thermal expansion. It may also increase the risk of thermal fatigue and reduce the lifespan of the equipment. Therefore, reheat temperatures must be carefully controlled to balance efficiency gains with material limitations.

  6. 6.Why is it important to control the moisture content at the turbine exhaust in the Rankine cycle?Application

    Controlling the moisture content at the turbine exhaust is important to prevent erosion and damage to the turbine blades. High moisture content can lead to water droplet formation, which can cause mechanical wear and reduce the efficiency and lifespan of the turbine. Reheating helps to reduce this moisture content by increasing the steam temperature during expansion.

  7. 7.What are the advantages of using multiple feedwater heaters in the Rankine cycle with regeneration?Application

    Using multiple feedwater heaters in the Rankine cycle with regeneration allows for more stages of feedwater heating, which increases the average temperature of heat addition. This improves the thermal efficiency of the cycle by reducing the amount of fuel needed to achieve the desired steam conditions. It also allows for better control of the feedwater temperature and reduces thermal stresses on the boiler.

  8. 8.Estimate the ideal efficiency of a reheat Rankine cycle: turbine inlet 15 MPa, 550 °C; reheat at 3 MPa back to 550 °C; condenser at 10 kPa.Numerical

    From steam tables: h₃ ≈ 3450.5 kJ/kg at 15 MPa, 550 °C; isentropic expansion to 3 MPa gives h₄ ≈ 2984 kJ/kg; after reheat h₅ ≈ 3569.6 kJ/kg with s₅ ≈ 7.377 kJ/kg·K; expansion to 10 kPa gives x₆ ≈ 0.897 and h₆ ≈ 2337.6 kJ/kg. Pump work is v_f·ΔP ≈ 0.00101 × 14 990 ≈ 15.1 kJ/kg, so h₂ ≈ 206.9 kJ/kg. Turbine work is 466.5 + 1232.0 = 1698.5 kJ/kg and heat input is (3450.5 − 206.9) + (3569.6 − 2984.0) = 3829.2 kJ/kg. Efficiency ≈ (1698.5 − 15.1)/3829.2 ≈ 0.44, or about 44%.

  9. 9.If the condenser pressure in a Rankine cycle with reheat and regeneration is increased, what effect does it have on the cycle efficiency?Application

    Increasing the condenser pressure in a Rankine cycle generally decreases the cycle efficiency. This is because a higher condenser pressure results in a higher temperature at which heat is rejected, reducing the temperature difference between the heat source and sink. This decreases the overall thermal efficiency of the cycle.

  10. 10.Roughly how much does a single reheat improve an ideal Rankine cycle at 15 MPa, 500 °C and 10 kPa, if the steam is reheated at 3 MPa back to 500 °C?Numerical

    Working both cycles with steam tables: the simple cycle gives an exhaust quality of about 0.76 and an efficiency of about 41.4%. With reheat at 3 MPa to 500 °C, the exhaust quality rises to about 0.88 and the efficiency to about 42.8%. So efficiency improves by only about 1.4 percentage points, while the exhaust moisture falls from about 24% to 12%. The answer an interviewer wants is that reheat is mainly a moisture-control measure with a modest efficiency bonus.

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