ICE Lecture 2

8/14/2019 ICE Lecture 2

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Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE

TERMODYNAMIC AND CYCLING

1. First Law Analysis ofEngine Cycle-Energy Balance

a). Indicated thermal efficiency ( t ).

Indicated thermal efficiency is the ratio of energy in the indicated horse power to fuel

energy.

hpfuel

ihp t =

valuecalorificfuel/min xofmass

4500xihp=

b). Mechanical efficiency ( m )

Mechanical efficiency is the ratio of brake horse power (delivered power) to the indicated

horse power (power provided to the piston)

ihp

bhpm =

and bhpihpfhp =

7

Fuel in System boundary

Air in

Engine

Qt

Work out

Exhaust

Energyin

fuel

ihp

bhp

Energy lost in exhaust, coolant, radiation etc

Energy loss in fiction, pumping etc

Enginebhpihp

friction


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c). Brake thermal efficiency ( tb ).

Brake thermal efficiency is ratio of energy inbrake horse powerto the fuel energy.

hpfuel

bhp

tb

=

valuecalorificfuel/min xofmass

4500xbhp=

The brake thermal equals the product of the indicated thermal efficiency t and the

mechanical efficiency m .

mttb x =

d). Volumetric efficiency ( V )

conditionpressureandretemperatuintakeatvolumecylinderbydrepresentechargeofmass

indicatedactuallychargeofmassV =

e). Specific fuel consumption.

The fuel consumption characteristics of an engine are generally expressed in terms of

specific fuel consumption in grams per horsepower-hour. Brake specific fuel

consumptionand indicated specific fuel consumption, abbreviated as bsfc and isfc, are

the specific fuel consumptions on the basis of bhp and ihp, respectively.

f). Fuel-air (F/A) or air-fuel (A/F) ratio.

The relative proportions of the fuel and air in the engine are very important from the

standpoint of combustion and efficiency of engine. This expressed either as the ratio of the

mass ofthe fuel to that ofthe air.

ratioairfueltricstoichiome

ratioairfuelactualFr

=

Stoichiometric = a chemically correct is mixture that contains just enough air for complete

combustion of all fuel.

2. Useful Thermodynamic Relations

The following are the useful thermodynamic relations used in the analysis of air standard

cycles.

a). For ideal gas cycle the working fluid is a perfect gas which follows the law

mRTpV = , or RTpv =

where p is the pressure, V volume, v specific volume, m mass, R gas constant and Tabsolute temperature (0Kelvin).

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b). For perfect gas

J

Rcc VP =

where cP (= 0,24) is the specific heat at constant pressure and cV (= 0.17) is the specific

heat at constant volume. The ratio 4.1c

c

V

p== will be designated by the symbol .

c). From the perfect gas law, it can be seen that an isothermal process will follow the

relationship

ttanconspv =

d). It is readily shown that for perfect gas the reversible adiabatic orisentropic process will

follow the relationship

ttanconspv =

e). The definition ofenthalpy h is given by the expression

pvuh +=

which for a perfect gas, becomes

RTuh +=

f). For a perfect gas internal energy u and enthalpy h are functions of temperature only

=2

1

T

TvdTcu =

2

1

T

TpdTch

g). In a compression process, if p1, V1, and T1 represent the initial conditions p2, V2, and T2 the

final conditions are given by

( ) n/1n

1

2

1n

2

1

1

2

p

p

V

V

T

T

=

=

where n is the index of compression.

For reversible adiabatic or isentropic compression n = .

h). Forisothermal process of a perfect gas, the change in u and h is zero. Therefore, for both

flow and non-flow process

1

2isothermal

v

vlogmRTWQ ==

where Q is the heat interchange and W the work done

i). The work done in a non-flowpolytrophic process is given by

( )

1n

TTmR

1n

VpVpW 212211

=

=

9

u + pv


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where m = mass of gas

The work transfer during flow process is given by

( )

1n

TTmRn xW 21

=

j). The heat transferto any fluid can be evaluated from

== dTcTdsQ nrevwhere cn = specific heat of the fluid in which subscript n refers to the property which

remains constant during the process.

k). For any general process, according to the first law of thermodynamics,

fornon-flow process UWQ =

and forflow process HWQ =

l). For any cycling process

addedtrejectedadded QxQQQW ===

Where the symbol refers to over the cycle and t is the thermal efficiency.

added

tQ

W=

THE CARNOT CYCLE

(Carnot is a French Engineer)

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During the isentropic process bc and da the heat transfer form or to the working

substance is zero. Therefore, heat transfer takes place during isothermal process ab and cd

only.

Let r= ratio ofexpansion Vb/Va during process ab

= ratio ofcompression Vc/Vd during process cd

If the ratio of expansion and compression are not equal it would be a closed cycle.

Now, consider 1 kg of working substance:

Heat supplied during process ab, rlogRTrlogvpq e1eaac =

Heat rejected during process cd, rlogRTrlogvpq e2eccd =

Work done = heat supplied heat rejected

= rlogRTrlogRT e2e1

Thermal efficiency of the Carnot cycle,

pliedsupheat

workdonecarnot =

rlogRT

rlogRTrlogRT

e1

e2e1 =

1

2

1

21

T

T1

T

TT=

=

peraturHigher tem

T=

Carnot cycle on T-s diagram.

On T-s diagram the two isothermal processes ab and cdare represented by horizontal lines

and two isentropic processes bc and adby vertical lines.

The heat supplied during the isothermal process ab is given by

)s(sTssbaareaq 121211 ==

Similarly, the heat rejected during the isothermal process cd is given by

)s(sTssdcareaq 122212 ==

Hence we have thermal efficiency of Carnot cycle

( ) ( )

( )121

122121carnot

ssT

ssTssT

=

1

2

1

21

T

T1

T

TT=

=

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Net work output = (T1 T2)(s2 s1)

Gross workof expansion = work done during process ab + work done during process bc.

For isothermal process Q = W

i.e., Wab = Qab = area under line ab on T-s diagram

= T1(s2-s1)

Forisentropic process from b and c

Wbc = ub - uc

Therefore, for a perfect gas

( )21vbc TTcW =

( )( )

( ) ( )21v121

1221

TTcssT

ssTTratioWork

+

=

Relative work outputs of various piston engine cycles is given by mean effective

pressure (mep or pm), which is defined as the constant pressure producing the same net work

output whilst causing the piston to move through the same swept volume as in the actual cycle

Let pm = mean effective pressure

Vs = swept volume

W = net work output per cycle

Then,volumestroke

cycleperdoneworkpm =

ss V

pdV

V

W ==

Also,diagramtheoflength

diagramindicatortheofareapm =

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ICE Lecture 2