Glossary

10.1 Rankine cycle and its modifications

7 min read•july 30, 2024

The is the backbone of power plants, converting thermal energy into mechanical work. It consists of four main components: , , , and , each playing a crucial role in the cycle's efficiency and power output.

Modifications to the basic Rankine cycle, such as reheating, regeneration, and superheating, can significantly improve its performance. These enhancements increase , , and steam quality, making power plants more effective and economical in generating electricity.

Rankine cycle components and processes

Basic Rankine cycle components

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  • The basic Rankine cycle consists of four main components: pump, boiler, turbine, and condenser
    • Pump raises the pressure of the working fluid () to the boiler pressure
    • Boiler converts the high-pressure liquid water into superheated steam by adding heat at constant pressure
    • Turbine extracts work from the superheated steam, reducing its pressure and temperature
    • Condenser converts the low-pressure steam back to liquid water by rejecting heat at constant pressure

Thermodynamic processes in a Rankine cycle

  • The working fluid (water) undergoes four processes in a basic Rankine cycle:
    1. Isentropic compression in the pump (liquid water)
    2. Constant-pressure in the boiler (liquid to superheated steam)
    3. Isentropic expansion in the turbine (superheated steam)
    4. Constant-pressure in the condenser (steam to liquid water)
  • The phase change of the working fluid from liquid to vapor and back to liquid allows for efficient heat transfer and work extraction
    • Latent heat of vaporization enables high heat transfer rates in the boiler
    • High enthalpy difference between superheated steam and liquid water maximizes work output in the turbine

Thermal efficiency and Carnot efficiency

  • Thermal efficiency of a basic Rankine cycle is determined by the ratio of net work output to
    • Net work output is the difference between turbine work and pump work
    • Heat input is the energy transferred to the working fluid in the boiler
  • Carnot efficiency sets an upper limit for the thermal efficiency of a Rankine cycle operating between a given set of high and low temperatures
    • Actual Rankine cycles have lower efficiencies due to irreversibilities (friction, heat transfer across finite temperature differences, non-isentropic processes)

Rankine cycle performance analysis

Applying the First and Second Laws of Thermodynamics

  • (energy balance) is applied to analyze each component in the Rankine cycle
    • Consider heat transfer, work, and changes in enthalpy for each component
    • Steady-flow energy equation: Q−W=ΔHQ - W = \Delta H
  • Second Law of Thermodynamics is used to determine irreversibilities and losses in the cycle
    • Entropy generation due to friction, heat transfer across finite temperature differences, and non-isentropic processes
    • Isentropic efficiency of turbine and pump: ηturbine=hin−hout,actualhin−hout,isentropic\eta_{turbine} = \frac{h_{in} - h_{out,actual}}{h_{in} - h_{out,isentropic}}, ηpump=hout,isentropic−hinhout,actual−hin\eta_{pump} = \frac{h_{out,isentropic} - h_{in}}{h_{out,actual} - h_{in}}

Improving Rankine cycle efficiency

  • Increase the average temperature at which heat is added to the working fluid
    • Increase boiler pressure (supercritical Rankine cycles)
    • Increase turbine inlet temperature (superheating)
  • Decrease the average temperature at which heat is rejected from the working fluid
    • Lower condenser pressure (vacuum conditions)
    • Use a lower temperature cooling medium (river water, seawater)
  • Minimize irreversibilities in the cycle components
    • Reduce friction losses in pipes and components
    • Improve heat exchanger effectiveness (boiler and condenser)

Steam quality and turbine performance

  • Steam quality at the turbine outlet is a critical parameter for turbine performance and longevity
    • Excessive moisture (low steam quality) can cause erosion and damage to turbine blades
    • Maintain steam quality above 90% at the turbine outlet for safe and efficient operation
  • Reheat cycles can improve steam quality at the turbine outlet
    • Steam is reheated after partial expansion in the turbine, increasing its temperature and quality
    • Reheating also increases the average temperature of heat addition, improving cycle efficiency

Rankine cycle modifications and efficiency

Reheating

  • Steam is expanded in stages, with additional heat input between the stages
    • Increases the average temperature of heat addition
    • Improves steam quality at the turbine outlet
    • Increases cycle efficiency and work output
  • Reheat pressure is optimized based on the trade-off between efficiency gains and increased complexity/cost

Regeneration (feedwater heating)

  • Extract a portion of the steam at intermediate points in the turbine
    • Use extracted steam to preheat the feedwater before it enters the boiler
    • Reduces the amount of heat input required in the boiler
    • Increases cycle efficiency by reducing irreversibilities in the boiler
  • Open feedwater heaters (direct contact) and closed feedwater heaters (heat exchangers) are used for regeneration
    • Multiple feedwater heaters at different pressure levels can be employed for better heat recovery

Superheating

  • Heat the steam to higher temperatures before it enters the turbine
    • Increases the work output and efficiency of the cycle
    • Improves steam quality at the turbine outlet
    • Limited by the maximum allowable temperature of the boiler and turbine materials (creep and corrosion resistance)

Lowering condenser pressure

  • Reduce the condenser pressure (and thus the temperature) to increase cycle efficiency
    • Decreases the average temperature of heat rejection
    • Requires larger and more expensive condensers
    • May be limited by the available cooling medium temperature (ambient air, cooling water)

Combined cycles (e.g., Rankine-Brayton)

  • Utilize the waste heat from a gas turbine (Brayton cycle) to generate steam for a Rankine cycle
    • Gas turbine exhaust acts as the heat source for the steam generator
    • Increases the overall efficiency by maximizing the use of high-temperature heat
    • Achieves higher efficiencies than either cycle alone (up to 60% in modern combined cycle power plants)

Energy and mass balances in Rankine cycles

Applying the steady-flow energy equation

  • First Law of Thermodynamics for open systems: Q−W=ΔH+ΔKE+ΔPEQ - W = \Delta H + \Delta KE + \Delta PE
    • In most cases, changes in kinetic energy (KE) and potential energy (PE) are negligible
    • Steady-flow energy equation simplifies to: Q−W=ΔHQ - W = \Delta H
  • Apply the steady-flow energy equation to each component of the Rankine cycle
    • Pump: Wp=m˙(hout−hin)W_p = \dot{m}(h_{out} - h_{in})
    • Boiler: Qb=m˙(hout−hin)Q_b = \dot{m}(h_{out} - h_{in})
    • Turbine: Wt=m˙(hin−hout)W_t = \dot{m}(h_{in} - h_{out})
    • Condenser: Qc=m˙(hin−hout)Q_c = \dot{m}(h_{in} - h_{out})

Using thermodynamic property tables and charts

  • Steam tables and thermodynamic property charts are used to determine the state properties of the working fluid at various points in the cycle
    • Properties include temperature, pressure, specific volume, enthalpy, and entropy
    • Interpolation may be necessary for intermediate states
  • Mollier diagram (enthalpy-entropy chart) is particularly useful for visualizing the Rankine cycle processes
    • Isentropic processes appear as vertical lines on the Mollier diagram
    • Constant-pressure processes (boiler and condenser) appear as nearly horizontal lines

Calculating mass flow rate and cycle efficiency

  • Mass flow rate of the working fluid is determined based on the desired power output and the specific work of the turbine and pump
    • m˙=Pnetwnet=Pnetwt−wp\dot{m} = \frac{P_{net}}{w_{net}} = \frac{P_{net}}{w_t - w_p}
  • Thermal efficiency of the Rankine cycle is the ratio of net work output to heat input
    • ηth=WnetQin=Wt−WpQb\eta_{th} = \frac{W_{net}}{Q_{in}} = \frac{W_t - W_p}{Q_b}
    • Can also be expressed in terms of specific enthalpy differences: ηth=(h3−h4)−(h2−h1)h3−h2\eta_{th} = \frac{(h_3 - h_4) - (h_2 - h_1)}{h_3 - h_2}

Analyzing the effect of operating parameters

  • Boiler pressure: Increasing boiler pressure generally improves cycle efficiency
    • Higher pressure increases the average temperature of heat addition
    • Supercritical Rankine cycles operate above the critical point of water (22.1 MPa)
  • Condenser pressure: Lowering condenser pressure improves cycle efficiency
    • Lower pressure reduces the average temperature of heat rejection
    • Limited by the available cooling medium temperature and the size/cost of the condenser
  • Turbine inlet temperature: Higher turbine inlet temperature increases cycle efficiency and work output
    • Limited by the maximum allowable temperature of the boiler and turbine materials
    • Superheating is used to achieve higher turbine inlet temperatures while maintaining acceptable steam quality

Solving problems with Rankine cycle modifications

  • Reheating: Analyze the as two separate Rankine cycles in series
    • First cycle: from the boiler to the high-pressure turbine and the reheater
    • Second cycle: from the reheater to the low-pressure turbine and the condenser
    • Total work output is the sum of work from both turbine stages
  • Regeneration: Account for the extraction of steam at intermediate points in the turbine
    • Extracted steam reduces the mass flow rate through the remaining turbine stages
    • Feedwater heaters increase the enthalpy of the feedwater, reducing the heat input required in the boiler
    • Perform energy balances on each feedwater heater to determine the extraction mass flow rates
  • Combined cycles: Analyze the gas turbine (Brayton) cycle and the steam (Rankine) cycle separately
    • Gas turbine exhaust heat is the input for the steam generator in the Rankine cycle
    • Total power output is the sum of the gas turbine and steam turbine outputs
    • Overall efficiency is the ratio of the total power output to the heat input to the gas turbine

Key Terms to Review (22)

Boiler: A boiler is a device used to generate steam or hot water by transferring heat from a fuel source to water. It plays a crucial role in various thermodynamic cycles, especially in converting thermal energy into mechanical energy. The efficiency and design of the boiler significantly affect the overall performance of systems like steam power plants and combined gas-vapor cycles.
Carnot Efficiency Equation: The Carnot efficiency equation defines the maximum possible efficiency that a heat engine can achieve operating between two thermal reservoirs. It is given by the formula $$ ext{Efficiency} = 1 - \frac{T_C}{T_H}$$, where $$T_C$$ is the absolute temperature of the cold reservoir and $$T_H$$ is the absolute temperature of the hot reservoir. This concept connects deeply with heat engines and their thermal efficiency, illustrating how no engine can be more efficient than a Carnot engine, which operates on a reversible cycle known as the Carnot cycle. Understanding this equation is essential for analyzing real-world cycles like the Rankine cycle, which often seeks to approach Carnot efficiency through modifications and optimizations.
Condenser: A condenser is a heat exchanger used to condense vapor into liquid by removing heat from the vapor, usually through contact with a cooler surface or fluid. This process is crucial in various thermodynamic cycles and systems, enabling efficient heat transfer and phase change essential for energy conversion, refrigeration, and air conditioning.
Enthalpy calculations: Enthalpy calculations involve determining the total energy of a thermodynamic system, which includes internal energy and the product of pressure and volume. This concept is crucial in analyzing energy transfer during processes such as heating, cooling, phase changes, and chemical reactions. In the context of thermodynamic cycles, especially the Rankine cycle, enthalpy helps assess the efficiency and performance of power generation systems by evaluating energy input and output at different stages.
First Law of Thermodynamics: The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another, which means the total energy of an isolated system remains constant. This principle underlies various processes, cycles, and energy interactions that involve heat, work, and mass transfer in different systems.
Heat addition: Heat addition refers to the process of transferring thermal energy into a working fluid within a thermodynamic cycle, causing an increase in temperature and internal energy. This process is crucial for converting thermal energy into mechanical work, allowing systems to perform useful tasks. Heat addition typically occurs at a constant pressure or volume, depending on the specific cycle, and plays a vital role in the overall efficiency and performance of various thermodynamic systems.
Heat input: Heat input refers to the total amount of thermal energy supplied to a system, particularly in the context of energy conversion processes such as heat engines. This energy is crucial as it determines the amount of work that can be extracted from a system, ultimately influencing its overall performance and efficiency. Understanding heat input helps in analyzing how energy is transformed and utilized in various thermodynamic cycles, including those used in power generation and refrigeration.
Heat rejection: Heat rejection refers to the process of releasing heat from a system to its surroundings, typically during the operation of thermal cycles. This concept is crucial in thermodynamic systems, as it directly impacts efficiency and performance. In cycles like the Rankine cycle, heat rejection occurs in the condenser, where steam releases its latent heat and transforms back into liquid, enabling the cycle to continue efficiently.
Ideal Rankine cycle: The ideal Rankine cycle is a thermodynamic cycle that converts heat into work, typically used in steam power plants. It consists of four processes: isentropic expansion in a turbine, isobaric heat addition in a boiler, isentropic compression in a pump, and isobaric heat rejection in a condenser. This cycle is essential for understanding how thermal energy can be efficiently transformed into mechanical energy through various modifications to improve performance.
Isentropic process: An isentropic process is a thermodynamic process that occurs at constant entropy, meaning there is no heat transfer into or out of the system, and it is reversible. This concept plays a crucial role in analyzing various cycles, where it simplifies the calculations of efficiency and performance by assuming idealized conditions without entropy changes. Isentropic processes are often used to represent idealized transformations in real-world systems, linking them to key principles in energy conversion and thermodynamic efficiency.
P-v diagram: A p-v diagram is a graphical representation of the relationship between pressure (p) and volume (v) for a substance during various thermodynamic processes. It allows for the visualization of different states and changes of state that a fluid undergoes, making it an essential tool for analyzing cycles and processes such as compression, expansion, and phase changes. These diagrams help illustrate key concepts like work done during processes and efficiency in thermal systems.
Pump: A pump is a mechanical device used to move fluids, such as liquids or gases, from one place to another by imparting energy to the fluid. In thermodynamics, particularly within the context of the Rankine cycle and its modifications, pumps are essential for circulating working fluids and ensuring efficient energy transfer throughout the system.
Rankine cycle: The Rankine cycle is a thermodynamic cycle that converts heat into work through a series of processes involving a working fluid, typically water or steam. It consists of four main processes: isentropic compression, isobaric heat addition, isentropic expansion, and isobaric heat rejection, making it a foundational concept in the study of heat engines and energy conversion systems.
Refrigerants: Refrigerants are substances used in cooling systems that undergo phase changes to absorb and release heat, thereby providing refrigeration. They play a crucial role in various thermodynamic cycles, including the Rankine cycle and gas refrigeration cycles, where they facilitate the transfer of heat from one location to another to achieve desired temperature reductions.
Regenerative cycle: A regenerative cycle is a thermodynamic process that enhances the efficiency of power cycles by reusing a portion of the exhaust heat to preheat the working fluid before it enters the boiler. This process increases the overall efficiency of the system by reducing the amount of fuel needed to generate steam, thus optimizing energy use and minimizing waste. The regenerative cycle is often applied in steam power plants and is closely related to variations of the Rankine cycle and other vapor power cycles.
Reheat Cycle: A reheat cycle is a thermodynamic process where steam is expanded in a turbine, then partially condensed and reheated before being sent back to another turbine for further expansion. This method increases the overall efficiency of steam power plants by utilizing heat that would otherwise be wasted, improving thermal efficiency and allowing for greater power output.
Steam: Steam is the gaseous form of water that occurs when water is heated to its boiling point, transforming from a liquid state to a vapor. It plays a crucial role in various thermal cycles, especially in energy generation, where it acts as the working fluid that transfers heat energy from the heat source to perform mechanical work in turbines. This vapor is essential in driving turbines and generating electricity, making it a key component in many power plants and thermal systems.
T-s diagram: A t-s diagram, or temperature-entropy diagram, is a graphical representation that illustrates the relationship between temperature and entropy for a thermodynamic system. This diagram is essential in visualizing phase changes, analyzing thermodynamic cycles, and understanding the efficiency of various processes in energy systems.
Thermal efficiency: Thermal efficiency is a measure of how well an energy conversion system, such as a heat engine, converts heat energy into useful work. It is defined as the ratio of the useful work output to the heat input, typically expressed as a percentage. This concept is crucial for evaluating and optimizing the performance of various thermodynamic cycles and systems.
Turbine: A turbine is a mechanical device that converts fluid energy into mechanical work, typically by rotating blades driven by a flowing fluid such as water, steam, or gas. This conversion is crucial for various applications, particularly in energy generation and propulsion systems, where turbines play a significant role in harnessing energy from different sources.
Water: Water is a vital substance that acts as a working fluid in various thermal systems, serving as the medium for heat transfer and energy conversion. Its unique properties, such as high specific heat capacity, high latent heat of vaporization, and ability to exist in three phases (solid, liquid, gas) under standard conditions, make it an ideal choice for applications in power cycles and refrigeration systems.
Work output: Work output refers to the useful energy or work produced by a system as it converts energy from one form to another, typically in the context of thermodynamic cycles. This concept is critical in evaluating the performance and efficiency of various energy conversion devices, where maximizing work output is often a primary goal.
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