Engine Performance lecture

8/17/2019 Engine Performance lecture

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Engine Performance

Section 2


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2

BC

L

TC

ls

a

B

( ) 2/1222 sincos θ θ alas −+=

The cylinder volume at any crank angle is:

)(4

2

sal B

V y AV V ccc −++=+= π

When the piston is at TC (s= l+a) the cylinder

volume equals the clearance volume Vc

Geometric Properties

For most engines B ~ L

(“square engine”)

Connecting rod

VC

y Piston displacement: y = l + a - s

Compression ratio:

c

d c

TC

BC c

V

V V

V

V r

+==

Maximum displacement, or swept, volume:

L B

V d 4

2π =

Wrist pin


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BC

L

TC

l

VC

s

a

B

Average piston velocity:

Average piston speed for standard auto engine is

about 15 m/s. Ultimately limited by material

strength. Therefore engines with large strokes run

at lower speeds

“Over square engines” (B > L) with light pistons

have higher rev limits

Geometric Properties

( )( )

−+=

2/122 sin/

cos1sin

2 θ

θ θ

π

alU

U

p

p

( ) 2/1222 sincos θ θ alas −+=

dt dsU p =Instantaneous piston velocity:

=

s

rev

stroke

m

rev

stroke LN U p 2


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R = l/a

Piston Velocity vs Crank Angle

TC BC

R=3


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Piston Acceleration

Piston displacement is:

For most modern engines (a/l)2 ~ 1/9

Using series expansion approximate (1-ε)1/2 ~ 1-(ε/2) and subst θ = ωt

So

Substituting

yields

differentiating

2/1

2

2

sin1cos

−+= θ θ la

las

−+= t

lalt as ω ω 2

2

sin2

cos

2/)2cos1(sin2 t t ω ω −=

−−+=)2cos1(

4cos

2

t l

alt as ω ω

+= t

l

at a

dt

sd ω ω ω 2coscos2

2

2


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Piston Inertia Force

The inertia force is simply the piston mass multiplied by the acceleration

+−=−= t

l

at am

dt

sd mForce Inertia ω ω ω 2coscos2

2

2

Primary term Secondary term

• The maximum force occurs at TC, θ = ωt = 0 F ~ amω 2

• The primary term varies at the same speed as the crankshaft

and the secondary term varies at twice the crank shaft speed

• For a very long connecting rod (a/l)


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Torque and Power

Torque is measured off the output shaft using a dynamometer.

Load cell

Force FStator

Rotor

b

N

The torque exerted by the engine is T:

W

)341.1k 1()( :units )2( hpW W J s

rev

rev

rad T N T W ==

⋅⋅=⋅= π ω

J NmbF T =⋅= :units

The power delivered by the engine turning at a speed N andabsorbed by the dynamometer is:

Note: ω is the shaft angular velocity in units rad/s


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The term brake power , , is used to specify that the power is

measured at the output shaft, this is the usable power delivered bythe engine to the load.

bW

Brake Power

iW

The brake power is less than the power generated by the gas in

the cylinders due to mechanical friction and parasitic loads (oil

pump, air conditioner compressor, supercharger, etc…).

The power produced in the cylinder is termed the indicated

power , .

Torque is a measure of an engine’s ability to do work and power is

the rate at which work is done

Note torque is independent of crank speed.


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Indicated Work per Cycle

Given the cylinder pressure data over the operating cycle of the engine one

can calculate the work done by the gas on the piston. This data is

typically given as P vs V

∫= PdV W i

Compression

W0Intake

W>0

Exhaust

W


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Indicated Work per Cycle

Given the cylinder pressure data over the operating cycle of the engine one

can calculate the work done by the gas on the piston. This data is

typically given as P vs V

The indicated work per cycle is given by ∫= PdV W i

Compression

W0Intake

W>0

Exhaust

W 0

WB < 0

A

C


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Gross indicated work per cycle – net work delivered to the piston over

the compression and expansion strokes only:

Wi,g = area A + area C (>0)

Work per Cycle

Pump work – net work delivered to the gas over the intake and exhaust

strokes:

Wp = area B + area C (


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Indicated Work at WOT

The pressure at the intake port is just below atmospheric pressure

The pump work (area B+C) is small compared to the gross indicatedwork (area A+C)

Wi,n = Wi,g - Wp = area A - area B

Pintake

PintakePo


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Indicated Work at Part Throttle

The pressure at the intake port is significantly lower than atmospheric pressure

The pump work (area B+C) can be significant compared to gross indicated

work (area A+C)

Wi,n = Wi,g - Wp = area A - area B

Pintake


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Indicated Work with Supercharging

Engines with superchargers or turbochargers have intake pressures

greater than the exhaust pressure, yielding a positive pump work

Wi,n = area A + area B

Supercharge increases the net indicated work but is a parasitic load

since it is driven by the crankshaft

Pintake

Compressor


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Mechanical Efficiency

Some of the power generated in the cylinder is used to overcome engine

friction and to pump gas into and out of the engine.

The term friction power , , is used to describe collectively these power

losses, such that:

gi

f

gi

f gi

gi

bm

W

W

W

W W

W

W

,,

,

,1

−=

−

==η

f W

Friction power can be measured by motoring the engine.

bgi f W W W −= ,

The mechanical efficiency is defined as:


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Mechanical efficiency depends on pumping losses (throttle position) and

frictional losses (engine design and engine speed).

Mechanical Efficiency, cont’d

Typical values for automobile engines at WOT are:

90% @2000 RPM and 75% @ max speed.

Throttling increases pumping power and thus the mechanical efficiencydecreases, at idle the mechanical efficiency approaches zero.


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cyclecycle W T W N W T N W ∝⋅∝⋅∝ so and

1 kW = 1.341 hp

Rated brake power

Power and Torque versus Engine Speed at WOT

There is a maximum in the brake power

versus engine speed called the rated

brake power (RBP).

At higher speeds brake power decreases as

friction power becomes significant compared

to the indicated power f gib W W W

−= ,

Max brake torque There is a maximum in the torque versus

speed called maximum brake torque (MBT).

Brake torque drops off:

• at lower speeds due to heat losses

• at higher speeds it becomes more difficult to

ingest a full charge of air.


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Indicated Mean Effective Pressure (IMEP)

imep is a fictitious constant pressure that would produce the same

work per cycle if it acted on the piston during the power stroke.

R

p p

R

d i

d

Ri

d

i

n

U Aimep

n

N V imepW

N V

nW

V

W imep

⋅

⋅⋅=

⋅⋅=→

⋅⋅

==2

imep is a better parameter than torque to compare engines for design and

output because it is independent of engine size, Vd.

R

d

d

R

d

b

n

V bmepT

V

nT

V

W bmep

⋅⋅

=→⋅⋅

==π

π

2

2

Brake mean effective pressure (bmep) is defined as:


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The maximum bmep of a good engine design is well established:

Four stroke engines:

SI engines: bmep= 850-1050 kPa*

CI engines: bmep= 700 -900 kPa

Turbocharged SI engines: bmep= 1250 -1700 kPa

Turbocharged CI engines: bmep= 1000 - 1200 kPa

Two stroke engines:

Standard CI engines comparable bmep to four stroke

Large slow CI engines: 1600 kPa

*Values are at maximum brake torque and WOT

Note, at the rated (maximum) brake power the bmep is 10 - 15% less

Can use the maximum bmep in design calculations to estimate engine

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

engine speed.


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Maximum BMEP

The maximum bmep is obtained at WOT at a particular engine speed

Closing the throttle decreases the bmep

For a given displacement, a higher maximum bmep means more torque

For a given torque, a higher maximum bmep means smaller engine

Higher maximum bmep means higher stresses and temperatures in the

engine hence shorter engine life, or bulkier engine.

For the same bmep 2-strokes have almost twice the power of 4-stroke

2

d

R

d

b

V

nT

V

W bmep

⋅⋅== π


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Vehicle Engine

type

Displ.

(L)

Max Power

(hp@rpm)

Max Torque

(lb-ft@rpm)

BMEP at

Max BT(bar)

BMEP at

Rated BP(bar)

Mazda

Protégé LX

I4 1.84 122@6000 117@4000 10.8 9.9

Honda

Accord EX

I4 2.25 150@5700 152@4900 11.4 10.4

MazdaMillenia S

I4Turbo

2.26 210@5300 210@3500 15.9 15.7

BMW

328i

I6 2.80 190@5300 206@3950 12.6 11.5

Ferrari

F355 GTS

V8 3.50 375@8250 268@6000 13.1 11.6

Ferrari

456 GT

V12 5.47 436@6250 398@4500 12.4 11.4

Lamborghini

Diablo VT

V12 5.71 492@7000 427@5200 12.7 11.0

Typical 1998 Passenger Car Engine Characterist ics


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Road-Load Power

A part-load power level used for testing engines (fuel economy, emissions)

is the power required to drive a vehicle on a level road at a steady speed.

vvv Dav Rr S S AC g M C P ⋅+= )2

1( 2 ρ

*Modern midsize aerodynamic cars only need 5-6 kW (7-8 HP)

to cruise at 90 km/hr, hence the attraction of hybrid cars!

where CR = coefficient of rolling resistance (0.012 - 0.015)

Mv = mass of vehicle

g = gravitational acceleration

ρa = ambient air densityCD = drag coefficient (for cars: 0.3 - 0.5) Av = frontal area of the vehicle

Sv = vehicle speed

The road-load power , Pr , is the engine power needed to overcome

rolling resistance and the aerodynamic drag of the vehicle.


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Drag Force Parameters

Auto manufacturers can improve the drag force by reducing:

Vehicle frontal area:

2005 Corvette is 0.57 m2

Most cars around 0.8 m2

2006 Hummer H3 is 1.56 m2

Drag coefficient CD:

2004 Toyota Prius – 0.26

2005 Porsche Boxster – 0.29

1983 Audi 100 – 0.3

2006 Dodge Challanger – 0.332003 Hummer – 0.57

Formula 1 car – 0.7 to 1.1 (DRS)

http://en.wikipedia.org/wiki/File:Hummer-H3.JPGhttp://upload.wikimedia.org/wikipedia/commons/0/08/Chevrolet-Corvette-C6-2.jpghttp://www.bing.com/images/search?q=prius&FORM=IGRE1http://en.wikipedia.org/wiki/File:Raikkonen_Spain_2009.jpg


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Engine power requirements

F=Mvgα

hpkW S g M PvvC

4735)sin( ==⋅= α

For a 1500 kg car moving at 50 km/hr up a 10o incline:

F = Mva

For a 1500 kg car accelerating (constant) from 0-100 km/hr in 8 s:

hpkW S t S M Pvvva

207145)/( ==⋅=

Ferrari 430 Scuderia has 508 hp at 8500 rpm 4.3L V8 engine

1270 kg and 0-100 km/hr in 3.6 s requires 272 kW (389 hp)


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Automobile transmission

Automatic transmission – gears shift automatically based on input

data from the sensors on the engine and the transmission (e.g., enginespeed, vehicle speed, throttle position, brake pedal position)

Engine operates between 600 – 7000 rpm whereas car wheels rotate at

0 -1800 rpm

Manual transmission – operator shifts gears

Transmission produces high torque at low car speeds and also operatesat highway speeds with the engine operating in the same speed range

transmission changes the gear ratio as the car speeds up

Highest torque is obtained in the mid engine speed range while the

greatest torque is often required at the lowest wheel speed


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Differential provides

Further gear ratio (3:1)

Automobile transmission

Torque converter provides fluid dynamic coupling with torque multiplication during idle andacceleration


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Gears

Gears change the speed of rotation and torque transmitted between shafts

Consider a simple gear set consisting of two gears:

RiRo

ωiωo

Vc, Fc

i

o

R

R

GR =

GR R

R

R RV

ii

o

io

ooiic

ω ω ω

ω ω

=

=

==

ii

i

o

o

ooiic

T GRT R

RT

RT RT F

⋅=

=

== //

Gear ratio (GR) is the number of turns of the input shaft required to give one

revolution of the output shaft


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An automobile is more complicated because you need several gear

ratios so the car can accelerate smoothly (shift for power or fuel

economy?)

Automobile Transmission

Gear GR ωo/ωi To/Ti

1 3:1 1/3 3

2 2.5:1 2/5 5/23 1.5:1 2/3 3/2

4 1:1 1 1

5 (OD) 0.75:1 4/3 3/4

Manual transmission typically has five forward gears and a reverse

Automatic transmission uses two sets of planetary gears to give three

or four forward gear ratios and one reverse

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Manual transmission (two gears)

Bearings

Flywheel

Clutch

CRANKSHAFT

Starter

Splined

shaft/collar

Synchronizer

TO WHEELS


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Automatic transmission planetary gear system

A reduction, B overdrive, C reverse

Planet gears

linked by carrier

Input Out Stationary ωi:ωo

A Sun (S)

Planet

Carrier

(C)

Ring (R) 1 + R/S 3.4:1

B Planet

Carrier (C)

Ring (R) Sun (S)1 / (1 +

S/R)

0.71:1

C Sun (S) Ring (R)Planet

Carrier (C)-R/S -2.4:1

ring gear = 72 teeth and sun gear has 30 teeth.

Locking any two locks up the whole device at a 1:1 gear


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0

50

100

150

200

250

300

350

400

450

500

0 1000 2000 3000 4000 5000 6000 7000 8000

Engine speed (RPM)

T o r q u

e

( F t - l b )

Engine

1st gear (GR=3.54)

2nd gear (GR=2.13)

3rd gear (GR=1.36)

4th gear (GR=1.03)

5th gear (GR=0.72)

1999 Neon DOHC

4210 rpm

3610 rpm

st nd GR

GR1

1

2

2 ω ω =


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Specific Fuel Consumption

In engine testing the fuel consumption is measured in terms of the fuel

mass flow rate . f m

b

f

W

mbsfc

=

hr kW

g

W

misfc

i

f

⋅= :units

Clearly a low value for sfc is desirable since for a given power level

the lesser the fuel consumed the better it is.

The specific fuel consumption, sfc, is a measure of how efficiently thefuel supplied to the engine is used to produce power,

For transportation vehicles fuel economy is generally given as mpg, or

L/100 km (in the future gm of CO2/km).


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Brake Specific Fuel Consumption vs Engine Size

Bsfc decreases with engine size due to reduced heat losses from gas to

cylinder wall.

B L B

BL 1

olumecylinder v

areasurfacecylinder

released energy

lossheat2 ∝==

π

π

Note cylinder surface to volume ratio increases with bore diameter.


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Brake Specific Fuel Consumption vs Engine Speed

There is a minimum in the bsfc versus engine speed curve

b

f

W

mbsfc

=

At high speeds the bsfc increases due to increased friction i.e. smaller bW

iW

Bsfc decreases with compression ratio due to higher thermal efficiency

At lower speeds the bsfc increases due to increased time for heat

losses from the gas to the cylinder and piston wall, and thus a smaller


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Performance Maps

Performance map is used to display the bsfc over the engines full load

and speed range. Using a dynamometer to measure the torque and fuel

mass flow rate for different throttle positions you can calculate:

Constant bsfc contours from a

2 litre four cylinder SI engine

bmep@WOT

d

R

V

nT bmep

⋅⋅= π 2

b

f

W

mbsfc

= )2( T N W b ⋅⋅= π


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Engine Effic iencies

The time for combustion in the cylinder is very short, especially at high

speeds, so not all the fuel may be consumed

HV f

in

HV f

inc

Qm

Q

Qm

Q

ut l heat inptheoretica

t input actual hea

⋅=

⋅==

η

where Qin = heat added by combustion per cycle

mf = mass of fuel added to cylinder per cycle

QHV = heating value of the fuel (chemical energy per unit mass)

The combustion efficiency is defined as:

A small fraction of the fuel may not react and exits with the exhaust gas


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Engine Efficiencies (2)

The thermal effic iency is defined as:

HV f cinth

Qm

W

Q

W

⋅⋅===η

η cycle perinputheat

cycle perwork

HV f cinth

QmW

QW

⋅⋅===

η η

inputheatof rateout power

or in terms of rates

Thermal efficiencies can be given in terms of brake or indicated values

Indicated thermal efficiencies are typically 50% to 60% and brake thermalefficiencies are usually about 30%


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Engine Efficiencies (3)

Fuel conversion effic iency is defined as:

HV f HV f f

Qm

W

Qm

W

⋅=

⋅=

η

Note: η f is very similar to η th, difference is η th takes into account actual

fuel combusted.

W

msfc

f

=

HV f

Qsfc ⋅=

)(

1η

Note: η f is very similar to η th, difference is η th takes into account actual

fuel combusted.

Recall:

Therefore, the fuel conversion efficiency can also be obtained from:


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Volumetric Efficiency

Due to the short cycle time at high engine speeds and flow restrictions

through the intake valve less than ideal amount of air enters the cylinder.

N V

mn

V

m

d a

a R

d a

av

⋅⋅

⋅=

⋅

==

ρ ρ

η

air ltheoretica

inducted airactual

where ρa is the density of air at atmospheric conditions Po, To and for anideal gas ρ a =Po / RaTo and Ra = 0.287 kJ/kg-K (at standard conditions

ρa= 1.181 kg/m3)

The effectiveness of an engine to induct air into the cylinders is measured

by the volumetric efficiency:

Typical values for WOT are in the range 75%-90%, and lower when the

throttle is closed


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Air-Fuel Ratio

For combustion to take place the proper relative amounts of air and fuel

must be present in the cylinder.

For gasoline fuel the ideal AF is about 15:1, with combustion possiblein the range of 6 to 19.

For a SI engine the AF is in the range of 12 to 18 depending on the

operating conditions.

For a CI engine, where the mixture is highly non-homogeneous, the

AF is in the range of 18 to 70.

f

a

f

a

m

m

m

m AF

==

The air-fuel ratio is defined as


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Relationships Between Performance Parameters

By combining equations presented in this section the following additional

working equations are obtained:

)/1(

2

)/1(

)/1(

AF Qmep

n

AF QV T

n

AF QV N W

a HV v f

R

a HV d v f

R

a HV d v f

⋅⋅⋅⋅=

⋅

⋅⋅⋅⋅⋅=

⋅⋅⋅⋅⋅⋅=

ρ η η

π

ρ η η

ρ η η

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Engine Performance lecture