Simulation Studies of Combustion in a Constant-Mass Variable-Volume Combustion Chamber

A numerical simulation code was used to conduct a systematic study of the effects of fuel-air equivalence ratios in the range 0.7 ≤ φ ≤ 1.4 and compression ratio, rc = 8.0 on key operating parameters, such as pressure, rate of change of pressure, ‘/dt’ flame extinction temperature, burn rate frequency, combustion efficiency, ηb, source term, mass burn fractions and heat loss in a simulated 5.734 liter, V8 spark-ignition engine. The data shows that the burn rate characteristics of the fuel and oxidizer are qualitatively perfectly correlated. The results also show that as flame extinction/flameout is approached, the fuel consumption rate, Rfu increases rapidly with temperature for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4. The average burn rate frequency (per second), fbr(1/s) varies from 11.2 ≤ fbr ≤ 137.0 for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4 The results further show that the fastest fuel consumption rate was for fuel-air equivalence ratio, φ = 1.4 in the time interval, t such that 0.0 ≤ t ≤ 0.61 ms while the slowest corresponds to φ – 0.7 and the corresponding time interval was 0.0 ≤ t ≤ 3.98 ms. Moreover, the data shows that for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4 the fuel consumption rate increases monotonically after the initial ignition delay period. The combustion efficiency, ηb of the engine under investigation were found to be in the range of 94.1% ≤ ηb ≤ 94.4% for lean mixtures, that is, for φ < 1.0;the corresponding values of combustion efficiency, ηb for fuel-rich mixtures were in the interval 93.8% ≤ ηb ≤ 94.1%. The other results from this study are summarized in the conclusion.


INTRODUCTION
The main source of environmental pollution in urban centers of the world can be traced to emissions produced by vehicles which are powered by internal combustion engines (ICEs).These pollutants originate from non-ideal combustion processes which are common in internal combustion engines and their formation is influenced byboth the engine operating parameters (for example, engine temperature, speed, load, air-fuel ratio, ignition delay, spark timing, exhaust gas recirculation, etc.) as well as the fuel composition.Internal combustion engine emissions consist of volatile organic compounds (VOCs), carbon monoxide (CO), nitric oxide (NO) and nitrous oxide (NO 2 ) which are collectively referred toas oxides of nitrogen (NO X ), particulate matter (PM), carbon dioxide (CO 2 ) and water vapor (H 2 O).Volatile organic compounds (VOCs) and (NO X ) form photochemical smog in the atmosphere, and (CO) and (PM) have been identified as having adverse health effect on human beings.The impacts of fossil fuel combustion permeate many areas of our lives, in particular, it relatestothe economy, sustainability, variation of climatic conditions and energy utilization.In view of the foregoing issues, research efforts are now been concentrated on designing cost effective, safe, efficient and non-polluting combustion devices for a variety of fossil fuels with a view to keeping cost reasonable while protecting the environment and sustaining our standard of living.
A thorough understanding of combustion at a fundamental and engineering perspective is required so as to be able to improve the design of engine combustion systems.Detailed understanding of engine combustion is a difficult undertaking that entails a comprehensive knowledge of the chemical sciences, thermodynamics, heat transfer, fluid dynamics and advanced mathematics.For example, a complete comprehension of the most elementary turbulent flame requires detailed knowledge of turbulent reacting flow, a phenomenon which is highly intractable and is presently an active area of rigorous research efforts.Since it is impossible to wait until such a time that adequate knowledge of combustion dynamicsin ICE is attained, engineers who are tasked with designing combustion devices have turned to using a combination of science, experimentation, numerical simulation and experience in order to look for practicable solutions.In choosing the thermodynamic models that are normally used for engine combustion simulations we rely on some implicit understanding of the physical and chemical mechanisms they contain.Since the description of the most relevant and important aspects of the engine processes are usually incorporated into these models, the models have been found to performed extremely well and they are ideally suited for initial parametric studies Numerical modeling of internal combustion (reciprocating and rotary) engines involve thermodynamics, fluid mechanics, turbulence, heat transfer, combustion, chemical reactions and numerical analysis.In simulating the ICE, various levels of approximation have been used to predict the performance of internal combustion engines.Studies range from simple air standard cycles to complex three dimensional models which employ turbulence, chemical reactions, spray dynamics, heat transfer models, etc.In general, the numerical models of internal combustion engine can be classified into four categories, namely, zerodimensional single zone, zero-Dimensional/one-Dimensional single zone models, quasi-dimensional multi-zone models and multidimensional models.In zero-one-Dimensional models, the ICE is represented as a network of pipes (intake and exhaust manifolds) with "devices" that simulate different parts of the machine (valves, cylinders, pipe junctions, etc.) interconnecting them.For zero-dimensional models, the vast majority of the properties are averaged over the total volume of the combustion chamber and there is no spatial information.
A zero-dimensional single-zone model is capable of predicting engine performance and fuel economy accurately with a high computational efficiency.The major weakness of single-zone models is their inability to accurately simulate wave propagation into pipes and manifolds which the volumetric efficiency strongly depend upon.Furthermore, these models cannot account for the temporal and spatial variation of temperature and fuel spray in the mixture.It is worth mentioning that both the temporal and spatial variation of temperature and fuel spray is crucial in predicting harmful species formed during the combustion process.
In view of the foregoing, multi-dimensional models, such as the KIVA family of Fortran-based Computational Fluid Dynamics code which was developed by Los Alamos National Laboratory [1] is being used to resolve the combustion chamber space into fine grids, thus providing a considerable amount of spatial information.However, multi-dimensional models still employ phenomenological sub-models to describe physical processes such as fuel spray, turbulence, combustion, etc. that are present during the combustion process.
There is presently an intermediary method between zero-dimensional and multi-dimensional models that is called quasi-dimensional.Multi-zone models [2]can be effectively used to simulate innovative engine combustion systems, by combining the advantages of zerodimensional models and multi-dimensional models.These models are capable of providing the spatial information required to predict emission products with minimal requirement on computing resources.

LITERATURE REVIEW
The current pressure on automotive engine manufacturers to improve on internal combustion engine's fuel efficiency while simultaneously achieving acceptable emission levels has encouraged a lot of research activities in this field.The reviewspresented in this section describe various strategies that are presently beingused to study ICE combustion processes.
It is a well-known fact that heat transfer affects the performance and phasing of internal combustion engines.Empirical relationships and equilibrium wallfunction models are usually employed in engine simulations to predict wall heat transfer.However, numerous studies have shown that significant errors usually occur due to the failure of the underlying assumptions employed in deriving these equilibrium wall-function models.Non-equilibrium wall-function models have been found to provide a more accurate way of predicting the near-wall region heat transfer of incylinder flows.
In order to buttress this fact, [3]conducted a study in which simultaneous high-speed high-resolution particle image velocimetry and heat-flux measurements were employed in an optically accessible engine.The experiments were performed under both motored and fired conditions at two different engine speeds.The experimental data were utilized to assess the performance of different heat transfer models in predicting the thermo-viscous boundary layer.These models include commonly used heat transfer correlations, equilibrium and modified wall-function models and the non-equilibrium wall model which was recently developed.It was found that the equilibrium wall-function significantly under predicts the heat flux under both motored and fired conditions whereas, the non-equilibrium wall model was found to adequately capture the structure and dynamics of both momentum and thermal boundary layers in comparison with experimental measurements.It was concluded that the performance of the non-equilibrium wall model was superior to those of empirical correlation wall functions and the equilibrium model.
A quasi one-dimensional numerical code which was based on fuel-air cycle analysis was developed by [4]and used to predict the performance of two-and four-stroke fuel-inducted engines.The study was undertaken in order to provide boundary conditions for a finite element analysis which was used to predict thermal and mechanical loading of carbon-carbon pistons which was designed to be usedfor advanced internal combustion engine prototype.The simulation code was able to predict the required boundary conditions, namely, the gas pressure, temperature and heat transfer coefficients as a function of crank angle, as well as the indicated and brake power outputs, thermal efficiency and mean effective pressure.The code employs variable specific heat calculation throughout the operational cycle.The compression of an air-fuelresidual gas mixture was calculated followed by a finite rate burn, where the burn duration was calculated on the basis of the turbulent flame speed and cylinder geometry.The authors also used the code to study the tendency for engine knock or auto-ignition.The authors concluded that the code produced results which were in good agreement with actual engine operational data.
Lucchini et al. [5] presented a comprehensive approach which was developed using an open-source computational fluid dynamics code.In order to minimize the pre-processing time and preserve the accuracy of the results, algorithms for automatic mesh generation of spray-oriented grids were developed and applied to different combustion chamber geometries.The Lagrangian approach was used to describe the spray evolution while the combustion process was modeled by employing detailed chemistry and turbulence-chemistry interaction.The proposed numerical code was first tested by simulating cold flow thereafter; it was used to compute reacting flows in a constant-volume vessel, where the operating conditions mimicking those of heavy-duty diesel engines were simulated.Finally, the authors used their code to model two different load points and two piston bowl geometries.Experimental validations of these results were carried out by comparing the computed and experimental data with the cylinder pressure, heat release rate and pollutant emissions (NO X , CO and UHC) of a real engine.The simulated results were found to reproduce the measured data reasonably well.
The other efforts that are actively being researched in order to provide better understanding of combustion efficiency and effective control of combustion emissions can be found in references [6][7][8][9][10][11][12][13][14]and the references contained in them.
This paper is organized as follows; the introduction is presented in section 1, followed by the literature review in section 2. Section 3 presents the objectives of the present study, while section 4 details the engine simulation model while the modeling of the combustion process is described in section 5.The details concerning the setup and implementation of the numerical solution, initial and boundary conditions applied, internal consistency checksand convergence criteria are presented in section 6.The results of the parametric studies are presented in section 7. Finally, the conclusions are presented in section 8.

OBJECTIVE OF THE PRESENT STUDY
The control and optimization of combustion are crucial to fulfilling various legislations concerning the environment and the future enhanced performance required of internal combustion engines.Increasing break mean effective pressure at high loads and extending the operating range of advanced combustion engines appear to be the most promising way of reducing fuel consumption and pollutant emissions simultaneously.In view of this, comprehensive computational fluid dynamics tools are usually used to predict the complex interactions of the various phenomenological processes, such as fuelair mixing, unsteady diffusion combustion and formation of noxious species prevailing within the combustion chamber of an ICE.Detailed kinetics, consistent spray models and high quality grids are usually necessary in order to perform high quality predictive and parametric simulation studies which can be used either for design or diagnostic purposes.In view of the foregoing, the objective of this study is to use chemical kinetics and various fuel-air equivalent ratios to investigate the variation of concentration of products of combustion and tempe-rature within the combustion chamber of an ICE.The ultimate goal of this work is to gainsome understanding of combustion characteristics in ICEs in order to be able to optimize the design of future engines.

THE ENGINE CYCLE SIMULATION MODEL
In an internal combustion engine a substantial portion of the combustion processes take place when the inlet and exhaust valves are closed simultaneously.Since there is no inflow or outflow, we can model this situation as a constant-mass combustion reactor/bomb with temporal variation of mixture properties.The equations describing the combustion processes can therefore be reduced to their zero-dimensional, unsteady models.It is worth mentioning that the volume of a constant-mass combustion reactor/bomb may or may not have temporal variation.
As stated above, the objective of the present study is to model constant-mass combustion reactor, as for example, in ICE by simplifying the unsteady, threedimensional equations which are given below.
This will facilitate the computation of the time history of the reacting mixture from its initial reactant state to its final product state.In general, the product state may or may not be in equilibrium.The main utility of these simplified models are to provide a means of studying the fundamental physics behind the combustion processes in these devices.The results obtained from these models cannot be depended upon solely for practical designs; however, they do provide guidance on the main dynamics inherent in the constant-mass combustion reactor/bomb.

Conservation of mass equation
The law of conservation of mass for bulk fluid mixtures is given by: ( ) ( ) where ρ m is the mixture density, u j is the fluid velocity with j = 1,2,3, x j is the coordinate in three mutually perpendicular directions and t is the time.

Conservation of species
The equation of mass transfer of the species can be written as: where k is the number of species, ω is the mass fraction, D is the mass diffusivity and R k is the volumetric generation rate from chemical reaction.
When Equation ( 2) is summed over all species k of the mixture; Equation (1) is obtained.This can be explained as follows: from Dalton's law, . Therefore, on summing over all species k, Equation (2) reduces to: ( ) On comparing Equation (3) with Equation (1), Equation (3) becomes exactly equal to Equation (1) when 0 . The physical interpretation of this is that when some species are generated by for example a chemical reaction, some others are consumed.This implies that there is no net mass generation in the bulk fluid.

Conservation of chemical elements
It can be shown that the mass fraction η α of chemical element α in the mixture of a chemical reaction mechanism containing k species, is given by [13]: where η α,k is the mass fraction of element α in species k.
In a manner analogous to species convection, diffusion, generation and consumption/destruction so also are the elements in a chemical reaction.However, the chemical elements can neither be destroyed nor created/generated in view of the principle of conservation of element (law of definite proportions).Therefore, the transport equation for any chemical element α will have no source term.Hence, the conservation of element equation is given by: ( ) ( ) Notice that the diffusion coefficient D for the elements is assumed to be equal to those of the species [14].

Energy equation
In combustion calculations, it is more convenient to use the enthalpy or the temperature forms of the energy equation.It can be shown that the energy equations in enthalpy and temperature forms are given by [15]: and the energy equation in terms of temperature is: where T is the temperature, p m c is the specifi heat at constant pressure of the mixture, h m is the enthalpy of the mixture, h k is the enthalpy of species k, k eff = k m + k t is the effective conductivity, k m is the conductivity of the mixture and k t is the turbulent conductivity, rad Q and other Q are the volumetric generation/dissipation from radiation and other sources respectively.The viscous dissipation function is Φ v and μ is the molecular viscosity.
The following important remarks concerning the energy equation in temperature form are worth mentioning: 1.

∑
is the net volumetric rate of heat generation as a result of chemical reaction.For a simple chemical reaction (SCR),

R H
Δ where H c is the enthalpy of formation.
2. If we assume that the specific heats of all species are equal, that is, 7) is also zero because 0 3. The viscous dissipation terms μΦ v are significant only in high Mach number flows.Similarly, the Dp/Dt term is important in compressible flows particularly when shock waves are present.

MODELING COMBUSTION IN ICE
In internal combustion engines, the combustion taking place at the top dead center position can be modeled as a constant mass constant volume process whereas when the engine is in the normal operational mode, the combustion dynamics can be treated as a constant mass variable volume process.
In a spark ignition engine, the combustion of fuel-air mixture is initiated at the top dead center (TDC) position or at a few crank angle degrees before top dead center.The combustion process usually continues over quite a few crank angle degrees into the power stroke, however, the mass of the combustion products remain essentially constant while the combustion chamber volume changes.Furthermore, heat from the combusting gases is transferred to the coolant through the cylinder walls.
During normal operation of a spark ignition engine, the equation of bulk mass becomes: From [15], it can be shown that: where: ( ) ( ) is the angular velocity of the crank in rad/s, and N is in revolutions per minute and l and c are the lengths of the connecting rod and crank respectively, x 0 is the clearance height at TDC, x p is the instantaneous position of the piston, A c is the cross-sectional area of the combustion cylinder and u p is the speed of the piston at any instant of time/crank angle.The crank angle, θ is measured clockwise and θ = 0 is the top dead center position while θ = 180° corresponds to the bottom dead center (BDC) position.
From the foregoing, Equation ( 8) can be expressed as: Furthermore, by using Equation ( 8), Equations ( 9) and ( 10) simplify to: , , , andthe energy equation becomes: ( ) where dV p dt represents the work transfer by the pressure the combusting gases exert on the piston head, F, OX and P represent the fuel, oxidizer and combustion products respectively.Equation ( 12) can be further simplified to Equations ( 13) and ( 14): ( ) Therefore, the processes taking place in a spark ignitionengine can be modeled with Equations ( 10), ( 11), ( 14) and or (15).
In order to put a closure to this model it is necessary to stipulate physical models for wall heat transfer and combustion product pressure In an internal combustion engine, the pressure-crank angle history is normally determined from in-cylinder measurements or the pressure could be obtained from: where R m is the gas constant for the mixture.The wall heat transfer can be modeled as [16]: where the heat transfer coefficient α is usually obtained from measurements.It varies with time and locations along the surfaces of the engine combustion chamber.
Because of this, spatially averaged coefficients are normally used for preliminary studies.The other variables appearing in Equation ( 17) are defined below: and the subscript g and 0 refer to gas and conditions at the BDC when intake valve closes, p u is the mean piston speed, d is the diameter of the combustion chamber and p ad is the isentropic compression or expansion pressure which obeys the relation pV γ = constant.
For internal combustion engine studies, [17] recommend that the correlation given below should be used for α: 0.2 0.8 0.8 0.53 0.82 The derivation of the models presented so far assume that temperature and mass fractions are uniform all over the combustion chamber volume at all times.That is, the state of the products of combustion is assumed to be isotropic; this type of representation is referred to as thermodynamic model.However, in practical combustion devices, the ignition process creates substantial spatial and temporal variations of temperature and mass fractions as the flame front propagates through the unburned mixture.Sometimes, the air-fuel mixture resulting from pressure and temperature rise during the compression stroke, may auto-ignite, thereby leading to engine knock, which most often causes substantial damage to the pistoncrank assembly.It is for this reason that an accurate model of the rate of pressure rise is highly important.

Modeling ICE combustion dynamics as a constant mass variable volumeprocess
As stated above, in an internal combustion engine, ignition is initiated a few crank angle degrees BTC and a greater portion of the fuel-air mixture is burnt at constant volume while the combustion of the remaining unburnt charge propagates further into parts of the expansion stroke.Therefore, strictly speaking, in a constant mass reactor, combustion can either be approximated as a constant-volume or a variable-volume process.In the constant mass variable volume scenario, the combustion chamber volume, will vary with time and it can be determined from the speed, of the engine and the dimensions of the connecting rod and crank which are connected to the piston.In the present paper parametric studies of the effects of fuel-air equivalent ratio on pressure and temperature history as well as on the products of combustion was undertaken for the combustion processes in an internal combustion engine.Variable volume combustion chambermodels as well as appropriately transformed versions of Equations ( 1) to (18) were employed in the present work.

Simulation combustion in an ICE chamber as a constant-mass variable-volume reactor
The scenario used to illustrate the constant mass variable volume combustion process is as described and implemented below.
A mixture of n-octane, (C 8 H 18 ) and moist air ( φ = 1.0, x H2O = 0.03) is drawn into an engine at T = 300K and p = 1.01325 bar.The engine speed in revolutions per minute is 1400 rpm.The engine cylinder bore, d = 101.6mm and stroke length, L = 88.4 mm.The crank radius, c = 44.2mm, and connecting rod length, l = 144.92mm.Assume that at TDC (or θ = 0), the mass fractions and pressure correspond to T = 1000 K as calculated below.Assume a single step reaction model and T w = 650 K. Investigate the time/crank angle histories of T,p and mass-fractions ω f , ω O2 , ω CO2 , and ω H2O , α, and q w until the end of power stroke for equivalence ratios, 0.7 ≤ φ ≤ 1.4which is equivalent to air-fuel ratio, AFR, in the range; (10.76 ≤ AFR ≤ 21.53) and compression ratio, r c = 8.0.The objective is to simulate the combustion of fuel-air mixture in a constant-mass variable volume combustion chamber until flame extinction (that is, fuel is totally consumed).Furthermore, the examination of heat loss, combustion efficiency, η b and the corresponding crank angle at which the fuel or oxygen is totally consumed (that is, end of combustion) were also investigated.
In order to simulate the conditions described above and to keep computational effortssimple, the following assumptions regarding the thermodynamics and the chemical kinetics in the combustion chamber of an ICE were made: 1. One-step global kinetics and the following engineering approximation for global reaction was made [18]: [ ] where 4. In the present study stoichiometric air-fuel ratio is 15.05 and combustion is constrained to stichiometric or lean burn conditions.
The value of the parameters, A, a u E R , m and n were chosen in such a manner that they give the best agreement when experimental and predicted flame speeds and flammability limits are compared [19].

Comments
a.The use of global kinetics is hard to justify for modeling combustion in spark ignition engines.However, the only justification for using this model was to illustrate principles while acknowledging that our results may not be very precise.In order to achieve more comprehensive results, computational fluid dynamics codes such as [20] are normally used.b.Assumptions 2 and 3 provide values that give reasonable estimates.

NUMERICAL SOLUTION
In order to simulate the situation described in section 5.2, we proceed as follows: For the case under consideration, Equation (11) transforms to: ( ) ( ) From Equation ( 12), we get: , or ( ) ( ) Therefore: ( ) From the foregoing, the net consumption rate of C 8 H 18 is given by: [ ] Since a single-step global mechanism which also referred to as simple chemical reaction is assumed in the present study, then: 1 kg of fuel + r st kg of oxygen → (1 + r st ) kg of products (29) Where r st is the stoichiometric ratio and is defined as: ( ) From the stoichiometric combustion of n-octane, ( ) On combining Equations ( 21) to (27), we get: 1 1 From Equations (31) to (34), With the initial values/conditions known, Equation (27) becomes: where: ( ) In order to complete the modeling of the right hand side (RHS) of Equation ( 36 , where p j c is evaluated as a function of temperature, T at each instant of time during the computation of Equation (36).Finally, ( ) , where . The volume is computed as shown in Equation (37), From Equation (37), the instantaneous values of can be computed.Furthermore, Equation (36) can now be expressed as: In the present study the Euler's integration computational method was used to solve the resulting model, that is, Equation(38), at every instant of time.The timestep, Δt which was used in this study was 10 -5 s.However, Δt was gradually reduced as T* = (T-T i )/(T ad -T i ) → 1.0, in order to preserve accuracy.Simulations were terminated when 8 18 C H ω ≤ 0 and the flame is extinguished, that is fuel is totally consumed.

Initial conditions
In order to complete the necessary input information, the relevant initial conditions for the first order differential equation which describes the interactions between temperature, pressure and mass fractions are specified thus: • Initial conditions -temperature: T = T i = T amb • (rc) 0.4 at t = 0 • Initial conditions -pressure: p = p i = p amb • (rc) 1.4

Convergence criteria
For the zero dimensional model used in the present study, convergence was obtained after 21 iterations at each time step.The local truncation, discretization and global errors are on the order of O(Δt 2 ), O(Δt) and O(Δt) respectively for the Euler integration scheme.In view of these, convergence criterion was set to a tolerance value of 10 -6 .Therefore, complete calculations are repeated until the final values converge to within the specified tolerance with the initial values.

RESULTS
The results presented in this study were obtained from a simulated 5.734 liter, V8 engine.Table 1 below lists the engine specifications, operating conditions and fuel input parameters.The data presented shows the temporal variation of several important parameters which are useful for characterizing the performance of internal combustion engines at various fuel-air equivalence ratios, φ .The quantities are combustion chamber pressure, rate of change of combustion chamber pressure with time, combustion chamber temperature, combustion efficiency, η b , flame extinction temperature, heat lossand variation of mass fractions of fuel, water vapor, carbon dioxide and oxidizer.The operating conditions investigated are clearly annotated in Figures 1 -12.
Comprehensive discussions of how well the model reproduces the effects of fuel-air equivalence ratio on the combustion characteristics mentioned aboveare presented in the paragraphs that follow.Fuel-air equivalence ratios, φ 0.7 ≤ φ ≤ 1.4 Figures 1 and 2 show the variation of mass burn fraction of fuel and oxygen with time for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4.The data shows that the burn rate characteristics of the fuel and oxidizer are qualitatively perfectly correlated.The characteristics in Figures 1 and 2 show that as flame extinction/flameout is approached, the fuel consumption rate, R fu increases rapidly with temperature (see Figures 3 and 4) for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4.Figure 1shows that the average burn rate frequency (per second), f br (1/s) varies from 11.2 ≤ f br ≤ 137.0 for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4.This is due to the fact that, in a fuel-lean mixture, the flame extinction/flameout limit is governed by the fuel mass fraction.Whereas, in a fuel-rich mixture the flame extinction/flameout limit is controlled by the oxygen mass fraction.It is worth mentioning that in a fuel-rich mixture, the assumption of a single-step reaction is not strictly valid due to dissociation.Therefore, in order to have a closure (that is, the equality of number of equations and the number of species) the watergas reaction must be included in the reaction mechanism.The visual evidence of the foregoing is clearly captured in Figures 1 and 2.
The variation of fuel consumption rate and flame temperature with time for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4 are shown in Figures 3 and 4.
Figure 3 shows that the fastest fuel consumption rate is for fuel-air equivalence ratio, φ = 1.4in the time interval, t such that 0.0 ≤ t ≤ 0.61 ms while the slowest corresponds to φ = 0.7 and the corresponding time interval is 0.0 ≤ t ≤ 0.61 ms.Moreover, Figure 3 shows that for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4, the fuel consumption rate increases monotonically after the initial ignition delay period.Furthermore, Figure 3 shows that the fuel consumption rate is highly dependent on the fuel-air equivalent ratio.The computer model used for this study accurately replicate these trends which have been observed in actual internal combustion engine experimental measurements [19].Figures 3 and 4 showthat after the initial flame development time intervals, which correspond to 0.0 ≤ t ≤ 0.61 ms, 0.0 ≤ t ≤ 0.79 ms, 0.0 ≤ t ≤ 1.11 ms and 0.0 ≤ t ≤ 3.98 ms for fuel-air equivalence ratios 1.4, 1.2, 1.0, 0.8 and 0.7 respectively, the remaining charge in the combustion is then consumed almost instantaneously as evidenced in the rapid rise in flame temperature shown in Figure 4.As can be seen from Figure 4 the time rate of change of temperature is steepest for fuel-air equivalence ratio, φ = 1.4 and least for φ = 0.7.The temporal variation of the characteristics of combustion chamber pressure and rate of change of pressure for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4 are shown in Figures 5 and 6 respec-tively.The figures show that as fuel-air equivalence ratio increases the pressures and the rate of change of pressure increases proportionately as well.However, it can be seen from Figure 5 that at fuel-air equivalence ratios in the range 0.8 ≤ φ ≤ 1.4, the rise in both pressure and rate of change of pressure are quite smooth and somewhat gradual for most portions of the combustion processes, thereafter, a rapid consumption of the remaining charge ensues.However, for fuel-air equivalence ratio φ = 0.7 the pressure characteristics decrease over the flame development time interval and then recover somewhat during the final period of spontaneous charge consumption.This could be attributed to the fact that substantial amount of heat was transferred to the combustion wall due to very slow charge consumption rate.The shapes of the pressure and rate of change of pressure as combustion progresses (Figures 5 and 6) are positively correlated with the temperature characteristics (Figure 4) for fuel-air equivalence ratios, 0.8 ≤ φ ≤ 1.4, except for the case where φ = 0.7.The possible reason for this deviation was stated above.
The results show that it took about 0.61, 0.79, 1.11, 1.89 and 3.98 ms for fuel-air equivalence ratios 1.4, 1.2, 1.0, 0.8 and 0.7 respectively, for the in-cylinder combustion dynamics to reach T* = 1.0.In the last 0.01 ms, for all the fuel-air equivalence ratios investigated the rate of change of pressure, dp dt lies in the range 3.23 × 10 10 ≤ dp/dt ≤ 2.19 × 10 11 Pa/s, while the corresponding flame temperatures vary within the limit 1910 ≤ T ≤ 2810 K.The rapid change in temperature and pressure with corresponding high rate of consum-ption of fuel-oxidizer (C 8 H 18 -O 2 ) mixture characterizes thermochemical explosion, that is, engine knock.This phenomenon is due to the extremely fast interaction between the energy released and the corresponding temperature rise from the combustion reaction which in turn feeds back to produce constantly increasing reaction rates because of the dependence of temperature on the reaction rate, that is, (-E a /RT), where E a is the activation energy.The results of flame extinction temperatures versus fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4 are shown in Figure 7. Figure 7 shows that flame extinction temperatures are positively correlated with fuel-air equivalence ratios.Furthermore, the data show that the simulated temperatures are fairly higher than those typically observed in real internal combustion engines for fuel-air equivalence ratios, φ in the range 1.2 ≤ φ ≤ 1.4.This discrepancy could be attributed to the fact that the effects of wall quenching and radiation were not taken into consideration in the present model since the model was largely designed for initial preliminary/exploratory studies.
The characteristics presented in Figures 4, 7 and 8 can be summarized as follows; increasing fuel concen-tration and temperature results in an increase in flame temperature with concomitant increase in the rate of energy generation.Conversely, when the concentration of oxidizer is reduced, flames with high values of fuel concentration and temperature will require high convective energy losses to induce flame extinction.Equally true; flames with low fuel concentration and temperature are more predisposed to kinetic extinction.Flame extinction is a factor limiting combustion performance in internal combustion engines.Some of the techniques such as advanced fuel-air mixing strategies exhaust gas recirculation (EGR) and staged injections which are used for achieving low emissions in ICEs can be adversely affected by flame extinction.Flame extinction is highly influenced by the operating conditions, for example, local fuel-air equivalence ratio and the reaction kinetics of the fuel.The studies of flame extinction are central to flame characterization and response analysis.Furthermore, such studies do provide data for validation of kinetic reaction mechanisms.High performance engines and propulsion systems frequentlyoperate at extreme conditions near or below the flammability boundary in order to improve energy efficiency and reduce emission.The flammability limit is governed by fuel kinetics and flame radiation.Due to the preferential diffusion effect, fuels with smaller Lewis numbers can burn beneath the flammability limit if strained.That is, a strained/stretched flame can burn leaner than un-strained flames.In summary, flame extinction temperature can serve as a guide to the impact of fuel composition on the extinction strain rate.
Figure 8 shows the graph of the variation of the source term (heat release rate) with combustion duration for fuel-air equivalence ratios, 0.7 ≤ φ ≤ 1.4.From Figure 8 it can be seen that the source term is highest for fuel-air equivalence ratio of φ = 1.4 and least for φ = 0.7 with the magnitudes of other source terms in between, that is, source terms for fuel-air equivalence ratios, 1.0 ≤ φ ≤ 1.4.Furthermore, Figure 8 shows that the leaner a fuel-air mixture is, the longer it takes to burn.It can also be seen from Figure 8 that little changesin fuel-air equivalence ratio, ( φ ~ 0.1) lead to significant changes in the heat release rate.This observation is due to the fact that the relationship between chemical reaction rate and the equivalence ratio is highly non-linear, especially at lean conditions, that is, at φ < 1.0.One of the most important properties of a combustion process is the heat release rate since it characterizes the amount of thermal energy that can be obtained from the oxidation of a fuel/hydrocarbon.The spatial distribution of the source term (heat release rate) is able to provide information concerning localized hot spots which can be used to identify areas of the combustion chamber which might be susceptible to uncontrolled ignition.Moreover, the source term (heat release rate) is very important for understanding and predicting combustion instability.Figure 9 shows the result of combustion efficiency versus fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4.From Figure 9 we can see that combustion efficiency, η b of the engine under investigation are in the range of 94.1% ≤ η b ≤ 94.4% for lean mixtures, that is, for φ < 1.0.Furthermore, since there is insufficient air for complete oxidation of all the fuel in fuel-rich mixtures, that is, for φ > 1.0, the combustion efficiency steadily decreases as the mixture strength becomes richer.As shown in Figure 9, the values of combustion efficiency, η b for fuel-rich mixtures are in the interval 93.8% ≤ η b ≤ 94.1%.In internal combustion engines combustion efficiency is to a very large extent independent of other engine operating and design variables, as long as the engine combustion process remains stable.It is worth mentioning that, in general, compression ignition engines often operate lean and typically have combustion efficiencies of approximately 98%.It is the combustion dynamics elucidated in Figure 9 that provided the impetus for employing lean combustion in most combustion technology applications, such as boilers, burners, furnaces, gas turbines and combustion chambers of internal combustion engines.The various areas of applications mentioned above most often strive to take advantage of the fact that combustion processes operating under lean fuel conditions, that is, φ < 1.0 do have very high combustion efficiency and impressively low emission levels.Since the flame temperatures are generally very low, pollutant formation and emissions such as, NO X are usually very low.
Furthermore, when lean-burn is carried out with excess air for hydrocarbon oxidation, complete combustion of the fuel normally follows, with a concomitant reduction in unburned hydrocarbon and carbon monoxide emissions.However, because of slow reaction dynamics, instabilities, extinction, low heat release rate and sensitivity to mixing that usually characterize lean-burn conditions, the realization of these improvements and achieving the requirements of real combustion systems is usually a formidable undertaking.
In general, the characteristics shown in Figure 9 and similar ones can be used to explore the performance of state-of-the-art combustion technologies utilizing fuelair equivalence ratios, φ < 1.0 and their advantages in achieving present and future requirements of combustion systems.
The characteristics shown in Figure 10 is the relationship between heat loss and combustion duration for fuel-air equivalence ratios, 0.7 ≤ φ ≤ 1.4. in the internal combustion engine been studied.Figure 10 shows that for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4, the rate of heat loss during the combustion period increases monotonically with fuel-air equiva-lence ratio.This could be due to the fact that as the fuel-air equivalence ratio increases the combustion chamber wall and residual gas temperatures increase as well.Furthermore, higher temperatures during the engine cycle results in copious production of radicals during the early stages of combustion; this can sometimes lead to auto-ignition.It is worth stating that maximum temperature and rate of heat loss for the engine under consideration appear to occur at an equivalence ratio of φ = 1.4.From various measurements that have been carried out on real engines and other practical combustion devices, maximum temperature and hence rate of heat loss has often occurred on the rich side of stoichiometric.A plausible explanation for this is as follows: for equivalence ratios, φ ≤ 0.7, the combustion process is limited by the amount of fuel available whereas at equivalence ratios, φ > 1.0, the oxidation process is governed by the quantity of oxygen available.
At intermediate equivalence ratios, that is, 0.7 ≤ φ ≤ 1.4 the combustion process is constrained somewhat by the ease of forming free radicals.It can then be surmised that operating an internal combustion engine slightly rich implies that there is sufficient fuel available to realize this.The interactions of these factors combine to cause the observed characteristics of the rate of heat loss for equivalence ratios in the interval 0.7 ≤ φ ≤ 1.4.
As stated above the maximum rate of heat loss occurs at an equivalence ratio, φ = 1.4 which is higher than for most spark ignited engines which have equivalence ratio, φ = 1.1.This may have to do with the fact that turbulence, mixing characteristics of the combustion chamber and radiative heat loss were not included in our model.
The graphs of mass fractions of carbon dioxide (CO 2 ) and water vapor (H 2 O) produced versus combustion durationfor fuel-air equivalence ratios, 0.7 ≤ φ ≤ 1.4.are shown in Figures 11 and 12 respectively.The graphs show that the trends are positively correlated to a very high degree with fuel consumption rate, see Figure 3.It can be seen from Figures 11 and 12 that the least amount of carbon dioxide (CO 2 ) and water vapor (H 2 O) were produced at fuel-air equivalence ratios in the range, 0.7 ≤ φ ≤ 1.0.This could be due to that fact that the combustion duration was somewhat slow with the concomitant low rate of the carbon dioxide (CO 2 ) and water vapor (H 2 O) production.

CONCLUSION
A numerical simulation code was used to investigate the effects of fuel-air equivalence ratio on some of the important performance characteristics of a 5.734 liter, V8 spark-ignition engine.The combustion process is based on a constant mass variable volume thermodynamic model.The simulation results are valuable in the initial conceptual design phase, during experimental /testing analysis and in diagnosing field problems.The trends of ICE performance characteristics captured by this code were quite similar both qualitatively and quantitatively to their experimentally observed counterparts.The findings from this study gave a comprehensive insight into the relationship between equivalence ratio and the engine performance characteristics investigated in this study.The results are shown in Figures 1 to 12.
In specifics, the conclusions from this study can be summarized as follows: 1.The model used in this study can be used to investigate the variation of key operating parameters, such as pressure, rate of change of pressure, dp/dt flame extinction temperature, combustion efficiency, η b , source term, mass burn fractions and heat loss with fuel-air equivalence ratio, φ .2. The data shows that the burn rate characteristics of the fuel and oxidizer are qualitatively perfectly correlated.The results also show that as flame extinction/flameout is approached, the fuel consumption rate, R fu increases rapidly with temperature for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4.

5.
The results show that the fastest fuel consumption rate was for fuel-air equivalence ratio, φ = 1.4 in the time interval 0.0 ≤ t ≤ 0.61 ms while the slowest corresponds to φ = 0.7 and the corresponding time interval was 0.0 ≤ t ≤ 3.98 ms Moreover, the data shows that for fuel-air equivalence ratios, φ in the range 0.7≤φ ≤ 1.4 the fuel consumption rate increases monotonically after the initial ignition delay period.6.The computed characteristics show that after the initial flame development time intervals, which correspond to 0.0 ≤ t ≤ 0.61 ms, 0.0 ≤ t ≤ 0.79 ms, 0.0 ≤ t ≤ 1.11 ms and 0.0 ≤ t ≤ 3.98 ms for fuel-air equivalence ratios 1.4, 1.2, 1.0, 0.8 and 0.7 respectively, the remaining charge in the combustion chamber was then consumed almost instanta-neously as evidenced in the rapid rise in flame temperature shown in Figure 4.As can be seen from Figure 4 the time rate of change of tempe-rature is steepest for fuel-air equivalence ratio, φ = 1.4 and least for φ = 0.7.7. The results show that as fuel-air equivalence ratio increases the pressures and the rate of change of pressure increases proportionately as well.However, it can be seen from Figure 5 that at fuel-air equivalence ratios in the range 0.8 ≤ φ ≤ 1.4, the rise in both pressure and rate of change of pressure are quite smooth and somewhat gradual for most portions of the combustion processes, thereafter, a rapid consumption of the remaining charge ensues.
Conversely, for fuel-air equivalence ratio φ = 0.7 the pressure characteristics decrease over the flame development time interval and then recover somewhat during the final period of spontaneous charge consumption.8.The results show that it took about 0.61, 0.79, 1.11, 1.89 and 3.98 ms for fuel-air equivalence ratios 1.4, 1.2, 1.0, 0.8 and 0.7 respectively, for the in-cylinder combustion dynamics to reach T* = 1.0.In the last 0.01 ms, for the all fuel-air equivalence ratios investigated the rate of change of pressure, dp/dt lies in the range 3.23 × 10 10 ≤ dp/dt ≤ 2.19 × 10 11 Pa/s, while the corresponding flame temperatures vary within the limit 1910 ≤ T ≤ 2810 K. 9.The data shows that the simulated temperatures were fairly higher than those typical observed in real internal combustion engines for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4.

ПРОУЧАВАЊЕ СИМУЛАЦИЈЕ САГОРЕВАЊА У КОМОРИ ЗА САГОРЕВАЊЕ ПРИ КОНСТАНТНОЈ МАСИ И ПРОМЕНЉИВОЈ
) can be transformed to: 25, n = 1.5, k G is the global rate coefficient, E a is the activation energy, R u is the universal gas constant, T is temperature in Kelvin, m and n are exponential parameters, x and y are the number of carbon and hydrogen atoms respectively in the fuel.2. The specific heats at constant pressure of the fuel, air and products are constant and equal, that is, the mixture, M m = 29.3. Isentropic compression, that is, γ = 1.4 is assumed.Furthermore, it was assumed that p j c = p m c = 1200 J K kg ⋅ and mixture molecular mass, M m = 29.