Factors Determing Ignition and Efficient Combustion in Modern Engines Operating on Gaseous Fuels13For lower gaps and compression ratios the secondary voltage can be decreased.Therequired secondary voltage as a function of compression pressure is presented in Figure6for different gaps of spark plug electrodes from 0.3 to 0.9 mm.If one assumes that the electrical energy E is delivered during period t to a certain smallvolume V near spark plug with the temperature of the charge Ti and pressure pi andconcentration of CNG fuel adequate to the air excess coefficient 2, it is possible to calculatethe change of the charge temperature in this space.On the basis of the law of gas state andbalance of energy the specific internal energy u of the charge in the next step of calculation isdefined.(11)u, = Ui-1 +dEwhere i is the step of calculations and dE is the energy delivered from the spark plug in steptime dt. The internal energy is function of the charge mass m and temperature T, wheremass m in volume Viscalculated from thefollowing dependency:m=P-V(12)R-T,and gas constant R is calculated on the mass concentration g of the n species in the mixtureMass of thecharge consists of the fuel mass myand air mass ma,whichmeans:(13)m=m,+m,For the mixture that contains only air and fuel (in our case CNG), the equivalent gasconstant is calculated as follows:R=Z8r·R;=8·R,+8f-Rf(14)1In simple calculations the local relative air-fuel ratio is obtained from the localconcentrationofairandfuel:m.元=(15)K.mjwhere K is stoichiometric coefficient for a given fuel. For the CNG applied during theexperiments K-16.04 [kg air/kg CNG]. At assumption of the relative air-fuel ratio themasses offuel mf and air ma canbeobtained from thefollowingformulas:AKm(16)mj"K+1m,=mzK+iAfter substitution of the fuel and air masses to the equation (10) the equivalence gasconstantRisdefinedonlyiftheisknown
Factors Determing Ignition and Efficient Combustion in Modern Engines Operating on Gaseous Fuels 13 For lower gaps and compression ratios the secondary voltage can be decreased. The required secondary voltage as a function of compression pressure is presented in Figure 6 for different gaps of spark plug electrodes from 0.3 to 0.9 mm. If one assumes that the electrical energy E is delivered during period to a certain small volume V near spark plug with the temperature of the charge T1 and pressure p1 and concentration of CNG fuel adequate to the air excess coefficient , it is possible to calculate the change of the charge temperature in this space. On the basis of the law of gas state and balance of energy the specific internal energy u of the charge in the next step of calculation is defined. i i 1 u u dE (11) where i is the step of calculations and dE is the energy delivered from the spark plug in step time d. The internal energy is function of the charge mass m and temperature T, where mass m in volume V is calculated from the following dependency: 1 1 p V m R T (12) and gas constant R is calculated on the mass concentration g of the n species in the mixture. Mass of the charge consists of the fuel mass mf and air mass ma, which means: mm m a f (13) For the mixture that contains only air and fuel (in our case CNG), the equivalent gas constant is calculated as follows: 1 n R gR gR g R ii aa f f (14) In simple calculations the local relative air-fuel ratio is obtained from the local concentration of air and fuel: a f m K m (15) where K is stoichiometric coefficient for a given fuel. For the CNG applied during the experiments K=16.04 [kg air/kg CNG]. At assumption of the relative air-fuel ratio the masses of fuel mf and air ma can be obtained from the following formulas: 1 f m m K 1 a K m m K (16) After substitution of the fuel and air masses to the equation (10) the equivalence gas constant R is defined only if the is known
14InternalCombustionEngines(a.K-R.+R)(17)RaK+ForwholevolumeVthe internal energyatthebeginningof theignition is definedas:u,=-m-c,T-R.T-PEV.(18)cRRTThe chargepressureduring compressionprocess increasesas function of thecrank anglerotationfromprtop.When oneknowstheengine'sstrokeSand diameterDofthecylinderandcompressionratioitispossibletodeterminethechangeofpressurefromstartpointtoanother point.If the heat transfer will be neglected the pressure change in the cylinder canbeobtained froma simple formula as a function of timet and engine speed n (rev/min):dp=30 k-1kdv.(19)dt元n.V.(k-1dtwhere V.is volumeof the cylinder at crank angleandk is specific heat ratio (cp/c)For simplicityof calculations it was assumed thatduring compression strokethe specificheatratio for small period isconstant(k1.36)and cylinder volumechangeswithkinematics of crank mechanism.Delivery of electrical energy to the local volume results onthe increase of local internal energy and changing of temperature T, which can bedetermined from the following energy equation:dTde(20)mc, T,=m:c, T- +de or m.c-aTheelectrical energy can be performed in a different way:with constant value during time t(rectangular form or according to the reality in a triangular form as shown in Figure 7.El in Jamodt [s]maxAFigure 7.Variation of electrical power from spark plug
14 Internal Combustion Engines 1 1 R KR R a f K (17) For whole volume V the internal energy at the beginning of the ignition is defined as: 1 1 11 1 1 vvv pV pV U mc T c T c RT R (18) The charge pressure during compression process increases as function of the crank angle rotation from p1 to p. When one knows the engine’s stroke S and diameter D of the cylinder and compression ratio it is possible to determine the change of pressure from start point to another point. If the heat transfer will be neglected the pressure change in the cylinder can be obtained from a simple formula as a function of time t and engine speed n (rev/min): 30 1 1 c c dp k k dV dt n V k dt (19) where Vc is volume of the cylinder at crank angle and k is specific heat ratio (cp/cv). For simplicity of calculations it was assumed that during compression stroke the specific heat ratio for small period is constant (k 1.36) and cylinder volume changes with kinematics of crank mechanism. Delivery of electrical energy to the local volume results on the increase of local internal energy and changing of temperature T, which can be determined from the following energy equation: m c T m c T de vi vi1 or v dT de m c dt dt (20) The electrical energy can be performed in a different way: with constant value during time (rectangular form or according to the reality in a triangular form as shown in Figure 7. Figure 7. Variation of electrical power from spark plug
Factors Determing Ignition and Efficient Combustion in Modern Engines Operating on Gaseous Fuels15If the total electrical energy amounts E and duration of sparking lasts t (1.8 ms) then for thefirst case the local power is E/t for whole period t of the sparking.For the second caseelectrical power from the spark plug changes and for the first period can be expressed as:t 2E(21)N,TtmaxForthesecondperiodtheelectricalpowercanbedeterminedasfollows:1- 2·E(22)N.=-The temperature of the charge near the spark plug during the period t is computed asfollows:1-N(t)-dt(23)dT=m-c,For thefirst case (rectangular form) of variation of electrical power the change of the chargetemperature iscomputed from thefollowingdependency1.E.atdT=(24)mc,tFor the second case (triangular form of power)thetemperature of the local charge iscalculatedasfollows:1 perioda.1t2E.dt(25)dT=?m.C,tmaxb.2nd periodt112.EdtdT=(26)tm·c,1-muxtAt assuming of specific volumetric heat cas constant in a small period rthetemperature ofthe local charge is simply obtained by integration ofgiven above equations as function oftimet(t=o..t)E_t1.T=T, +(27)m-C,t
Factors Determing Ignition and Efficient Combustion in Modern Engines Operating on Gaseous Fuels 15 If the total electrical energy amounts E and duration of sparking lasts (1.8 ms) then for the first case the local power is E/ for whole period of the sparking. For the second case electrical power from the spark plug changes and for the first period can be expressed as: max 2 I t E N t (21) For the second period the electrical power can be determined as follows: max 1 2 1 II t E N t (22) The temperature of the charge near the spark plug during the period is computed as follows: 1 ( ) v dT N t dt m c (23) For the first case (rectangular form) of variation of electrical power the change of the charge temperature is computed from the following dependency: 1 v E dT dt m c (24) For the second case (triangular form of power) the temperature of the local charge is calculated as follows: a. 1st period max 1 2 v t E dT dt mc t (25) b. 2nd period max 1 1 2 1 v t E dT dt m c t (26) At assuming of specific volumetric heat cv as constant in a small period the temperature of the local charge is simply obtained by integration of given above equations as function of time t (t = 0 . ) 1 1. v E t T T m c (27)
16InternalCombustionEnginesE(28)2a.T=T +m-c.12.E(29)2b.T=C+m-C, 1_ max2TThe constant Cis calculated for theinitial conditions fort/r=trm/twiththe end temperaturefor 1st period as an initial temperature for 2nd period. The three cases are performed in a non-dimensional time t/t.Because compression stroke in 4-stroke engine begins usually pa=45oCA ABDC and thus the cylinder volume [3] can be calculated at , crank angle as follows:V-+1+gd(30)-cos(180-,)- -cos2(180-）8-1244The simple calculations of the increment of the local temperature in the region of the sparkplug were done at certain assumptions given below:swept volume of the cylinder-450 cm,compression ratio-12,crank constant -0.25,diameterof sparking region-1mm,height ofsparking region -1 mm, closing of inlet valve - 45° CA ABDC, start angle of ignition - 200CA BTDC.For calculation the air-gas mixture was treated as an ideal gas (methane CHa and air at=1.4). Two ignition systems were considered with ignition energy 40 and 60 mJ atassumptionof:1constant sparking power (rectangularform) in period t=2 ms2.variablesparkingpower (triangularform)inperiodt=2ms.The results of calculations are performed in Figure 8 for those two ignition systems,respectively.It was assumed that compression process begins after closing of the inlet valvewithconstantcoefficientofcompressionpolitropek=1.36.sparking power=constignition20degBTDCignition20degBTDCnaturallyaspiratedengine2000020000E=60mJE=40mJ16000E=60mJE=40mJ2Bnjd12000adu8000eesoaedn40004000000.20.40.60.80.4A0.8cal time+HSmensional timef-l(a)(b)Figure 8. Increment of the local temperature in the region of the spark plug for two ignition systems: a)with constant sparking power, b)with variable sparking power (triangular form)
16 Internal Combustion Engines 2 1 max 2 . v E t a TT mc t (28) max 1 2 2. 1 2 1 v Et t b TC m c t (29) The constant C is calculated for the initial conditions for t/ = tmax/ with the end temperature for 1st period as an initial temperature for 2nd period. The three cases are performed in a nondimensional time t/. Because compression stroke in 4-stroke engine begins usually a=45 CA ABDC and thus the cylinder volume [3] can be calculated at i crank angle as follows: 1 cos(180 ) cos2(180 ) 12 4 4 s s a ii V V V (30) The simple calculations of the increment of the local temperature in the region of the spark plug were done at certain assumptions given below: swept volume of the cylinder - 450 cm3, compression ratio – 12, crank constant - 0.25, diameter of sparking region - 1 mm, height of sparking region - 1 mm, closing of inlet valve - 45 CA ABDC, start angle of ignition - 20 CA BTDC. For calculation the air-gas mixture was treated as an ideal gas (methane CH4 and air at =1.4). Two ignition systems were considered with ignition energy 40 and 60 mJ at assumption of: 1. constant sparking power (rectangular form) in period =2 ms 2. variable sparking power (triangular form) in period =2 ms. The results of calculations are performed in Figure 8 for those two ignition systems, respectively. It was assumed that compression process begins after closing of the inlet valve with constant coefficient of compression politrope k=1.36. Figure 8. Increment of the local temperature in the region of the spark plug for two ignition systems: a) with constant sparking power, b) with variable sparking power (triangular form) (a) (b)
Factors Determing Ignition and Efficient Combustion in Modern Engines Operating on Gaseous Fuels17In the moment of the sparking start thepressure in the cylinderamounts 1.577MPa attemperature 726 K. Theoretical consumption of the air for combustion of 1 Nm of thenatural gas amounts 9.401 Nm.Forgiven concentration of the air and fuel (CNG) in themixture the gas constant is R=-296.9 J/(kg K) and calculated mass of charge in the regionamounts0.465e-8kg.Asshowninbothfiguresthefinaltemperatureintheregionisthesame for two considered variations of power.If the volume of the sparking regiondecreases the local temperature will increase, however ignition of the mixture depends onconcentration of thefuel in the air.The final temperature does not depend on the shape ofthe ignition power during sparking but only on the total energy released during thesparking.Inthegapoftheelectrodesatignition energy60mJameantemperatureamountsalmost 17000Kafter2ms and at 40mJ amounts12000K.This is enough toignitethemixture.6.DeterminationofthermalefficiencyOnlya small part of thedelivered energy from the second circuit is consumed bygaseousmedium, which is observed by increase of the temperature 4T and thus also internal energyEi. The thermal efficiency of the ignition system is defined as ratio of the increase of internalenergy and energy in the secondary circuit ofthe ignition coil:AE,_AE,·E,(31)=n,neTth=-EEEwhere Er is the energy in the primary circuit and mpis the total efficiency and n is the electricefficiency of the ignition system. The increase of the internal energy in volume V with initialpressure pi can bedetermined as follows:AE,=m-c,-AT(32)Assuminga constant mass and individual gas constant R, the temperatureafter ignition canbe definedfrom the gas state equation.At small change of the gas temperature from Tito T2the volumetric specific heat c,has the same value. In such way it is possible to determine theincrease of the internal energy:AE,-P-VC, (T-T)=P-V.P2(33)R-TR·TPAftersimplificationthisequationtakestheform:LV(34)AE -c (P2-P)-"C,4pThe increase of the internal energy depends on the sparking volume, gas properties and apressure increment in this volume.Because of constantvolumeandknown R and ctheunknown value is only the increment of the pressure p.The direct method of measurement
Factors Determing Ignition and Efficient Combustion in Modern Engines Operating on Gaseous Fuels 17 In the moment of the sparking start the pressure in the cylinder amounts 1.577 MPa at temperature 726 K. Theoretical consumption of the air for combustion of 1 Nm3 of the natural gas amounts 9.401 Nm3. For given concentration of the air and fuel (CNG) in the mixture the gas constant is R=296.9 J/(kg K) and calculated mass of charge in the region amounts 0.465e-8 kg. As shown in both figures the final temperature in the region is the same for two considered variations of power. If the volume of the sparking region decreases the local temperature will increase, however ignition of the mixture depends on concentration of the fuel in the air. The final temperature does not depend on the shape of the ignition power during sparking but only on the total energy released during the sparking. In the gap of the electrodes at ignition energy 60 mJ a mean temperature amounts almost 17000 K after 2 ms and at 40 mJ amounts 12000 K. This is enough to ignite the mixture. 6. Determination of thermal efficiency Only a small part of the delivered energy from the second circuit is consumed by gaseous medium, which is observed by increase of the temperature T and thus also internal energy Ei. The thermal efficiency of the ignition system is defined as ratio of the increase of internal energy and energy in the secondary circuit of the ignition coil: 1 2 21 i i th o e E EE E EE (31) where E1 is the energy in the primary circuit and 0 is the total efficiency and e is the electric efficiency of the ignition system. The increase of the internal energy in volume V with initial pressure p1 can be determined as follows: i v E mc T (32) Assuming a constant mass and individual gas constant R, the temperature after ignition can be defined from the gas state equation. At small change of the gas temperature from T1 to T2 the volumetric specific heat cv has the same value. In such way it is possible to determine the increase of the internal energy: 1 12 21 1 1 1 11 iv v pV pV p E cTT c T T RT RT p (33) After simplification this equation takes the form: iv v 2 1 V V E cpp c p R R (34) The increase of the internal energy depends on the sparking volume, gas properties and a pressure increment in this volume. Because of constant volume and known R and cv the unknown value is only the increment of the pressure p. The direct method of measurement