Chapter 2Chapter 2Operating Characteristics

2-1 Engine Parameters2 2 Work2-2 Work2-3 Mean Effective Pressure2 4 T d P2-4 Torque and Power2-5 Dynamometers2-6 Air-Fuel Ratio and Fuel-Air Ratio2-7 Specific Fuel Consumptionp p2-8 Engine Efficiencies

1

Important engine characteristicsp gFactors important to an engine user are:

1. The engine’s performance over its operating range range 2. The engine’s fuel consumption within this operating range and the cost of the required fueloperating range and the cost of the required fuel3. The engine’s noise and air pollutant emissions within this operating range4. The initial cost of the engine and its installation5. The reliability and durability of the engine, its maintenance requirements, and how these affect engine availability and operating costs

1

engine availability and operating costs

Engine performance is more preciselyEngine performance is more precisely defined by:

1. Maximum power (or Maximum torque) p ( q )available at each speed within the useful engine operating rangeg p g g2. The range of speed and power over which engine operation is satisfactoryg p y

1

Crank Shaft Crank Shaft with Pistonwith Piston

22--1 1 Engine Engine ggParametersParameters

B = boreL = stroke

a = crank offsetl = connecting rod lengthL = stroke

a = crank offsets = piston position

= crank angleθ

Vd = displacement volume

crank angleVc = clearance volumeθ

d p

2Figure 2-1 Piston and cylinder geometry of reciprocating engine.

TABLE 2-1 Typical engine operating parametersTABLE 2 1 Typical engine operating parameters

If an engine has bore = stroke, we call it “square engine”.

If bore (B) > stroke, referring to “over square”. Stroke length L2aL =

3If bore (B) < stroke, referring to “under square”.

Stroke length L(2 1)2aL (2-1)2aL =

The distance s between crank axis and wrist pin axis is given byand wrist pin axis is given by

θθ 222 sina-cos a s l+=

where: a = crankshaft offsetl = connecting rod length

anglecrank =θ

(2-2)

g

Do you think a piston ever stops while an engine operates?

Yes / No Question

Mean piston speed is :(2-3)where: N = crankshaft speedLNS p 2=

The instantaneous piston speed S is obtained :The instantaneous piston speed Sp is obtained :

(2-4)ds/dt Sp = ( )p

as a function of crank angle for various R values, whereInstantaneous piston speed relative to average piston speedas a function of crank angle for various R values, where R = l/a, l = connecting rod length, a = crankshaft offset.

The ratio of instantaneous piston speed divided by the average piston speed can then be written as

(2-5)

speed can then be written as

⎥⎦

⎤⎢⎣

⎡−

+= 2/122 )sin(cos1sin

2 θθθπ

RS

S

p

p

R is the ratio of connecting rod length to crank offsetwhere: R = l/a (2-6)

⎦⎣ )sin(2 θRS p

R is the ratio of connecting rod length to crank offset

Displacement or displacement volume Vd is the volume displaced

VVV (2 7)

Displacement, or displacement volume Vd is the volume displaced by the piston as it travels from BC to TC:

TDCBDCd V - VV = (2-7)

Displacement can be given for one cylinder or for the entire :engine. For one cylinder Displacement can be given for one cylinder or for the entire :

(2 8)L/4)B(V 2d π= (2-8)L/4)B(Vd π=

For an engine with Nc cylinders: (2-9)

where: B = cylinder boreL /4)B(N V 2

cd π=

S = strokey

Nc = number of engine cylinders

clearance volume Vc

c g y

TDCc V V = (2-10)

(2-11)dcBDC V V V += (considering each cylinder) ( )

The compression ratio of an engine is defined as :

cdcTDCBDCc )/VV(V/VV r +== (2-12)

7

The cylinder volume V at any crank angle is:)/4)(( 2 l (2-13)

where: Vc = clearance volumes)-a/4)(B( VV 2

c ++= lπSame s we just seen !

B = borel = connecting rod length a = crank offset s = piston position

This can also be written in a non-dimensional form by dividing byVc , substituting for l, a, and s, and employing the definition of R:

]sin-R-cos-11)[R-(r1 VV/ 22c2

1c θθ++= (2-14)

Vc , substituting for l, a, and s, and employing the definition of R:

])[( c2c ( )

R l /where: rc = compression ratio

8R = l / a

The cross-sectional area of a cylinder and the surface area of ay

(2-15)flat-topped piston are each given by:

2p /4)B( A π= ( )

The combustion chamber surface area is:

p )(

where A is the cylinder head surface area which will be

s) - a B( A A A pch +++= lπ (2-16)

where Ach is the cylinder head surface area, which will beSomewhat larger than Ap.

Then if the definitions for r, a, l, and R are used. Eq. (2-16) can berewritten as:

]sin R - cos - 1 BL/2)[R(A A A 22pch θθπ +++= (2-17)

rewritten as:

9

2-2 Torque and PowerTorque T is normally measured with dynamometer. Torque is a measure of engine’s ability to do work.

where: F = force exerted on statorFb =T (2-18)

b = length of moment arm

Fi 2 2 S h i f i i l f d i10

Figure 2-2 Schematic of principle of dynamometer operation

2-2 Torque And Power

(2 19)

Power P delivered by the engine and absorbed by dynamometer.

N2P T

where: N = crankshaft rotational speed

(2-19)N2P Tπ=

p

The engine power measured as described is called b k Pbrake power, Pb.

11

Figure 2-3 Power and

Motors L35 Vortec V6torque curves of General

engine.

hp 1.341 kW 1 =

12

13engine.Figure 2-4 1996 General Motors L35 4300 Vortec V6 spark ignition

Figure 2-5 Brake power and torque of a typical auto-q ypmobile reciprocating engineas a function of engine

14speed. g

2-3 Indicated Work per CycleP d f h i h li d i l f hPressure data for the gas in the cylinder over operating cycle of the .

Figure 2-6 An indicator diagram plots cylinder pressure as a function of combustion chamber volume over a 720° cycle for a

15

function of combustion chamber volume over a 720° cycle for a typical four stroke cycle SI engine.

Force due to gas pressure on the moving piston generates the work inan IC engine cycle.

∫∫ == dx PA Fdx W p (2-20)

an IC engine cycle.

where: P = pressure in combustion chamber A = area against which the pressure acts

x = distance the piston moves Ap = area against which the pressure acts

dV dx Ap = (2-21)And

dV is the differential volume displaced by the piston so work done

∫ (2 22)

dV is the differential volume displaced by the piston, so work donecan be written:

∫= dV P W (2-22)

Indicated work per cycle is obtained by integrating around a 16

p y y g gcurve to obtain area enclosed on the diagram.

Fi 2 7 F t k l f t i l SI i l tt d P V17coordinates at (a) wide open throttle

Figure 2-7 Four-stroke cycle of typical SI engine plotted on P-V

Gross indicated work is work delivered to piston over the compression and expansion processes

C areaA area Wgross += (2-23)

Net indicated work is work delivered to piston over the entire cycle

B area -A area C) B (area-C)A (area Wnet =++= (2-24)

over the entire cycle

Pumping work is work delivered to piston over the intake and exhaust processes

Carea area B Wpump += (2-25)

and exhaust processes

18

19charger or turbocharger, plotted on P-v coordinates. Figure 2-8 Four-stroke cycle of a SI engine equipped with a super-

Power per cylinder is related to the indicated Power per cylinder is related to the indicated work per cycle by Indicated power

NW

R

ici n

NWP ,=

N : crank shaft rotational speednR: the number of crank revolutions for each

power stroke per cylinder power stroke per cylinder For four-stroke engine = 2For two-stroke engine = 1

lbf/sec-ft 550 BTU/hr 2545 kW 0.7457 hp 1 ===

hp 1.341 kW 1 =

20

p

Indicated Power Brake PowerPower that is generated Usable power delivered Power that is generated inside the combustion chamber giving force th t t di tl th

Usable power delivered by the engine to the loadA il bl that acts directly on the

pistonAvailable at a crankshaft

Indicated power and Brake powerIndicated power and Brake power

Actual power available at the crankshaft is called brake powerPb.

fib P- P P = (2-27)

where: Pi = indicated power generated inside combustion chamber

Pf = power lost due to friction and parasitic loads called friction power

The ratio of brake work at the crankshaft to indicated work in the

PPPP

combustion chamber defines the mechanical efficiency of an engine:

i

f

i

fi

i

bm P

P1P

PPPP −=

−==η (2-28)

21

Road Load PowerRoad-Load Power

The road-load power is the power required to drive aThe road-load power is the power required to drive a vehicle on a level road at a steady speed. This power overcomes the rolling resistance which arises from f i ti f ti d d i d f th hi lfriction of tires and aerodynamic drag of the vehicle.

Road Load PowerRoad-Load Power

SSACMCP )1( 2νννν ρ SSACgMCP DaRr )

2( 2+=

RC

νM= coefficient of rolling resistance (0.012 < CR < 0.015)

= mass of vehicle

gaρ

= acceleration due to gravity

= ambient air density

DC

νA= drag coefficient (for cars 0.3 < CD < 0.5)

= frontal area of vehicle

= vehicle speedνS = vehicle speed

Road Load PowerRoad-Load Power

2-4 Mean Effective Pressure An average or mean effective pressure (mep) is defined by dividing the work per cycle by the cylinder displacement volume:

(2-29)

or in term of power P

g p y y y pdc/V w mep =

(2-30)or in term of power, P

NR

VPn mep =

where: nR = 1 for 2-stroke cycle = 2 for 4-stroke cycle

N k h f i l d

NdV

N = crank shaft rotational speedVd = displacement volume

(2-31)If brake work is used, brake mean effective pressure is obtained:

)/(/Vwbmep db NVnP dRb==22

(2 31))/(/Vwbmep dbc, NVnP dRb

Example 2.1 A four-stroke automotive spark-ignition (SI) engine is designed to provide a maximum brake torque of 150 N m with thedesigned to provide a maximum brake torque of 150 N⋅m with the brake mean effective pressure of 925 kPa in the mid-speed range (~ 3,000 rev/min). Estimate( , )

1) engine displacement2) bore and stroke (assume bore equals stroke)3) maximum brake power if the mean piston speed is 15 m/s

Pnmep R= NTP π2=andNV

mepd

NTP π2=and

RTnmep

28.6=Thus

dVp

max28.6b

TnV Rd =

maxbmep

925150228.6 ××

= 3dm2=925

LBV 24π For 4 cylindersLBVd2

44= For 4 cylinders

Since B = L (as assumed)6

3 102 −×B Since B = L (as assumed)π

3 =B

mmLB 86==

Pnbmep R310×

=NV

bmepd

=

max= db

NbmepVP

s/m15maxP =S

max2max LNS P =310max ×R

b nP

kW70872800 ××P

maxmax

rev/s87max =N

kW70102 3bmax

=×

=P

2-5 Air-Fuel Ratio And Fuel-Air RatioAir-fuel ratio (AF) and fuel-air ratio (FA) are parameters used to

d ib h i ifafa m/m /mm AF

••

==••••

describe the mixture ratio:

where: ma = mass of air mf = mass of fuel

1/AF m/m m/m FA afaf ===

a f

air of rate flow mass ma =•

fuel of rate flow mass mf =•

φ

ideal or stoichiometric fuel air:Equivalence ratio is defined as the actual ratio of fuel-air toideal or stoichiometric fuel-air:

actstoichstoichact /(AF) (AF) /(FA)(FA) ==φ

23

2-6 Specific Fuel Consumption

Specific fuel consumption is defined by:

P/m sfc f

•

= (2-35)•

power engine=P engine into flow fuel of rate m :where f =

•

pg

Brake power gives brake specific fuel consumption:

bP/m bsfc f

•

= (2-36)

24

bsfcbsfc

Figure 2-9 Brake specific fuel consumption as a function of engine

25speed.

Figure 2 9 Brake specific fuel consumption as a function of engine

2-7 Fuel Conversion Efficiency fηRatio of work produced per cycle to amount of energy supplied

per cycle that can be released in combustion process

HVfHVRf

R

HVf

cf Qm

PNQnm

NPnQW

W&&

===/

/η

fm mass of supplied fuel

HVQ heatig value of fuel

sfcP

mf&=fromP

fηHVsfcQ

1=thus

fη )()(1MJ/kgmg/J HVQsfc

= )()(3600

MJ/kghg/kW HVQsfc ⋅=

with units:

26)()( MJ/kgmg/J HVQsfc HV

2-8 Volumetric EfficiencyParameter used to measure the effectiveness of the induction process

Only used with four-stroke engines which have a distinct induction process

V/

Volumetric efficiency is defined as:

NV/•

daav V/m ρη =

where: ma = mass of air into the engine (or cylinder) for one cycle

NnR daav V/m ρη =or

engine theintoair of flow state-steady m =•

a

a g ( y ) y

conditionscatmospheriatevaluateddensityair=ρ

V = displacement volume

conditionscatmospheriat evaluateddensity air =aρoutside the engine

N = engine speed b f l ti l

Vd = displacement volume Again, seen before !

27

nR = number of revolutions per cycle

b d t fi d d itstandard values of surrounding air pressure and temperature can be used to find density:

T ( t d d) 298 K 25 °C 537 °R 77 °FPo (standard) = 101 kPa = 14.7 psia

ooa /RTP=ρ

To (standard) = 298 K = 25 °C = 537 °R = 77 °F

ooaρ

where: Po = pressure of surrounding air

To = temperature of surrounding air R = gas constant for air = 0.287 kJ/kg-K g g

= 53.33 ft-lbf/lbm-°R

kg/m1 181airofdensitytheconditionsstandardAt 3=ρ

.lbm/ft 0.0739

kg/m1.181air ofdensity the,conditionsstandardAt 3

a

=

=ρ

28

2-9 Correction Factors for Power and Volumetric Efficiency

Pressure of dry Vapor pressure Temperature

air

736.6 mmHg 9.65 mmHg 29.4°c29.0 inHg 0.38 inHg 85°F

29

For 1D steady flow past orifice

2/1)1(/2

0 2 ⎪⎬

⎫⎪⎨

⎧⎥⎤

⎢⎡

⎟⎟⎞

⎜⎜⎛

⎟⎟⎞

⎜⎜⎛

+γγγ

γ ppPAm E&000

0

1 ⎪⎭

⎬⎪⎩

⎨⎥⎥⎥

⎦⎢⎢⎢

⎣⎟⎟⎠

⎜⎜⎝

−⎟⎟⎠

⎜⎜⎝−

=γγ

pp

pp

RTm E

Tpm ∝&T

Indicated Power

miFsi PCP ,, =

2/1

⎟⎞

⎜⎛Tp

,

,⎟⎟⎠

⎞⎜⎜⎝

⎛−

=s

m

mm

dsF T

Tpp

pC

ν

PPCP mfmiFsb PPCP ,,, −=

V l t i Effi iVolumetric Efficiency

2/1T∝νη2/1kT=νη

2/1, ss kT=νη

2/1, mm kT=νη

2/1,

⎟⎟⎠

⎞⎜⎜⎝

⎛= ss

TTνη

,⎟⎠

⎜⎝ mm Tνη

2/1

⎟⎞

⎜⎛ T 2/1

⎞⎛,, ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

m

sms T

Tνν ηη

2/1

⎟⎟⎠

⎞⎜⎜⎝

⎛=′

m

sF T

TC

2-10 Emissions

•

Specific Emissions : rates of pollutant per unit power

bNOxNOx /m (SE) P•

=

CO /m(SE) P•

= bCOCO /m (SE) P=

/m (SE) bHCHC P•

=(2-42)

/m (SE) bpartpart P•

=

gm/hrin emissions of rate flow m :where =•

powerbrake=P powerbrakeb =P

29

Emissions Index : emission rate is normalized by fuel flow rate

[kg/sec] m[gm/sec]/m (EI) fNOxNOx

••

=

y

[kg/sec] m[gm/sec]/m (EI) fCOCO

••

=(2 43)

[kg/sec] m[gm/sec]/m (EI) fHCHC

••

=(2-43)

[kg/sec] m[gm/sec]/m (EI) fpartpart

••

=

30