Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 129 (2015) 873 – 878
International Conference on Industrial Engineering
Diesel Engine operating cycle optimization with simulation of combustion process by double-Wiebe function Kamaltdinov V.G.*, Lysov I.O., Nikiforov S.S. South Ural State University, 76, Lenin Avenue, Chelyabinsk, 454080, Russian Federation
Abstract The model and the program for analysis of the operating cycle with two fuel combustion laws according to Wiebe I.I. are developed. The calculation of the transport diesel engine with the Common-Rail system for gasoline direct injection is performed. The optimal heat generation law for the maximum pressure reduction in the cylinder and the improvement of indicator values of the diesel engine is specified. © 2015 The Authors. Published by Elsevier Ltd. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE(http://creativecommons.org/licenses/by-nc-nd/4.0/). 2015). Peer-review under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE-2015) Keywords: diesel engine, calculation, operating cycle, indicator values, maximum combustion pressure, simulation, double-Wiebe function, combustion process, combustion type factor, initial period, main period, fuel rate
1. Introduction The fuel combustion process in heavy transport diesel engines has two significant periods. It’s most pronounced at the diesel engines with the Common-Rail system for gasoline direct injection. The existing mathematical models of the combustion process with one combustion law according to I.I. Wiebe [1,2] are in appreciable error in determination of the maximum heat generation rate in the initial period of the process. That’s why in most cases the models with two combustion laws according to I.I. Wiebe are applied for modeling of the operating cycle of heavy transport diesel engines [3,4, etc.]. They enable one to indicate duration of significant periods and peculiarities of changing the heat generation rate in them. The known mathematical models yield different results during the
* Corresponding author. Tel.: +7-951-777-00-11; +7-967-863-40-18. E-mail address:
[email protected]
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE-2015)
doi:10.1016/j.proeng.2015.12.113
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evaluation of the spent fuel rate in the initial and main periods of the combustion process. Thus, the need for introduction of a new parameter, namely a fuel rate, which takes part in the fuel combustion in the initial period, from the general cyclic fuel supply have become imminent. A new model and the program for calculation of the operating cycle with two fuel combustion laws according to I.I. Wiebe in transport diesel engines with the CommonRail injection system has been developed at the Department of Internal-Combustion Engines of South Ural State University. 2. New model of the combustion process calculation in the diesel engine The new mathematical model of the combustion process calculation in the transport diesel engines with the accumulator fuel delivery system is based on the following formula:
x
ª §M ° 1p ) u ®1 exp « c¨ ¨ M z1 p « ° ¬ © ¯
· ¸ ¸ ¹
m1 p 1 º ½
ª §M » °¾ 1 ) u °®1 exp « c¨ 2 p »° « ¨ M z2 p ° ¼¿ ¬ © ¯
· ¸ ¸ ¹
m2 p 1 º ½
» °¾ »° ¼¿
where ĭ is a fuel rate, which takes part in combustion in the initial period, from the general cyclic supply; ij1p, ij2p is angle of crankshaft rotation, the beginning of burning out in the initial and main periods; ijz1p, ijz2p is duration of the initial and main periods of the combustion process; m1p, m2p is indicators of the type of initial and main periods of the combustion process. According to the form this mathematical model is similar to the combustion process model developed by N. Kojima [3]. But in the new model the start of the main period is not connected with the start of the fuel combustion in the initial phase. It enables one if necessary to simulate the start of heat generation in the main period earlier than in the initial one. It expands the opportunities to take into consideration special characteristics of the fuel injection, its distribution in the combustion chamber and its preparation for ignition in heavy diesel engines with the CommonRail injection system. The fuel burnup in each period is specified independently by its type indicators, the start and the duration of the combustion process, as well as by the fuel rate, which takes part in each period of the combustion. The change of these parameters enables one to simulate different combustion laws depending on the set restraints on parameters of the operating cycle. The total rate of the fuel combustion in the cylinder is determined by composition of combustion rates in the initial and main periods. If ĭ=0 or ĭ=1, the combustion rate has one maximum according to the combustion law of I.I. Wiebe. If the value of F lies in the range from 0 to 1, the combustion rate has two maximums, typical for the working process of modern transport diesel engines with the Common-Rail injection system (Fig. 1). The calculation of diesel working cycle is produced step-by-step from the point 1 (the beginning of the step) to the point 2 (the end of the step) by well-known method [5]. Herewith, the following equation for definition of the pressure in the diesel cylinder on each step of the calculation is used [5]:
p2
2 'Qcomb 'Qwell § k 1 · p1 ¨ v1 v2 ¸ m k 1 © ¹ k 1 v2 v1 k 1
where ǻQcomb, ǻQwell – fuel burn energy and heat transfer through the wells of cylinder head, piston and sleeve consequently; m – gas mass in the cylinder; p, v – pressure and specific volume of gas in cylinder; k=Cp/Cv – the indicator of adiabat.
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Fig. 1. Differential characteristic of fuel burn: ș1p, ș2p – angle of crankshaft rotation, the beginning of burning out in the initial and main periods; dx/dij, dx1p/dij, dx2p/dij – the fuel burn speed is summarized, in the initial and main periods consequently
The fuel burn energy on the step of working cycle calculation (from the point 1 to the point 2) is defined by a well-known expression: 'Qcomb
'mcomb [ H U
where 'm comb – fuel mass whichh has burned on the calculation step from the point 1 to the point 2; ȟ – effective combustion ratio; Hu – the lowest fuel heat content. Heat transfer through the wells of cylinder head, piston and sleeve is calculated according to the NewtonRichmann law: 'Qwell
D1 F1 T1 TW 'M 6n
where Į1 – the coefficient of heat transfer from the working fuel to the wells; F1 ɢ Tw – square and the temperature of the cylinder volume surface at the beginning of the calculation step; Ɍ1 – the gas temperature at the beginning of the calculation step; n – the rate of crankshaft rotation; ǻij – the angle of the crankshaft turn per calculation step. The described mathematical model is taken as a basis of the methods and algorithm of “Working cycle calculation program of the “Double-Wiebe function” diesel” engineering software. With the help of this program the influence of F-value, indicators of combustion characteristics, the beginning and duration of the combustion process in the initial and main periods on the diesel engine working cycle indicators were defined. There are results of diesel working cycle calculation with different fuel share values taking part in the combustion in the initial period are given on the Figure 2. The increase of this share from 0,1 to ~0,3 when the other parameters are unchangeable leads to essential improvement of the indicator values and essential increase of the maximum gas pressure in the diesel cylinder. The best indicator values are gotten when ĭ=0,38: average cycle indicator pressure pi=1,801 MPa, fuel flow indicated density gi=177,7 gramm/kilowatt-hour, indicated efficiency Și=0,4793. The maximum pressure in the cylinder pmax equals to 18,1 MPa. The further increase of F till 0,45 leads to the degradation of indicator values and the growth of maximum pressure in cylinder pmax to 18,8 MPa.
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Fig. 2. Dependance of parameters pmax, Și, pi, gi on fraction of fuel ĭ (fi)
Fig. 3 shows measurement charts of the in-cylinder pressure and heat release rate at different values of the proportion of fuel involved in combustion at the initial stage. Here it is seen that the larger the proportion of fuel is the higher the maximum heat release rate in the initial period and the smaller the maximum heat release rate in the main period are. This results in an increase of pressure rise rate and the increase of the maximum pressure in the cylinder.
Fig. 3. Charts of pressure change P in the cylinder and heat release rate Q at different ĭ (fi)
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Obviously in a real transport diesel with fuel-handling system fuel the fraction of fuel involved in combustion in the initial stage depends on pilot fuel injection. The greater the portion of the fuel in the pilot fuel injection is the greater the value of the fraction of fuel is ĭ. Thus, the use of the developed program allows to plan the amount of fuel in the pilot fuel injection at the stage of design. Fig. 4 shows the results of calculating the working cycle of a diesel at different rates of the combustion character in the initial m1 and main m2 periods. The increase of m1 from 0,1 to 1,1 (while other parameters remain constant) leads to a slight improvement of indicator values and preservation of the same maximum gas pressure in the cylinder of a diesel. That means that the law of fuel combustion in the initial period does not affect the performance of a diesel. This is due to the short duration of the initial period of the combustion. The increase of m2 from 0,1 to 1,1 (while other parameters remain constant) leads to a significant deterioration of the indicator values (indicated coefficient of efficiency Și and indicated mean pressure are reduced by ~ 11%) and reduction of the maximum gas pressure in the cylinder of a diesel from 19,6 to 14,4 MPa (by ~ 26.5%). That means that the law of fuel combustion in the main period significantly affects the performance of a diesel. This is due to the long duration of the main period of the combustion.
Fig. 4. Influence of values of combustion character m1 (1) and m2 (2) on parameters Pmax, Și, Pi, gi
3. Conclusions According to the results of the performed work the author makes the following conclusions: 1. The model and calculation program of the working cycle with two laws of combustion by Ivan Ivanovich Wiebe for transport diesel engines with the Common-Rail system of direct injection has been developed. 2. The novelty of the model of combustion process is the introduction of a new parameter – the fraction of fuel which is involved in the combustion of fuel in the initial period from the total cyclic delivery. The fact that the start of the main combustion period is not associated with the start of the combustion in the initial phase has also become an innovation in the field. 3. Best indicator values have been obtained when the fraction of fuel involved in combustion in the initial period has had the value of about 0,38. 4. The value of the indicator of the combustion character in the initial period almost has no effect on the indicator values of a diesel engine and the maximum pressure in the cylinder. 5. The value of the indicator of the combustion character in the main period significantly affects the indicator values of a diesel and the maximum pressure in the cylinder. 6. The given model of the combustion process allows to perform search engineering calculations for transport diesel engines with the accumulator fuel-handling system and to plan the value of a pilot fracture of fuel at the stage of design.
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Acknowledgements The given work is written with the support of the Federal Target Program “Research and Development in Priority Areas of the Development of Scientific and Technological Complex of Russia for 2014-2020”. References [1] I. I. Wiebe, Novoe o rabochem cikle dvigatelej. [New on the Working Cycle of Engines]. Moscow, Mashgiz Publ., 1962. 272 p. [2] I.I. Wiebe, Brennverlauf und Kreisprozess von Verbrennungsmotoren, VEB Verlag Technik, Berlin, 1970. [3] T. Murayama, N. Kojima, Y. Satomi, A simulation of diesel engine combustion noise, SAE Technical Paper 760552 (1976) 16 p. [4] E. A. Lazarev, Osnovnyie printsipyi, metodyi i effektivnost sredstv sovershenstvovaniya protsessa sgoraniya topliva dlya povyisheniya tehnicheskogo urovnya traktornyih dizeley: monografiya. [Fundamentals Principles, Methods, and Effectiveness of the Means of Improvement of Combustion Process for the Raise of the Technological Level of Tractor Diesel Engines: Monograph]. Chelyabinsk: South Ural St. Univ. Publ. (2010) 288. [5] V. G. Kamaltdinov, Utochnennaya metodika rascheta parametrov rabochego tela na puskovyih rezhimah dizelya. [Refined Methods of Calculation of Parameters of a Working Body on Starting Operating Mode of Diesel Engines]. Dvigatelestroenie. (2008) (232-2), 31–34.
