Benzin motorlarında indirgenmiş kinetik model uygulaması

Abstract

Çok boyutlu reaktif akış programlan, içten yanmalı benzin motorlarının geliştirme çalışmalarında, yakıt sarfiyatının düşürülmesi, egzoz emisyonlarının azaltılması ve vuruntu simülasyonu gibi amaçlarla kullanılmaktadır. Şimdiye kadar yapılan geliştirmelerle gaz hareketlerinin çok boyutlu olarak modellenmesi tatminkar seviyede yapılabilmektedir. Fakat, günümüze kadar hem yanma üzerine fiziksel bilgi yetersizliğinden hem de var olan fiziksel bilgilerin bu akış denklemleri ile beraber modellenmesi durumunda bilgisayar kapasitelerinin yetersizliği nedenr ile sözü edilen hedeflere hassas olarak varılması mümkün olamamıştır. Diğer taraftan, son yıllarda deney olanaklarındaki ilerlemeler sonucu, yanmanın elementer reaksiyonları, bu reaksiyonların hızları ve bu reaksiyonlarda yer alan bileşenler daha iyi gözlemlenebilmektedir. Bu bilgiler ışığında bir araya getirilen binlerce reaksiyon ve yüzlerce bileşen ile, yanmanın kapsamlı mekanizmaları ideal koşullarda oluşturulabilmektedir. Bu boyuttaki mekanizmaların hesap amaçlı kullanımı henüz mümkün değildir. Bu nedenle, ancak bu mekanizmalardan önemli reaksiyonlar ayrılarak oluşturulan indirgenmiş mekanizmalar akış denklemleri ile beraber çözülebilir. Bu durumda da birtakım reaksiyonların ihmal edilmesi, reaksiyon hız parametrelerindeki yanlışlıklar ve hesap güçlükleri nedeni ile bu güne kadar ancak özel koşullarda kullanılabilen, az sayıda reaksiyon içeren ve tek boyutlu gaz akış çözümleri kullanan modeller gerçekleştirilebilmiştir. Bu çalışmada, önce akış denklemlerinin nasıl çözüldüğü özetlenmiş, sonra yanmanın elementer reaksiyonlarının nasıl oluşturulduğu, bu reaksiyonlarda yer alan bileşenlerin özellikleri ve reaksiyonlara ait hız parametrelerinin nasıl belirleneceği tartışılmıştır. Daha sonra, bu reaksiyonların akış denklemleri ile beraber çözüm yöntemleri incelenmiş, mümkün olan ekonomik çözüm için gerekli indirgenmiş mekanizmanın oluşturulması aşamaları anlatılmıştır. Seçilen indirgenmiş yanma mekanizması ve akış çözüm programı, birlikte kullanıldığında çok hızlı reaksiyonların görece yavaş reaksiyonlarla beraber çözülmesi gerektiğinden diferansiyel denklem çözümleri klasik yöntemlerle mümkün olamamaktadır. Bu tip denklemlerin çözümü için önerilen yöntemlerin de akış çözümleri ile beraber kullanılması mümkün olmadığından mekanizmada ikinci bir basitleştirme yapılarak hızlı reaksiyonlar standart çözüm yönteminden ayrı bir yöntemle çözülerek sistemin stiff özelliği giderilmeye çalışılmıştır. Bu ayrım motor çevriminin farklı noktalarında farklı reaksiyonlar seçilerek yapılmıştır. Çünkü farklı bileşenlerin farklı zamanlarda dengeye ulaşması söz konusudur. Bu ayrım da gerçekleştirildikten sonra, oluşturulan model neticeleri deney koşulları ile karşılaştırılmış ve sınırlı çalışma şartlarında deney motorunun P-v diyagramı, alev hızı ve egzoz emisyonu seviyeleri ile uyumlu neticeler alınmıştır. Daha ayrıntılı araştırmalar için yerel özelliklerin incelenmesine de çalışılmıştır. Sonuç olarak, oluşturulan çözüm yönteminin sınırlı çalışma koşulları için global araştırmalarda kullanılmasının mümkün olduğu anlaşılmıştır.

For more than 30 years, zero or one-dimensional thermodynamic cycle simulation of the internal combustion engines has been effectively in use for parametric studies. However, the demands on more detailed and accurate analyses of phenomena such as mixture formation, pollutant emission or knocking requires two or three- dimensional models which include comprehensive chemical reaction models for ignition, combustion and knocking. Therefore, in the recent years, numerical simulation of the flow field and the combustion in the cylinder of the internal combustion engines has become an important instrument for research and development efforts. Two or more dimensional models are more universal models and have the ability to solve the problem with a parameter set independent of the operating conditions. If a more or less simple chemical kinetic model is used with a simple geometry, then a solution can be obtained for a reasonable expense. Nevertheless, the solution will be time consuming and requires very high computer performance, if the geometry is complex and the chemical model is comprehensive. This is because of the use of the three dimensional mesh system with very large number of grid points increases the number of the conservation and the chemical kinetic equations to be solved. In most cases, these equations must be solved in every mesh cell using very short time steps. For combustion studies in CI engine (or direct injection SI engine), the governing equations of spray mixing, droplet distribution and vaporization in the combustion chamber must also be solved. This makes the problem more complex and harder to solve with an acceptable accuracy. Numerical simulation of the in-cylinder phenomena requires the simultaneous applications of the flow, thermodynamics and the chemical reaction equations and forces the limits of the knowledge of the disciplines. The methods of analyses and solutions need to be adapted to some extent according to the special demands of the application field. The governing partial differential equations, to be solved for a reactive flow, are the conservation equation of mass, momentum, energy and chemical species. The equation of state couples the pressure with temperature. The source terms of the Gas Phase Continuity Equation must be obtained from the droplet vaporization model in case of fuel injection into the compressed air. On the other hand, the source terms of energy and species equation are calculated from the solution of the kinetic equations. All equations are time-dependent and solved under the condition of moving xm boundaries. In many cases, the stability of the solution constrains the source terms and the space and time scale. If for example 30-40 cells are used for each direction and if 30 chemical species are present in the reaction model, then approximately 1.000.000.000 coupled partial differential equations must be solved simultaneously in each time step. In addition to this, coupled kinetics equations more than the number of the chemical species must also be solved at each time interval in every cell. Chemical kinetics of the combustion in internal combustion engines can be modeled by ordinary differential equations, which can be written in the general form given below: - L=/i (concentrations, reaction rates) Here, i denotes the species considered, concentrations cover all species which take part in reaction and reaction rates are forward and backward rates. These ordinary differential equations can be solved by numerical integration over the time. However, each chemical rate equation has its own time scale for an accurate solution. In most cases, very different time scales must be used both for different equation and during the development of the solution (the so-called stiffness problem). Reaction rates, on the other hand, are generally expressed in modified "Arrhenius" form, that is with pre-exponential temperature dependence. k=ATaexp(-E/RT) Most of the (binary) reactions occurring during the ignition and combustion of the internal combustion engine fuels depend on the temperature only through the exponential term. However, at high temperatures the pre-exponential rate coefficient must be corrected using a pre-exponential temperature dependence term. Some times, it may be more convenient to express the reaction rates with suitable functions of temperature. Another difficulty related to the reaction rates is the pressure dependence of the rates of many unimolecular decomposition and recombination reactions. However, some bimolecular reactions exhibit weak pressure dependence as well. Reaction rates are principally obtained, within some uncertainty limits, by experiments. Adequate kinetics models give results which agree with the experiments and which are valid for the given temperature and pressure interval. If there is big difference between measured and calculated concentrations then this is mostly because of the unrealistic kinetic model. However, sometimes the experimental rate constants may also be inaccurate. This is possible especially for reactions with components of which concentration can not be measured easily and accurately. In these cases, the theoretical rate or model calculations can sometimes help to decide for the true value of the reaction rate. It is also possible to by pass this difficulty with an adequately reduced kinetic model. A mechanism describing the whole reaction set consists of the elementary steps, which lead from Reactant State to end products. Enormous numbers of reaction must be considered for a theoretically complete mechanism. However, some xiv elementary steps do not occur at all and many occur at a very slow rate so that they do not affect the combustion process. In recent years, two kind of research dealing with internal combustion engines have been carried out with in different sources to improve the capability of reactive flow codes using more realistic combustion models. Some of them try to use comprehensive kinetic mechanism with one or quasi- dimensional flow solvers such as HCT (Lund, 1978). The aim of this kind of works was to correct the combustion model of the reactive problems. The major difficulty to use these kind of comprehensive mechanisms with flow calculation was the solution of species continuity equations with energy equations. Today, comprehensive kinetic mechanisms for hydrocarbon fuels such as iso-octane have hundreds of elementary reactions and thousands of species. Meanwhile, some reaction rate data and some rare radical properties have uncertainties because of the lack of experimental data and theoretical knowledge. With this profile, there is no successful attempt to use comprehensive kinetic mechanism with flow calculations. To simplify the problem, some research had been carried out to reduce the full kinetic mechanism. There are two major ways to do this. One is to apply sensitivity analysis to the kinetic mechanism of a specific problem and then eliminate less important or rare reactions and species while preserving major species and vital reactions. For example, Westbrook at al. (1981) in their study modeled the wall quenching phenomena with reduced kinetic mechanism to understand the major source of exhaust hydrocarbon emissions from internal combustion engines. The other approach is the use of formal kinetic structures such as Shell model in the flow calculations. Formal kinetic structures having few independent variables simplify the problem of conservation equations but they still not to be able to solve energy balance of the flow calculations. Important examples of this kind of study are Li at al. (1996), Natarajan and Bracco (Griffiths, 1995). On the other hand, some researchers try to use reduced kinetic mechanisms with multi-dimensional flow codes. Reactive flow codes for example KIVA (Amsden at al. 1989) and SPEED (Adomson at al. 1990) already gave reasonable solutions on the flow field. However, with their global one step reaction model they were not capable of explaining local phenomenon such as pollutant formation and autoignition. In recent years, at Engine Research Center of Wisconsin University Kong at al. (1995) add some subroutines in KIVA to improve the combustion or autoignition models. With successful application of formal Shell structure, KIVA used to model out various local phenomenon in internal combustion engines especially diesel engines. In other research, application of reduced chemical kinetic mechanisms successfully explained some low temperature fields in internal combustion engines. To give the turbulence effect to the combustion model some other researchers tried to use recent aspects of turbulence such as "flamelet", "Large-Eddy Simulation". The major problem of multi-dimensional reactive calculations with turbulence is how to calculate the reaction rates. In literature, reaction rate data is always measured or calculated in laminar or no flow conditions. However, turbulence effects greatly change these rates. Turbulence effects can be modeled with two major aspects in nonpremixed or premixed turbulence models. Nonpremixed flame models (formerly classified as diffusion flame models) either simplify the problem by using equilibrium chemistry or directly calculation of xv turbulent reaction rates with some other means of turbulence such as flamelet. The flamelet reaction rates can be calculated by using PDF approach. Premixed flames can also uses flamelet applications or model the turbulence effects by Large-Eddy Simulation. In future, if the computer speeds and storage capacities provide the researchers the ability of using fine meshes so that minimum turbulence scales can be modeled, direct numerical simulation models might be usable. No direct uses of comprehensive kinetic mechanism have been reported yet to explain both species conservation and energy balance with multidimensional flow calculations. The aim of this work was to use a reduced chemical kinetic mechanism with a multidimensional flow calculation for modeling internal combustion engines. In this work, a reduced chemical model (Moses at al., 1995) was applied to CONCHAS (Cloutman, 1982). The original one-step, 11 species model was replicated with a multi-step mechanism of 149 chemical reaction and 40 species. The first step of this work was maintaining species and reaction data. CONC AS uses species Enthalpy of Formation table as JANAF (Stull and Prophet, 1971) but this source does not have some species like radicals, which is in the mechanism. This data have been obtained from other sources like Burgess at al. (1995) and was adapted for use with the CONCHAS algorithm. The results are as expected inaccurate for major species concentration, flame temperature and the flame speed. While investigating source of inaccuracy, it was found that some reactions have greater time scales comparing to others. For conditions in internal combustion engine, this model can not be realistic if fast reactions calculated separately. The partial equilibrium approximation was used for this purpose. Partial Equilibrium Approximation Method proposed by Amsden (1979) for iso-octane combustion in internal combustion engine flow calculations is an efficient tool if the fast reactions selected properly. This means the reactions for partial equilibrium must be selected separately and these reactions must have fast reaction rates both reverse and forward directions. In this study firstly, the reactions proposed by Cloutman at al. (1982) was used while equivalent H2-O2 reactions in the kinetic mechanism taken out. This configuration gave incorrect flame speeds and incorrect P-a diagrams for all estimated the concentrations of major species. Than, some elementary reactions in the original mechanism were calculated by partial equilibrium approach. Several reaction configurations were tested to compare the flame speed and major species concentrations predicted with the experimental values. However, in most cases convergence problems occurred. In some cases concentration levels of some species like 02 was not correctly estimated at the end of expansion stroke although the flame speed and concentrations at the end of the combustion process were correct. Several investigators like Heywood (1988) and Newhall (1969) have reported the same problem. This report explains that for internal combustion engine conditions different species reaches their equilibrium concentration at different periods. This gives an idea of using different equilibrium reactions at different time steps in each computational cell. First, the equilibrium model proposed by Newhall (1969) was tried for expansion conditions. The results were appropriate for engine exhaust conditions. If these reactions set in equilibrium then no combustion occurs. Then the most promising combustion reaction set used with expansion reaction set proposed by Newhall. First, the transition from one equilibrium set to another is made at same xvi crack angle for all grid points. Good concentration values were obtained during both combustion and expansion conditions. However, concentration and pressure discontinuities have occurred in the transition point. So the transition was made at each grid point according to grid fuel concentrations. Successful results are achieved by making the transition at 5-degree crank angle after reaching zero fuel concentration at every grid points. With this configuration, the grid optimization was made. The starting grid configuration was set at 38x15. With this configuration, the reaction rates have to be adjusted in order to obtain a realistic flame speeds. Adjustments were made by multiplying all the rate coefficients by same number so that the P-ct diagrams fitted with the experimental results. This adjustment needed because, if the number of grid points is less then a realistic value, the heat transfer between grid points could not be simulated successfully. To understand this effect and to get more realistic heat transfer rates finer grid configurations such as 76x30, 51x20 and 18x7 were also tested. Grid number adjustment made by preserving the dx/dy ratio. This means grid number at each axis changed by same ratio. Results of this investigation show that finer meshes in the order of 76x30 must be used to achieve reasonable P-a with non- adjusted rate coefficients. This kind of refinement is also necessary for more realistic flow-flame interactions. The wall quenching effect and deformation of flame front due to the flow instabilities were made visible with temperature counters of 76x30, 51x20 grid configurations. Nevertheless, this grid refinement accepted as not economic because of the computation times, which was in the order of 48 or 96 hours. However, if one wants to use this model for explaining local phenomenon such as hydrocarbon production mechanism caused by wall quenching or autoignition finer grids than 76x30 must be used. The results for 38x15 configuration further investigated as if major species concentrations be consistent with experimental results. Qualitatively good results were observed for Fuel, C02, H2O, 02, CO, OH, H, H2 and O concentrations. This agreement graphed for individual grids and total molar concentrations. This model also gave good results for both compression and expansion strokes. With this configuration, some rare species concentrations were also plotted to explain hydrocarbon formation and deformation mechanisms of internal combustion engines. Most of these species reaches their maximum concentrations in the mid- combustion period and consumed quickly. However, some small hydrocarbons do not reaches zero concentrations even after combustion was ended. These species types and concentrations were in agreement with the test results. Nevertheless, these results can not be quantitatively tested with experimental results. Because this kind of comparison needs experimental data of these rare species concentration in the engine at different crank angles which are not available yet. Fuel history tables of this study is also presented. However, one must be made proper fuel definition to compare these graphs with real engine. For example, the carbon monoxide not treated as fuel in this study, which may be combustible. Than, the effects of excess air coefficients on flame speed and concentrations were calculated and compared with experimental values. Flame structures at TDC for different excess air coefficient were presented to explain flame speed values. Gradually faster flames were observed for ^=1 to X=0.85. The flame location of xvn X=O.S was behind the X,=0.85. It can explained so that flame travels faster as X decreases up to A,=0.85 but than the flame speed is slows down. Nevertheless, the pressure vs. crank angle diagrams of different air excess coefficients shows inconsistent results with above explanations about flame speeds. It was observed from these diagrams that maximum pressure is obtained with A. = 1. The position and value of maximum pressure of X < 1 indicates that there is no significant relation between air excess coefficient and maximum pressure. The molar concentrations of major species were also plotted for comparison. In this diagrams. The carbon monoxide emissions at the peek values and at the exhaust conditions increase as the X decreases. This was expectable result for internal combustion engines. Other major components concentrations also shows related results. It must be noted that air excess coefficient effects on the concentrations and flame speed could only be investigated for the values of X below unity. Qualitatively good results were obtained with these values. However, the selection of partial equilibrium reactions not suitable if the model is applied to lean conditions. It is clear from these results that, with his configuration the optimization and automation of selection of partial equilibrium reactions must be integrated into the model in order to use it at different operating conditions. The contents of this thesis is as follows: - In Chapter 2., the methods for simulation of flow field and turbulence was reviewed. - The chemical kinetics concepts, which were used in this model, are introduced in Chapter 3. - The construction of a chemical kinetic mechanism was outlined in Chapter 4. The solution methods for flow equations with chemical kinetic mechanism may found in Chapter 5. - Reduction methods and types of reduced chemical kinetic mechanism were outlined in Chapter 6. - In Chapter 7., recent studies about application of reduced chemical kinetic mechanism into flow calculations were reviewed. - The model construction steps and solution results were introduced in Part 8.