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 V2= V3 and V4 = V1

� 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

Diesel Cycle

� Cut off ratio rc

� 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, P2 = P3 and P4 = P1

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

Regeneration

� Effectiveness

� 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

� 2nd 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: