Mixture Preparation in a Small Engine Carburator Peter Dittrich, Frank Peter MBtech Powertrain GmbH, Germany ABSTRACT The objective of this work is related to the problem of mixture preparation in a carburator of a small 1 cylinder - 2 stroke engine. A enhanced KIVA3v code has been modified in order to get a geometrically simplified but relatively fast and reliable numerical diagnostics tool. Emphasis was placed on idle speed investigation with an unsteady outflow boundary condition. Mixture formation for closed throttle near the nozzle hole was investigated experimentally with a VideoScope System with the goal to derive proper boundary conditions for the numerical investigation. Kiva3v served as a proper an reliable investigative tool to successfully study all relevant physical phenomena i.e. wall-film, spray breakup as well as providing robust numerical integration for several engine cycles. INTRODUCTION Mixture preparation for a small one-cylinder engine with less than 50 ccm at low speed still poses an engineering problem especially when dealing with the problem of engine stalling. From fluid dynamic point of view, the process of a mixture preparation at idle speed load conditions is a quite complex unsteady task. We have been focused mainly on the following location of a liquid injector flow pattern behind the throttle Gasoline drops injected with a small velocity close to throttle s hole into the tube are transported by the flowing stream of air towards the continuously opened and closed outlet. One part of the drops evaporate, other parts stay in a liquid phase and finally some drops stick at the wall and create the wall-film. KIVA3V AS AN INVESTIGATION TOOL An open source compressible, thermodynamic, multi-face and multi-component code KIVA3vrel.2, originally developed at Los Alamos Laboratory, has been used. Even if the original code is suitable mainly for the internal combustion engine calculations, it is a relatively simple task to adapt the code in order to handle the problem of a carburator flow. An accurate spray model is crucial for the air-fuel mixing predictions in a gas-spray system. The following sub-models have been utilized: a) drop wave-breakup sub-model, giving the drop sizes and their distribution, b) droplet turbulent dispersion sub-model, c) drop evaporation submodels, dealing with a change of droplet radius, d) drop interaction sub-model (collisions and coalescences), e) spray wall interaction submodel, reflecting the drops from a solid wall or transforming the drops into the wall-film according to a specific conditions based on the Weber number and the Reynolds number of the impinging droplet. The sub-models b,c,d,e are implemented in the KIVA code, see the KIVA documentation, and have been individually tested. On the other hand, the sub-model a has been programmed in addition, Reitz (1987). DROP BREAKUP SUB-MODEL This sub-model is based on a linearized Kelvin- Helmholtz instability of a stationary, round liquid jet immersed into a quiescent, incompressible gas. The result is a general dispersion equation which relates the growth rate of an initial surface perturbation to its wavelength. Under the assumption that the size of the stripped off product droplets is proportional to the length of the fastest growing surface wave, Λ, and that the rate of droplet generation is proportional to the maximal jet disturbance growth rate, Ω, one obtains the expression for the radius, r, and the time constant, τ, of the stripped off product droplets as τ = 3.726 B Λ Ω a 1 a, r = B 0 Λ ( B 0 Λ a), where denotes the parent drop radius and the constants read B = 0.61 0, B = 10 1. These constants are valid for diesel sprays, for which the breakup sub-model has been originally developed. The rate of change of the radius of the parent drop, a, is given by an exponential law da = ( a r) / τ, r a dt by which the parent drop approaches the stripping drop size asymptotically and its mass decrease is 1
compensated by real creation of product droplets of size r. Notice, due to the uncertainty of the physics of the flow inside the injector and in its vicinity, the breakup time constant B 1 cannot be determined a priory for the nozzle carburator injection. PROBLEM DEFINITION A real shape of the carburator is shown in figure 1. It has been geometrically simplified to be able to create a block structured hexahedral 3D grid by the KIVA pre-processor, see figure 2. Figure 3: Detailed view of the throttle at idle speed mode with the experimental set-up for the videoscope system. Figure 1: Longitudinal section over a real carburator, the throttle is on the right and the choke on the left side. Figure 4: Simplification of the throttle with a small hole, a clipped view. The area of the hole in the throttle is about 2 2 mm. Notice, presence of the choke is not taken into account in all simulations. In reality, the inlet part of the carburator is connected to the filter, not modeled here. On the other hand, the carburator outlet part is connected to a pipe which directs the mixture into a crankcase. The simplified shape of this pipe is shown in figure 5 which also presents the whole 3D-computational domain. Figure 2: Shape simplification of the outer geometry, scale in [cm]. On the next two figures 3 and 4, one can see the inner part of the carburator, for the experimental setup and the numerical simplification. Figure 3 shows the closed throttle with the throttle hole, the idle-speed nozzle, and the Video endoscope (lower right) and the light source (upper side). For the experimental investigations, triggered images acquisition with very low exposure tolerances were taken (AVL 513D). Figure 5: The whole computational domain with carburator and a simplified shape of the outlet pipe. BOUNDARY CONDITIONS The main flow through the above system is driven by the unsteady time and the periodically 2
repeating pressure profiles imposed at the inlet and the outlet parts of the geometry, shown in figure 6. The flow is supposed to be from left to right. All the simulations have been performed in four cycles that in total take 87 ms. The pressure signal is based on experimentation. Figure 7b: The injection flat-shape velocity profiles for liquid fuel. Figure 6: Inlet/outlet pressure profiles at idle speed conditions, black line inlet (filter), red line outlet (crankcase), blue line open outlet (four cycles). One can see that the inlet pressure is constant and approximately equal to the atmospheric pressure. However, the outlet pressure changes as the outlet boundary is continuously opened and closed, hence only the blue part is really applied. The timing for outlet boundary is: opening 2.73 ms, closing 9.87 ms, periodicity 21.43 ms. Also the wall temperature is set to 300 K everywhere in the model (top boundary of mesh). LIQUID INJECTION The liquid fuel is gasoline and it is injected just behind the throttle s hole. Since we deal with flow at idle speed conditions, the injection velocity is supposed to be rather small in order to have the relative velocity between the air stream and the drops high enough. The air stream is significantly accelerated behind the throttle s hole and it leads to breakup of drops and consequently to their evaporation. Note that, the timing for liquid injection is in accord with timing of the outlet boundary (fig. 7a,b). The amount of injected fuel is 5 mg per each cycle and all the drops are injected in one size that corresponds to the hole (in the wall behind the throttle) exit diameter of 0.5 mm. This mass is divided into 300 discrete parcels. The drop initial temperature is 310 K and the injection direction is inclined about 30 deg from the z-axis towards the outlet boundary. The default injector position has distance of Zinj=2.8 cm from the inlet. MESH REFINEMENT STUDY Three different grids have been tested, see figures 8, 9, 10, and the resulting mass flow rate profiles have been compared, see figure 11 1. coarse grid in total 38.000 cells 2. middle grid in total 104.000 cells 3. fine grid in total 205.000 cells Figure 8: Coarse grid, 23x23 cell in cross-section. Figure 7a: Two images from videoscope at idle speed, left side event with no liquid penetration present, right side with fuel vapor complete coverage of nozzle. Figure 9: Middle grid, 34x34 cells in crosssection. 3
occur and only the droplet breakup instead is dominant. This approach leads to the rapid increase of droplets enhancing the process of liquid evaporation. Figure 10: Fine grid, 50x50 cells in cross-section. The above figures represent a clipped view from the inlet towards the outlet part of the computational domain. FLOW PATTERN The flow pattern behind the throttle rapidly changes as the outlet boundary continuously opens and closes. However, a typical vortex flowstructure develops very quickly behind the throttle and it remains there slowing down its rotation even when the outlet boundary is already fully closed. In the next figures 12, 13 and 14, one can see the section-cut over the domain colored by streamwise velocity component (scale in [cm/s]) together with the velocity vectors at different time instances during the fourth injection cycle. The part upstream of the throttle is cut off out from figures for better clarity. Figure 11: Mass flow rate profiles; negative inlet, positive outlet; black coarse grid, red middle grid, blue fine grid. In figure 11, one can see the characteristic overshot in outflow profiles, which occur right after the outlet opening. These peaks slightly increase from cycle to cycle, however the difference between the last two is not so high for the middle grid case. Also the difference between the fine and middle grid results seems to be very small. Because of the exuberant increase of computing time for the finest grid and with respect to the relatively small change in accuracy all the other simulations have been performed on the middle grid arrangement. NUMERCIAL COLLISION MODELING Numerical collision modeling has been studied in many recent investigations. It has been observed, that the collision frequency is proportional to the droplet cell density. Therefore, for the same injection configuration a mesh refinement leads to a higher droplet cell density, which then increases the collision frequency and improves the number of coalescences. This process however counteracts with droplet atomization, thus leading to larger droplets, Tanner (1995). Moreover, the collision model increases the CPU time of the simulation. Due to these reasons, we have decided to switch off the collision model completely, so that no coalescence phenomena Figure 12: Flow pattern, time 67.6 ms, outlet boundary starts to open. Figure 13: Flow pattern, time 70.6 ms, outlet boundary fully open. Figure 14: Flow pattern, time 74.6 ms, outlet boundary fully closed. FUEL EVAPORATION Liquid fuel starts to evaporate just after the injection beginning. This process is strongly supported by the drop breakup. It occurs mainly due to shear acting on the drop surface which results from a high relative velocity between the air stream and the liquid. In figures 15, 16 and 17, one can see a half of the computational domain cut through the XZ-plane 4
again at different time instances of the fourth injection cycle. Several features are captured in these figures and they are summarized in the following points: dots represent discrete parcels colored by their temperature, scale in [K] shadow structures correspond to an isovolume of the fuel vapor mass-fraction ( mfrac >0.4) iso-lines of stream-wise velocity component in the XZ-plane In figure 15, the majority of drops have been injected already during the cycle before (3 rd one). They stay at the wall, contributing to the wall-film and they have a temperature about 300 K. The vapor is situated mainly in the down-stream part of the domain and it is created mainly due to the wall-film evaporation at this time. However, a new set of liquid starts to be injected, see the red parcels having the initial temperature about 310 K. Figure 15: Fuel evaporation, time 67.6 ms, outlet boundary starts to open. In figure 16, there are already a lot of new drops injected, significantly contributing to the fuel vapor cloud. At this time, the outlet boundary is fully open, however the cloud is located in the lower part of the domain only. This is due to the vortex flow pattern behind the throttle. Figure 17: Fuel evaporation, time 74.6 ms, outlet boundary fully closed. WALL-FILM BEHAVIOR The wall-film time changes can be seen in the following figures 18,19, and 20, again related to a different time instances of the fourth injection cycle. The wall-film here is visualized as an isovolume of the wall-film height ( height >1e-4 cm). The figures show the inside view from the liquid injector (red parcels) towards the outlet. Each time when the layer of cells at the outlet boundary (during its opening) is activated as fluid cells, all the mass of liquid in the wallfilm attached to these cells is added to the total mass of liquid fuel that is transported away from the computational domain. Thus the total mass of liquid is conserved. In figure 18, the wall-film is present mainly in the down-stream part of the outlet pipe. New liquid parcels are injected, as outlines by the red dots in the lower-left corner of the figure. One can see, there is no wall-film at the lower strip of the outlet boundary indicating its partially open state. In figure 19, the outlet is fully open, so the grid at the outlet boundary is completely visible. Finally, in figure 20, the outlet is completely closed and it is already covered by a new wall-film from the remaining drops still arriving there. For a better visibility, the drops are switched off in figures 19 and 20. Figure 16: Fuel evaporation, time 70.6 ms, outlet boundary fully open. In figure 17, no new drops are injected. Most of the remaining ones are going to be adhered to the wall after a while. The vapor cloud is now transported towards the throttle due to the flow pattern and the vapor mass fraction is going to become more homogeneous behind the throttle. Figure 18: Wall-film creation, time 67.6 ms, outlet boundary starts to open. 5
Figure 24: Off z-axis configuration, injector distance from the inlet Zinj=2.8 cm. Figure 19: Wall-film creation, time 70.6 ms, outlet boundary fully open. Figure 20: Wall-film creation, time 74.6 ms, outlet boundary fully closed. EFFECT OF INJECTOR ORIGIN The liquid injector has been placed at 4 different positions behind the throttle s hole as it can be seen in the following figures 21, 22, 23 and 24, all for the same time. Figure 21: On z-axis configuration, injector distance from the inlet Zinj=2.4 cm. Figure 22: On z-axis configuration, injector distance from the inlet Zinj=2.8 cm, default. Figure 23: On z-axis configuration, injector distance from the inlet Zinj=3.2 cm. CONCLUDING POINTS A detailed time dependent 3D-numerical study has been performed in order to analyze the flow and processes of fuel evaporation and wall-film creation during a mixture preparation in a carburator. The KIVA3v - code has been partially adapted to handle this problem A mesh refinement study, including three different grids, has been evaluated. As a result, the optimal grid has been chosen for all the other simulations. However the creation of the basic iprep-file for the KIVA pre-processor has been tedious at first. Newer versions of KIVA may prove helpful in adding more grid refinement on unstructured meshes at the throttle hole. The effect of the injector position has been investigated. The results have been reported in terms of cumulative fuel vapor and liquid mass profiles. The numerical modeling shows the capability to rapidly investigate the evaporation process behind the throttle, thus allowing the investigation for further improvements of idle-speed performance for two-stroke engines. REFERENCES [1] KIVA-documentation: http://www.lanl.gov/orgs/t/t3/codes/kiva.shtml [2] Tanner F. X.: Liquid Jet Atomization and Droplet Breakup Modeling of Non-Evaporating Diesel Fuel Sprays, SAE Technical Paper 97050. [3] Stanton D. W., Lippert A. M., Reitz R. D., Rutland Ch.: Influence of Spray-Wall Interaction and Fuel Films on Cold Starting in Direct Injection Diesel Engines, SAE Technical Paper 982584. [4] Reitz R. D.: Modeling Atomization Processes in High-Pressure Vaporizing Sprays, Atomization and Spray Technology, 3, 309. [5] Reitz R.D., Bracco F.V.: Mechanism of atomization of a liquid jet, Physics of Fluids, vol 25, 1982. 6