air-standard power cycles (open cycle) the brayton cycle...

Lecture note for general thermodynamics, 2003

School of Mechanical Engineering, ChungAng University

OVERVIEWOVERVIEW

POWER CYCLEPOWER CYCLE

••The The RankineRankine Cycle Cycle ••thermal efficiency thermal efficiency ••effects of pressure and temperatureeffects of pressure and temperature

••Reheat cycleReheat cycle••Regenerative cycleRegenerative cycle••Losses and CogenerationLosses and Cogeneration

••AirAir--Standard Power Cycles (open cycle)Standard Power Cycles (open cycle)••The The BraytonBrayton cyclecycle••Simple gasSimple gas--turbine cycle with regeneratorturbine cycle with regenerator••Gas turbine power cycle configurationsGas turbine power cycle configurations••Jet propulsionJet propulsion

••Reciprocating Engine Power CyclesReciprocating Engine Power Cycles••Otto cycleOtto cycle••Diesel cycleDiesel cycle••StirlingStirling cyclecycle

REFRIGERATION SYSTEMSREFRIGERATION SYSTEMS

••VaporVapor--compression refrigeration cycle compression refrigeration cycle ••Actual vaporActual vapor--compression refrigeration cycle compression refrigeration cycle ••Ammonia absorption refrigeration cycleAmmonia absorption refrigeration cycle••AirAir--standard refrigeration cyclestandard refrigeration cycle

OTHER SYSTEMS : combinedOTHER SYSTEMS : combined--cycle power and refrigeration systemscycle power and refrigeration systems



11.8 AIR11.8 AIR--STANDARD POWER CYCLESSTANDARD POWER CYCLES

So far, we studied idealized four-process cycles

A. External-combustion engine : liquid – phase change – gas : closed cycleB. Internal combustion engine – ex) automotive engine (diesel, gasoline engines), gas-turbine engines ; working fluid is always gas. : open cycle – inlet to exhaust (focuses our attention on air pollution problem.

IC engine operates on the so-called open cycle – but we may consider closed cycle that closely approximate the open cycles. : air-standard cycle based on the following assumptions

- A fixed mass of air is the working fluid throughout the entire cycle, and the air is always an ideal gas. Thus, there is no inlet process or exhaust process.- The combustion process is replaced by a process transferring heat from an external source.- The cycle is completed by heat transfer to the surroundings ( in contrast to the exhaust and intake process of an actual engine)- All processes are internally reversible- An additional assumption is often made that air has a constant specific heat, recognizing that this is not the most accurate model.

Main goal of this approach is to examine qualitatively the influence of a number of variables on performance. : mep (mean effective pressure), efficiency

A. A. BraytonBrayton cyclecycle



Standard Standard BraytonBrayton cyclecycle

• Two const-P processes (combustor, and approximated condensed process) + two isentropic processes (compressor, turbine)• Rankine cycle using a single phase, gaseous working fluid – Brayton cycle • Ideal cycle for the simple gas turbine

( )( )

( )( )

( )

4 1 1 4 1

3 2 2 3 2

11 /

2 2 1

/ 11 1 1

/ 111 1

/

PLth

H P

k k

C T T T T TQQ C T T T T T

TT P P

η

−

− −= − = − = −

− −

= − = −

( ) ( )

4 3

1 2

3 2

4 1

/ 1 / 1

2 2 3 3

1 1 4 4

2 3

1 4

,

1 1

k k k k

here we noteT TT T

P PP P

P T P TP T P TT TT T

− −

− = −

=

⎛ ⎞ ⎛ ⎞= = =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

=

∵

2 1

2 1

3 4

3 4

scomp

turbs

h hh h

h hh h

η

η

−=

−

−=

−

• Large amount of compressor work• Exam 11.6



11.10 GAS11.10 GAS--turbine cycle with a regeneratorturbine cycle with a regenerator

( )( )

3

3 4

net t cth

H H

H P x

t P

w w wq q

q C T T

w C T T

η −= =

= −

= −

• Ericsson cycle

For ideal regeneratorFor ideal regenerator 4,t H xw q T T= =

( )( )

( )( )

( )( )

2 1 1 2 1

3 4 3 4 3

( 1) /2 1

1( 1) /

3 1 2

( 1) /

1 2

3 1

/ 11 1 1

1 /

/ 11

1 /

1

Pcth

H P

k k

k k

k k

th

C T T T T Twq C T T T T T

P PTT P P

T PT P

η

η

−

−

−

− −= − = − = −

− −

⎡ ⎤−⎣ ⎦= −⎡ ⎤−⎣ ⎦

⎛ ⎞= − ⎜ ⎟

⎝ ⎠

11.11 Gas11.11 Gas--turbine power cycle turbine power cycle configurationsconfigurations



JET PROPULSIONJET PROPULSION



11. 13 Reciprocating Engine Power Cycles11. 13 Reciprocating Engine Power Cycles•• Otto cycleOtto cycle•• Diesel cycleDiesel cycle•• StirlingStirling cyclecycle

Some definitions and Some definitions and termsterms

Bore B : cylinder diameterBore B : cylinder diameterCrank angleCrank angleTDC : Top dead centerTDC : Top dead centerBDC : bottom dead centerBDC : bottom dead centerClearance volumeClearance volumeDisplacement volumeDisplacement volumeCompression ratioCompression ratioAirAir--fuel ratiofuel ratioMean effective pressure (Mean effective pressure (mepmep))

max min

max min

max min

max min

2( )

/

( )

( )

60 60

crank

displ cyl cyl cyl

v

net mef

net net meff

cyl net meff displ

S RV N V V N A S

r CR V V

w Pdv P f v v

W mw P V V

RPM RPMW N mw P V

=

= − =

= =

= = −

= = −

= −

∫

11. 14 The Otto cycle11. 14 The Otto cycle

11

2 1 1 3

1 2 3 4

3 4

2 1

kkT V V TT V V T

T TT T

−−⎛ ⎞⎛ ⎞

= = =⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

∴ =

4 1 4 1

3 2 3 2

( ) ( )1 1 1( ) ( )

H L L vth

H H v

Q Q Q mC T T T TQ Q mC T T T T

η − − −= = − = − = −

− −



( )( )

111

2

1 4

2 3

11 1 1

,

kth v k

v

v

T rT r

V Vwhere rV V

η −

−= − = − = −

= =

Thermal efficiency of the Otto Thermal efficiency of the Otto cycle as a function of compression cycle as a function of compression ratioratio

NOTE 1; NOTE 1; 1. higher compression ratio, higher 1. higher compression ratio, higher thermal efficiencythermal efficiency2. detonation occurs at very high 2. detonation occurs at very high compression ratio, compression ratio, -- negative negative respect in actual engines : strong respect in actual engines : strong pressure wave (spark knock)pressure wave (spark knock)

NOTE 2 ; Deviation of actual engine from airNOTE 2 ; Deviation of actual engine from air--standard cyclestandard cycle1. specific heat 1. specific heat –– increases with temperatureincreases with temperature2. combustion process is present 2. combustion process is present –– incomplete : producing pollutant incomplete : producing pollutant such as such as NoxNox, Soot, and particulate matter (PM), Soot, and particulate matter (PM)3. inlet and outlet processes + a certain amount of work is requ3. inlet and outlet processes + a certain amount of work is required ired because of pressure dropsbecause of pressure drops4. considerable heat transfer4. considerable heat transfer5. 5. irreversibilitiesirreversibilities (pressure and temperature gradients)(pressure and temperature gradients)

11. 15 The Diesel Cycle (Compression Ignition 11. 15 The Diesel Cycle (Compression Ignition –– CI engine)CI engine)

4 1

3 2

1 4 1

2 3 2

( )1 1( )

( / 1)1( / 1)

L Pth

H P

Q C T TQ C T T

T T TkT T T

η −= − = −

−

−= −

−



NOTENOTE

1. there is no knocking problem because only air is compressed 1. there is no knocking problem because only air is compressed during the compression strokeduring the compression stroke2. constant pressure 2. constant pressure –– heat transferring (combustion process)heat transferring (combustion process)CfCf) Otto cycle ) Otto cycle –– constant volume processconstant volume process

Some lossesSome losses-- pumping losspumping loss-- some losses during inlet and exhaust processessome losses during inlet and exhaust processes-- heat transferheat transfer-- not constant pressure process during combustion processnot constant pressure process during combustion process

11. 16 11. 16 StirlingStirling cycle cycle

NOTENOTE

1. Strictly, the 1. Strictly, the StirlingStirling cycle engine is not an internalcycle engine is not an internal--combustion engine combustion engine but externalbut external--combustion engine with regenerationcombustion engine with regeneration

2. Two gas chambers are connected to pistons2. Two gas chambers are connected to pistons3. Constant volume process 3. Constant volume process –– heat transferred by external combustorsheat transferred by external combustors

http://www.geocities.com/~rrice2/



OVERVIEWOVERVIEW

POWER CYCLEPOWER CYCLE

••The The RankineRankine Cycle Cycle ••thermal efficiency thermal efficiency ••effects of pressure and temperatureeffects of pressure and temperature

••Reheat cycleReheat cycle••Regenerative cycleRegenerative cycle••Losses and CogenerationLosses and Cogeneration

••AirAir--Standard Power Cycles (open cycle)Standard Power Cycles (open cycle)••The The BraytonBrayton cyclecycle••Simple gasSimple gas--turbine cycle with regeneratorturbine cycle with regenerator••Gas turbine power cycle configurationsGas turbine power cycle configurations••Jet propulsionJet propulsion

••Reciprocating Engine Power CyclesReciprocating Engine Power Cycles••Otto cycleOtto cycle••Diesel cycleDiesel cycle••StirlingStirling cyclecycle

REFRIGERATION SYSTEMSREFRIGERATION SYSTEMS

••VaporVapor--compression refrigeration cycle compression refrigeration cycle ••Actual vaporActual vapor--compression refrigeration cycle compression refrigeration cycle ••Ammonia absorption refrigeration cycleAmmonia absorption refrigeration cycle••AirAir--standard refrigeration cyclestandard refrigeration cycle

OTHER SYSTEMS : combinedOTHER SYSTEMS : combined--cycle power and refrigeration systemscycle power and refrigeration systems



11.18 Vapor11.18 Vapor--Compression Refrigeration CycleCompression Refrigeration Cycle

4 processes

1-2 : isentropic compression (pump)2-3 : constant pressure heat rejection (condenser)3-4 : adiabatic throttling process (irreversible)4-1 : constant pressure evaporation (heat absorption)

Cycle performance : Coefficient of Performance (COP) ,L H

c c

q qw w

β β ′= =

Working Fluids (Refrigerants)

Ammonia & Sulfur-Dioxide (early days) – but not used ; highly toxic and dangerous

Chlorofluorocarbons (CFCs) – CCl2F2 (Freon-12, Genatron-12) ; R-11 and R-12: but destroying the protective ozone layer of the stratosphere

The most desirable fluids – HFCs (CFCs containing hydrogen) R-22

Two important considerations when selecting refrigerant working fluids

A. Temperature at which refrigeration is neededB. Type of equipment to be used



Deviation of the Actual VaporDeviation of the Actual Vapor--Compressor Refrigeration Cycle Compressor Refrigeration Cycle from the Ideal Cyclefrom the Ideal Cycle



Ammonia Absorption Refrigeration Cycle Ammonia Absorption Refrigeration Cycle –– 흡수식흡수식 냉동기냉동기

The AirThe Air--Standard Refrigeration CycleStandard Refrigeration Cycle



The AirThe Air--Standard Refrigeration Cycle (for aircraft cooling)Standard Refrigeration Cycle (for aircraft cooling)

The Air Refrigeration Cycle utilizing a heat exchangerThe Air Refrigeration Cycle utilizing a heat exchanger

CombinedCombined--Cycle Power and Refrigeration SystemCycle Power and Refrigeration System



Combined Combined Brayton/RankineBrayton/Rankine Cycle Power SystemCycle Power System

air-standard power cycles (open cycle) the brayton cycle...

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