Gas Power Cycles

Power Cycles   Ideal Cycles, Internal Combustion      Otto cycle, spark ignition Diesel cycle, compression ignition Sterling & Ericsson cycles Brayton cycles Jet-propulsion cycle Ideal Cycles, External Combustion  Rankine cycle

Modeling

Ideal Cycles  Idealizations & Simplifications  Cycle does not involve any friction    All expansion and compression processes are quasi-equilibrium processes Pipes connecting components have no heat loss Neglecting changes in kinetic and potential energy (except in nozzles & diffusers)

Carnot Cycle

Carnot Cycle

Gas Power Cycles   Working fluid remains a gas for the entire cycle Examples:    Spark-ignition engines Diesel engines Gas turbines

Air-Standard Assumptions     Air is the working fluid, circulated in a closed loop, is an ideal gas All cycles, processes are internally reversible Combustion process replaced by heat-addition from external source Exhaust is replaced by heat rejection process which restores working fluid to initial state

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

Engine Terms     Top dead center Bottom dead center Bore Stroke

Engine Terms    Clearance volume Displacement volume Compression ratio

Engine Terms  Mean effective pressure (MEP)

Otto Cycle      Processes of Otto Cycle: Isentropic compression Constant volume heat addition Isentropic expansion Constant volume heat rejection

Otto Cycle

Otto Cycle  

Ideal

Otto Cycle Four internally reversible processes     1-2 Isentropic compression 2-3 Constant-volume heat addition 3-4 Isentropic expansion 4-1 Constant-volume heat rejection

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

Otto Cycle  Thermal efficiency of ideal Otto cycle:  Since V 2 = V 3 and V 4 = V 1  Where r is compression ratio k is ratio of specific heats

Otto Cycle

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

Diesel Cycle

Diesel Cycle      Processes of Diesel cycle: Isentropic compression Constant pressure heat addition Isentropic expansion Constant volume heat rejection

Diesel Cycle  For ideal diesel cycle  With cold air assumptions

 Cut off ratio r c Diesel Cycle  Efficiency becomes

Brayton Cycle   Gas turbine cycle Open vs closed system model

Brayton Cycle  Four internally reversible processes  1-2 Isentropic Compression (compressor)    2-3 Constant-pressure heat addition 3-4 Isentropic expansion (turbine) 4-1 Constant-pressure heat rejection

Brayton Cycle  Analyze as steady-flow process  So  With cold-air-standard assumptions

Brayton Cycle  Since processes 1-2 and 3-4 are isentropic, P 2 = P 3 and P 4 = P 1 where

Brayton Cycle

Brayton Cycle  Back work ratio  Improvements in gas turbines  Combustion temp   Machinery component efficiencies Adding modifications to basic cycle

Actual Gas-Turbine Cycles  For actual gas turbines, compressor and turbine are not isentropic

Regeneration

Regeneration   Use heat exchanger called recuperator or regenerator Counter flow

 Effectiveness Regeneration  For cold-air assumptions

Brayton with Intercooling, Reheat, & Regeneration

 Brayton with Intercooling, Reheat, & Regeneration For max performance

Ideal Jet-Propulsion Cycles

Ideal Jet-Propulsion Cycles  Propulsive power  Propulsive efficiency

Turbojet Engines   Turbofan: 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

Jets     Afterburner: addition to turbojet Ramjet: use diffusers and nozzles Scramjet: supersonic ramjet Rocket: carries own oxidizer

Second Law Issues    Ideal Otto, Diesel, and Brayton cycles are internally reversible 2 nd Law analysis identifies where losses are so improvements can be made Look at closed, steady-flow systems

Second Law Issues  For exergy and exergy destruction for closed system :  For steady-flow system :

Second Law Issues  For a cycle that starts and end at the same state: