ET375 Applied Thermodynamics 09 Thermodynamic Cycles Introduction to Gas Cycles 12/1/131rm

Thermodynamic Cycles 1. Power Cycles – designed to generate a net positive work output – often simply referred to as engines Examples: gas engines, diesel engines 2. Refrigeration Cycles – designed to provide heating or cooling Examples: Refrigerator and air-conditioner to provide cooling, and heat pump to provide heating (usually for residential buildings) 12/1/132rm

Examples of systems using Thermodynamic Cycles Gasoline engines Diesel engines Jet engines Gas-turbine power plants Refrigeration Air-conditioning 12/1/133rm

Categories Gas Cycle – here the “working fluid” always remains in the gaseous phase – e.g. in an automobile engine, the working fluid is a mixture of gasoline vapor and air Vapor Cycle – here, the working fluid is alternately condensed and vaporized – e.g. steam power plants use water as the working fluid to generate most of the electricity across the world; similarly, vapor-compression refrigeration cycles are widely used for refrigeration (vapor cycles are not considered any further in these notes) 12/1/13rm4

Consideration of energy contributions in analysis of thermodynamic cycles For turbines, pumps and compressors, changes in KE and PE of the working fluid are usually neglected, because these are much smaller compared to the amount of work done For heat exchangers – such as boilers, condensers and evaporators – velocity changes are kept as low as possible to avoid large changes in KE, and to avoid pressure drops affecting changes in PE For diffusers, nozzles, etc designed specifically to create significant changes in the velocity of the working fluid, changes in KE must be included in analysis and application of energy conservation principles 12/1/13rm5

Efficiency of Power Cycles Power cycle – Thermal Efficiency – ratio of the net work output during the cycle to the heat transfer to the working fluid from the high-temperature reservoir during the cycle 12/1/13rm6

Efficiency of Refrigeration Cycles Refrigeration Cycle – Coefficient of Performance = ratio of the heat transfer to the system from the low- temperature reservoir to the work required to operate the refrigerator Heat Pump Cycle – Coefficient of Performance = ratio of heat transfer from the system to the high- temperature reservoir to the work required to operate the heat pump 12/1/13rm7

Ideal vs. Actual Cycles Ideal cycle – impossible to build – consists entirely of internally reversible processes – complicating factors such as friction and other sources of internal irreversibilities are ignored – often used as a first approach to analyzing thermodynamic cycles – note: although internally reversible, ideal cycles are not necessarily totally reversible, therefore the efficiency is less than that of a Carnot cycle operating between the same temperature limits, in other words, ηCarnot > ηideal > ηactual Actual cycle – contains irreversibilities – real life situation 12/1/13rm8

Air Standard Analysis Applicable only to gas cycles Assumptions: 1.The working fluid properties are the same as those of air 2.The working fluid is an ideal gas 3.The combustion process is replaced by heat transfer to the cycle from a high-temperature reservoir 4.The exhaust process is replaced by heat transfer from the cycle to a low-temperature reservoir 5.No intake and exhaust strokes – therefore, heat transfer is under constant volume conditions 6.All processes are internally reversible 12/1/13rm9

Ideal Gas Cycles Gas Carnot Cycle Stirling Cycle Ericsson Cycle Otto Cycle Diesel Cycle Gas Turbine Cycles 12/1/13rm10

Gas Carnot Cycle 12/1/13rm11

(Totally Reversible) Stirling Cycle 12/1/13rm12

The Stirling Cycle Two reversible, isothermal processes (1-2, 3-4) PLUS two reversible, constant volume processes where non-isothermal heat transfer occurs (2-3, 4-1) Employs regeneration processes – during which (a) heat transfer to an energy-storage device is used to cool the working fluid during one portion of the cycle, and (b) the stored energy is used in another portion of the cycle to heat the working fluid The ideal regeneration processes are not isothermal, but the heat transfer occurs through an infinitesimally small temperature difference …continued … 12/1/13rm13

The Stirling Cycle … contd-2 During process 1-2 the working fluid undergoes isothermal compression at TC, and heat transfer from the fluid to the low-temperature reservoir occurs During process 2-3 the energy stored in the generator is transferred to the working fluid, so that it undergoes constant-volume heating During process 3-4 the working fluid is heated by the high- temperature reservoir and expands isothermally at TH During process 4-1 the volume of the working fluid remains constant, its temperature decreases from TH to TC, and it transfers heat to the regenerator for storage 12/1/13rm14

The Stirling Cycle … contd-3 Since there is no heat transfer from the regenerator to the surroundings, the heat transfer to the regenerator during process 4-1 is exactly equal in magnitude to the heat transfer to the working fluid during process 2-3, i.e. ΔQ41 = - ΔQ23 In other words, all the heat added to the working fluid externally from the hot reservoir takes place isothermally during process 3-4, and all the heat rejected by the working fluid to the cold reservoir takes place isothermally during process 1-2 Therefore, the thermal efficiency of the Stirling Cycle is the same as that of the Carnot Cycle 12/1/13rm15

(Totally Reversible) Ericsson Cycle 12/1/13 rm16

The Ericsson Cycle … contd-2 Two reversible, isothermal processes (1-2, 3-4) PLUS two reversible, constant pressure processes (2-3, 4-1) Process 3-4 is isothermal and energy is added to the working fluid via heat transfer QH from the high-temperature reservoir at TH During process 4-1 the working fluid is compressed at constant pressure, and transfers heat to the regenerator until its (working fluid’s) temperature drops to TC During process 1-2 the working fluid is compressed isothermally at TC as it rejects heat Qc to the low-temperature reservoir During process 2-3 the working fluid expands at constant pressure and absorbs the energy stored in the regenerator Heat transfer from the regenerator to the working fluid during process 2-3 is equal to the heat transfer to the regenerator during process 4-1, i.e. Q23 = -Q41 12/1/13rm17

Thermal Efficiency Comparison The Carnot, Stirling and Ericsson Cycles are all totally reversible cycles Therefore, they each have the same thermal efficiency if operating between the same temperature reservoirs Thus, 12/1/13rm18

Internal Combustion (IC) Engine Spark-ignition (SI) or Compression-ignition (CI) In SI engines, the mixture of fuel and air is ignited by an external source such as a spark plug In CI engines, the mixture is compressed to a high pressure and a temperature that is higher than the ignition temperature, so that it ignites spontaneously as fuel is injected into the cylinder Examples of SI engines are 2-stroke, 4-stroke and Wankel cycle gasoline engines Diesel engines are classified as CI engines 12/1/13rm19

Piston-Cylinder Terminology Bore, Stroke Bottom dead center Top dead center Clearance volume = VTDC Displacement volume = VBDC - VTDC Compression ratio r = VBDC/VTDC Mean effective pressure MEP = Wnet/ Disp Vol 12/1/13 rm20

Four-Stroke Spark-Ignition IC Engine 12/1/13rm21

Ideal Otto Cycle 12/1/13rm22

The Ideal Otto Cycle …. Contd-2 Use a closed piston-cylinder assembly as model Ideal Otto cycle consists of internally reversible processes Closely resembles spark-ignition IC engine, even though real-life irreversibilities are not considered in the ideal model The compression (1-2) and expansion (3-4) processes are assumed to be isentropic (internally reversible, adiabatic) The combustion process (2-3) and the exhaust process (4-1) are imagined to be internally reversible, constant volume processes – here we have heat transfer but no work (v=const) The working fluid is heated during combustion, and cooled during the exhaust process 12/1/13rm23

Actual Spark-Ignition IC Engine Cycle 12/1/13 rm24

Thermal efficiency of ideal, cold air- standard Otto cycle as a function of compression ratio 12/1/13rm25

Ideal Diesel Cycle Spontaneous combustion causes extended ignition of the fuel-air mixture – combustion occurs continuously while fuel is injected into the cylinder, and the fuel continues to burn as the piston recedes from the TDC Spontaneous combustion happens because the mixture is compressed to a very high pressure and its temperature increases and causes ignition Uses fuel injectors (instead of spark plugs as in SI engines) Piston stroke is longer than in SI engines to provide a greater compression ratio 12/1/13rm26

Ideal Diesel Cycle ….contd-2 4 Internally Reversible Processes: Isentropic Compression Constant Pressure Heat Addition Isentropic Expansion Constant Volume Heat Rejection 12/1/13 rm27

Gas Turbine Power Plants Favorable power-to-weight ratio – advantage in transportation where weight is critical (aircraft, marine, etc) Also used in stationary power plants Assumptions used in analyzing the basic gas turbine cycle: - Air, as an ideal gas, is the working fluid throughout - Combustion is replaced with heat transfer from an external source Can operate as either (a) open (to the atmosphere) or (b) closed system 12/1/13rm28

Gas Turbine Power Plants ….contd-2 12/1/13rm29

Air Standard Ideal Brayton Cycle Air-standard cycle Each component piece is an open system with one inlet and one outlet Compression and expansion are modeled as isentropic Heat addition and heat rejection are modeled as isobaric 12/1/13 rm30

Basic components of an open system gas turbine Process 1-2: air drawn into compressor, where its temperature and pressure increase Process 2-3: after air leaves compressor, fuel is added and the mixture ignited in the combustion section (const pressure addition of heat) Process 3-4: high- temperature high-pressure working fluid passes through the turbine section, where energy is extracted from it in order to rotate the turbine shaft (work) 12/1/13 rm31

Open vs. Closed Brayton Cycle In the open Brayton cycle, the gases leave the turbine section and are exhausted to the atmosphere Some of the work produced in the turbine section is used to operate the compressor, and the remainder can be used to power an external device In the closed Brayton cycle, the exhaust process is replaced by a constant-pressure cooling process (heat exchanger) Although gas turbine power plants operate in an open cycle, it is assumed to operate in a closed cycle in engineering analysis, because in a closed system the working fluid executes a complete thermodynamic cycle 12/1/13rm32

Jet Propulsion Cycles In gas turbines used for jet aircraft propulsion, the entire work output from the turbine is used to operate the compressor and auxiliary systems such as electric generators and hydraulic systems In other words, the net work output of the cycle is zero The gases that exit the turbine at a relatively high pressure are subsequently accelerated in a nozzle to provide the thrust to propel the aircraft. 12/1/13rm33

Stationary Power Plant Cycles In gas turbines used in stationary power plants for power generation, the excess power produced by the turbine after powering the compressor is used to rotate an electric generator 12/1/13rm34

Turbojet applications, with and without afterburners 12/1/13 rm35