LES/FMDF of Spray Combustion in Internal Combustion Engines

Transcription

1 LES/FMDF of Spray Combustion in Internal Combustion Engines Araz Banaeizadeh *, Harold Schock, and Farhad Jaberi Department of Mechanical Engineering Michigan State University, East Lansing, MI, Abstract The two-phase filtered mass density function (FMDF) model is employed for large-eddy simulation (LES) of turbulent spray combustion in internal combustion (IC) engines. The LES/FMDF is implemented with an efficient, hybrid numerical method. In this method, the filtered compressible Navier-Stokes equations in curvilinear coordinate systems are solved with a generalized, high-order, multi-block, compact differencing scheme. The spray and the FMDF are implemented with Lagrangian methods. The LES/FMDF methodology has been used for simulations of turbulent combustion in a rapid compression machine (RCM) and in a direct-injection spark-ignition (DISI) engine. For both RCM and DISI engine, the complex interactions among turbulent velocity, fuel droplets and combustion are shown to be well captured with the LES/FMDF. The results for the DISI engine indicate that the size, velocity, evaporation and combustion of the sprayed fuel droplets are strongly affected by the unsteady, vortical motions generated by the incoming air during the intake stroke. In turn, the droplets are found to change the in-cylinder flow structure. Introduction Complicated combinations of turbulent boundary and shear layers and highly unsteady vortical motions with substantial cycle-to-cycle variations (CCV) in internal combustion (IC) engines make the large eddy simulation (LES) an excellent candidate for numerical simulations of fluid flow in these engines. However, most numerical studies conducted so far for in-cylinder flow calculations have been based on Reynolds-averaged Navier-Stokes (RANS) simulations and only few LES of IC engines have been reported. For instance, Haworth et al. [1] conducted LES of nonreacting flow in a relatively simple engine, composed of an axisymmetric -cylinder assembly and a non-moving central valve. Sone et al. [2] and Lee et al. [3] simulated turbulent mixing and combustion in direct injection gasoline and diesel engines with KIVA-3V [4] software as a LES model. They found the predicted LES results to be closer to experimental data than RANS results. Jhavar et al. [5] also simulated turbulent combustion in an IC engine via a KIVA-based LES model. Their simulations of flow in a CAT 3401 engine indicate that the LES is able to predict CCV to some extent, which the RANS is unable to do. They also compared the heat release rate profiles obtained by LES and RANS with the corresponding experimental data, and found the LES predictions to be closer to experiment than RANS. Rapid compression machine (RCM) is a simple device which is used for studying the compression and ignition in IC engines. Wurmel et al. [6] and Mittal et al. [7] used the STAR-CD [8] software for two-dimensional (2D) RANS simulations of RCM. In both works, a creviced was used for minimizing the non-uniform temperature effects generated by corner vortices in front of the flat. Mittal et al. reported that the predictions of RANS with k ε turbulent model are not in good agreement with the experimental data. In this work, LES of two different flows are conducted with our new two-phase combustion model, termed the filtered mass density function (FMDF) [9-13]. The first simulated flow involves the compression and reaction of air or air-ethanol mixture in RCM. The second one describes the two-phase turbulent combustion in a 3-valve direct-injection spark-ignition (DISI) engine. Mathematical Formulation and Computational Method In the LES/FMDF model, the conservative form of filtered compressible Navier-Stokes equations in curvilinear coordinate system [12] is solved with Eulerian finite difference schemes. The unclosed subgrid-scale (SGS) terms, which appear in the filtered equations, are closed by gradient-type closures [14,15]. In conventional * Corresponding author: banaeiza@egr.msu.edu Associated Web site: Proceedings of the 6th U.S. National Combustion Meeting

2 LES methods, the filtered equations for the scalars are solved together with mass and momentum equations. In the scalar equations, the chemical source/sink terms are not closed and need modeling. Here, the subgrid combustion model is based on the FMDF methodology. The chemical source/sink terms are determined exactly with the knowledge of FMDF. The spray (droplet) field is simulated with a Lagrangian model. In this model, the evolution of the droplet displacement vector, velocity vector, temperature, and mass is governed by a set of non-equilibrium Lagrangian equations [16]. The effects of droplets on the carrier gas are included via a series of source/sink terms in the gas continuity, momentum, energy and scalar equations. These source terms are evaluated by volumetric averaging and interpolation of the Lagrangian variables. In the previous applications of LES/FMDF [9-12], the effect of pressure on the scalar FMDF was not considered. This effect could be ignored at low Mach number or constant pressure combustion. In IC engines or supersonic flows, pressure variation can be significant, and should be included in the FMDF formulation. In this work, the FMDF equation is modified to include the pressure effect. More details are given below in the results section. The discretization procedure of the carrier fluid is based on the compact parameter finite difference scheme, which yields up to sixth-order spatial accuracies. The time differencing is based on a third-order low-storage Runge- Kutta method. The FMDF is implemented via stochastic differential equations (SDEs). The most convenient method of solving these SDEs is via the Lagrangian Monte Carlo (MC) procedure [9]. With the Lagrangian procedure, the FMDF is represented by an ensemble of computational elements or particles which are transported in the physical space by the combined actions of large scale convection and diffusion (molecular and subgrid). In addition, changes in the composition space occur due to SGS mixing, droplet evaporation, and chemical reaction. All of these are implemented by a set of SDEs. These SDEs are fully consistent with the original FMDF transport equation. The Lagrangian FMDF represents the gas scalar fields and is used to evaluate the local values of temperature, density and species mass fractions at droplet locations. The droplets in turn modify the species concentration and temperature values of the Monte Carlo particles due to mass, momentum and energy coupling. Hence, the three-way coupling between the carrier gas velocity field, the FMDF scalar field and droplet field are included in the computations. Lagrangian spray equations are solved with nonequilibrium evaporation models via numerical methods similar to that used for FMDF. Spray droplet break-up was performed by the hybrid Kelvin-Helmholtz (KH)/Rayleigh-Taylor (RT) model [18-20]. It is assumed that, the size of initial droplets or parent blobs are equal to the injector nozzle diameter, this rough assumption is then corrected by the KH primary break-up model. After this stage the particles undergo a secondary break-up by the RT accelerative instability model [17]. Results The LES model is applied here to two flow configurations: (1) an RCM, and (2) a realistic singlecylinder DISI engine with moving intake and exhaust valves and. The RCM is a relatively simple compression machine and recently built at MSU s Energy and Automotive Research Laboratory. The stroke and bore of MSU s RCM is 25.4 and 5 cm, respectively. The operational compression ratio is 21. In order to have a uniform temperature distribution in the cylinder, a creviced head is used. The RCM is modeled with a 4-block grid system; the 3D and 2D views of the grid is shown in Fig. 1 (a) and (b), respectively. During the compression, we keep the same number of grids, but compress them as the moves. At the beginning of compression, it is assumed that the in-cylinder mixture is either a homogeneous charge of evaporated ethanol with equivalence ratio of 0.5 or pure air at initial temperature of 393 K and atmospheric pressure. The walls are assumed to be adiabatic. Here, we are interested in fluid dynamics and (single-phase) combustion in RCM. To include the pressure effect, the total derivative of pressure Dp/Dt, as computed by the filtered Eulerian carrier-gas equations are interpolated and added to the corresponding MC particles in the FMDF. Consistency of the temperature predicted by Eulerian carrier-gas equations, solved by the finite difference (FD) method, with the Lagrangian MC temperature in LES/FMDF are dependent on the inclusion of Dp/Dt in the FMDF. This is clearly observed in Fig. 2, where the spatial variations of the air temperature along the RCM centerline are shown. At different times or locations, the values of temperature, predicted by FD and MC are compared in Fig. 2. In this figure, the solid lines, squares, and circles denote the FD, MC with Dp/Dt, and MC without Dp/Dt results, respectively. A comparison between the two MC methods, indicate the critical role of pressure in the FMDF equation when used for the RCM simulation. There seems to be a perfect consistency between the FD and MC parts of the LES/FMDF model with Dp/Dt term included. Despite some vortical fluid flow motions between and cylinder head, the temperature distribution is almost uniform throughout the cylinder. Similar observations are made in the reacting case for an ethanol-air mixture. 2

3 For more complex flows, we consider the in-cylinder flow in a 3-valve DISI engine. The engine has two intake valves and one bigger exhaust valve, with valves being tilted with respect to the. The maximum lifts of the intake and exhaust valves are 11 and 12 mm, respectively. This engine was simulated with the fixed RPM of 2500 and the mean speed of 12.5 m/s. To achieve a high quality grid for a moving, complex cylinder head and moving valves, a multi-block grid was developed. Inside the cylinder, the grid consisted of 32 initial parts which were then merged to form a 9-block grid system as shown in Fig. 3 (a). In this grid system, each valve has a separate block to move in/out and there are three blocks for every three intake/exhaust valves and the corresponding manifolds. By adding the valve and manifold grids to the cylinder grids, an 18-block grid system was created as shown in Fig. 3 (b). As valves move up and down, their corresponding blocks move at different speed (relative to speed) than the surrounding blocks. Therefore, the overlap grids are no longer aligned and some interpolation for transferring the data between the blocks is required. Flow in the 18-block grid was simulated for several cycles using 18 CPUs. After 5 continuous cycles, spray begins at crank angle of 79 o and continued up to crank angle of 148 o. The injector has 8 nozzles which are located between the intake valves. The nozzle diameter is 50 μ m. As described before, the initial fuel droplet or blob has a diameter equal to the nozzle diameter, before it undergoes primary and secondary break-up. Fuel droplets are injected toward the region under the exhaust valve. The droplet distribution patterns during the injection process (at crank angle of 100 o ) are shown in Fig. 4. Those droplets which reach the are modeled to randomly bounce back or to stick to the as a liquid film. Droplets mainly beak up during the intake and early compression stroke period (between crank angles of 79 o o ), but high level of fuel evaporation starts in the middle of compression period as the temperature increases. Combustion is initiated by activating a spark plug in the cylinder head, when the crank angle is 340 o. The spark plug is modeled with a source term in the FMDF equation. This source term increases the energy of MC particles that are close to the spark plug. Consistency of the gas temperature is evident in Fig. 5, where the radial variations of the instantaneous temperature at top dead center (TDC), as predicted by FD and MC, are compared. There is a good agreement between the two methods. The volume-averaged values of in-cylinder temperature for three cases of, (a) motored without spray, (b) motored with spray, and (c) a case with spray and ignition are shown in Fig. 6. Evaporation of the fuel droplets in the case with spray slightly decreases the volume-averaged temperature compared to that in case without spray. Combustion of fuel after ignition increases the in-cylinder volume-averaged temperature to its peak value at TDC, as expected. The FD and MC values of the temperature are shown to be consistent in all three cases. Conclusions The flow in a rapid compression machine (RCM) and a direct-injection spark-ignition (DISI) engine involving complex geometries and moving boundaries were simulated with the newly developed two-phase LES/FMDF model. By adding pressure effect to the FMDF equation, consistency between the Eulerian and Lagrangian parts of the FMDF model was established during the gas compression and constant-volume combustion in RCM. Similar consistency was established in the DISI engine simulations, employing a unique 18- block grid. This indicates the accuracy of the numerical method. For the DISI engine, the analysis of spray and combustion effects on the volume-averaged temperature and vorticity fields indicates that the spray increases the in-cylinder vorticity, while its effect is opposite on the temperature. While the predicted RCM results compare well with the existent experimental data, a more detailed quantitative comparison with the experiment is not possible at this time due to lack of such data. Acknowledgements Financial support for this work was provided by the US Department of Energy and Michigan Economic Development Corporation. Computational resources were provided by the Michigan State University High Performance Computing Center. References [1] D.C. Haworth, K. Jansen, Computers & Fluids 29 (2000) [2] K. Sone, S. Menon, J Eng for Gas Turbines and Power 125 (2003) [3] D. Lee, E. Pomraning, C. J. Rutland, SAE paper [4] A. Amsden, KIVA-3, Los Alamos National Laboratory Report LA MS. [5] R. Jhavar, C. Rutland, SAE paper [6] J. Wurmel, J.M. Simmie, Comb. Flame 141 (2005) [7] G. Mittal, C.-J. Sung, Comb. Flame 145 (2006) [8] PROSTAR Version , Copyright , Computational Dynamics, Ltd. [9] F. A. Jaberi, P. J. Colucci, S. James, P. Givi, S. B. 3

4 Pope, J. Fluid Mech. 401 (1999) [10] S. James, and F. A. Jaberi, Comb. Flame 123 (2000) [11] P. Givi, AIAA J. 44 (2006) [12] A. Afshari, F. A. Jaberi, T. I-P. Shih, AIAA J. 46 (2008) [13] A. Banaeizadeh, A. Afshari, H. Schock, F. Jaberi, DETC , ASME Int l. DET and CIE Conf., Brooklyn, New York, August 3-6, [14] R. Germano, U. Piomelli, P. Moin, W. H. Cabot, Phy. Fluids A 3 (1991) [15] D. K. Lilly, Phy. Fluids A 3 (1992) 633. [16] R. S. Miller, J. Bellan, J. Fluid Mech. 384 (1999) [17] C. Baumgarten, Mixture Formation in IC Engines. Springer (2006). [18] M. Chen, S. Das, and R.D. Reitz, SAE paper , [19] J. C. Beale, and R. D. Reitz, Atomization and Sprays, 9 (1999) [20] G. Stiesch, G.P. Merker, Z. Tan, and R.D. Reitz, SAE paper Temperature (K) FD MC with Dp/Dt MC no Dp/Dt X(m) Fig. 2. Consistency of temperature obtained from finite difference (FD) and Monte Carlo (MC) data at different locations during the compression in the RCM. (a) (a) (b) (b) Fig. 1. 3D and 2D views of the 4-block computational grid used for LES of the RCM. Fig. 3. 3D and 2D views of the 18-block computational grid used for LES of the 3-valve DISI engine. 4

5 Temperature (K) Motored Spray Combustion Crank Angle Fig. 4. 3D contour plots of temperature and the fuel droplets in the DISI engine at crank angle of 100 o. Exhaust manifold and are not shown. Fig. 6. Volume averaged temperature in the DISI engine for the case without spray and combustion (green line with squares), with spray and no combustion (blue line with triangles), and with spray and combustion simulations (orange line with circles). Temperature (K) FD MC R(m) Fig. 5. Consistency of temperature obtained from finite difference (FD) and Monte Carlo (MC) data in FMDF. Radial profiles in the DISI engine at TDC are shown. 5