Using Representative Interactive Flamelets in Three- Dimensional Modeling of the Diesel Combustion Process Including Effects of Heat Transfer C. Hergart Ford Research Center Aachen H. Barths,. Peters Institut für Technische Mechanik RWTH Aachen Abstract Three-dimensional modeling of the diesel combustion process offers a way of gaining a deeper understanding of the physical and chemical processes occurring in a DI diesel engine. Although substantial advances in the field have been made in recent years, the current status is still not satisfactory and no model can be considered fully predictive. Most models employed in describing transient, turbulent reacting two-phase flows tend to focus on either the fluid dynamic aspect of the problem or the chemistry. The Representative Interactive Flamelet (RIF) model features a very detailed description of the chemistry without having to resort to a simplified treatment of the turbulent flow. This is made possible by separating the turbulent and chemical time scales. The model is based on the laminar flamelet concept, which views a turbulent flame as an ensemble of thin, locally onedimensional flame structures. Laminar values of species mass fractions are converted into turbulent equivalents by following a pre-assumed PDF-approach of the conserved scalar, which is the mixture fraction. In this study a two-component model fuel composed of 30% α-methynaphtalene and 70% n-decane was used to represent diesel fuel. A reaction mechanism comprising 118 species and 519 elementary reactions was used to describe the chemistry in the gas phase. The soot model includes a detailed description of benzene and Polycyclic Aromatic Hydrocarbons (PAH) in the gas phase and employs a method of statistical moments to describe formation, surface growth, coagulation, condensation and oxidation of soot particles. Having been applied successfully to numerous engine simulations in the past, the focus of this investigation was to further improve the soot predictions of the RIF model by including effects of heat transfer in the flamelet calculation. Local flame quenching in the vicinity of the, relative to the hot combustion gases, cold cylinder wall is believed to be a main contributor to engine-out soot emissions. In order to capture such local effects an enthalpy defect, accounting for the heat loss from a certain region of the combustion chamber, was introduced. The enthalpy defect can be viewed as an additional flamelet parameter. The model was applied to simulate the combustion at part load in a small-bore single-cylinder HSDI diesel engine and the computational results were compared to experimental data. Introduction As the emissions legislation becomes increasingly stringent, the need to develop a better understanding of the in-cylinder processes that governs the composition of the exhaust gas is imperative. Many concepts aimed at describing the combustion in a DI diesel engine have been proposed in the past, but none can claim to be fully predictive. The extent to which the chemistry of the combustion process can be treated accurately is often limited by computational power. In this study, the Representative Interactive Flamelet (RIF) model was employed to describe ignition, combustion and emissions. A particularly attractive feature of the RIF-model is its capability of separating the chemical time scales from the turbulent ones. This offers a significant saving in the required computational effort. Assuming that the chemical reactions occur in thin layers with length and time-scales much smaller than the those associated with the smallest turbulent eddies, the governing equations can be written as functions of a single conserved scalar, the mixture fraction. Species and temperature are obtained as a function of this independent variable in the laminar flamelet. Information about the turbulent mean values is contained in the mixture fraction probability density function (PDF). The latter is pre-assumed to be described by the, in nonpremixed turbulent combustion, commonly employed β-pdf. For a thorough discussion on the mathematical framework of the model reference is given to Peters pioneering work [16].
The decoupling of the chemical and turbulent time scales enables a very detailed treatment of the chemistry. In this study a two-component reference fuel was used to represent diesel. A reaction mechanism comprising 118 species and 519 elementary reactions accounting for low-temperature degenerate chain branching leading to auto-ignition, high temperature fuel oxidation, and formation and consumption of nitrogen oxides was used [16,18]. The soot model includes a detailed description of benzene and Polycyclic Aromatic Hydrocarbons (PAH) in the gas phase [12] and employs a method of statistical moments to describe formation, surface growth, coagulation, condensation and oxidation of soot particles [7]. The aim of the present study was to improve the prediction of soot emissions at part load by accounting for heat losses to the wall. This was accomplished by introducing an additional flamelet parameter, the so-called enthalpy defect. The improved model has been used to simulate the combustion process in the small-bore Ford DIATA (Direct Injection Aluminum Through-bolt Assembly) engine. In the first section of this paper a way of accounting for wall heat losses, and evaporation in the flamelet is presented. ext, the scope of the analytical study is outlined. This is followed by the results and discussion, preceding the summary and conclusions of the study. Introducing an enthalpy defect to the laminar flamelet concept The flamelet equations constitute a parabolic set of coupled partial differential equations and as such the solution is governed by initial and boundary conditions and the time-dependent scalar dissipation rate. It has been shown by several groups [3,7,12] that a flamelet cannot adjust instantaneously to changes in the flamelet parameters. This initial finding made the interactive flamelet approach supersede the use of stationary flamelet libraries. In the Eularian Particle Flamelet Model proposed by Barths et. al [24] and discussed at length in [5], the probability of finding flamelets attached to fluid is calculated by Eulerian equations. The purpose is to track several different flamelets, each having its own unique history of the scalar dissipation rate, which is a flamelet parameter of profound importance. The use of several flamelets thus models a distribution function of the scalar dissipation rate. On their path through the combustion chamber, the flamelets will also be subjected to wall heat transfer. This effect is accounted for by an additional flamelet parameter, the so-called enthalpy defect, which is defined in the following manner: q = h h ad h where ad is the Favre turbulent mean of the enthalpy that results from an adiabatic volume change and does not take heat transfer, evaporation and viscous dissipation into account, ρ Dh Dt ad = Dp Dt (1) (2) while h is the turbulent mean of the turbulent enthalpy as calculated in KIVA 3V: D h Dp µ t ρ = + h + ρε + Qs Dt Dt Sc (3) The third term on the right-hand side of equation 3 describes heat loss due to viscous dissipation and can be neglected for our purpose. In this paper, the main objective is to investigate the effect of heat transfer on the soot oxidation, which mainly occurs at instants when all of the fuel has already been vaporized. Therefore, Q s was also neglected here. The second term on the right-hand side describes enthalpy diffusion. Integrating the enthalpy diffusion over the whole volume of the combustion chamber, will yield the heat flux to the wall, Q & WHF. This wall heat flux is distributed over the flamelets present in the calculation based on their relative wall fraction. Thus the following entity will hold: Q& WHF = ρ qˆ& (4)
where qˆ& is the Favre-averaged specific enthalpy defect averaged over flamelet. Here the suffix denotes flamelet out of several flamelets. Assuming that the complete enthalpy defect can be looked upon as wall heat losses in the present study, the following expression relating it to the mixture fraction appears adequate: q& ( Z ) = α ) [ Z T ] T ( wall (5),which is commonly used to describe the heat flux transferred to a solid surface at temperature T wall from a flowing fluid stream at steady flow conditions [10]. flamelet and α is the corresponding heat transfer coefficient. q& is the laminar enthalpy defect per unit time of Equation (5) describes the distribution of the laminar enthalpy defect over mixture fraction space. This is related to the global in equation 4, through the mixture fraction PDF in the wall region of flamelet : q& ˆ Z 1 1 r = = q& ( Z) P( Z, x) I dadz Z 0 A = A 144424443 Pwalllayer ( Z) (6) Where I is the probability of finding flamelet at a given location and A is the total surface area of the flamelet facing the combustion chamber. Thus, Pwalllayer (Z ) expresses the probability of finding a certain value of Z in a specific flamelet at the wall. If no part of the flamelet is in contact with a wall, distribution qˆ& is zero and the q& (Z) will automatically become zero for all values of Z. Inserting (5) into (6) and assuming a heat transfer coefficient constant over the flamelet, the latter can be evaluated as: α = Z = 1 Z = 0 ˆ q& [ T ( Z ) T ] wall P walllayer ( Z ) dz (7) Once the enthalpy defect is known as a function of the mixture fraction, the flamelet temperature equation, omitting indices for the flamelets, can be modified to include heat losses: 2 T χ T ρ ρ 2 t 2 Z 1 c p i χ ρ 2c 1 p 1 him& i + ρ q& c p t cp p T c p Z Z i ( Z ) = 0 χ ρ 2Le i c c pi p Yi Z T Z + (8) The first term is the instationary temperature change, the second term is the heat diffusion, whose diffusion coefficient is the scalar dissipation rate. The third and fourth terms expresses convection in mixture fraction space, which arises as a consequence of different diffusion in physical space between the mixture fraction and the temperature. The fifth term is the chemical source term, the sixth is the instationary pressure change and finally, the last term is the enthalpy defect per unit time. The flamelet equations are obtained by applying a universal coordinate transformation of the Crocco-type to the instantaneous governing equations for species and temperature [16].
Scope of analysis The present study aims at displaying the effect of local wall heat losses, accounted for through the enthalpy defect, defined in the previous section on the prediction of engine-out soot. To serve this purpose a threedimensional combustion simulation was performed of the Ford DIATA engine. At the start of the calculation, the combustion chamber consists of a single flamelet, over which the wall heat losses are evenly spread. At a certain time, where soot oxidation starts to dominate over soot formation, a new flamelet is introduced in a wall region where soot is present. The wall heat losses are distributed over the two flamelets according to their relative portion of wall cells. It should be noted that the enthalpy defect is defined in units of energy per unit time and mass, so that the defect will be greater the smaller the mass of the region from which the energy is being withdrawn. The flamelets subsequently mix with each other due to the turbulence. Analogous to the method described by Barths et. al [5], a marker equation for the flamelets is solved in the CFD-code, allowing to track them in their path through the turbulent flow field. Thus it was possible to account for the limited time a burning flamelet is exposed to regions of high wall heat losses. A calculation of the kind described above was compared with a baseline case where no enthalpy defect was accounted for. umerical results Table 1. Engine facts and data for simulations To serve the demonstration of the concept, a part load operating point was chosen for the analytical study, since part load soot emissions, due to the very small difference between two large numbers representing the Engine Displacement Bore Stroke Ford DIATA 300 cm 3 70 mm 78 mm processes of soot formation and oxidation, Injector nozzle 6-hole constitute a particular prediction challenge at ozzle hole diameter 0.124 mm present. Table 1 summarizes some engine Injection pressure 800 bar data and information pertaining to the Spray cone angle [deg] 150 operating point. The two-component model fuel, commonly referred to as the IDEA-fuel, consisting of 30% α-methylnapthalene and Engine speed 2000 RPM 70 % n-decane, has been shown to represent Fuel Two-component model fuel diesel well [4]. The size of a grid cell was (IDEA) approximately 1.1 mm in the radial direction and 3 degrees in the azimuthal direction. Due to the centrally located vertical injector, only a 60-degree sector was simulated in order to reduce the computational effort. 25 000 Injected mass EGR-rate Start of injection Injection duration [deg] 5 mg (partload) 30 % -2 deg. Before TDC 7 computational cells were used for the Lagrangian description of the spray. All models deviating from the standard KIVA-3V sub-models, documented in [1,2], have been summarized in table 2. Table 2 - Summary of modifications to standard KIVA-3V Standard KIVA-3V Modified KIVA-3V Ignition - RIF [16,19] Combustion Arrhenius RIF Emissions Soot formation based on Surovikin [23], Oxidation according to agle and Strickland-Constable [15] RIF Heat transfer Including effects of compressibility Law-of-the-wall and unsteadiness [20]* Wall impingement Rebound-slide with enhanced one droplet breakup [14]* Drop drag Spherical drop Distorting drops [11]* Spray atomization and droplet TAB-model Surface-wave-growth [21]*
breakup Figures 1-4 show contour plots of the soot as a function of engine crank angle in planes cutting through the spray. Attention should be paid to the different color scaling! As can be seen, there is a region of soot arriving at the wall of the combustion bowl at around 8 crank angle degrees after Start Of Injection (SOI). The soot appears to remain close to the wall for a relatively long time. At 14 crank angle degrees (12 degrees after TDC) a new flamelet is introduced in the bowl wall regions where soot is present. Figure 5 displays the distribution of this flamelet at the instant where it was introduced. Figure 1 Figure 2 Figure 3 Figure 4 Due to the strongly different enthalpy defects of the two flamelets, completely different flamelet solutions are obtained after some time. Here, we will focus on the soot predictions. Fig. 7 shows the soot density in units of [mg/m 3 ] as a function of engine crank angle in the two flamelets (flamelet 2 was initiated 12 crank angle degrees after TDC). Superimposed is also the global, weighted soot density. As a result of the heat transfer the temperature in the flamelet closest to the wall is reduced, accompanied by a decline in OH-radicals, which are known to be the most significant species in oxidizing soot under conditions relevant to diesel combustion [22]. Therefore soot oxidation in this flamelet is inhibited as confirmed by the significantly higher soot density of this
flamelet in fig. 7. In mixture fraction space, the effect of eliminating the OH-radicals is to tear down the wall preventing soot from breaking through to the lean side. The soot oxidation in the flamelet accounting for the bulk of the mass (approximately 94%) is seen to progress way into the expansion stroke and little soot remains at exhaust valve opening. Thus, we conclude that the soot remaining in the cylinder at the time of exhaust valve opening originates from the flamelet originally located in the wall region depicted in fig. 5. At exhaust valve opening, the two flamelets are relatively well mixed with each other, i.e. there is no wall-flamelet and the thermodynamic conditions prevailing in the flamelets would offer little explanation as to why one flamelet would contain more soot than the other. It is obvious that the path which the flamelets have taken through the flow field is of major importance. Fig. 6 shows iso-surfaces of flamelet 2 (initial wall flamelet) colored by the soot concentration at 72.0 degrees after TDC. Interpreting the figure, we see that a region of relatively high soot concentration is captured in the bowl near the wall. This is soot that has been transported from another wall region where it was formed. The depicted flamelet also has a region of slightly lower soot density (colored green) located in the squish region (in the volume between the iso-surfaces). This is soot that originates from the cold wall regions of flamelet 2 early in the expansion stroke. Fig. 8 shows a comparison between a calculation including the enthalpy defect and one without. As can be seen, the simulation including the defect comes closer to the experimentally measured value of 1.5 mg/m 3. Further improvement could be expected by better resolving regions of high wall heat transfer by including more flamelets in the calculation. Figure 5 - Initial location of flamelet 2 (wall flamelet) iso-surface colored by soot Figure 6 - late distribution of flamelet 2 ("wall flamelet") - iso-surfaces colored by soot
Figure 7 - Soot density in different flamelets Figure 8 Effect of including an enthalpy defect Conclusions and summary A way of accounting for local heat transfer losses in the combustion chamber of a DI diesel engine was proposed in the framework of the Representative Interactive Flamelet (RIF) model. This was accomplished by introducing a so-called enthalpy defect, which can be looked upon as an additional flamelet parameter. The model is based on the recently developed Eulerian Particle Flamelet Model, in which flamelets, represented by computational particles are monitored in their path through the turbulent flow field, thus taking the temporal development of the flamelet parameters into account. The simulations suggest that soot reaches the walls of the combustion chamber approximately 8 degrees after the start of injection. A flamelet located in these near-wall regions containing soot will experience very different enthalpy defects from one located in the center of the combustion chamber. As a consequence of the significant amount of energy withdrawn from the wall-flamelet, the pool of OH-radicals will eventually be depleted, thus impairing further oxidation of the soot. The study shows that the flamelet, accounting for 6% of the mass, initially located at the wall is responsible for essentially all the soot emitted. Future work will focus on improving the resolution of regions of high wall heat transfer by including more flamelets and refining the strategy determining how to distribute the global enthalpy defect over the various flamelets. Acknowledgement Ford Research Center Aachen, Germany (FFA) would like to acknowledge the very fruitful collaboration with the Institut fuer Technische Mechanik at RWTH Aachen under the supervision of Prof. orbert Peters, without whose assistance the presented work had not been possible. FFA would also like to thank the Engine Research Center in Wisconsin and Prof. Reitz for putting their version of KIVA-3V, from which some of the models used in this work have been taken (marked with an asterisk in table 2), at our disposal.
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