Week 8 Gas Power Cycles

Gas Power Cycles

Power CyclesIdeal Cycles, Internal CombustionOtto cycle, spark ignitionDiesel cycle, compression ignitionSterling & Ericsson cyclesBrayton cyclesJet-propulsion cycleIdeal Cycles, External CombustionRankine cycle

Modeling

Ideal CyclesIdealizations & SimplificationsCycle does not involve any frictionAll expansion and compression processes are quasi-equilibrium processesPipes connecting components have no heat lossNeglecting changes in kinetic and potential energy (except in nozzles & diffusers)

Carnot Cycle

Carnot Cycle

Gas Power CyclesWorking fluid remains a gas for the entire cycleExamples:Spark-ignition enginesDiesel enginesGas turbines

Air-Standard Assumptions Air is the working fluid, circulated in a closed loop, is an ideal gasAll cycles, processes are internally reversibleCombustion process replaced by heat-addition from external sourceExhaust is replaced by heat rejection process which restores working fluid to initial state

Cold-Air-Standard AssumptionAir has constant specific heats, values are for room temperature (25C or 77F)

Engine TermsTop dead centerBottom dead centerBoreStroke

Engine TermsClearance volumeDisplacement volumeCompression ratio

Engine TermsMean effective pressure (MEP)

Otto CycleProcesses of Otto Cycle:Isentropic compressionConstant-volume heat additionIsentropic expansionConstant-volume heat rejection

Otto Cycle

Otto CycleIdeal Otto CycleFour internally reversible processes1-2 Isentropic compression2-3 Constant-volume heat addition3-4 Isentropic expansion4-1 Constant-volume heat rejection

Otto CycleClosed system, pe, ke 0 Energy balance (cold air std)

Otto CycleThermal efficiency of ideal Otto cycle:

Since V2= V3 and V4 = V1

Where r is compression ratiok is ratio of specific heats

Otto Cycle

Spark or Compression IgnitionSpark (Otto), air-fuel mixture compressed (constant-volume heat addition)Compression (Diesel), air compressed, then fuel added (constant-pressure heat addition)

Diesel Cycle

Diesel CycleProcesses of Diesel cycle:Isentropic compressionConstant-pressure heat addition Isentropic expansionConstant-volume heat rejection

Diesel CycleFor ideal diesel cycle

With cold air assumptions

Diesel CycleCut off ratio rc

Efficiency becomes

Brayton CycleGas turbine cycleOpen vs closed system model

Brayton CycleFour internally reversible processes1-2 Isentropic Compression (compressor)2-3 Constant-pressure heat addition3-4 Isentropic expansion (turbine)4-1 Constant-pressure heat rejection

Brayton CycleAnalyze as steady-flow process

So

With cold-air-standard assumptions

Brayton CycleSince processes 1-2 and 3-4 are isentropic, P2 = P3 and P4 = P1

where

Brayton Cycle

Brayton CycleBack work ratioImprovements in gas turbinesCombustion tempMachinery component efficienciesAdding modifications to basic cycle

Actual Gas-Turbine CyclesFor actual gas turbines, compressor and turbine are not isentropic

Regeneration

RegenerationUse heat exchanger called recuperator or regeneratorCounter flow

RegenerationEffectiveness

For cold-air assumptions

Brayton with Intercooling, Reheat, & Regeneration

Brayton with Intercooling, Reheat, & RegenerationFor max performance

Ideal Jet-Propulsion Cycles

Ideal Jet-Propulsion CyclesPropulsive power

Propulsive efficiency

Turbojet EnginesTurbofan: for same power, large volume of slower-moving air produces more thrust than a small volume of fast-moving air (bypass ratio 5-6)Turboprop: by pass ratio of 100

JetsAfterburner: addition to turbojetRamjet: use diffusers and nozzlesScramjet: supersonic ramjet Rocket: carries own oxidizer

Second Law IssuesIdeal Otto, Diesel, and Brayton cycles are internally reversible2nd Law analysis identifies where losses are so improvements can be madeLook at closed, steady-flow systems

Second Law IssuesFor exergy and exergy destruction for closed system:

For steady-flow system:

Second Law IssuesFor a cycle that starts and end at the same state: