Engine Performance

Section 2

BCLTClsaqBThe cylinder volume at any crank angle is:Compression ratio:When the piston is at TC (s= l+a) the cylinder volume equals the clearance volume VcMaximum displacement, or swept, volume:Geometric PropertiesFor most engines B ~ L (square engine)Connecting rodVCyPiston displacement: y = l + a - s

Average and instantaneous piston velocity are:Where N is the rotational speed of the crank shaft in units revolutions per secondAverage 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 than those with small strokes run at higher speeds.Geometric Properties

R = l/aPiston Velocity vs Crank Angle

Piston AccelerationPiston displacement is:

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

Using series expansion approximate (1-e)2 ~ 1-(e/2) and subst = wt

So

Substituting

yields

differentiating

Piston Inertia ForceThe inertia force is simply the piston mass multiplied by the accelerationPrimary termSecondary term The maximum force occurs at TC, = wt = 0 F = -amw2

The primary term varies at the same speed as the crankshaftand the secondary term varies at twice the crank shaft speed

For a very long connecting rod (a/l)

Torque and PowerTorque is measured off the output shaft using a dynamometer.Load cellForce FStatorRotorbNThe torque exerted by the engine is T:

Torque and PowerTorque is measured off the output shaft using a dynamometer.The torque exerted by the engine is T:The power delivered by the engine turning at a speed N and absorbed by the dynamometer is:Note: w is the shaft angular velocity in units rad/s

Torque is a measure of an engines ability to do work and power is the rate at which work is done

Note torque is independent of crank speed.

The term brake power, , is used to specify that the power is measured at the output shaft, this is the usable power delivered by the engine to the load.

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, etc)

The power produced in the cylinder is termed the indicated power, .Brake Power

Indicated Work per CycleGiven 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 CompressionW0IntakeW>0ExhaustW 0WB < 0

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)

Pump work net work delivered to the gas over the intake and exhaust strokes:

Wp = area B + area C (

Indicated power:

where N crankshaft speed in rev/snR number of crank revolutions per cycle= 2 for 4-stroke= 1 for 2-stroke

Power can be increased by increasing: the engine size, Vd compression ratio, rc engine speed, NIndicated PowerW

Indicated Work at WOTThe pressure at the intake port is just below atmospheric pressureThe pump work (area B+C) is small compared to the gross indicated work (area A+C)

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

Indicated Work at Part ThrottleThe pressure at the intake port is significantly lower than atmospheric pressureThe pump work (area B+C) can be significant compared to gross indicated work (area A+C)

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

Indicated Work with SuperchargingEngines with superchargers or turbochargers have intake pressuresgreater than the exhaust pressure, yielding a positive pump workWi,n = area A + area B

Supercharge increases the net indicated work but is a parasitic loadsince it is driven by the crankshaftPintakeCompressor

Mechanical EfficiencySome of the power generated in the cylinder is used to overcome enginefriction and to pump gas into and out of the engine.

The term friction power, , is used to describe collectively these power losses, such that:Friction power can be measured by motoring the engine.

The mechanical efficiency is defined as:

Mechanical efficiency depends on pumping losses (throttle position) andfrictional losses (engine design and engine speed).

Typical values for automobile engines at WOT are:90% @2000 RPM and 75% @ max speed.

Throttling increases pumping power and thus the mechanical efficiency decreases, at idle the mechanical efficiency approaches zero.Mechanical Efficiency, contd

There is a maximum in the brake power versus engine speed called the ratedbrake power (RBP).

At higher speeds brake power decreases as friction power becomes significant compared to the indicated power There is a maximum in the torque versus speed called maximum brake torque (MBT).

Brake torque drops off: at lower speeds do to heat losses at higher speeds it becomes more difficult to ingest a full charge of air.Max brake torque1 kW = 1.341 hpRated brake powerPower and Torque versus Engine Speed at WOT

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.imep does not depend on engine speed, just like torqueimep is a better parameter than torque to compare engines for design and output because it is independent of engine size, Vd.

Brake mean effective pressure (bmep) is defined as:

The maximum bmep of good engine designs is well established:

Four stroke engines:

SI engines: bmep= 850-1050 kPa* CI engines: bmep= 700 -900 kPaTurbocharged SI engines: bmep= 1250 -1700 kPaTurbocharged CI engines: bmep= 1000 - 1200 kPa

Two stroke engines:

Standard CI engines comparable bmep to four strokeLarge 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 above maximum bmep in design calculations to estimate engine displacement required to provide a given torque or power at a specified speed.

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

Typical 1998 Passenger Car Engine Characteristics

VehicleEnginetypeDispl.(L)Max Power(HP@rpm) Max Torque(lb-ft@rpm)BMEP atMax BT(bar)BMEP atRated BP (bar)MazdaProtg LXL41.839122@6000117@400010.89.9Honda Accord EXL42.254150@5700152@490011.410.4Mazda Millenia SL4Turbo2.255210@5300210@350015.915.7BMW328iL62.793190@5300206@395012.611.5FerrariF355 GTSV83.496375@8250268@600013.111.6Ferrari456 GTV125.474436@6250398@450012.411.4LamborghiniDiablo VTV125.707492@7000427@520012.711.0

Road-Load Power A part-load power level useful for testing car engines is the power requiredto drive a vehicle on a level road at a steady speed.

The road-load power, Pr, is the engine power needed to overcome rolling resistance and the aerodynamic drag of the vehicle.Where CR = coefficient of rolling resistance (0.012 - 0.015)Mv = mass of vehicleg = gravitational accelerationra = ambient air densityCD = drag coefficient (for cars: 0.3 - 0.5)Av = frontal area of the vehicleSv = vehicle speed

*Modern midsize aerodynamic cars only need 5-6 kW (7-8 HP) power to cruise at 90 km/hr, hence the attraction of hybrid cars!

Specific Fuel Consumption For transportation vehicles fuel economy is generally given as mpg, orL/100 km.

In engine testing the fuel consumption is measured in terms of the fuel mass flow rate .

The specific fuel consumption, sfc, is a measure of how efficiently the fuel supplied to the engine is used to produce power, Clearly a low value for sfc is desirable since for a given power levelless fuel is consumed

Brake Specific Fuel Consumption vs Engine Size Bsfc decreases with engine size due to reduced heat losses from gas to cylinder wall. Note cylinder surface to volume ratio increases with bore diameter.

Brake Specific Fuel Consumption vs Engine Speed At high speeds the bsfc increases due to increased friction i.e. smaller

At lower speeds the bsfc increases due to increased time for heatlosses from the gas to the cylinder and piston wall, and thus a smaller

Bsfc increases with compression ratio due to higher thermal efficiency There is a minimum in the bsfc versus engine speed curve

Performance MapsPerformance 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 two-liter four cylinder SI enginebmep@WOT

Engine Efficiencies The time for combustion in the cylinder is very short so not all the fuel may be consumed

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

The combustion efficiency is defined as:Where Qin = heat added by combustion per cyclemf = mass of fuel added to cylinder per cycleQHV = heating value of the fuel (chemical energy per unit mass)

Engine Efficiencies (2) The thermal efficiency is defined as: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 thermal efficiencies are usually about 30%

Engine Efficiencies (3) Fuel conversion efficiency is defined as:Note: hf is very similar to hth, difference is hth takes into account actual fuel combusted.

Recall:

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

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.

The effectiveness of an engine to induct air into the cylinders is measured by the volumetric efficiency:where ra is the density of air at atmospheric conditions Po, To and for an ideal gas ra =Po / RaTo and Ra = 0.287 kJ/kg-K (at standard conditions ra= 1.181 kg/m3)

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

Air-Fuel Ratio For combustion to take place the proper relative amounts of air and fuel must be present in the cylinder.

The air-fuel ratio is defined as The ideal AF is about 15:1, with combustion possible in 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.

Relationships Between Performance ParametersBy combining equations presented in this section the following additionalworking equations are obtained: