INDICATED WORK PER CYCLE

Pressure data for the gas in the cylinder over the operating

cycle of the engine can be used to calculate the work transfer

from the gas to the piston. The cylinder pressure and

corresponding cylinder volume throughout the engine cycle

can be plotted on p – V diagram.

The indicated work per cycle Wc,i is obtained by integrating

the curve to obtain the area enclosed on diagram:

With two-stroke cycle, the application is straightforward.

With the addition of inlet and exhaust strokes the four-

stroke cycle , some ambiguity for is introduced as two

definitions of indicated output are used:

Gross indicated work per cycle Wc,ig. Work delivered to the

piston over the compression and expansion strokes only.

Net indicated work per cycle Wc,in. Work delivered to the

piston over the entire four strokes cycle.

The work transfer between the piston and the cylinder gases

during the inlet and exhaust strokes and is called the

pumping work Wp.

The pumping work transfer will be from piston to the

cylinder gases if the pressure during the intake stroke is less

than the pressure during the exhaust stroke, this is the

situation with naturally aspirated engines.

The pumping work transfer will be from the cylinder gases

to the piston if the exhaust stroke pressure is lower than the

intake pressure, which is normally the case with highly

loaded turbocharged engines.

The power per cylinder is related to the indicated work per

cycle by:

Where:

N engine speed

nR is the number of crank revolutions for each stroke per

cylinder. For four-stroke cycle nR = 2, for two stroke cycle

nR =1.

This power is the indicated power, it differ from the brake

power (measured) by the power absorbed in overcoming

engine friction, driving engine accessories and ( in the case of

gross indicated power) the pumping power.

pdVWi,c

R

i,c

in

NWP

Indicated parameters are used primarily to identify the

impact of the compression, combustion, and expansion

processes on engines performances.

The gross indicated output is, the most appropriate

definition. It represents the sum of useful work available at

shaft and the work required to overcome all the engine

losses.

The term brake and indicated are used to describe other

parameters such as mean effective pressure, specific fuel

consumption, and specific emissions in a manner similar to

that used for work per cycle and power.

MECHANICAL EFFICIENCY

A part of gross indicated work per cycle or power is used to

expel exhaust gases and induct fresh charge. An additional

portion is used to overcome the friction of bearings, pistons,

and other mechanical components of the engine, and to drive

the engine accessories.

All of these power requirements are grouped together and

called friction power Pf.

Pig =Pb + Pf

The ratio of brake power Pb (or useful) delivered by engine

to the indicated power is called the mechanical efficiency m.

m = Pb / Pig = 1 – (Pf / Pig)

MEAN EFFECTIVE PRESSURE

An useful relative engine performance measure is obtained

by dividing the work per cycle by the cylinder volume

displaced per cycle.

The parameter so obtained has units of force per unit area

and is called the mean effective pressure.

Work per cycle = P.nR / N

Where: P – power; nR – (2 for four stroke cycle, 1 for two

stroke cycle); N – crankshaft rotational speed.

Then:

fm

mep = P.nR / Vd.N

mep(kPa) = P(kW)nR103 / Vd(dm

3)N(rev/s)

Mean effective pressure can also be expressed in terms of

torque by using the relationship:

mep(kPa) = 6.28 nR T(N.m) /Vd(dm3)

The maximum brake effective pressure of good engine

designs is well established, and is essentially constant over a

wide range of engine sizes. Thus, the actual bmep that a

particular engine develops can be compared with this norm,

and the effectiveness with which the engine designer has

used the engine’s displaced volume can be assessed.

Also, for design calculations, the engine displacement

required to provide a given torque or power, at a specified

speed can be estimated by assuming appropriate values for

bmep for particular application.

For naturally aspirated SI engine: maximum values for

bmep are in the range 850 to 1050 kPa at the engine speed

where maximum torque is obtined( about 3000 rpm).

At maximum rated power , bmep value are 10 to 15% lower.

For turbocharged automotive SI engines the maximum

bmep is the 1250 to 1700 kPa At the maximum rated power,

bmep is in the 900 to 1400 kPa range.

For naturally aspirated four-stroke diesels, the maximum

bmep is in the 700 to 900 kPa range , with the bmep at the

maximum rated power about 700 kPa.

Turbocharged four-stroke diesel maximum bmep values are

in the range 1000 to 1200 kPa; for turbocharged aftercooled

engines this can rise to 1400 kPa. At maximum rated power,

bmep is 850 to 950 kPa.

Two stroke cycle diesels have comparable performance to

four –stroke cycle engine.

SPECIFIC FUEL CONSUMPTION AND EFFICIENCY

The fuel consumption is measured as a flow rate – mass flow

per unit time

An useful parameter is the specific fuel consumption –sfc-

the fuel flow rate per unit power output. It measure how

efficiently an engine is using the fuel supplied to produce

work:

With units,

Low values of sfc are obviously desirable.

The fuel energy supplied which can be released by

combustion is given by the mass of fuel supplied per cycle

times the heating value of fuel. The heating value of fuel,

QHV, defines its energy contents. It is determined in a

standardized test procedure in which a known mass of fuel is

fully burned with air , and thermal energy released by the

combustion process is absorbed by a calorimeter as the

combustion products cool down to their original

temperature.

This measure of energy of an engine’s efficiency, which will

be called the fuel conversion efficiency f is given by:

Where mf is the mass of fuel inducted per cycle.

Substitution for power to mass flow per unit time into

relationship of fuel conversion efficiency, gives

QHV – fuel heating value

P

msfc f

)kW(P

)h/g(m)h.kW/g(sfc f

HVfHVRf

R

HVf

cf

Qm

P

Q)N/nm(

)N/n.P(

Qm

W

HV

fQsfc.

1

)kg/MJ(Q)h.kW/g(sfc

3600

HV

f

Typical heating values for commercial hydrocarbon fuels

used in engines are in the range 42 to 44 MJ / kg.

Thus, specific fuel consumption is inversely proportional to

fuel convertion efficiency for normal hydrocarbon fuels.

AIR / FUEL AND FUEL / AIR RATIOS

The ratio of the air mass flow rate to the fuel mass flow rate

and

The ratio of the fuel mass flow rate to the air mass flow rate

define the engine operating conditions:

and

For the conventional SI engine using gasoline fuel:

12 A / F 18 ( 0.056 F / A 0.083 )

For the CI engines with diesel fuel:

18 A / F 70 (0.014 F /A 0.056)

VOLUMETRIC EFFICIENCY

The intake system: the air filter, carburetor, throttle plate

(in SI engine), intake manifold, intake port, intake valve

restricts the amount of fresh charge (air or air-fuel mixture)

which an engine of given displacement can induct.

The parameter used to measure the effectiveness of an

engine’s induction process is the volumetric efficiency v.

Volumetric efficiency is used only with four-stroke cycle

engine which have a distinct induction process.

f

a

m

m)F/A(ratio.fuel/Air

a

f

m

m)A/F(ratio.air/Fuel

Volumetric efficiency is defined as the volume flow rate of air

into the intake system divided by the rate at which volume is

displaced by piston:

where: a,i - the inlet air density.

An alternative equivalent definition for volumetric efficiency

is:

Where: ma – the mass of air inducted into cylinder per cycle.

Maximum values of v for naturally aspirated engines are in

the range 80 – 90 %.

The volumetric efficiency for diesels is somewhat higher

than for SI engines.

ENGINE SPECIFIC WEIGHT AND SPECIFIC VOLUME

These parameters indicate the effectiveness with which the

engine designer has used the engine materials and packaged

the engine components.

and

NV

m2

di,a

av

di,a

av

V

m

powerrated

weightengineweightSpecific

powerrated

volumeenginevolumeSpecific

CORRECTION FACTORS FOR POWER AND

VOLUMETRIC EFFICIENCY

The pressure, humidity, and temperature of the ambient air

induced into an engine , at a given engine speed, affect the

air mass flow rate and the power output.

The basis for the correction factor is the equation for one-

dimensional steady compressible flow through an orifice or

flow restriction of effective area AE.

In deriving this equation, it has been assumed that the fluid

is an ideal gas with constant R (constant gas) and that the

ratio of specific heats (cp / cv = ) is constant.

p0 and T0 are the total pressure and temperature upstream

of restriction and p is the pressure at the throat of the

restriction

If, in the engine, p / p0 is assumed constant at wide-open

throttle, then for a given intake system and engine , the mass

flow rate of dry air varies as:

For mixtures containing the proper amount of fuel to use all

the air available, the indicated power at full throttle Pi will

be proportional to the dry air flow rate.

Thus if

Pi,s = CF.Pi,m

The subscripts s and m denote values at standard and

measured conditions.

The correction factor CF is given by:

where:

2/1/)1(

0

/2

00

0E ]})p

p()

p

p[(

1

2{

RT

pAm

0

0a

T

pm

2/1

s

m

m,vm

d,s

F)

T

T(

pp

pC

ps,d - standard dry air absolute pressure

pm – measured ambient air absolute pressure

pv,m – measured ambient water vapor partial pressure

Tm – measured ambient temperature, K

Ts – standard ambient temperature, K

The rated power is corrected (Pb,s) by using the correction

factor to correct the indicated power and making the

assumption that the friction power is unchanged:

Pb,s = CF Pi,m – Pf,m

Volumetric efficiency is proportional to

Since a is proportional to p/T, the correction factor for

volumetric efficiency, CF’ is

RELATIONSHIPS BETWEN PERFORMANCES

PARAMETERS

For power P:

For four stroke engines, volumetric efficiency can be

introduced:

For torque T:

For mean effective pressure:

aa/m

2/1

m

s

m,v

s,v'

F)

T

T(C

R

HVaf

n

)A/F(NQmP

2

)A/F(QNVP i,aHVdvf

4

)A/F(QVT i,aHVdvf

mep = fvQHVa,i(F/A)

The power per unit of piston area is called the specific

power:

Or, if the mean piston speed is introduced, the specific

power is

Specific power is proportional to the product of mean

effective pressure and mean piston speed.

These relationships illustrate the direct importance to engine

performance of:

1) high fuel conversion efficiency

2) high volumetric efficiency

3) increasing the output of given displacement engine by

increasing the inlet air density

4) maximum fuel/air ratio that can be usefully burned in the

engine

5) high mean piston speed

ENGINE DESIGN AND PERFORMANCE DATA

Engine rating usually indicate the highest power to give

satisfactory economy, emissions, reliability, and durability.

Maximum torque, and the speed at which it is achieved, is

usually given also.

1) At maximum or normal rated point:

-Mean piston speed. Measures comparative success in

handling loads due inertia of the parts and/or engine

friction.

2

)A/F(NLQ

A

P i,aHVvf

p

4

)A/F(QS

A

P i,aHVpvf

p

-Brake mean effective pressure. In naturally aspirated

engines bmep is not stress limited. It then reflects the

product of volumetric efficiency(ability to induct air),

fuel/air ratio (effectiveness of air utilization in combustion),

and fuel conversion efficiency.

In supercharged engines bmep indicates the degree of

success in handling higher gas pressure and thermal load.

-Power per unit piston area. Measures the effectiveness with

which the piston area is used, regardless of cylinder size.

-Specific weight. Indicates relative economy with which

materials are used.

-Specific volume. Indicates relative effectiveness with which

engine space has been used.

2) At all speed at which the engine will be used with full

throttle or with maximum fuel pump setting:

-Brake mean effective pressure. Measures ability to

obtain/provide high air flow and use it effectively over the

full range.

3) At all useful regimes of operations and particularly in

those regimes where the engine is run for long period of

time:

-Brake specific fuel consumption or fuel conversion

efficiency.

-Brake specific emissions.