Chapter 2: Engine Performance Measures

BAE 517 - Lecture 2

Terminology

Mean Effective Pressure Fuel Use Efficiency Specific Fuel Consumption

Fuel Equivalent Power

600,3gf

fe

HmP

Pfe - fuel equivalent power (kW)

mf – fuel mass flow rate (kg/h)

Hg – gross heating value of fuel (kJ/kg) No. 2 Diesel – 45,000 kJ/kg

.

Example

What is the Pfe of an engine consuming 30.0 kg/h of No. 2 diesel fuel?

s

h

kJ

skW

kg

kJ

L

kg

h

LkW

3600

1

1

1000,45840.07.35375

Fig. 2.1: Power flows in an engine.

Alternate Fuel Equivalent Power

600,3gff

fe

HqP

qf – fuel consumption rate (L/h)

f – fuel density (kg/L)

Indicated Power

000,120eeime

i

NDpP

Pi – Indicated power (kW)

pime – indicated mean effective pressure

De- engine displacement (L)

Ne- crankshaft speed (rpm)

Burning fuel produces high pressure on the piston, multiplied by the piston area produces a forces to drive the piston downward.

Engine Displacement

000,1

LnAD p

e

Ap – area of piston (cm2)

L – stroke length (cm) n – number of cylinders

The total swept volume of the engine is calculated as,

Example

Assume the six-cylinder engine from the previous problem has a cylinder bore of 11.67 cm and a stroke of 12.00 cm. If the engine is running at 2,200 rev/min, and pime is 1,200 kPa, what is the indicated power?

000,14

600.1267.1170.7

2

cmcm

LDe

000,120

200,270.7000,124.169

rpmLkPakWPi

Brake Engine Power

000,60

2 ebb

NTP

Pb – brake power (kW)

Tb – torque at flywheel (N.m)

Early engine development utilized a “prony brake” for the determination of engine power at the flywheel. Brake power is determined as,

Example

Continuing from the previous example, assume the “brake torque” at the flywheel is 625 N.m. What is the “brake power” in kW?

000,60

200,262520.144

rpmmNkWPb

Friction Power

bif PPP

Pf – friction power (kW)

The difference between “indicated power” and “brake power” is termed “friction power.” This loss is associated with the internal friction of the engine, along with the power to drive the injection pump, fuel pump, water pump, fan, alternator and air conditioner compressor.

Example

From the previous example, what is the friction power (kW)?

kWkWkWPf 0.1444.1694.25

Fig. 2.2: Engine P-V diagram with indicated mean effective pressure.

Brake Mean Effective Pressure

ee

bbme ND

Pp

000,120

pbme – brake mean effective pressure (kPa)

Brake mean effective pressure can not be measured within the engine. However it can be calculated as,

Example

From the previous example, what is the brake mean effective pressure (kPa)?

rpmL

kWkPapb 200,270.7

0.144000,120024,1

Brake Toque

4bmee

b

pDT

Tb – brake torque (N.m)

Note: The above equation is only good for 4-stroke engines. The denominator must be changed to 2 for two-stroke engines.

By combining the previous two equations, brake torque can be approximated as,

Friction Mean Effective Pressure

ee

ffme ND

Pp

000,120

A variation on previous equations yields,

pfme – friction mean effective pressure (kPa)

Example

From the previous example, what is the friction mean effective pressure (kPa)?

rpmL

kWkPapb 200,270.7

4.25000,120180

Friction Mean Effective Pressure

2

21 10001000

ee

ofme

NA

NAAp

Ao, A1, and A2 are constants for a specific engine.

For CI engines, friction mean effective pressure is estimated as,

Engine Efficiencies

fe

bbt

i

bm

fe

iit

P

Pe

P

Pe

P

Pe

Indicated thermal (eit), mechanical (em), and brake thermal (ebt) efficiencies are determined as,

Example

What are the indicated, brake and thermal efficiencies for the on-going example?

kW

kWe

kW

kWe

kW

kWe

bt

m

it

0.375

0.144384.0

4.169

0.144850.0

0.375

4.169452.0

Specific Fuel Consumption

X

f

P

mXSFC

XSFC – specific fuel consumption (kg/kWh). X must always be specified when reporting

these values (i.e., I for indicated)

Fuel consumption of an engine reported in L/h or kg/h because these values ignore engine load. A better measure of fuel consumption is,

Specific Fuel Consumption Variations

ISFC – indicated specific fuel consumption BSFC - brake specific fuel consumption PSFC – PTO specific fuel consumption DSFC – drawbar specific fuel consumption

Specific Fuel Consumption (Alternate)

XtgeHXSFC

600,3

Alternately, specific fuel consumption can be determined as,

Example

What are the “indicated” and “brake” specific fuel consumptions for the engine noted in the previous examples?

kW

hLkWhLBSFC

kW

hLkWhLISFC

0.144

/7.35/248.0

4.169

/7.35/211.0

Engine Speed Control

Most engines (CI and SI) are equipped with some form of governor.

Mechanical governors have been utilized since the days of James Watt (steam engines).

Much of the terminology is the same for both mechanical and electronic governors.

Fig. 2.3: Illustration of mechanical governor action.

Terminology

High Idle Point (A) – maximum speed of unloaded engine.

Governor’s Maximum Point (C) – governor is unable to affect fuel delivery beyond this point.

Governor-Control Region (right of C) – speed of engine controlled by governor in this region.

Load-Control Region (left of C) – engine speed is controlled by torque load on engine.

Governor Regulation – measure of how well a governor maintains a constant speed.

Governor Regulation

GMHI

GMHI

NN

NNg 200Re

Reg – governor regulation (%) Mechanical Governor – 6% is possible Electronic Governor – 1% is possible

NHI – engine high idle speed (rpm)

NGM – engine speed at governor’s maximum (rpm)

“Governor regulation” is calculated as,

Engine Torque Generation

4

206.0

fmeef

e

fitGi

fib

pDT

N

meHT

TTT

Tb – brake engine torque (N.m)

Ti – indicated engine torque (N.m)

Tb – friction torque (N.m)

By rearranging the previous equations it is possible to develop the following relationships describing engine torque,

Engine Torque Notes

Friction torque varies with pmef, which in turn varies with engine speed.

The governor controls the amount of fuel added to the engine and therefore controls indicated torque (for the control range of the governor).

In the load control region, friction torque fall as engine speed decreases, and therefore brake torque increases.

Accessories that add to the friction torque at higher engine speeds help to increase brake torque as the engine is loaded.

Fuel added per cycle in the load control range (increased volumetric efficiency of injection system) adds to the torque reserve of the engine.

Fig. 2.4: Performance Map of Over-fueled Engine

Engine Performance Map Notes

Manufacturer’s plot engine performance maps to aid off-road equipment designers.

The torque envelope is defined by the torque-speed curve of the engine when run with the governor set at maximum speed.

A family of constant power curves is plotted within the envelope by solving for brake torque from the eq. in Slide 10.

Engine Performance Map Notes

Over-fueling occurs in the region where BSFC rises with increasing torque.

Some engines are never over-fueled (minimum BSFC occurs above torque envelope).

The lowest BSFC is 0.278 kg/kWh. Performance maps can be generated by

collecting data on torque, speed, and fuel consumption, and then plotting contours by hand.

Alternate Performance Map Generation Method

4

4

3

3

2

2

1

1 000,1000,1000,1000,1

1

1600,3

eeeeoe

en

b

itoit

bme

fme

itg

NB

NB

NB

NBBNf

NfT

ee

p

p

eHBSCF

For any CI engine, the following equations can be fit to a specific engine providing a limited engine performance data set is collected (approximately 50 points).

Optimizing Engine Performance

Engines are most efficient at or near peak load.

Efficiency drops with a reduction in torque load.

At zero brake torque, all fuel energy is expended in engine friction.

Lower rated engine speeds provide lower BSFC, and at the same time reduce torque reserve – design compromise.

Optimizing Engine Performance

Partial load fuel economy can be improved by shifting to higher gear to reduce engine speed. Engine initially operated at 20 kW and

2250 rpm results in BSFC of 0.400 kg/kWh.

Shifting to a higher gear reduces engine speed to 1850 rpm, at 20 kW, resulting in a new BSFC of 0.325 kg/kWh.

Improved Fuel Economy at Partial Load

Initial Setting

Higher Gear

Homework Set No. 1

Do problems 2.1, 2.3, 2.5, 2.7, 2.9, 2.10, and 2.15 at the end of Chapter 2 for next Tuesday.