gas power cycles 1 (1)

7/26/2019 Gas Power Cycles 1 (1)

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MECH 351 PM Wood-Adams Fall 2006

Classification of Thermodynamic

Cycles

We can classify thermodynamic cycles

according to their desired output:

the state of the working fluid:

or whether or not the working fluid is

replaced in each cycle

Power cycles vs. refrigeration cycles

Gas cycles vs. vapor cycles

Closed cycles vs. open cycles


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Heat engines

Internal combustion:

the heat is supplied tothe working fluid by

burning the fuel within

the system boundaries

e.g. automobile

engines

External combustion:

heat is supplied to theworking fluid from a

source external to the

system

e.g. steam power

plants

We can also classify heat engines in terms of

how the heat is supplied to the working fluid.


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Analysis of gas cycles

actual gas power cycles are difficult to

analyze because of non-idealities such asfriction and non-equilibrium conditions

We make simplifications and strip thecycle of internal irreversibilities. Then we

end of with an ideal cycle that closely

resembles the actual cycle.


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Simplification of a real process to allowfor analysis


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Analysis of gas power cycles The working fluid remains a gas through

out the entire cycle.

Examples of such cycles: spark-ignitionengines, diesel engines, conventional gas

turbines. All of these engines are internal

combustion engines. This means that the

working fluid undergoes chemicalreactions in the cycle:

air + fuel combustion gases


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Air standard assumptionsSet of assumptions that we make in the analysis

of internal combustion engines: the working fluid is air which is an ideal gas

all processes of the cycle are internally

reversible the combustion process is replaced by a heat-

addition process from an external source

the exhaust process is replaced by a heatrejection process that restores the working fluidto its initial state (i.e. we consider a closed cycle)


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Reciprocating engines

top dead center: position

of piston when it forms

smallest volume in cylinder

bottom dead center:position of piston when it

forms largest volume in

cylinder


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Volumes

TDC

BDC

min

max

VV

VVr ==

Compressionratio:


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Mean effectivepressure

A fictitious pressurethat, if it acted on

the piston over the

entire power stroke,

would produce the

same amount of net

work as the actual

cycle.


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Classification of reciprocating engines

Spark ignition (SI): combustion is

initiated by a spark plug. Ideal cycle is theOtto cycle.

Compression ignition (CI): air-fuelmixture is self ignited as a result of

compressing the mixture above its self

ignition temperature. Ideal cycle is theDiesel cycle.


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4 stroke spark ignition engine

Actual

cycle


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4 stroke spark ignition engine

Ideal cycle


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2 stroke reciprocatingengine

Same for 4 functionsare executed in just 2

strokes: the power

stroke and the

compression stroke.


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Otto CycleApply the air-standard assumptions to SI engines we

get the idealized version: the Otto cycle

Process 1-2: isentropic compression, Process 2-3: constant

volume heat addition, Process 3-4: isentropic expansion,

Process 4-1: constant volume heat rejection.


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Analysis of Otto Cycle:

Ideal gas w/ constant Cv.

The cycle is

executed in aclosed system,

i.e. a cylinder.

( )23v

23in

TTc

uuq

==

( )14v

14out

TTcuuq=

=


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Thermal efficiency of the Otto cycle

Constant Cv

1k

in

netotto,th

r11

qw

==

How do we derive this?

compression ratio


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Isentropic relations for ideal gas

with constant specific heat

k

2

1

consts1

2

k)1k(

1

2

consts1

2

1k

2

1

consts1

2

v

v

P

P

PP

TT

vv

TT

=

=

=

=

=

=v

p

C

Ck=

These equations are used torelate the properties of the states

before and after the isentropic

expansion and compression

processes.


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th of the ideal Otto cycle

k=1.4

The maximum

feasible compressionratio is limited by

engine knock. This is

when the fuel and air

mixture is compressedbeyond its autoignition

temperature and

premature ignition

occurs.


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Specific heat ratio and th

Air at room temperature

smaller molecule, argon

larger molecule, ethane

Working fluid in real engines contains

larger molecules and it is used at much

higher temperatures. Both result in lower

th. A typical value is about 25 to 30%.


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Analysis of isentropic processes when

specific heat varies with temperature

Cannot use the isentropic ideal gas relations

Instead we use Table A.17 and reduced pressure (Pr)or reduced volume (vr) to relate the properties of thestates before and after an isentropic process.

We can also use ideal gas law to find temperature

We find u from Table A.17

1r

2r

ttanconss1

2

P

P

P

P == 1r

2r

ttanconss1

2

v

v

v

v ==


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Example 8-2 An ideal Otto cycle has a compression ratio of 8.

At the beginning of the compression process, air

is at 100 kPa and 17C, and 800 kJ/kg of heat istransferred during the heat addition process.

Accounting for the variation in specific heats with

temperature, determine (a) the maximum temperature and pressure that

occur during the cycle,

(b) the net work output,

(c) the thermal efficiency and

(d) the mean effective pressure for the cycle.


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Example 8-2

gas power cycles 1 (1)

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