Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE

TERMODYNAMIC AND CYCLING

1. First Law Analysis of Engine Cycle-Energy Balance

a). Indicated thermal efficiency ( tη ).

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

energy.

hp fuel

ihpη t =

valuecalorific fuel/min x of mass

4500 x ihp=

b). Mechanical efficiency ( mη )

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

horse power (power provided to the piston)

ihp

bhpm =η

and bhpihpfhp −=

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Fuel inSystem boundary

Air in

Engine

Qt

Work out

Exhaust

En

ergy

in f

uel

ihp

bh

p

Energy lost in exhaust, coolant, radiation etc

Energy loss in fiction, pumping etc

Enginebhpihp

friction

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c). Brake thermal efficiency ( tbη ).

Brake thermal efficiency is ratio of energy in brake horse power to the fuel energy.

hp fuel

bhpη tb =

valuecalorific fuel/min x of mass

4500 x bhp=

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

mechanical efficiency mη .

mttb η x ηη =

d). Volumetric efficiency ( Vη )

condition pressure and re temperatuintakeat volumecylinder by drepresente charge of mass

indicatedactually charge of massηV =

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

consumption and 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 of the fuel to that of the air.

ratioair fuel tricstoichiome

ratioair fuel actualFr −

−=

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 T

absolute 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 ==γ will be designated by the symbol γ .

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 or isentropic process will

follow the relationship

ttanconspv =γ

e). The definition of enthalpy 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

T vdTcu ∫=∆ 2

1

T

T pdTch

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 = γ.

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

flow and non-flow process

1

2isothermal v

vlog mRTWQ ==

where Q is the heat interchange and W the work done

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

( )1n

TTmR

1n

VpVpW 212211

−−

=−−

=

9

u

u + pv

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where m = mass of gas

The work transfer during flow process is given by

( )1n

TTmRn x W 21

−−=

j). The heat transfer to any fluid can be evaluated from

∫ ∫== dTcTdsQ nrev

where 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,

for non-flow process UWQ ∆=−

and for flow process HWQ ∆=−

l). For any cycling process

addedtrejectedadded Q x ηQQΣQΣW =−==

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

addedt Q

ΣW=∴η

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 of expansion Vb/Va during process ab

= ratio of compression 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 =η

rlogRT

rlogRTrlogRT

e1

e2e1 −=

1

2

1

21

T

T1

T

TT−=

−=

peraturHigher tem

ΔT=

Carnot cycle on T-s diagram.

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

and two isentropic processes bc and ad by vertical lines.

The heat supplied during the isothermal process ab is given by

)s(s Ts s b a areaq 121211 −==

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

)s(s Ts s d c areaq 122212 −==

Hence we have thermal efficiency of Carnot cycle

( ) ( )( )121

122121carnot ssT

ssTssT

−−−−

=η

1

2

1

21

T

T1

T

TT−=

−=

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Net work output = (T1 – T2)(s2 – s1)

Gross work of 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)

For isentropic 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

cycleper donework pm =

ss V

pdV

V

W ∫==

Also, diagram theoflength

diagramindicator theof areapm =

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