İçten yanmalı motorlarda motor çevrimlerinin bilgisayarla modellenmesi

Abstract

Bu çalışma da içten yanmalı motor çevrimlerinin bilgisayarla modellemesi yapılarak, farklı verilerde sonuçların karşılaştırılması imkanı sağlanmıştır. Çalışmanın ilk bölümünde, içten yanmalı motorların genel tanımı verilmiştir. İkinci bölümde, içten yanmalı motorların sınıflan dırılması, çalışma şekilleri verilmiştir. Uç uncu bölümünde» dört zamanlı bir motorda dolgu değişiminin önemi, dolgu değişimini etkileyen faktörler, silindire giren ve silindirden çıkan gazların analitik incelenip uygun formasyonun elde edilmesi verilmiştir. Dördüncü bölümde, dolgu değişiminin matematik mo del lenmesi ve bilgisayar modunda kullanılır hale geti rilişi gösterilmiştir. Besinci bölümde, içten yanmalı motorlarda yanma ola yı incelenmiş ve nümerik çözüm için ampirik denklem elde edi lmistir. Altıncı bölümde, ısı transferi hakkında genel bil giler verilmiş.icten yanmalı motorlara en uygun ampirik denklemler verilmiştir. Yedinci bölümde, matematik model lemenin Basic prog ramlama dili ile yazılmış programın çalışması verilmiş tir.

Internal -combustion engines are classified accord ing to the cycle of operations and the mode of combustion. There are two cycles of operation, namely, the two-stroke and the four -stroke cycle. There are two modes of combustion, namely, spark ignition and compression ignition. The cycle of operations can be subdivided into the gas exchange process, where the product of combustion are exhaused and replaced by a fresh charge, and the power process, in which the charge is compressed, ignited and the hot gas expanded to produce useful work. A contribution to the useful work may or may not be produced in the gas exchange process. In thermodynamic terms, during the gas exchange process the cylinder is an open system and during the power process it is a closed system. In the four -stroke cycle the gas exchange process takes place in approximately two strokes of the piston, In the two-stroke cycle the gas exchange process takes place at the and ofoutword stroke and the beginning of the inward stroke. The power process in a four stroke cycle engine is made up of approximately two strokes; and in the two-stoke cycle part of the inwardstroke and the part of the outward stroke. In the four stroke cycle engine the gas exchange process is caused by the pumping action of the piston motion, al tough there may be interactions with the intake and exhaust system; in the two-stoke cycle, the gas exchange process is almost wholly controlled by the gas dynamic interactions between the intake and the engine cylinder. It is convenient to analyse the mode of operations commencing with the gas exchange process and the following with the power process. The sequence of events is : 1- Gas exchange process a- Exhaust b- Charcing 2- Power process a- Compression Jo- Combuotion c- Expansion The equivalent constant-volume fuel -air cycle represents the limit which can be approached by spark - ignition engines. Figure 1 shows, qualitatively, how an actual indicator diagram from a spark -ignition engine differs from that of the equivalent fuel -air cycle. In constructing the equivalent cycle it is taken to coincide in temperature, pressure, and composition at a point, such as x, about midway in the compression stroke. With this assumption, and since the actual compression process is nearly isentropic, the compression lines of the two cycles coincide very closely up to point a, at which ignition causes the pressure of the real cycle to rise sharply. After combustion starts the pressure of the real cycle rises along a line such as a-b. Point b is taken where the expansion line becomes tangent to an isentropic line parallel to that of the fuel -air cycle. Experince shows that in well-adjusted engines point b is the point at which the charge becomes fully inflamed and combustion is virtually complete. Figure 1. Cycle losses - - - Equivalent fuel -air cycle A Actual cycle B Cycle with time loss only C Cycle with heat loss only x is the point of measurement of vol ume y-z is isentropic through point b exhaust blowdown loss. pressure, temperature and VII As the charge expands, the expansion line falls below the isentropic line, due to heat loss. At point c the exhaust valve starts to open, and the pressure falls rapidly as the piston approaches bottom center. Possible causes of the observed differences between the actual and the fuel -air cycle include the following: 1. Leakage 2. Incomplete combustion 3. Progressive burning 4. Time losses; that is, losses due to piston motion during combustion 5. Heat losses 6. Exhaust loss; thatis, the loss due to opening the exhaust valve before dead center. 1. LEAKAGE: Except at very low piton speeds, leakage in well adjusted engines is usually insignificant. Leakage can be estimated by measuring blow by, that is, the mass flow of gases from the crankcase breather. 2. INCOMPLETE COMBUSTION: By this term is meant failure to reach theoretical chemical equilibrium before the exhaust valve opens. Experience shows that with spark - ignition engines there is always some incomplete ly burned material in the exhaust, probably due to quenching of the combustion process on the relatively cool surfaces of the combustion chamber. In well -design ed and well-adjusted engines the resultant loss in efficiency is very small except, perhaps, at light loads and idling. however, the unburned material in the ex haust may be an important cause of " smog " and odor. 3. PROGRESSIVE BURNING : 1) Normal combustion in spark - ignition engines starts atone or more ignition points and continues by means of moving flame fronts which spread from these points at measurable time rates. 2) Combustion is virtually complete when the flame fronts have passed through the entire charge. 3) The time required for the combustion process varies with fuel composition, combustion-chanber shape and size {including number and position of ignition points}, and engine operating conditions, one of the most important of which is engine speed. Fortunatelly, combustion time varies nearly inversely as speed, so that the crank angle occupied by combustion tends to remain constant as speed varies. VIII 4.) Best power and efficieny are obtained when ignition is so timed that points at C a) and <.' b) of Figure 1. are at substantially the same crank angle from top center. C This means that the cylinder volume at these points is the same. } Since the movement of a flame requires a certain amount of time, it is evident that eve if the piston remained stationary during combustion different parts of the charge would burn at different times. To explain the mechanism of progressive burning, its effect will be computed by using the assumptions of the fuel- air cycle for each infinitesimal portion of the charge. The assupptions are listed below : 1) The piston motion during combustion is neglig ible 2} At any instant the pressure in all parts of cylinder is the same 3) Chemical reaction occurs only at the flame front 4. TIME LOSS : By this term is meant the loss of work due to the fact that the piston moves during the combustion process. 5. HEAT LOSS : By this term is meant the loss of work due to heat flow from the gases during the compression and expansion stroke. In most cases heat transfer during the compres sion stroke up to the point at which combustion starts appears to be a negligible quantity. 6. EXHAUST LOSS : There is always an appreciable loss due to the fact that the exhaust valve starts to open at a. point, such as in Fig 1., before bottom center. Such early opening is re quired in order to minimize the exhaust -stroke loss in four -stroke engines and in order to allow time for scawenging in two-stroke engines. 1. CALCULATION OF INLET PORTS AND EXHAUST PORTS : The energy equation can be written as follows, if the gas t* or air) at the pressure ( Pi ) enters to the IX cylinder at the pressure ( P2 ) from the wide area. INLET EXHAUST Figure 2. Inlet and exhaust ports. w w e ) - C 1 + e ) =Pv -Pv 2 2 2 11 CI. I) let the gas be ideal gas, then CP P v = R T = k, R = C - C P v P v 1 1 k-1 C 1. 25 e = 2 P v 2 2 k-1 CI. 3) Hence, w P v 2 2 k-1 w' P v - c - - + i-î- > = P v - P v 11 2 2 k-1 CI. 4) At the surface Ac, the pressure, velocity and specific volume can be written as in order P, v and v. mm m Initially velocity can be neglected and it is true that we deal with the real velocity C w ) rng k v - P V ) I 11 2 2' w = C I 2 v CPv-Pv)J Cl.S) a k-1 Thus we can now calculate the mass flow rate through the inlet par t -area, dm n, = = Velocity * Area * Density ' dt m=w*C*A*p (LEO i rng c a m m and by means of the equation of ideal gas and by assuming the flow isenytopic, we can find as a final solution for mass flow rate; k P ¦ A ( 2 - i- } m. = )j. A. I 2 - J C 1. 70 k-1 P 2..-/ k-1 2 / k ( k + l > / k CCP/P) -CP-P> > C1.E0 ml ml yt. : Multiplied coefficient of the inlet ports orifis y.' : Coefficient of flow or Nusselt at the inlet ports Then, it can be written another form as in the computer - program at the end of the study. 1/2 m = fj yj. A p C 2 R T ) C 1. 9> İ V. t \. J. \. In the same way, mass flow rate through the exhaust port can be written. XI 1. '2 m=uy>ApC2RT> C 1. 1 0) Q & £* ö & G fj : Multiplied coefficient of the exhaust ports orifis y : Coefficient of flow or Nussel t at the exhaust port 2. MATHEMATIC MODEL OF INLET AND EXHAUST GAS In this study the flow is assumed that, is steady-one dimensional flow. Thus, tempertature and pressure can be calculated by means of the pressure difference C APa ) or temperature difference ( ATs). Mass rate equation : S m. = £ m CI. 11) then dm = dm. - dm + dm C 1. 1 2) c t e f dm : Fuel mass difference dm : Inlet- gas difference L dm : Exhaust gas difference dm : Cylinder gas difference c - and energy equation» dC m u ) = dm. h. - dm i - P dV - dQ - dÇ> CI. 13} c c it a e c c w f Some assumptions : - In the time difference C dt) or angle difference C d#), cylinder pressure (Ps), exhaust enthalpy Ch ) and inlet enthalpy Ch.) are constants. - The gas mixture in the cylinder is uniform and its velocity is constant. XII After some calculations, as unity energy, enthalpy, mass, density, volume, rate of volume, combustion term and heat transfer term, it can be written the latest case of energy equation that is used in computer program. It is convinient and easy to calculate so that some short forms are accepted in this formulation. A = i dm. 1 dm dtp 6 n dt A = h - u 2 i c A * A CI. 14) 1 2 B = ı dm 1 dm dtp 6 n dt B = h -u =P / p 2 c c c c B = B * B CI. IS) 1 2 dV C = P - CI. 16) c dtp dQ D = CI. 17) dtp dQ E = İ C 1. 1 8) d# XIII and all calculated terms above C A,B,C,D.E ) can be in serted in general equation; dT d<£ m G & v A-B-C-D+E C 1. 1 95 3. CALCULATION OF THE MATHEMATIC MODEL CALCULATION STEP BY STEP: - Volume at the beginning of compression is calculated CV 3, CO With ideal gas equation p = P / R / T CO CO CO density and mass are calculated. m = p V CO CO CO - Ai, Ae can be selected by menu given in the program or some experimantal documents. - y.. v*. C, h, u, dm./ dd>. h, t e v ı. c l a dm / d# thus all unknowns are calculated, - So that C ATc / A^ )i is calculated for first step by means of the C1.19> equation, - After L$ temperature will be as T = T + AT Cl CO cl - This calculation must be repeated to reduce the mistake of calculation. But in this case mean temperature must be taken, XIV T = C T + T ) / 2 cim go el T is used as the first step value cim AT AT = C 5 A0 &4> then, T = T + AT Cl CO cl Thus Tci is calculated and pressure at the every step can be calculated as explained above.