Chapter 2 Operating Characteristics 2-1 Engine Parameters 2-22 Work 2-3 Mean Effective Pressure 2-4 Torque and Power 2-5 Dynamometers 2-6 Air-Fuel Ratio and Fuel-Air Ratio 2-7 Specific Fuel Consumption 2-8 Engine Efficiencies 1
Important engine characteristics Factors important to an engine user are: 1. The engine s performance over its operating range 2. The engine s fuel consumption within this operating range and the cost of the required fuel 3. The engine s noise and air pollutant emissions within this operating range 4. The initial cost of the engine and its installation 5. The reliability and durability of the engine, its maintenance requirements, and how these affect engine availability and operating costs 1
Engine performance is more precisely defined by: 1. Maximum power (or Maximum torque) available at each speed within the useful engine operating range 2. The range of speed and power over which engine operation is satisfactory 1
Crank Shaft with Piston
2-1 Engine Parameters B bore L stroke l connecting rod length a crank offset s piston position θ crank angle V c clearance volume V d displacement volume d Figure 2-1 Piston and cylinder geometry of reciprocating engine. 2
TABLE 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 L If bore (B) < stroke, referring to under square. L 2a 3
Stroke length L L 2a (2-1) The distance s between crank axis and wrist pin axis is given by s a cosθ + l 2 - a 2 sin 2 θ where: a crankshaft offset l connecting rod length θ crank angle (2-2)
Do you think a piston ever stops while an engine operates? Yes / No Question
Mean piston speed is : S p 2LN where: N crankshaft speed (2-3) The instantaneous piston speed S p is obtained : S p ds/dt p (2-4)
as a function of crank angle for various R values, where Instantaneous piston speed relative to average piston speed as 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 S p π cosθ sinθ (2-5) 1 + 2 2 1/ S p 2 ( R sin θ ) 2 where: R l/a (2-6) R is the ratio of connecting rod length to crank offset Displacement, or displacement volume V d is the volume displaced by the piston as it travels from BC to TC: V V - V (2-7) d BDC TDC Displacement can be given for one cylinder or for the entire : engine. For one cylinder V d 2 ( π /4)B L (2-8)
For an engine with N c cylinders: 2 V N ( π /4)B L d c where: B cylinder bore S stroke N c number of engine cylinders (2-9) clearance volume V c V c V TDC (2-10) V BDC Vc + Vd (considering each cylinder) (2-11) The compression ratio of an engine is defined as : r V /V (V + c BDC TDC c V d )/V c (2-12) 7
The cylinder volume V at any crank angle is: 2 V V + ( πb /4)( l a -s) (2-13) c + where: V c clearance volume B bore l connecting rod length a crank offset s piston position Same s we just seen! This can also be written in a non-dimensional form by dividing by V c, substituting for l, a, and s, and employing the definition of R: 1 2 2 V/ V c 1+ (r c -1)[R + 1- cosθ - R - sin θ ] (2-14) 2 where: r c compression ratio R l / a 8
The cross-sectional area of a cylinder and the surface area of a flat-topped piston are each given by: 2 A (2-15) π /4)B p ( The combustion chamber surface area is: A A + A + π B( l a - s) (2-16) ch p + where A ch is the cylinder head surface area, which will be Somewhat larger than A p. Then if the definitions for r, a, l, and R are used. Eq. (2-16) can be rewritten as: A A ch + A p + ( π BL/2)[R + 1- cosθ - R 2 2 sin θ ] (2-17) 9
2-2 Torque and Power Torque T is normally measured with dynamometer. Torque is a measure of engine s ability to do work. T Fb where: F force exerted on stator b length of moment arm (2-18) Figure 2-22 Schematic of principle of dynamometer operation 10
2-2 Torque And Power Power P delivered by the engine and absorbed by dynamometer. P 2π N T (2-19) where: N crankshaft rotational speed The engine power measured as described is called brake power, P b. 11
Figure 2-3 Power and torque curves of General Motors L35 Vortec V6 engine. 1 kw 1.341hp 12
Figure 2-4 1996 General Motors L35 4300 Vortec V6 spark ignition engine. 13
Figure 2-5 Brake power and torque of a typical auto- mobile reciprocating engine as a function of engine speed. 14
2-3 Indicated Work per Cycle Pressure 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 typical four stroke cycle SI engine. 15
Force due to gas pressure on the moving piston generates the work in an IC engine cycle. W Fdx PAp dx (2-20) where: P pressure in combustion chamber And Ap dx A p area against which the pressure acts x distance the piston moves dv (2-21) dv is the differential volume displaced by the piston, so work done can be written: W P dv (2-22) Indicated work per cycle is obtained by integrating g around a curve to obtain area enclosed on the diagram. 16
Figure 2-7 Four-stroke cycle of ftypical SI engine plotted on P-V coordinates at (a) wide open throttle 17
Gross indicated work is work delivered to piston over the compression and expansion processes W gross area A + area C (2-23) Net indicated work is work delivered to piston over the entire cycle W net (area A + C) - (area B + C) area A - area B (2-24) Pumping work is work delivered to piston over the intake and exhaust processes W pump area B + area C (2-25) 18
Figure 2-8 Four-stroke cycle of a SI engine equipped with a super- charger or turbocharger, plotted on P-v coordinates. 19
Power per cylinder is related to the indicated work per cycle by Indicated power P i W N : crank shaft rotational speed n R : the number of crank revolutions for each power stroke per cylinder c, i For four-stroke engine 2 For two-stroke engine 1 n R N 1 hp 0.7457 kw 2545 BTU/hr 550 ft - lbf/sec 1 kw 1.341hp 20
Indicated Power Power that is generated inside the combustion chamber giving force that t acts directly on the piston Brake Power Usable power delivered by the engine to the load Available at a crankshaft Indicated power and Brake power
Actual power available at the crankshaft is called brake power P b. P P - P (2-27) b i f where: P i indicated power generated inside combustion chamber P f power lost due to friction and parasitic loads called friction power The ratio of brake work at the crankshaft to indicated work in the combustion chamber defines the mechanical efficiency of an engine: Pb Pi Pf Pf η m 1 (2-28) P P P i i i 21
Road-Load Power The 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 friction of tires and aerodynamic drag of the vehicle.
Road-Load Power 1 2 Pr ( CR Mν g + ρa CD Aν Sν ) S 2 ν C R M ν g ρ a C D A ν S ν coefficient of rolling resistance (0.012 < C R < 0.015) mass of vehicle acceleration due to gravity ambient air density drag coefficient (for cars 0.3 < CD < 0.5) frontal area of vehicle vehicle speed
Road-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: mep w c /V d (2-29) or in term of power, P Pn R mep V d N where: n R 1 for 2-stroke cycle 2 for 4-stroke cycle N crank shaft rotational speed V d displacement volume (2-30) If brake work is used, brake mean effective pressure is obtained: bmep w c, b/vd PbnR /( Vd N ) (2-31) 22
Example 2.1 A four-stroke automotive spark-ignition (SI) engine is designed 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 displacement 2) bore and stroke (assume bore equals stroke) 3) maximum brake power if the mean piston speed is 15 m/s Thus PnR mep and P 2 πnt Vd N 6.28n R T mep V d V d 6.28nRT bmep max max 6.28 2 150 925 2 dm 3
2 V d For 4 cylinders 2 4 π B L For 4 cylinders 4 2 10 B 3 π B L 86 6 mm Since B L (as assumed) P bmep P b max PnR V d bmepv n R 3 10 N d N 10 800 2 87 3 2 10 b max max 3 70kW S P 15m / s max S P 2LN max N max max 87 rev/s
2-5 Air-Fuel Ratio And Fuel-Air Ratio Air-fuel ratio (AF) and fuel-air ratio (FA) are parameters used to describe the mixture ratio: AF m /m m / m FA a f a f f / ma mf / ma m 1/AF where: m a mass of air Equivalence ratio ma mass flow rate of ideal or stoichiometric fuel-air: φ φ (FA) air m f mass of fuel mf mass flow rate of is defined as the actual ratio of fuel-air to act /(FA) stoich (AF) stoich /(AF) act fuel 23
2-6 Specific Fuel Consumption Specific fuel consumption is defined by: m where : f rate of sfc mf /P (2-35) P engine power fuel flow into engine Brake power gives brake specific fuel consumption: bsfc mf /P b (2-36) 24
bsfc Figure 2-9 Brake specific fuel consumption as a function of engine speed. 25
2-7 Fuel Conversion Efficiencyη f Ratio of work produced per cycle to amount of energy supplied per cycle that can be released in combustion process η f Wc W Q f HV m& f PnR / N n / NQ R HV m& f P Q HV m f Q HV mass of supplied fuel heatig value of fuel from thus sfc η f m& f P 1 sfcq HV with units: η f 1 sfc ( ) Q ( MJ/kg ) mg/j HV sfc( g/kw h 3600 ) Q HV MJ/kg) ( 26
2-8 Volumetric Efficiency Parameter used to measure the effectiveness of the induction process Only used with four-stroke engines which have a distinct induction process Volumetric efficiency is defined as: η m / ρ V v a a d or m a steady -state flow of η v n R ma / ρ a V d N where: m a mass of air into the engine (or cylinder) for one cycle air into the engine ρ a air density evaluated at atmospheric conditions outside the engine V d displacement volume N engine speed n R number of revolutions per cycle Again, seen before! 27
standard values of surrounding air pressure and temperature can be used to find density: P o (standard) 101 kpa 14.7 psia T o (t (standard) d) 298 K 25 C 537 R 77 F ρ a ρ P o /RT o where: P o pressure of surrounding air T o temperature of surrounding air R gas constant for air 0.287 kj/kg-k 53.33 ft-lbf/lbm- R At standard conditions, 0.0739 lbm/ft 3. the density of air ρ a 1.181kg/m181kg/m 3 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 c 29.0 inhg 0.38 inhg 85 F 29
For 1D steady flow past orifice 2 1/ 1) ( 2/ 0 2 + γ γ γ γ p p P A m E & 0 0 0 0 1 γ p p p p RT m E T p m & T
Indicated Power m i F s i P C P,, 2 1/ T p,, s m m m d s F T T p p p C ν P P C P m f m i F s b P P C P,,,
Volumetric Efficiency i η ν T 1/ 2 η ν kt 1/ 2 1/ 2 η ν, s kts 1/ 2 η ν, m ktm η ν, s η ν, m T T s m 1/ 2 1/ 2 T,, 1/ 2 s η ν s η ν T m s T C m F T m
2-10 Emissions Specific Emissions : rates of pollutant per unit power (SE) (SE) (SE) NOx m NOx / CO mco m / Pb HC mhc / P b P b (2-42) (SE) part mpart / P b where : m flow rate of emissions in gm/hr P brake b power 29
Emissions Index : emission rate is normalized by fuel flow rate (EI) NOx m NOx [gm/sec]/ m f [kg/sec] (EI) (EI) CO HC mco mhc [gm/sec]/ m [gm/sec]/ m f [kg/sec] f [kg/sec] (2-43) (EI) part mpart [gm/sec]/ m f [kg/sec] 30