Gas Power CyclesGas Power Cycles

Power CyclesPower Cycles

Ideal Cycles, Internal CombustionIdeal Cycles, Internal Combustion Otto cycle, spark ignitionOtto cycle, spark ignition Diesel cycle, compression ignitionDiesel cycle, compression ignition Sterling & Ericsson cyclesSterling & Ericsson cycles Brayton cyclesBrayton cycles Jet-propulsion cycleJet-propulsion cycle

Ideal Cycles, External CombustionIdeal Cycles, External Combustion Rankine cycleRankine cycle

ModelingModeling

Ideal CyclesIdeal Cycles Idealizations & SimplificationsIdealizations & Simplifications

Cycle does not involve any frictionCycle does not involve any friction All expansion and compression All expansion and compression

processes are quasi-equilibrium processes are quasi-equilibrium processesprocesses

Pipes connecting components have no Pipes connecting components have no heat lossheat loss

Neglecting changes in kinetic and Neglecting changes in kinetic and potential energy (except in nozzles & potential energy (except in nozzles & diffusers)diffusers)

Carnot CycleCarnot Cycle

Carnot CycleCarnot Cycle

Gas Power CyclesGas Power Cycles

Working fluid remains a gas for the Working fluid remains a gas for the entire cycleentire cycle

Examples:Examples: Spark-ignition enginesSpark-ignition engines Diesel enginesDiesel engines Gas turbinesGas turbines

Air-Standard Assumptions Air-Standard Assumptions

Air is the working fluid, circulated in a Air is the working fluid, circulated in a closed loop, is an ideal gasclosed loop, is an ideal gas

All cycles, processes are internally All cycles, processes are internally reversiblereversible

Combustion process replaced by heat-Combustion process replaced by heat-addition from external sourceaddition from external source

Exhaust is replaced by heat rejection Exhaust is replaced by heat rejection process which restores working fluid to process which restores working fluid to initial stateinitial state

Cold-Air-Standard AssumptionCold-Air-Standard Assumption

Air has constant specific heats, Air has constant specific heats, values are for room temperature values are for room temperature (25°C or 77(25°C or 77°F)°F)

Engine TermsEngine Terms

Top dead centerTop dead center Bottom dead Bottom dead

centercenter BoreBore StrokeStroke

Engine TermsEngine Terms

Clearance volumeClearance volume Displacement Displacement

volumevolume Compression ratioCompression ratio

Engine TermsEngine Terms

Mean effective Mean effective pressure (MEP)pressure (MEP)

Otto CycleOtto Cycle

Processes of Otto Cycle:Processes of Otto Cycle: Isentropic compressionIsentropic compression Constant-Constant-volumevolume heat addition heat addition Isentropic expansionIsentropic expansion Constant-Constant-volumevolume heat rejection heat rejection

Otto CycleOtto Cycle

Otto CycleOtto Cycle

IdealIdeal Otto Cycle Otto Cycle Four internally Four internally

reversible processesreversible processes 1-2 Isentropic 1-2 Isentropic

compressioncompression 2-3 Constant-volume 2-3 Constant-volume

heat additionheat addition 3-4 Isentropic 3-4 Isentropic

expansionexpansion 4-1 Constant-volume 4-1 Constant-volume

heat rejectionheat rejection

Otto CycleOtto Cycle

Closed system, pe, ke ≈ 0 Closed system, pe, ke ≈ 0 Energy balance (cold air std)Energy balance (cold air std)

Otto CycleOtto Cycle

Thermal efficiency of ideal Otto cycle:Thermal efficiency of ideal Otto cycle:

Since Since VV22= V= V33 and and VV44 = V = V11

Where r is compression ratioWhere r is compression ratio

k is ratio of specific heatsk is ratio of specific heats

Otto CycleOtto Cycle

Spark or Compression IgnitionSpark or Compression Ignition

Spark (Otto), air-fuel Spark (Otto), air-fuel mixture compressed mixture compressed (constant-volume heat (constant-volume heat addition)addition)

Compression (Diesel), Compression (Diesel), air compressed, then air compressed, then fuel added (constant-fuel added (constant-pressure heat pressure heat addition)addition)

Diesel CycleDiesel Cycle

Diesel CycleDiesel Cycle

Processes of Diesel cycle:Processes of Diesel cycle: Isentropic compressionIsentropic compression Constant-Constant-pressurepressure heat addition heat addition Isentropic expansionIsentropic expansion Constant-Constant-volumevolume heat rejection heat rejection

Diesel CycleDiesel Cycle

For ideal diesel cycleFor ideal diesel cycle

With cold air assumptionsWith cold air assumptions

Diesel CycleDiesel Cycle

Cut off ratio rCut off ratio rcc

Efficiency becomesEfficiency becomes

Brayton CycleBrayton Cycle

Gas turbine cycleGas turbine cycle Open vs closed Open vs closed

system modelsystem model

Brayton CycleBrayton Cycle

Four internally Four internally reversible processesreversible processes 1-2 Isentropic 1-2 Isentropic

Compression Compression (compressor)(compressor)

2-3 Constant-pressure 2-3 Constant-pressure heat additionheat addition

3-4 Isentropic 3-4 Isentropic expansion (turbine)expansion (turbine)

4-1 Constant-pressure 4-1 Constant-pressure heat rejectionheat rejection

Brayton CycleBrayton Cycle

Analyze as steady-flow processAnalyze as steady-flow process

SoSo

With cold-air-standard assumptionsWith cold-air-standard assumptions

Brayton CycleBrayton Cycle

Since processes 1-2 and 3-4 are Since processes 1-2 and 3-4 are isentropic, Pisentropic, P22 = P = P33 and P and P44 = P = P11

wherewhere

Brayton CycleBrayton Cycle

Brayton CycleBrayton Cycle

Back work ratioBack work ratio Improvements in Improvements in gas turbinesgas turbines Combustion tempCombustion temp Machinery Machinery

component component efficienciesefficiencies

Adding Adding modifications to modifications to basic cyclebasic cycle

Actual Gas-Turbine CyclesActual Gas-Turbine Cycles

For actual gas For actual gas turbines, turbines, compressor and compressor and turbine are not turbine are not isentropic isentropic

RegenerationRegeneration

RegenerationRegeneration

Use heat Use heat exchanger called exchanger called recuperator or recuperator or regeneratorregenerator

Counter flowCounter flow

RegenerationRegeneration

EffectivenessEffectiveness

For cold-air For cold-air assumptionsassumptions

Brayton with Intercooling, Brayton with Intercooling, Reheat, & RegenerationReheat, & Regeneration

Brayton with Intercooling, Brayton with Intercooling, Reheat, & RegenerationReheat, & Regeneration

For max For max performance performance

Ideal Jet-Propulsion CyclesIdeal Jet-Propulsion Cycles

Ideal Jet-Propulsion CyclesIdeal Jet-Propulsion Cycles

Propulsive powerPropulsive power

Propulsive efficiencyPropulsive efficiency

Turbojet EnginesTurbojet Engines

Turbofan: for same power, large Turbofan: for same power, large volume of slower-moving air volume of slower-moving air produces more thrust than a small produces more thrust than a small volume of fast-moving air (bypass volume of fast-moving air (bypass ratio 5-6)ratio 5-6)

Turboprop: by pass ratio of 100Turboprop: by pass ratio of 100

JetsJets

Afterburner: addition to turbojetAfterburner: addition to turbojet Ramjet: use diffusers and nozzlesRamjet: use diffusers and nozzles Scramjet: supersonic ramjet Scramjet: supersonic ramjet Rocket: carries own oxidizerRocket: carries own oxidizer

Second Law IssuesSecond Law Issues

Ideal Otto, Diesel, and Brayton cycles Ideal Otto, Diesel, and Brayton cycles are internally reversibleare internally reversible

22ndnd Law analysis identifies where Law analysis identifies where losses are so improvements can be losses are so improvements can be mademade

Look at closed, steady-flow systemsLook at closed, steady-flow systems

Second Law IssuesSecond Law Issues

For exergy and exergy destruction For exergy and exergy destruction for closed for closed systemsystem::

For steady-flow For steady-flow systemsystem::

Second Law IssuesSecond Law Issues

For a cycle that starts and end at the For a cycle that starts and end at the same state:same state: