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Performance parameters
- 1. Engine Geometry VC TC B L ( s = a cosθ + l − a sin θ 2 2 2 )1/ 2 Cylinder volume when piston at TC (s=l+a) BC defined as the clearance volume Vc The cylinder volume at any crank angle is: l s πB 2 V = Vc + (l + a − s ) 4 Maximum displacement, or swept, volume: θ πB 2 a Vd = L 4 Compression ratio: VBC Vc + Vd For most engines B ~ L (square engine) rc = = VTC Vc
- 2. Mean and Instantaneous Piston Speeds VC TC ( 2 s = a cosθ + l − a sin θ 2 2 ) 1/ 2 B Average and instantaneous piston speeds are: L U p = 2 LN BC ds Up = dt l Where N is the rotational speed of the crank shaft s in units revolutions per second Up π cosθ = sin θ 1 + θ Up 2 ( ( l / a ) 2 − sin 2 θ ) 1/ 2 a 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 those with small strokes can run at higher speeds.
- 3. Piston Speeds vs Crank Angle R = l/a
- 4. Engine Torque and Power Torque is measured using a dynamometer. b Stator Force F Rotor N Load cell The torque exerted by the engine is: T = F b with units: J The power Wdot delivered by the engine turning at a speed N and absorbed by the dynamometer is: Wdot = ω T = (2π N) T w/units: (rad/rev)(rev/s)(J) = Watt Note: ω is the shaft angular velocity with units: rad/s
- 5. Indicated Work Given the cylinder pressure data over the operating cycle of the engine one can calculate the work done by the gas on the piston. The indicated work per cycle is Wi = ∫ PdV WA > 0 WB < 0 Compression Power Exhaust Intake W<0 W>0 W<0 W>0
- 6. Indicated Power Indicated power: Wdoti = Wi N / nR w/units: (kJ/cycle) (rev/s) / (rev/cycle) where N – crankshaft speed in rev/s nR – 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, N
- 7. Mechanical Efficiency Some of the power generated in the cylinder is used to overcome engine friction. The friction power is used to describe these losses: Wdotf = Wdoti - Wdotb Friction power can be measured by motoring the engine. The mechanical efficiency is defined as: ηm = Wdotb / Wdoti = 1- (Wdotf / Wdoti ) Mechanical efficiency depends on throttle position, engine design, and engine speed. Typical values for car engines at WOT are 90% @2000 RPM and 75% @ max speed.
- 8. Power and Torque versus Engine Speed Rated brake power There is a maximum in the brake power versus engine speed called the rated brake power. 1 kW = 1.341 hp At higher speeds brake power decreases as friction power becomes significant compared to the indicated power Max brake torque 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.
- 9. 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 = Wi / Vd = (Wdoti nR) / (Vd N) so Wdoti = imep Vd N / nR = imep Ap Up / (2 nR) imep does not depend on engine speed, just like torque. imep is a better parameter than torque to compare engines for design and output because it is independent of engine speed, N, and engine size, Vd. Brake mean effective pressure (bmep) is defined as: Wb 2π ⋅ T ⋅ nR bmep ⋅ Vd bmep = = → T= Vd Vd 2π ⋅ nR
- 10. Maximum BMEP Wb 2π ⋅ T ⋅ nR bmep = = Vd Vd • 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
- 11. Specific Fuel Consumption • For transportation vehicles fuel economy is generally given as mpg, or liters/100 km. • In engine testing the fuel consumption is measured in terms of the fuel mass flow rate mdotf. • The specific fuel consumption, sfc, is a measure of how efficiently the fuel supplied to the engine is used to produce power, bsfc = mdotf / Wdotb isfc = mdotf / Wdoti w/units: g/(kW hr) • Clearly a low value for sfc is desirable since at a given power level less fuel will be consumed
- 12. Brake Specific Fuel Consumption vs 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. cylinder surface area 2πrL 1 = 2 ∝ cylinder volume πr L r
- 13. Brake Specific Fuel Consumption vs Speed • There is a minimum in the bsfc versus engine speed curve • At high speeds the bsfc increases due to increased friction • At lower speeds the bsfc increases due to increased time for heat losses from the gas to the cylinder and piston wall • Bsfc increases with compression ratio due to higher thermal efficiency
- 14. 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 you can calculate: bmep = 2π T nR / Vd Wdotb = 2π N T bsfc = mdotf / Wdotb bmep@WOT Constant bsfc contours from a two-liter four cylinder SI engine
- 15. Combustion Efficiency • The time for combustion in the cylinder is very short so not all the fuel may be consumed or local temperatures may not support combustion • A small fraction of the fuel may not react and exits with the exhaust gas • The combustion efficiency is defined as actual heat input divided by theoretical heat input: ηc = Qin/ (mf QHV) = Qdotin / (mdotf QHV) 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)
- 16. Thermal Efficiency ηth = work per cycle / heat input per cycle ηth = W / Qin = W / (ηc mf QHV) or in terms of rates… ηth = power out/rate of heat input ηth = Wdot/Qdotin = Wdot/(ηc mdotf QHV) • 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%
- 17. Arbitrary Efficiency ηo = Wb / (mf QHV) = Wdotb / (mfdot QHV) Note: ηo is very similar to ηth, the difference is that ηth takes into account only the actual fuel combusted. Recall that sfc = mdotf / Wdotb Thus ηo = 1 / (sfc QHV)
- 18. Volumetric Efficiency • Due to the short cycle time and flow restrictions 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 which is the ratio of actual air inducted divided by the theoretical air inducted: ηv = ma / (ρa Vd) = nR mdota / (ρa Vd N) where ρa is the density of air at atmospheric conditions Po, To for an ideal gas ρa =Po / RaTo and Ra = 0.287 kJ/kg-K (at standard conditions ρa= 1.181 kg/m3) • Typical values for WOT are in the range 75%-90%, and lower when the throttle is closed
- 19. Air-Fuel Ratio • For combustion to take place, the proper ratio of air and fuel must be present in the cylinder. •The air-fuel ratio is defined as AF = ma / mf = mdota / mdotf • The ideal AF is about 15:1, with homogenous 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 and the AF is in the range of 18 to 70.