Chapter 9 POWER AND REFRIGERATION CYCLES Copyright © 2012 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Fundamentals.

Chapter 9POWER AND REFRIGERATION

CYCLES

Copyright © 2012 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Fundamentals of Thermal-Fluid Sciences 4th Edition in SI Units

Yunus A. Çengel, John M. Cimbala, Robert H. TurnerMcGraw-Hill, 2012

Lecture slides by

Mehmet Kanoğlu

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Objectives• Evaluate the performance of gas power cycles.

• Develop simplifying assumptions applicable to gas power cycles.

• Review the operation of reciprocating engines.

• Solve problems based on the Otto and Diesel cycles.

• Solve problems based on the Brayton cycle and the Brayton cycle with regeneration.

• Analyze vapor power cycles in which the working fluid is alternately vaporized and condensed.

• Investigate ways to modify the basic Rankine vapor power cycle to increase the cycle thermal efficiency.

• Analyze the reheat vapor power cycles.

• Analyze the ideal vapor-compression refrigeration cycle.

• Discuss the operation of refrigeration and heat pump systems.

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9-1 BASIC CONSIDERATIONS IN THE ANALYSIS OF POWER CYCLES

Modeling is a powerful engineering tool that provides great insight and simplicity at the expense of some loss in accuracy.

Most power-producing devices operate on cycles.

Ideal cycle: A cycle that resembles the actual cycle closely but is made up totally of internally reversible processes is called an.

Reversible cycles such as Carnot cycle have the highest thermal efficiency of all heat engines operating between the same temperature levels. Unlike ideal cycles, they are totally reversible, and unsuitable as a realistic model.

Thermal efficiency of heat engines:

The analysis of many complex processes can be reduced to a manageable level by utilizing some idealizations.

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The ideal cycles are internally reversible, but, unlike the Carnot cycle, they are not necessarily externally reversible. Therefore, the thermal efficiency of an ideal cycle, in general, is less than that of a totally reversible cycle operating between the same temperature limits. However, it is still considerably higher than the thermal efficiency of an actual cycle because of the idealizations utilized.

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The idealizations and simplifications in the analysis of power cycles:

1. The cycle does not involve any friction. Therefore, the working fluid does not experience any pressure drop as it flows in pipes or devices such as heat exchangers.

2. All expansion and compression processes take place in a quasi-equilibrium manner.

3. The pipes connecting the various components of a system are well insulated, and heat transfer through them is negligible.

Care should be exercised in the interpretation of the results from ideal cycles.

On both P-v and T-s diagrams, the area enclosed by the process curve represents the net work of the cycle.

On a T-s diagram, the ratio of the area enclosed by the cyclic curve to the area under the heat-addition process curve represents the thermal efficiency of the cycle. Any modification that increases the ratio of these two areas will also increase the thermal efficiency of the cycle.

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9-2 THE CARNOT CYCLE AND ITS VALUE IN ENGINEERING

P-v and T-s diagrams of a Carnot cycle.

The Carnot cycle is composed of four totally reversible processes: isothermal heat addition, isentropic expansion, isothermal heat rejection, and isentropic compression.

For both ideal and actual cycles: Thermal efficiency increases with an increase in the average temperature at which heat is supplied to the system or with a decrease in the average temperature at which heat is rejected from the system.

A steady-flow Carnot engine.

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9-3 AIR-STANDARD ASSUMPTIONS

The combustion process is replaced by a heat-addition process in ideal cycles.

Air-standard assumptions:

1. The working fluid is air, which continuously circulates in a closed loop and always behaves as an ideal gas.

2. All the processes that make up the cycle are internally reversible.

3. The combustion process is replaced by a heat-addition process from an external source.

4. The exhaust process is replaced by a heat-rejection process that restores the working fluid to its initial state.

Cold-air-standard assumptions: When the working fluid is considered to be air with constant specific heats at room temperature (25°C).

Air-standard cycle: A cycle for which the air-standard assumptions are applicable.

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9-4 AN OVERVIEW OF RECIPROCATING ENGINES

Nomenclature for reciprocating engines.

• Spark-ignition (SI) engines

• Compression-ignition (CI) engines

Compression ratio

Mean effective pressure

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9-5 OTTO CYCLE: THE IDEAL CYCLE FOR SPARK-IGNITION ENGINES

Actual and ideal cycles in spark-ignition engines and their P-v diagrams.

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Schematic of a two-stroke reciprocating engine.

The two-stroke engines are generally less efficient than their four-stroke counterparts but they are relatively simple and inexpensive, and they have high power-to-weight and power-to-volume ratios.

T-s diagram of the ideal Otto cycle.

Four-stroke cycle1 cycle = 4 stroke = 2 revolutionTwo-stroke cycle1 cycle = 2 stroke = 1 revolution

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The thermal efficiency of the Otto cycle increases with the specific heat ratio k of the working fluid.

Thermal efficiency of the ideal Otto cycle as a function of compression ratio (k = 1.4).

In SI engines, the compression ratio is limited by autoignition or engine knock.

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9-6 DIESEL CYCLE: THE IDEAL CYCLEFOR COMPRESSION-IGNITION ENGINES

In diesel engines, the spark plug is replaced by a fuel injector, and only air is compressed during the compression process.

In diesel engines, only air is compressed during the compression stroke, eliminating the possibility of autoignition (engine knock). Therefore, diesel engines can be designed to operate at much higher compression ratios than SI engines, typically between 12 and 24.

1-2 isentropic compression

2-3 constant-volume heat addition

3-4 isentropic expansion

4-1 constant-volume heat rejection.

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Thermal efficiency of the ideal Diesel cycle as a function of compression and cutoff ratios (k=1.4).

Cutoff ratio

for the same compression ratio

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QUESTIONS ???

Diesel engines operate at higher air-fuel ratios than gasoline engines. Why?

Despite higher power to weight ratios, two-stroke engines are not used in automobiles. Why?

The stationary diesel engines are among the most efficient power producing devices (about 50%). Why?

What is a turbocharger? Why are they mostly used in diesel engines compared to gasoline engines.

P-v diagram of an ideal dual cycle.

Dual cycle: A more realistic ideal cycle model for modern, high-speed compression ignition engine.

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9-7 BRAYTON CYCLE: THE IDEAL CYCLE FOR GAS-TURBINE ENGINES

An open-cycle gas-turbine engine. A closed-cycle gas-turbine engine.

The combustion process is replaced by a constant-pressure heat-addition process from an external source, and the exhaust process is replaced by a constant-pressure heat-rejection process to the ambient air. 1-2 Isentropic compression (in a compressor)2-3 Constant-pressure heat addition3-4 Isentropic expansion (in a turbine)4-1 Constant-pressure heat rejection

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T-s and P-v diagrams for the ideal Brayton cycle.

Pressure ratio

Thermal efficiency of the

ideal Brayton cycle as a

function of the pressure ratio.

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The fraction of the turbine work used to drive the compressor is called the back work ratio.

The two major application areas of gas-turbine engines are aircraft propulsion and electric power generation.

The highest temperature in the cycle is limited by the maximum temperature that the turbine blades can withstand. This also limits the pressure ratios that can be used in the cycle.

The air in gas turbines supplies the necessary oxidant for the combustion of the fuel, and it serves as a coolant to keep the temperature of various components within safe limits. An air–fuel ratio of 50 or above is not uncommon.

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Development of Gas Turbines1. Increasing the turbine inlet (or firing) temperatures2. Increasing the efficiencies of turbomachinery components (turbines,

compressors):3. Adding modifications to the basic cycle (intercooling, regeneration or

recuperation, and reheating).

Deviation of Actual Gas-Turbine Cycles from Idealized Ones

The deviation of an actual gas-turbine cycle from the ideal Brayton cycle as a result of irreversibilities.

Reasons: Irreversibilities in turbine and compressors, pressure drops, heat losses

Isentropic efficiencies of the compressor and turbine

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9-8 THE BRAYTON CYCLE WITH REGENERATION

In gas-turbine engines, the temperature of the exhaust gas leaving the turbine is often considerably higher than the temperature of the air leaving the compressor.

Therefore, the high-pressure air leaving the compressor can be heated by the hot exhaust gases in a counter-flow heat exchanger (a regenerator or a recuperator).

The thermal efficiency of the Brayton cycle increases as a result of regeneration since less fuel is used for the same work output.

T-s diagram of a Brayton cycle with

regeneration.

A gas-turbine engine with regenerator.

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T-s diagram of a Brayton cycle with regeneration.

Effectiveness of regenerator

Effectiveness under cold-air standard assumptions

Under cold-air standard assumptions

Thermal efficiency of the

ideal Brayton cycle with and

without regeneration.

The thermal efficiency depends on the ratio of the minimum to maximum temperatures as well as the pressure ratio.

Regeneration is most effective at lower pressure ratios and low minimum-to-maximum temperature ratios.

Can regeneration be used at high pressure ratios?

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9-9 THE CARNOT VAPOR CYCLE

T-s diagram of two Carnot vapor cycles.

The Carnot cycle is the most efficient cycle operating between two specified temperature limits but it is not a suitable model for power cycles. Because:

Process 1-2 Limiting the heat transfer processes to two-phase systems severely limits the maximum temperature that can be used in the cycle (374°C for water)

Process 2-3 The turbine cannot handle steam with a high moisture content because of the impingement of liquid droplets on the turbine blades causing erosion and wear.

Process 4-1 It is not practical to design a compressor that handles two phases.

The cycle in (b) is not suitable since it requires isentropic compression to extremely high pressures and isothermal heat transfer at variable pressures.

1-2 isothermal heat addition in a boiler 2-3 isentropic expansion in a turbine 3-4 isothermal heat rejection in a condenser4-1 isentropic compression in a compressor

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9-10 RANKINE CYCLE: THE IDEAL CYCLEFOR VAPOR POWER CYCLES

Many of the impracticalities associated with the Carnot cycle can be eliminated by superheating the steam in the boiler and condensing it completely in the condenser.

The cycle that results is the Rankine cycle, which is the ideal cycle for vapor power plants. The ideal Rankine cycle does not involve any internal irreversibilities.

The simple ideal Rankine cycle.

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Energy Analysis of the Ideal Rankine Cycle

The efficiency of power plants in the U.S. is often expressed in terms of heat rate, which is the amount of heat supplied, in Btu’s, to generate 1 kWh of electricity. The thermal efficiency can be interpreted

as the ratio of the area enclosed by the cycle on a T-s diagram to the area under the heat-addition process.

Steady-flow energy equation

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9-11 DEVIATION OF ACTUAL VAPOR POWER CYCLES FROM IDEALIZED ONES

(a) Deviation of actual vapor power cycle from the ideal Rankine cycle. (b) The effect of pump and turbine irreversibilities on the ideal Rankine cycle.

The actual vapor power cycle differs from the ideal Rankine cycle as a result of irreversibilities in various components.

Fluid friction and heat loss to the surroundings are the two common sources of irreversibilities.

Isentropic efficiencies

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9-12 HOW CAN WE INCREASE THE EFFICIENCY OF THE RANKINE CYCLE?

The effect of lowering the condenser pressure on the ideal Rankine cycle.

The basic idea behind all the modifications to increase the thermal efficiencyof a power cycle is the same: Increase the average temperature at which heat is transferred to the working fluid in the boiler, or decrease the average temperature at which heat is rejected from the working fluid in the condenser.

Lowering the Condenser Pressure (Lowers Tlow,avg)To take advantage of the increased efficiencies at low pressures, the condensers of steam power plants usually operate well below the atmospheric pressure. There is a lower limit to this pressure depending on the temperature of the cooling medium

Side effect: Lowering the condenser pressure increases the moisture content of the steam at the final stages of the turbine.

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The effect of superheating the steam to higher temperatures on the ideal Rankine cycle.

Superheating the Steam to High Temperatures (Increases Thigh,avg)

Both the net work and heat input increase as a result of superheating the steam to a higher temperature. The overall effect is an increase in thermal efficiency since the average temperature at which heat is added increases.

Superheating to higher temperatures decreases the moisture content of the steam at the turbine exit, which is desirable.

The temperature is limited by metallurgical considerations. Presently the highest steam temperature allowed at the turbine inlet is about 620°C.

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Increasing the Boiler Pressure (Increases Thigh,avg)

The effect of increasing the boiler pressure on the ideal Rankine cycle.

For a fixed turbine inlet temperature, the cycle shifts to the left and the moisture content of steam at the turbine exit increases. This side effect can be corrected by reheating the steam.

A supercritical Rankine cycle.

Today many modern steam power plants operate at supercritical pressures (P > 22.06 MPa) and have thermal efficiencies of about 40% for fossil-fuel plants and 34% for nuclear plants.

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9-13 THE IDEAL REHEAT RANKINE CYCLEHow can we take advantage of the increased efficiencies at higher boiler pressures without facing the problem of excessive moisture at the final stages of the turbine?

1. Superheat the steam to very high temperatures. It is limited metallurgically.

2. Expand the steam in the turbine in two stages, and reheat it in between (reheat)

The ideal reheat Rankine cycle.

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The average temperature at which heat is transferred during reheating increases as the number of reheat stages is increased.

The single reheat in a modern power plant improves the cycle efficiency by 4 to 5% by increasing the average temperature at which heat is transferred to the steam.

The average temperature during the reheat process can be increased by increasing the number of expansion and reheat stages. As the number of stages is increased, the expansion and reheat processes approach an isothermal process at the maximum temperature. The use of more than two reheat stages is not practical. The theoretical improvement in efficiency from the second reheat is about half of that which results from a single reheat.

The reheat temperatures are very close or equal to the turbine inlet temperature.

The optimum reheat pressure is about one-fourth of the maximum cycle pressure.

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9-14 REFRIGERATORS AND HEAT PUMPS

The objective of a refrigerator is to remove heat (QL) from the cold medium; the objective of a heat pump is to supply heat (QH) to a warm medium.

The transfer of heat from a low-temperature region to a high-temperature one requires special devices called refrigerators.Another device that transfers heat from a low-temperature medium to a high-temperature one is the heat pump.Refrigerators and heat pumps are essentially the same devices; they differ in their objectives only.

for fixed values of QL and QH

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9-15 THE REVERSED CARNOT CYCLE

Schematic of a Carnot refrigerator and T-s diagram of the reversed Carnot cycle.

Both COPs increase as the difference between the two temperaturesdecreases, that is, as TL rises or TH falls.

The reversed Carnot cycle is the most efficient refrig. cycle operating between TL and TH.

It is not a suitable model for refrigeration cycles since processes 2-3 and 4-1 are not practical because Process 2-3 involves the compression of a liquid–vapor mixture, which requires a compressor that will handle two phases, and process 4-1 involves the expansion of high-moisture-content refrigerant in a turbine.

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9-16 THE IDEAL VAPOR-COMPRESSION REFRIGERATION CYCLEThe vapor-compression refrigeration cycle is the ideal model for refrigeration systems. Unlike the reversed Carnot cycle, the refrigerant is vaporized completely before it is compressed and the turbine is replaced with a throttling device.

Schematic and T-s diagram for the ideal vapor-compression refrigeration cycle.

This is the most widely used cycle for refrigerators, A-C systems, and heat pumps.

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An ordinary household refrigerator.

The P-h diagram of an ideal vapor-compression refrigeration cycle.

The ideal vapor-compression refrigeration cycle involves an irreversible (throttling) process to make it a more realistic model for the actual systems. Replacing the expansion valve by a turbine is not practical since the added benefits cannot justify the added cost and complexity.

Steady-flow energy balance

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9-17 ACTUAL VAPOR-COMPRESSION REFRIGERATION CYCLEAn actual vapor-compression refrigeration cycle differs from the ideal one owing mostly to the irreversibilities that occur in various components, mainly due to fluid friction (causes pressure drops) and heat transfer to or from the surroundings.

Schematic and T-s diagram for the actual vapor-compression refrigeration cycle.

DIFFERENCESNon-isentropic compressionSuperheated vapor at evaporator exitSubcooled liquid at condenser exitPressure drops in condenser and evaporator

The COP decreases as a result of irreversibilities.

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Summary• Basic considerations in the analysis of power cycles

• The Carnot cycle and its value in engineering

• Air-standard assumptions

• An overview of reciprocating engines

• Otto cycle: The ideal cycle for spark-ignition engines

• Diesel cycle: The ideal cycle for compression-ignition engines

• Brayton cycle: The ideal cycle for gas-turbine engines

• The Brayton cycle with regeneration

• The Carnot vapor cycle

• Rankine cycle: The ideal cycle for vapor power cycles

• Deviation of actual vapor power cycles from idealized ones

• How can we increase the efficiency of the Rankine cycle?

• The ideal reheat Rankine cycle

• Refrigerators and Heat Pumps

• The Reversed Carnot Cycle

• The Ideal Vapor-Compression Refrigeration Cycle

• Actual Vapor-Compression Refrigeration Cycle