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# COMBUSTIONENGINES ME328

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This 14 page Class Notes was uploaded by Dylan Olson II on Thursday October 29, 2015. The Class Notes belongs to ME328 at Wilkes University taught by S.Kalim in Fall. Since its upload, it has received 32 views. For similar materials see /class/230982/me328-wilkes-university in Mechanical Engineering at Wilkes University.

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Date Created: 10/29/15

Engine Characteristics Spark Ignition Engines 39339 Maximum torque at optimal spark timing 39339 Spark used to control combustion 39339 Advance spark timing earlier in cycle 39339 Retard spark timing later in cycle 39339 Fuel and air generally enter as a mixture 39339 Sometimes fuel is injected just before the spark Compression Ignition Engines 39339 Only air is pulled into cylinder Fuel injected just before combustion 39339 Fuel is metered to control the engine load 39339 Air flow at a given rpm is constant 39339 Higher compression ratios than SI engines 1224 39339 Fuel injected at about 20 BTDC 39339 After delay period autoignition 39339 Rapid pressure rise Strati ed Charge Engines 39339 Combines best features of SI and CI engines 39339 Fuel injection into cylinder 39339 Compression ratio of about 1215 don t want autoignition 39339 Load controlled by fuel mass flow rate 39339 Combustion controlled by spark ignition De nitions 39339 Maximum Rated Power the highest power an engine is allowed to develop for short operational periods 39339 Normal Rated Power highest continuous power is engine is allowed to make 2 Rated Speed crankshaft rpm at which rated power is developed Pollution 39339 Sources NOX l12 gkm CI is highest 4060 smog acid rain CO 5150 gkm S1 is highest 90 VOC 317 gkm S1 is highest 3050 smog 39339 National Ambient Air Quality Standards NAAQS 39339 Clean Air Act Amendments of 1990 CAAA 39339 Industrial Coordinated Rulemaking ICCR This module will address the following issues 1 Cylinder schematic and bore stroke crank radius TDC BDC and crank angle 2 Define the different rated conditions 1 Calculate engine volume piston speed and cylinder surface area as a function of crank angle 1 Calculate engine torque and hp from dynamometer tests 2 Define indicated brake and friction quantities 2 Define net and gross quantities 1 Calculate sfc AF vol eff and engine efficiency 1 Correct performance data for atmospheric conditions VBDC Vt max Total cylinder volume Vt Vd Vc Vd B2L VBDC VTDC For Multicylinder Engines Vd N0 E B 2 L 4 where Nc of Cylinders 0D lenth r Stroke S or L 2a I e Distance between crank axis 270 i 5N 90 a I and wrist pm aX1s OQ Qwristpin x p O Cranksha OO s 1 0 S a 1lE2 32 Sin2 9 2 LfBS itissquare engine SgtBLhe engine is under square and if SltB then it is over square 2 Bore B varies from 50 cm to 05 cm and BS Where 9 Crank angle 08 to 12 for small engines OP a Crankshaft radius PQ E Connecting rod radius or length The change in s with respect to 9 will give the piston speed as f9 Cylinder Heat Transfer Surface Area Variation with Crank Angle Combustion chamber surface Area A9 Ach Ap TEBEa s 216 Where Ach Cylinder head or Combustion chamber area and 7 AP P1ston Area B2 We already know that 89 a C089 VE2 a2 sin2 9 A9 Ach Ap TcBEa a cose m2 a2 sin2 e A9 AchAp 7Ba 1 cose za2 sin2 9 Such that AG Ach Ap 1 R cosG Cylinder Volume Variation With Crank Angle we V BW a s R2 sin29 2 17 We know that 5 a s al R cosG VR2 sin2 9 V9 Vc B2 a1 R cosG xR2 sin2 9 2 And 0 2 nzmzhn mB L4 V0 V0 V0 V0 TE 2 TE 2 TE 2 V0 r l Wthh glves Vc rel B L B 2agt B 4 4 4 2a So that volume in nondimensional form is L69 1rc lRl cos9 R2 sir129 c Where rc Compression ratio 8 to 12 for SI engines 12 to 24 for CI engines Figure 25 Notice that both CylinderArea and volume vary in the same fashion Piston Speed Vs Crank Angle Instantaneous Piston Speed Up or Sp Piston speed E dt d9 dt But 12 75 X re Y 27tN Therefore Sp 2 T N 3 eg min A A Need to differentiate T 0 Conversion lt Convert RPM to Radsec co N is rotational speed of the crankshaft in rpm Camshaft speed is one half the crankshaft speed for four stroke cycle engines NOW E i acos9VE2 a2sin29 d9 d9 Note that sin2 9 2 sinG cosG 2 Such that E a sine M a 511 L59 1 19 E2 32 SinZ 9 R2 sin2 6 SO that Sp 2 TEN asin9 Lse l R2 sin29 Finally therefore Up or Sp 2nLN sine L59 I R2 sin2 9 Mean Piston Speed 39339 Better than using rotational RPM and Instantaneous speed 39339 Gas ow velocities in the intake manifold and cylinder all scale with mean piston speed ozo Should be between 1 500 and 3000 min ozo Lower endis typical oflar eindustxial engines ozo High endis typical of automotive engines Calculating the Mean Piston Speed 3 7 i Vsywyie i mmvi is n 4w 9 r W E ZN 2 D ds r o 39 a WE IBZV360 ixilgo 360 ac05360 1 RI 7 sin 3 50 117 R 3180 acos180 7 1 r sin1180 aR r1 3 2Nn1RrR lxZNL So that Average Piston speed p or p nR S N Where N is in rpm and rig is the number of revolutions per cycle nR is 1 for twostroke and 2 for fourstroke cycle Lie U 2 7 2 such that 6 9 ZTELN sineJTe gsin 1 25 R2 75in2 0 ere R Za 3 to 4 for small engines and successively increases to 10 for larger engines Conversion Factors 1 L 10393 m3 10 cm3 61 in3 Example A square gasoline engine with a bore of 14inch operates on a compression ration of 9 and a connecting rod to crank ratio of 6 Determine the piston volume with respect to crank angle 9 B14i11 Ll4in i9 R6 V gtltl4i11 2155111 Li H83 x L It gtlt14in2 V61 2 Vd V6 gt VJ Vd V 2155 mquot V a Z 2694 m3 r 1 9 1 Lquot 179 2 V 1 31 1R 1 C089 R2 sin2 9 r 49 V511 i9 16 1 c039 36 sin e Graph of V vs 9 Bottom Dead Center Top Dead Center A400 300 A200 100 0 100 200 300 400 8 Thermodynamics of IC Engine Note The following text and figures are selected from various conventional and Internet sources listed at the end ofthis document The selected text and equations have been edited to present the material in a concise succinct and sequential manner Keywords Slider CrankModel Work Combustion Stoichiometry Fuels Determination of Qquot from HHV ofFuel Chemical Equilibrium Introduction to Engine Cycle Models Model ofBasic Otto Cycle Finite Heat Release Otto Cycle Determination of Fuel H eat Input QM Finite Heat Release Otto Cycle with Heat Transfer Work The work produced is due to the gas pressure on the piston Assuming that the pressure in the crank case is atmospheric then the gas pressure will be relative to the crank case pressure such that P Pgas 39 Pcrank case For a small displacement dx the work is dW The following relationship for dW can be developed dWFdxPAdxPdV For a nite volume change work is given by W jpdV The work can be represented per unit mass of fuel and air such that the speci c work w Wm and the speci c volume is v Vm This work W is called the indicated work represented as Wi Friction in the rings and bearings are included with a friction work Wf The work at the crankshaft is the brake work Wb The brake work is de ned as the indicated work less the friction work Wb Wi Wf Wb W The mechanical efficiency 11 is de ned as 11m W 71 f i W1 Mean Effective Pressure The pressure in the cylinder changes during the expansion stroke First increasing due to the heat addition and then decreasing due to the increase in cylinder volume We can de ne a mean effective pressure to determine the work W j39pdV Pmean Vd A mean effective pressure can be found for the indicated friction and brake work W W W Pmemi 1 1 1nd1cated Pmemf f f fr1ct10n Pmemb b b brake Vd Vd Va A naturally aspirated Otto cycle engine has a Pmemb N 1000 kPa If turbo charged the engine Pmemb can increase to above 1500 kPa Dr Kalim Supplementary Notes 2005ME328page 1 Introduction to Engine Cycles Some classic thermodynamic questions that cycle analysis addresses What is the cylinder pressure and temperature as a function of crank angle What is the work produced What is the mean effective pressure The above questions are answered by examining the thermodynamic properties of a piston cylinder system and the transfer of work and heat into and out of the system We will use different models to answer the above questions Each subsequent model increases in realism and complexity from the previous model The models will all assume a closed system with no gas exchange This means that the intake and exhaust strokes of a four cycle engine are not modeled They will be studied in the uid mechanics section The strokes to be studied in this section are the compression and expansion strokes The simplified spark ignition model is the Otto cycle which assumes all of the energy from the fuel is added to the engine instantaneously at the top dead center The second model is the Heat Release model which uses an empirical combustion relation for the combustion gas burn duration as a function of crank angle The third model is the Heat Release model with heat transfer which includes heat transfer to the cylinder walls as well as a finite heat release The simplest compression ignition model is the Diesel cycle which assumes all of the energy of the fuel is combusted at constant pressure The modern compression ignition engines operate on Dual cycle where combustion process is partly constant volume feature of Otto and partly constant pressure feature of Diesel Introduction The cycle is named after a German Nikolaus Otto who built the first spark ignition engine in 1876 Figure 1 shows schematically how the pressure varies during compression and expansion From 180 degrees a bottom dead center to 0 degrees top dead center the P upward motion of the piston compresses the airfuel 2 4 mixture The heat input for this model is assumed to 1 1 occur entirely at top dead center From 0 degrees to 180 degrees the expandmg gases move the p1ston 480 o 180 downward and produce work The heat re ectlon for a this cycle model is assumed to occur entirely at bottom dead center Figure 1 Basic Otto Cycle The air standard Otto cycle is modeled as a closed system with a fixed airfuel mass and uses the following process assumptions 12 Compression which is reversible and adiabatic Dr Kalim Supplementary Notes 2005ME328page 2 23 Heat addltlon from fuel Expanslrm whlch ls reverslble and adlabatlc 41 Heat rejectlon to cyllnderwal s i FirstLaw Analysis of the Ono Cycle Uslng the flrst law Process 12 6112 le 2 1 cvT2 Tl Slnce the process ls reverslble and adlabatlc lt ls also lsentroplc whlch leads to k H 2 v1 k 12 v2 P1 V2 Y Tl V2 1123 W23 3 CvlTa TZ Process 23 Pmcess34 34 W34W4 M3 CvlT4 T3 T4V3k711k71 11 T3 v4 r T Process4l q41 W41 1 4 Thermal Efficiency Derivation he overall efflclency for the cycle lndlcated thermal n ls glven by m Qm n n 1 cyquot an m C 7T TrT U Hyde Qnutlicv4 Tl1T4 Tl r Qm v z Tl Forlsentroplc Processes T3 rk T4 where k QCV Flgure 2 Thermal efflclency as a functlon ofr Note that T3 and P3 are the maxlmum cycle temperature and pressure Whlch rg rlrkquot and T2 T19 T3 7 T2 T4 7 me So that the Otto efflclency ls n 17 The ef clency ls plotted agalnstthe compresslrm ratlo ln Flgure 2 r A typlcal Value for an alr lel mlxture ls k 135 Dr Kiln SupplementaryNntesr zoosmmpage a3 Also Wm W34 W12 Cv T3 T4 CVT1Tz Cv T4 rk1 T4 Cv TlT1 rk1 Cv T4 rk1 1 Cv T1 1 rk1 Cvrk1 1 T4 T1 amp T3 T2 T4 T1rk 1 2 n Cvrk391 1 T4T1 Cvrk391T4T1 rk391 lrk391 1 7 1 k4 r Residual Mass Fraction In an ideal engine all the fuel is consumed in combustion Realistically this is not the case there will always be some amount of fuel that will be left unburned Due to this residual fuel remaining in the cylinder the initial and exhaust temperatures of the cycle will not return to their initial value Assuming the above definitions for the pressure and the temperature at given points in the cycle the Residual Mass Fraction xr can be given by f Kr H111 rc Te P4 where Te Exhaust temperature Pe Exhaust pressure rC Compression ratio In order to determine the residual mass fraction the exhaust pressure and temperature must be known The exhaust pressure is typically half of the intake pressure Pi 2P6 The exhaust temperature can be determined by assuming that the final mass in the cylinder expands k7 P k isentropically to the exhaust pressure Te T4 4 Using the 39 quot 39 39 J 39 J for and pressures from the first law analysis the J I F exhaust temperature and residual mass fraction can be determined by iterating Simple Finite Heat Release Model quotdeltaquot function Introduction We now account for finite burn 10000 t he quot1935 duration in which combustion occurs at 9b i and continues until Ge Figure 3 is a alga representation of this cycle The peak pressure will not be as high as the Otto cycle which has a quotdeltaquot function heat release The finite heat release model assumes that the heat input Q is delivered to the cylinder over a finite crank 7180 8b 0 6 angle 6 duration 5000 burn duration Figure 3 Heat Release Model Dr Kalim Supplementary Notes 2005ME328page 4 Derivation of Pressure versus Crank Angle for Finite Heat Release The differential first law for this model for a small crank angle change ins 6Q 6W dU Using the following de nitions 6Q heat release 6W PdV and dU m CV dT results in 6Q7PdVvadT The ideal gas equation is PV mRT so taking the derivative of T 3 deTPdVVdP Also dU m cv dT i V P dV VdP So that first law now becomes The 6Q 7 PdV CRv P dV VdP Further reduction 3 6Q 7 PdV P dV i V VdP Taking the derivative Wit 9 and further reduction 3 aQ1CVPdV CV dP d9 R d9 d9 Y Using R cp cV and k cpcv CV 1 and rearranging the energy equation becomes R 1 6 1 VdP k PdV d9 k 1 d9 k 1 d9 Or dP E g ELV d6 V d6 V d6 If we know the pressure P volume V and the heat released gradient we can compute the change in pressure Thus explicitly solving the equation for pressure as a function of crank angle Alternatively we can use experimental data for the pressure P and the volume V to determine the heat release term by solving for First the volume V and de 9 have to be defined From the slidercrank model we have a definition for cylinder volume V Both terms are only dependent on engine geometry lllrcilRlicoseifo2 isinze vc 2 V V V But re1 vd and vc dl v dl7dRlicos67R27sin26 ref ref Dr Kalim Supplementary Notes 2005ME328page 5 So taking the derivative with respect to the crank angle 9 results in V 1 2 d s1n9 lcos9 R2 sm2 9 09 2 For heat release term 81 3 the Wiebe function for the burn fraction is used f Xr1 eXp a Where f the fraction of heat added 9 the crank angle 90 angle of the start of the heat addition A9 the duration of the heat addition length of burn Normally a 5 and n 3 At the beginning of combustion f 0 and at the end the fraction is almost 1 The heat release 6Q over the crank angle change A9 is dQ df Qin d9 d9 Where Qin is the overall heat input Taking the derivative of the heat release function f with respect to crank angle gives the following definition of g If 9 S 90 df 0 So that with 12 and defined the pressure as a function of the crank 16 d8 angle can be solved What is Q Here is one method to determine Qin from given information for an engine For an automotive engine say the power per liter is given as 337XlO4 Wliter which is equivalent to 34 MWm3 after a unit conversion Doubling this value to include heat transfer results in approximately 60 MWm3 httpwwwinnerautocommainhtml Internal Combustion Engine E F Obert 1950 The Internal Combustion Engine C F Taylor and E S Taylor 1984 Internal Combustion Engine Fundamentals J B Heywood 1988 F ofSMtisti nl The 39 by RE Sonntag and GJ Van Wylen 1999 Internal Combustion Engine WW Pulkrabek 2004 httpwww taftan com the 39 ICNVIbpdm Dr Kalim Supplementary Notes 2005ME328page 6 h InternalV 39 Engine F J 7 I B Heywood 1988 Fundamentals of Statistical T hermaa namics by RE Sonntag and G Van Wylen1985 Engine Efficienc mf QH Qinideal HR 39HP Heat Availability Gibbs Energy G39R HR TR SR Availability as Natural Resource Second Law Ef ciency National mfg I 1 nrational ncntnm Closed System Energy Availability is Helmholtz Function A where A the maximum reversible work the work done against the surroundings U T S7U07T0 So and Wrevim A1 A2 ma1 a2 if AKE and APE are negligible Open System Energy Availability is Gibbs Function G where G the maximum reversible work the work done against the surroundings H TS H0 T0 so Natural Resource W revim G1 G2 g1 g2 if AKE and APE are negligible G is called the Natural Resource of the Chemical Energy in the Fuel is So that total chemical energy available to do the work is GReamms Gpmducts Beginning of i i i Compression Combustion Work in Avallablhty I i Irreversibilities I gt i Availablein I Exhaust BC Tc BC Dr Kalim Supplementary Notes 2005iVIE328page 1 THERMODYNAMICS FUNDAMENTALS 9 Cycle Process State Point or Path function IntensiveExtensive prop Pressure0a e amp absolutel OPEN Examples turbine compressor Example pistoncylinder diffuser condenser boiler arrangement rigid box etc feed water heater heat exchanger pump cooling tower etc Need Mass ow rate mpAV Need Mass 7 m I I I I I Extensive Q7WmAhmAkemApe 4 gtQ7WmAumAkemApe q7wAhAkeApe Intensive q7wAuAkeApe F or ideal gas n7l n Polytropic processes i For Isentropic processes use 11 k cpcV T1 V2 P1 Also use the process type of to determine state properties T P and V use ideal gas relationship PvRT or PVm RT ForNOVI Ideal gases go to Compressibility Chart PVm ZRT R cp 7 cV E M Q 01 q I Q is either calculated by energy equation or given in the problem or Qmf QHV Q de I Qlt0 when system looses heat Qgt0 when system gains heat m s l I W gt0 when work is given by the system turbine Wlt0 when work is given to W mdeV the system pump Pump work for water Wp VfPzP1 PzP1p 1 I Work is either calculated by integration or found by the energy equation or may be given in the problem I For ideal gas 7 use Tables or use CpTzT1 and ideal gas laws and given process to determine P T v etc as described above hu Pv Pv Flow work AH m Ah I For Water Steam only use tables no ideal gas laws Make sure to know which region the state is in compressed saturated or superheated Do you need to determine quality x I For ideal gas 7 use Tables or use CvTzT1 and use ideal gas laws and process to determine P T v etc as described above AU m Au I For Water Steam only use tables no ideal gas laws Make sure to know which region the state is in compressed saturated or superheated May be you need to determine quality x 2 V V2 Ake Ape gz They are either calculated by the formula or given in the problem AKE m 2 APE ng n cycl Wnet Qin Qout 5 fr Qin Qin Yh 7 Qout 7 Qout f f t f r in re lg W ea pump W an net Qout net Qout 39 Qin Dr Kalim Supplementary NotesME3222005

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