Modeling the Combustion Process of a Powerful

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 129 (2015) 488 – 494

International Conference on Industrial Engineering

Modeling the combustion process of a powerful diesel engine Kamaltdinov V.G.a*, Markov V.A.b, Lysov I.O.a b

a South Ural State University, 76, Lenin Avenue, Chelyabinsk, 454080, Russian Federation Bauman Moscow State Technical University, 5 2-ya Baumanskaya st., Moscow, 105005, Russian Federation

Abstract The authors develop models of the combustion process and a program for calculating the operating cycle of a powerful diesel engine with the set law of mixture formation. They also calculate how the temperature of a fresh charge after a charge air cooler impacts the operating cycle indicators of such an engine. Based on the results of the calculation, herein are constructed charts of in-cylinder pressure and heat release laws that accord with known experimental data. © 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). under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE-2015) Peer-review Keywords: powerful diesel, calculations, operating cycle, indicator parameters, the maximum combustion pressure, modeling, combustion process, molecules of fuel, the law of mixture formation, the temperature of the fresh charge, charge air cooler;

1. The peculiarities of combustion process in the diesel engine and models for its description It is admitted that at fuel combustion the reaction rate initially increases, but as the process unfolded under certain conditions, it decreases. By the simulation, theoretical and experimental research of the fuel combustion in the diesel engine it is determined that in the compression volume the two areas, the higher temperature area and the lower temperature area, are distinguished [1]. And in some areas the temperature reaches 3000ºK (with the average temperature 17001800ºK) and changes insignificantly within 50-60 degrees of the crankshaft position [2]. It indicates that when the temperature reaches 3000ºK, the processes of the carbon dioxide dissociation limit the further progress of the combustion, and in the expansion process the carbon monoxide afterburning sustain the higher temperature until it is

* 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.2015.12.159

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fully oxidized. The known models, which are used for mathematical formulation of the fuel combustion process in the internalcombustion engine, either consider this characteristics incompletely, or consider them in the implicit form. Therefore, the development of the combustion theory and making new models for the description of the real incylinder processes still remain urgent. All the known combustion process models may be divided into three principal groups: x models in which the heat generation process is described by the preset function of time or the crankshaft position; x models which describe in detail the kinetics of the combustion process; x models which are based on the application of the general kinetic law (Arrhenius equation). Simple and useful combustion process models among which I.I. Wiebe’s model became widespread refer to the first group [3]. The real variation of the parameters of the actuating medium (pressure, temperature and concentration of the reactants) in the combustion process are not considered in the models of this group. The combustion products dissociation heat losses are taken into consideration in the implicit form, as a rule, with the other heat losses which are expressed in terms of the heat utilization factor or the combustion efficiency factor. And the value of the dissociation heat losses is considered proportional to the part of the burnt fuel, and in the expansion process this heat doesn’t return to the actuating medium. The second group includes models that treat the fuel oxidation process by atmospheric oxygen as the combination of chemical reactions with the intermediate products generation [4,5]. For each similar reaction there are constants of reaction rate, activation energy and reagents concentration. It is too difficult to realize the models of this group in engineering computations as it demands great computational power. The third group includes models that describe the combustion process in general and consider such important physical parameters as the temperature of the actuating medium and the fuel and oxygen concentration [1]. Meanwhile, in the models of this group there is no direct accounting of inert components (nitrogen, combustion products, etc.) that, as it’s well-known, inhibits the combustion process. The key parameter of the process in these models is the combustion rate depending of the temperature and the concentration of the mixture active components. The relative quantity of the reactive fuel is not frequently used. The parameters that characterize the time factor of the combustion process are applied to determine integrated timing values: an ignition delay period estimation and combustion duration with the constant reaction rate or isothermal reaction [6]. However, to model a variable reaction rate with the constantly decreasing fuel and oxygen molecule concentration and considerable temperature rise, it is necessary to control the time dynamics of the combustion process variation. Therefore, it became necessary to introduce the fuel oxidation reaction time factor which allows to control the state of the actuating medium in the engine cylinder in any time (on any process stage). The Internal-Combustion Engine department of South Ural State University developed a new single-area model of the combustion process based on kinetic equations which more accurately considers the features of in-chamber processes of internal-combustion engines. 2. New models for computation of the fuel combustion process in the diesel engine 2.1. The Combustion Process Model The Combustion Process Model is based on the following points: x The whole combustion process is considered as a combination of successive oxidation reactions of active fuel molecules groups to carbon dioxide and water. These reactions progress according to Arrhenius equation and possess the energy that is larger than the conditional activation energy by the present temperature. x The quantity of reacting active fuel molecules in the group depends on the total quantity of fuel molecules, the current mixture temperature and the conditional activation energy that changes according to the burnt fuel ratio. x The conditional oxidation duration of active molecules in this group is considered dependent not only on the total quantity of fuel molecules but also such important for the combustion process parameters as the volume of the

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combustion chamber, the oxygen molecule quantity, the inert component molecule quantity (nitrogen, carbon dioxide, water, carbon monoxide, etc.) and the turbulence inside the combustion chamber. x The heat generating at oxidizing each active fuel molecule group is determined by the low fuel heat capacity and is consumed for the mixture temperature and pressure increase in the combustion area. x At each step of the computation the quantity of molecules of all the substances is corrected as a result of the fuel combustion, the oxygen consumption for combustion, carbon dioxide and water formation, formation of carbon monoxide and oxygen at dissociation and the further oxidation of carbon monoxide. The feature of the model is an introduction of the new parameter, the conditional duration of the fuel molecule oxidation reaction, which considers the time factor on the molecular level. When studying any process which develops with time, the timing parameter is used to trace the alteration of the phenomenon under study. In the internal-combustion engine the timing parameter is a crank angle in degrees (under the assumption of the steady rotation of the engine crankshaft). But when studying the combustion process when the crank angle is dependent on time and the compression volume value, this substitution is not always proper. The variation of the compression volume definitely results in the temperature variation in the cylinder and the concentration variation of the reactants and, consequently, the oxidation reaction rate. In this case it is impossible to identify the cause of the combustion rate alteration uniquely: either it is the result of the temperature and concentration variations, or it takes place with time. The new parameter eliminates this disadvantage as it considers the quantity of molecules of all the actuating medium components and the compression volume value in explicit form. The equation to obtain the relative duration of the reaction oxidation of the active fuel molecule group is as follows:

Wy

ZF const ˜ K1 ˜ K 2 ˜ V ˜ CFp ˜ COq 2

V , const ˜ K1 ˜ K 2 ˜ Z Fp 1 ˜ Z Oq 2

(1)

where ZF – the total quantity of fuel molecules in the volume under study V of the engine cylinder; const – the constant which considers the amount of collisions of active molecule reactants in time unit in volume unit; K1 – the coefficient which considers the influence of the inert components of the actuating medium and combustion products; K2 – the coefficient which regards the turbulence inside the combustion chamber, K2•1; CT=ZɌ/V ɢ CO2=ZO2/V – the concentrations of all the molecules of the fuel ZF and the oxygen ZO2 in the volume V respectively; p, q – exponents of power, and p+q=n – the kinetic index of the reaction, n=2. Coefficient K1 is taken from the equation which is derived from the dependence of the ignition delay period [7] from the oxygen concentration in the oxidant (Fig. 1): 6

K1

ZO 2 § · 1  ¨1  ¸ , © Z O 2  Z N 2  Z CO 2  Z H 2O  Z CO ¹

(2)

where Z N 2 , Z CO 2 , Z H 2O ɢ Z CO – the quantities of the nitrogen, carbon dioxide, water and carbon monoxide molecules in the rated volume V respectively. Coefficient K2 is worked in to model the influence of the combustion mixture motion (if it’s necessary). The active fuel molecule quantity (according to Arrhenius equation) is defined by the following expression:

dZ F

ZF

E  a RT ˜e

,

where Ea – the activation energy of fuel molecule. The quantity of the molecules which react at a computation step ǻij, is obtained from the equation:

(3)

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'Z i

dZ F ˜ 'M . W r ˜6˜n

(4)

Fig. 1. Influence of concentration of oxygen in an oxidizer on relative size of an ignition delay time [7]

The mass of the fuel combusted at a computation step ǻij, is derived from the equation: 'm comb

'Z i ˜ P F ˜ A0 ,

(5)

where ȝF – the fuel molecule mass, Ⱥ0 – Avogadro constant. The quantity of the heat generated by the fuel combustion at a computation step ǻij, is derived from the equation: 'Qcomb

'm comb ˜ [ ˜ H u ,

(6)

where ȟ - combustion effectiveness ratio coefficient; Hu – low heat value of the fuel. The more detailed description of the mathematical model is given in [8]. When the temperature in the fuel combustion area exceeds 1500-1700ºK, the carbon dioxide dissociation process starts to influence on the law of pressure changing in the cylinder through energy consumption on this process. Therefore, to model the combustion process in the real engine the carbon dioxide dissociation process model is developed, and it allows to determine energy dissipation and instant quantities of oxygen, carbon monoxide and carbon dioxide molecules in the engine cylinder. 2.2. The model of the dissociation process of carbon dioxide The model of the dissociation process of carbon dioxide generated at fuel combustion in the diesel engine cylinder under the conditions of non-stationary heat and mass exchange consists of equations for dissociation degree determination for quasi-equilibrium state according to V.V. Pomerantsev [9], the quantity of carbon dioxide molecules dissociated into carbon monoxide and oxygen molecules, and also energy consumptions on this process. It is considered that at temperature decreasing in the combustion area the dissociation process is going on in the opposite direction with heat generation by the carbon monoxide oxidation. The carbon dioxide molecule quantity ǻZCO2 dissociated per the computation step is determined through the dissociation degree Į at the current pressures, temperatures and the actuating medium composition. The dissociation degree Į is obtained as the solution of the cubic equation by the Viete-Cardan method:

D 3 D 2

2E 1  K P2

p

D

 3  4E  1  K P2

p

2  2E 1  K P2 p

0,

(7)

where p – the in-cylinder pressure; Ʉɪ – reaction equilibrium constant, is obtained from the equation 29791 0,324 ˜10 5 lg K 2p  0,169 ˜10 3 T   9,495 [10]; ȕ – relation of the sum of the mole quantities of nitrogen T T2

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NN2 and water NH2O to the quantity of carbon dioxide moles NCO2 in the actuating media at the beginning of the N N 2  N H 2O computation step: E . N CO 2 The equation (4) is obtained for the reaction N 2  H 2 O  2CO  O2 œ N 2  H 2 O  2CO 2 after the equilibrium establishing [11]. The energy consumptions on the dissociation of these molecules are determined according to the equation 'Qd

'Z CO 2 ˜ P CO 2 ˜ A0 ˜ E d

,

(8)

where P CO 2 – the molecule mass of carbon dioxide; Ed – the energy consumed on the dissociation of one carbon dioxide molecule. 2.3. The model of a operating cycle of the diesel engine The model of a operating cycle of the diesel engine assumes that the injected diesel fuel occupies only part of the current volume of the cylinder į. Its value and changes in the law are set on the basis of experimental data on the results of the tests of mixture formation at motorlass stand. In this part of į is distributed evenly all the fuel ZF, filed into the cylinder at the moment. For the calculation of step ǻij active molecules fuel dZF, defined by the formula (1) is the mass of fuel burned ǻmcomb by expression (2). Herewith heat release ǻQcomb is determined by expression (3), which is consumed (goes) to heat the working fluid in the cylinder. Calculations the operating cycle diesel engine is produced through the steps from point 1 (the beginning step) to point 2 (end of step) according to known method [3]. Herewith is used the following equation to determine the pressure in the cylinder of the diesel engine at each step of the calculation [11]:

p2

2'Qcomb  'Q well  'Q d · § k 1  p1 ¨ v1  v2 ¸ m ¹, © k 1 k 1 v2  v1 k 1

(9)

where ǻQwell – the heat transfer through the walls of the cylinder head, the piston, and the liner; m – in-cylinder gas mass; p, v – the in-cylinder gas pressure and specific volume; k=Cp/Cv – adiabatic index. The heat transfer through the walls of the cylinder head, the piston, and the liner is calculated under law NewtonRikhman 'Qwell

D1 F1 T1  TW 'M 6n

,

(10)

where Į1 – the in-cylinder heat transfer coefficient from gas to inner cylinder wall; F1 ɢ Tw – area and the surface temperature of cylinder volume at the beginning of the step of calculating; Ɍ1 – temperature of gas in the beginning of the calculating step; n – engine speed, ǻij – crank angle for a calculation step. The models described above are assumed as a basis of the methodic and algorithm of the program for engineering calculation of the operating cycle diesel engine with a given law of of mixture formation. The possibilities of the program are shown in the example calculation research the influence of temperature of a fresh charge after charge air cooler on the indicators operating cycle of a powerful diesel engine. Fig. 2 shows the results of calculation of the operating cycle of a diesel engine at different temperatures the actuating medium at the beginning of the compression Ta. The increase of this temperature from 360ºK to 430ºK at constant other parameters leads to a significant deterioration of indicated parameters and decrease of the maximum pressure of gases in the cylinder of a diesel engine. Best indicated parameters obtained at Ta = 360 K: mean

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indicated pressure of cycle pi = 2,29 MPa, the specific fuel consumption indicator gi = 180,6 g/kWh, indicated efficiency Și = 0,469. Maximum in-cylinder pressure pmax is 15.97 MPa. The deterioration of the indicated parameters and decreased of the maximum pressure in the cylinder occurs as a result of reduce the excess air ratio and changes of law heat release. The given dependence on rice. 2 will well be agreed with the experimental data on the influence of the temperature of a fresh charge after charge air cooler on indicated parameters of a operating cycle of a diesel engine of increased power.

Fig. 2. The dependence of the parameters pmax, Și, pi, gi from the temperature of the actuating medium at the beginning of compression

Fig. 3 shows curves of the calculated the in-cylinder pressure and the heat release rate at various temperatures of the actuating medium at the beginning of the compression Ta. Here it is seen that the higher the temperature Ta, the earlier the start of the combustion process and less the maximum heat release rate. When Ta = 360ºK the largest ignition delay period during which a larger quantity of fuel being prepared. This results in to increased the rate of pressure increase, increasing the maximum pressure in the cylinder and improve the indicated parameters of the operating cycle diesel engine. The maximum heat release rate in the main period (the second maximum) is almost does not change.

Fig. 3. Diagrams of variation of in-cylinder pressure and heat release rate at various temperatures Ta the actuating medium at the beginning of

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Diagrams of pressure in the cylinder and the laws of heat release produced by the developed calculation models will well be agreed with the experimental data obtained in the analysis of the indicated parameters of diesel engines increased power. This proves the possibility of using the developed mathematical models for engineering calculation of the operating cycle of the powerful diesel. Thus, the use of the developed program allows on the design stage to simulate and plan a rational law for of mixture formation for getting effective combustion process and the best indicated parameters of the operating cycle of the powerful diesel engine 3. Conclusion

We can make the following conclusions based on the results of the research. x The models and program for calculating the operating cycle of diesel engine with a given law of of mixture formation is developed. x The novelty of the combustion process model is the introduction of the new parameter considering the time factor in this process – the conventional duration of the fuel molecule oxidation reaction and the equation for its determination, in dependence on the oxygen, fuel, nitrogen and combustion products in the combustion chamber molecule quantity, the volume of the combustion chamber, the physicochemical property of the fuel. x The best indicated parameters the operating cycle of the powerful diesel engine produced at a temperature the actuating medium at the beginning of compression Ta = 360ºK and related to maximum cooling of the charge air cooler. x Diagrams of pressure in the cylinder of the powerful diesel engine and laws of heat release produced calculation of the developed models will well be agreed with the experimental data. x Using the developed program allows the design stage to simulate and plan a rational law for effective of mixture formation of the combustion process and the best indicators of the operating cycle of the powerful diesel engine. Acknowledgements

This work is carried out under support of the federal goal-oriented program “Research and development on priority directions of scientific-technological complex of Russia, 2014-2020”. References [1] R.Z. Kavtaradze, Lokalnyiy teploobmen v porshnevyih dvigatelyah, [Local heat exchange in piston engines]. Textbook for high schools, MSTU of N.E. Bauman Publ., Moscow, 2001. [2] A.K. Kostin, Teplonapryazhennost dvigateley vnutrennego sgoraniya, [Thermal stress of internal combustion engines]. Handbook, Mashinostroenie Publ., Leningrad, 1979. [3] I.I. Wiebe, Novoe o rabochem cikle dvigatelej, [New about the working cycle of the engines],Mashgiz Publ., Moscow, 1962. [4] Zhaolei Zheng, Mingfa Yao, Numerical study on the chemical reaction kinetics of n-heptane for HCCI combustion process. 85 (2006) 2605– 2615. [5] A. Bhave, M. Balthasar, M. Kraft, F. Mauss, Analysis of a natural gas fuelled homogeneous charge compression ignition engine with exhaust gas recirculation using a stochastic reactor model, Int. J. Engine Res. 5(1) (2004) 93–103. [6] D.A. Frank-Kamenetskiy, Diffuziya i teploperedacha v himicheskoy kinetike, [Diffusion and heat transfer in chemical kinetics], Science Publ., Moscow, 1987. [7] Pahl, Beiträage zur Erforschung des Zündproblenmes flüssiger Brennstoffe, München, 1927. [8] V.G. Kamaltdinov, Novaya model protsessa goreniya topliva v DVS, [New model of process of burning of fuel in an internal combustion engine], Dvigatelestroenie. 233(3) (2008) 17–20. [9] V.V. Pomerantsev, Osnovyi prakticheskoy teorii goreniya, [Bases of the practical theory of burning], Manual, Energiya Publ., Leningrad, 1973. [10] A.A. Ravdel', A.M. Ponomareva, Kratkiy spravochnik fiziko-himicheskih velichin, [Short reference book of physical and chemical sizes], Chemistry Publ., Leningrad, 1983. [11] V. Kamaltdinov, Combustion process modeling in HCCI engine. JSAE 20119118, SAE Technical Paper. 1(1789) (2011) 10.