Setting up a comprehensive CFD model of a small two stroke engine for simulation.
A two stroke spark ignition engine employs the power stroke itself to fill the cylinder with fresh charge. Due to this, the inlet charge also works as a medium to scavenge the exhaust products from the cylinder to be followed by the compression and ignition of the charge for the next cycle. This has both advantages and disadvantages. The simultaneous act of exhausting products of combustion and letting in fresh charge in to the cylinder is accomplished by incorporating ports in the cylinder wall which are opened and closed during the movement of the piston instead of the valves in the conventional four stroke engines involving many moving parts with the gears and operating mechanism to open and close the valves at appropriate time of the engine operating cycle.
The major advantage is that there is a power stroke for each revolution of the crank shaft and the disadvantage is the short circuiting of fresh charge into exhaust and escape of the fresh charge resulting in loss of thermal efficiency. Study of the scavenging flow helps in improving combustion, preventing short-circuiting of fresh charge into the exhaust and reducing emission of unburnt hydrocarbons to the environment though the exhaust. After Alfred Jante's  experiments to study the in-cylinder flow pattern in a two stroke engine, many attempts have been made including the use of model engines, flow visualization techniques and flow simulation. Experimental works have been limited to motoring and low speed conditions though some fired engine tests have also been reported. With the advent of personal computers, mathematical models are being applied to simulate the conditions inside the cylinder. The advantages of mathematical models are manifold. CFD allows accurate prediction of the effects of a change in a parameter of engine operation without the exorbitant cost of an experimental setup and in a comparatively shorter duration. Spatial and temporal values of the performance parameters are obtained in a CFD analysis for the entire study volume and the entire period. In this work, the steps involved in setting up a comprehensive model for a CFD study of the gas exchange process of a two stroke spark ignition engine have been described. Crankcase expansion and compression which is vital to the delivery of charge in to the cylinder has been modeled using available facilities of commercial CFD software. The predictions of the CFD study are compared with the results of a FLDV (Fiber Laser Doppler Velocimeter) experiment conducted by Yuji Ikeda [2, 3] et al on a 100cc SUZUKI 2 stroke production line engine for motoring and fired conditions.
Many researchers like Amden  et al, K. V. Reddy  et al, Chen Chengyou  et al, K. D. Raghunathan  et al, Epstein  et al, Todd D Fansier  et al, R Herweg  et al, and Y. G. Lai  et al have studied the two-stroke engine processes. But some of the main features of the present model like the simulation of the port opening and closing and simulation of the piston reciprocation have already been reported by Raghunathan et al and others. Additional feature of the model is the grid structure for the representative volume of the crankcase contents. The unique feature of the model is the simulation of simultaneous expansion and compression of the crankcase as the piston undergoes the compression and expansion strokes. Since the details of the exhaust system of the engine used in the experiment are not available exhaust system has been assumed with representative length and cross sections. To make the model as close as possible to the actual engine a crown piston top is used instead of a flat piston top employed in an earlier work .
The first step in a CFD methodology is the formulation of differential equations for the laws of nature governing the conservation laws, transport laws and source laws. These are generally partial differential equations. An example of such an equation is the Navier-Stokes equations governing viscous flows. Algebraic equations are far easier to solve than partial differential equations. By integrating the partial differential equations over a control volume, the relationship is converted to algebraic equations involving finite difference equations over a number of nodes between the boundaries of the region under consideration. In the age of fast computing facilities, solution algorithms are converted into computer programs and solved using appropriate initial and boundary conditions. Experimentally validated predictions from the CFD programs establish and enhance the reliability, accuracy and efficiency of such predictions. Gosman  et al have suggested that the predictions from mathematical models will depict physical reality with adequately formulated natural laws and finite difference equations, It has also been established that as the number of grids used tends to infinity the correctly formed finite difference equations approach those of the differential equations.
STARCD Methodology 
STARCD is a CFD tool for thermo fluids analysis employing the pre-processing, analysis and the post processing facilities. The main analysis code "STAR" stands for Simulation of Turbulent flow in Arbitrary Regions using efficient finite-volume solution algorithms. Steady and transient, laminar and turbulent flows, Newtonian and non-Newtonian, incompressible and compressible fluids, processes like heat, mass transfer and chemical reaction including combustion and flow in porous media etc. are some of the phenomena analyzed by STARCD. The pre-processing facility allows the user to set up the required solution domain in a model with body-fitted non-orthogonal meshes. The differential equations discussed above for the conservation of mass, momentum, energy etc. for the fluid flow are discretised by the finite-volume method. They are integrated over the individual computational cells and over a finite time increment in the case of transient problems and then approximated in terms of the cell centered nodal values of the dependent variables.
The steps involved in the development of the model are as follows:
(1) Selecting the model for final application based on the minimum errors after a routine grid checking operation from grids created from different modeling methods like (a) from Polar coordinates (b) using Patch method and (c) from Gambit software. Apart from the above, the layer thicknesses have also been varied from 0.25mm to 1mm. Trial runs have been executed to compare the results from 0.25, 0.5, and 1 mm layer models. Having found that the results are consistent thereby ensuring grid independence, 1mm layer model has been selected for saving computer time. The three basic models using polar coordinates, patch method and the Gambit software to create the basic grid structure of a flat top piston layer are shown in Fig 1, 2, & 3. One layer of 1mm crown top piston is shown in Fig. 4
(2) Extruding the grid structure for the displacement volume, the clearance volume and the equivalent crankcase volume.
(3) Developing and connecting exhaust ports to the cylinder after creating and connecting scavenge ports to the cylinder and the crankcase. The vertices of the cells at the ends of the ports connecting with the crankcase are merged with the crankcase so that they represent a common entity of crankcase volume. A plan view of the ports and the orientations with respect to the cylinder are shown in Fig. 5
(4) Writing the code for the moving mesh both for the crown piston and representative crankcase volume and creation of the ATTACH boundaries for scavenge / transfer and exhaust ports to facilitate connection and disconnection of the ports during simulated piston movement. The built-in moving mesh feature of the software enables the simulation of the piston movement of the predetermined layers in stipulated sequence from the BDC to the TDC and back. However the specific features of the software are to be modified to suit the model so that the compression and expansion of the cylinder and the simultaneous expansion and compression of the crankcase contents are simulated conforming to the positions of piston in an actual engine.
(5) Adapting the moving mesh code to suit the following select initial conditions and running the model for a full 360[degrees] crank rotation.
(a) Piston at BDC at time t=0.0 and not employing crankcase expansion and compression. (Fig. 6)
(b) Piston at BDC at time t=0.0 and simulating fully compressed crankcase at t=0.0 and starting to expand after exhaust port closure. (Fig. 7)
(c) Piston at TDC at time t=0.0 and simulating simultaneous crankcase compression up to exhaust port opening. (Fig. 8)
(d) Piston just above the scavenge ports at time t=0.0 and fully compressed crankcase at time t=0.0. (Fig. 9)
(e) Piston at about 60[degrees] BTDC at time t=0.0 when inlet reed valve is about to open with the fully expanded crankcase. (Fig. 10)
(f) Piston at BDC at time t=0.0 and simulating crankcase expansion from BDC itself effectively adding 98cc to crankcase volume when the piston reaches TDC. In this version of the model the analysis is split in to two parts. The second part of the analysis starts from TDC with initial conditions of the fluids set at the values reached at the end of the compression stroke from BDC to TDC but crankcase fluid is assigned atmospheric conditions. (Fig. 11)
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The grid checking results on the models have been listed out in Table 1. It is found that the trial model developed from Gambit contains the least number of errors. The cells with internal angles less than 45[degrees] and more than 135[degrees] of the SUZUKI 100cc Engine model have been due to the ports requiring certain amount of skew. The crack in the model is due to the ports in a detached state at times other than SO to SC. The critical microscopic errors in the model which have to be corrected before the software prepares the model geometrically for analysis are DUPLICATE CELLS SETS, NEGATIVE VOLUME CELLS, and COLLAPSED FACES. Since there were no errors in the model it was possible to run the analyses with the code defined ideal default constants of PISO solution algorithm, like relaxation factor for pressure correction at 0.9, corrector stages at 20, and corrector step tolerance at 0.25, thereby reducing the possibilities of errors introduced due to model building.
Basic Crown Model
The model with the crown top piston has been developed using Gambit software with available data culled out from the published work of Yuji Ikeda  et al. Some of the information not available in the paper has been extrapolated from details available for a similar Suzuki engine of lesser displacement volume. For example the orientation of the ports, the crankcase volume, connecting rod dimension etc. were assumed. The total area of cross section of the scavenge ports is reported in the paper  as 900[mm.sup.2] while the total area of cross section of the scavenge ports of the model developed is 850 [mm.sup.2].
(a) The curvature for the crown top piston model has been designed using the available data.
(b) The skews in the ports have been modeled to represent the actual engine as far as possible. However, small differences are bound to exist between model and the actual engine in the absence of detailed drawings.
(c) An adiabatic wall boundary is chosen for the cylinder and crankcase body. In this condition, no exchange of energy takes place across the wall. The option of specifying an equilibrium temperature of the body attained in an air-cooled environment has not been tried in this work.
(d) For ease of analysis, cylindrical crankcase has been modeled with the same diameter as that of the piston by which either in compression or expansion of the cylinder volume equal volume is subtracted or added to the crankcase volume respectively. The model differs from the actual engine only in the shape of the crankcase and the volume has been extrapolated from a similar Suzuki engine to nearly conform to the actual engine.
(e) The port connections with the cylinder have been styled to conform to the actual engine orientations and positions keeping the cross sectional area of scavenge ports nearly equal to that of the actual engine.
Ports and Crankcase
The engine described in the FLDV experiment has two scavenge ports on either side of the exhaust port and two ports of smaller cross sectional area opposite to the exhaust port. The nomenclature "scavenge ports" is used in the paper for all the above ports. The same terminology has been adopted in this work also to describe the ports. Crankcase volume has been approximated to about 333cc in the fully expanded condition. The adoption of the crankcase as a cylinder of equivalent volume will not greatly influence the analysis results since the port sizes and orientations have been maintained to match the actual engine. Hypothetically, though the displacement volume of the actual engine is 98cc, effective crankcase expansion may be considered to take place only when the volume is fully isolated after the closing of the scavenge port till the inlet reed valve opens which is normally 600 BTDC. Similarly effective crankcase compression may also be considered to start only after inlet reed valve closes at approximately 60 degrees ATDC and continue till the opening of scavenge port. However to study the efficacy of this hypothesis two sets of model simulation have been carried out. One of the analyses run is with a model assuming that cylinder compression takes place only after the exhaust port closure to the TDC equal to 30mm of the stroke and another version with simultaneous crankcase expansion from the scavenge port closure continuing up to the inlet reed opening. Another set of analysis is run with the cylinder compression assumed to start at BDC and continuing till TDC and the crankcase expansion to start at BDC and continuing till TDC.
Moving Mesh Code
In the version of the STARCD software used, the code for simulating the reciprocating piston has to be written manually. The provisions of the software in respect of the moving mesh needs to be suitably adapted to the requirement of the crown top piston. The problem gets further complicated for simulating simultaneous expansion and compression of the crankcase volume corresponding to the piston displacement. Having resolved this aspect of the simulation it becomes fairly easy to simulate the port opening and closing. This is accomplished by the Arbitrary Sliding Interface (ASI) facility that is in-built in the software which allows the boundaries to be shared by the ports and the corresponding piston cross sections so that physical connectivity is established during the port opening periods. Once the piston crosses these ports in its upward movement they are disconnected and act as individual walls.
The external cells of the displacement volume considered as cylinder contents for analysis has been selected as an adiabatic wall. Fixing an equilibrium temperature to the body has not been attempted in this work since the focus of the study is the velocity profile inside the cylinder and the crankcase pressure. All the ports connecting the cylinder wall have been designated as ATTACH boundaries as explained above. The extreme face of the extension from the exhaust port is designated as an Exhaust boundary. Different region types like Wall, Negative Inlet, Pressure and Outlet assigning different values for independent variables have been tried for this boundary to achieve the best match with the FLDV experiment curves. Many options were tried to represent the inlet reed principle in the model. The displacement volume of 98cc is represented by the expanded volume of the 50 layers of piston. This volume gets compressed during compression stroke and correspondingly crankcase volume expands developing negative pressure inside the crankcase. In an ideal situation pressure inside the crankcase becomes atmospheric after fresh charge enters through the inlet reed and starts getting compressed when the reed valve closes and the cylinder volume undergoes expansion. Letting in or injecting further amounts of charge therefore increases the mass held in the cylinder leading to the conclusion that no further charge is to be added through the inlet. The inlet boundary therefore has been designed as an adiabatic wall.
The number of initial conditions employed has been explained above. Many analyses have been carried out to establish the initial condition which provides the optimum agreement with the experimental values. Since the software automatically compresses the cylinder contents irrespective of whether the cylinder mass is isolated or not, it is very essential to adopt the different starts as mentioned above to observe the fluid behavior. In each of these instances barring that of the start at TDC, the initial pressure for Material 1 representing the cylinder contents has to be atmospheric. For the start at TDC the pressure and temperature values are initialized as per the values obtained while running the analysis with either option (a) or (b). And for the Material 2 representing the crankcase contents the pressure value has to be atmospheric barring that for option (b), namely starting the analysis at BDC the value has to be initialized as per the values obtained by employing other options. For the Material 3, the Exhaust contents, the initial value for pressure has been varied for observing the effect on the gas exchange process. It is to be noted that for the analysis with TDC start the crankcase pressure is initialized as atmospheric and the ports are all disconnected and hence the values are expected to reflect the actual conditions recorded and reported in the FLDV experiment.
As explained above, the analysis assumes the cylinder contents at 98cc of air with standard values of density. Whether the analysis is carried out with full throttle or part throttle, the initial volume at BDC remains the same which is equal to the displacement volume and the clearance volume put together. The variable which can simulate the throttling is the density of the charge which can vary the mass trapped in the cylinder at BDC. But the density of Material 1, the cylinder contents, is solved for the cell range and for every time step using ideal gas law and as a function of local pressure, temperature and species concentration. The method of adopting this for part throttling conditions has not yet been perfected. Hence the present analysis has been carried out for full throttle conditions only.
Results and Discussions
The representative results of the analysis carried out by running the crown piston top model of the 100cc SUZUKI spark ignition engine with all the initial positions of the piston listed above and with the various boundary conditions for an engine speed of 3000 rpm are given in the following graphs. (Fig. 12, 13) The crankcase pressure values are from a location near the scavenge port bend close to the port opening and the port velocity values are from a probe location in the centre of one of the scavenge ports 22mm below the edge of the port as in the FLDV experiment . It is seen that the values from CFD analysis almost match the FLDV values in the case of velocity and nearly so in the case of crankcase pressure. However there are minor deviations like the peak pressure values and the negative velocity values near crank angle corresponding to the scavenge port closing position.
There is also a phase lag in the FLDV values attributable to the inertia of the moving mass. Yuji Ikeda  et al in their work have explained that the negative values are due to leakage past the piston. Simulation of these crevices is rather a cumbersome exercise and is not attempted since the aim is only to verify if the model developed for the engine under consideration and run with initial and boundary conditions is able to represent the actual engine to a large extent. The gradual positive increase in crankcase pressures beyond the scavenge ports up to the inlet reed opening quite contrary to the expected drop in pressure due to expansion of crankcase volume while the cylinder contents are being compressed has not been explained by Yuji Ikeda  et al but could only be assumed to be due to the same phenomenon of leakage past piston and probably encountered in the experimental engine since results from other engine tests do not report this abnormal increase of crank case pressure during crankcase expansion .
The sharp drop in crankcase pressure seen in the experimental values but missing in the CFD results can be due to the inefficient emptying from cylinder to exhaust through the attachment boundary model in the code. It has not been possible to assign values and vary the parameters for this boundary. Improvements in the model with full exhaust system including the silencer etc. to study the effect of downstream conditions in the gas exchange process can possibly provide closer results. Location of exhaust pressure probe has not been specified in the details of the FLDV experiment2 and hence it has not been possible to compare exhaust pressure with results of CFD analysis. Negative crankcase pressures in the analysis graphs gradually increase beyond inlet reed opening but do not attain atmospheric conditions. It is possible to conclusively comment and modify the inlet conditions only after inlet system simulation with all the individual components in place. In actual working of the engine crankcase gets filled with fresh charge because of the negative pressure inside the crankcase due to which crankcase pressure tends to reach atmospheric conditions gradually some degrees before TDC and continues to be so for some degrees after TDC. The work to simulate this condition in the CFD software, STARCD, by overcoming certain inherent limitations is still incomplete.
Velocity patterns at the time of gas exchange between exhaust port opening to exhaust port closing are shown in Fig. 14, 15 and 16.
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It is clear that the gradual shift from negative pressure to near atmospheric pressure in the crankcase pressure cannot be reproduced in the CFD run. At best the values can match the figures of the FLDV experiment and the actual engine only up to the opening of the reed valve and after its closing. However the positive pressures can be simulated temporally and spatially to a great degree of agreement with actual values with the CFD analysis using an initial condition of near atmospheric pressure close to the inlet reed valve opening around 60[degrees] BTDC and the closing of the valve near about 60[degrees] ATDC. Since the scavenge port opening and closing positions are known accurately the crankcase compression reported in the analysis can be good guide and the velocity values obtained can be relied upon to work out improvements in the engine design. With further work and with improved versions of STARCD, the limitations experienced due to the software could be minimized and part throttling conditions could also be simulated and studied to achieve the ultimate goal of overcoming the biggest disadvantage in a two stroke engine, namely short circuiting.
 Jante., A., 1968, "Scavenging and other problems of two-stroke cycle sparkignition engines," Soc. Of Automot. Engineers Transactions, 77, pp. 1804-1824.
 Ikeda, Y., Hikosaka, M., and Nakajimi, T., 1991, "Scavenging flow measurements in a motored two-stroke engine by fiber LDV, " Soc. Of Automot. Engineers Transactions, 100, pp. 981-989.
 Ikeda, Y., Hikosaka, M., Nakajima, T., and Ohhira, T., 1991 "Scavenging flow measurements in a fired two-stroke engine by fiber LDV," Soc. Of Automot. Engineers Transactions, 100, pp. 990-998.
 Amden, A., A., Butler, T., D., O'Rourke, P., J., and Ramshaw, J., D., 1985, "KIVA-A comprehensive model for 2-D & 3-D engine simulations," Soc. Of Automot. Engineers Transactions, 94, pp. 4.1-4.15.
 Reddy, K., V., Ganesan, V., and Gopalakrishnan, K., V., 1986, "Under the roof of the cylinder head experimental study of the air movement in a two-stroke engine," Soc. Of Automot. Engineers Transactions, 95, pp. 1894-1919
 Changyou, C., and Wallace, F., J., 1987," A generalised isobaric and isochoric thermodynamic scavenging model," Soc. Of Automot. Engineers Transactions, 96:(4), pp. 933-947.
 Raghunathan, B., D., and Kenny, R.G., 1997, "CFD simulation and validation of flow within a motored two-stroke engine," Soc. Of Automot. Engineers Paper 970359.
 Epstein, P., H., Reitz, R., D., and Foster, D., E, 1991, "Computations of a 2-Stroke engine cylinder and post scavenging flows," Soc. Of Automot. Engineers Transactions, 100, pp. 1014-1028.
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 Lai, Y. G., Przekwas, A., J., and Sun. R., L., T., 1993,"Three-Dimentional Computation of the Scavenging Flow Process in a Motored Two-Stroke Engine," Soc. Of Automot. Engineers Transactions, 102, pp. 57-73.
 Hariharan, R., and Krishnamoorthy, J., 2006, "CFD study of turbulence and its enhancement on a small two-stroke engine model, "From Scientific Computing to Computational Engineering, Athens, Greece, pp. 356-363.
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Ramamoorthy Hariharan (1), N V Mahalakshmi (2) and Jeyachandran Krishnamoorthy (3)
(1) Department of Mechanical Engineering, C.E.G. Anna University Guindy, Chennai, 600 025 Email: firstname.lastname@example.org
(2) Department of Mechanical Engineering, C.E.G. Anna University, Chennai-25, India
(3) Formerly of Department of Mechanical Engineering, C.E.G. Anna University, Chennai-25, India
Table 1: The results of the operation of check grid command on the three trial models and the final SUZUKI 100cc Engine Model. SUZUKI ERRORS/WARNINGS POLAR PATCH GAMBIT 100cc TOTAL CELLS 115164 74529 67452 329130 IRREGULAR CELLS 1344 1344 0 0 DUPLICATE CELLS SETS 0 0 0 0 CONCAVE CELLS 0 0 0 0 CELLS WITH COLLAPSED 0 0 0 0 EDGES FACE WARPAGE GREATER 0 0 84 0 THAN 45.00 INTERNAL ANGLES <45 OR 17136 9936 6732 25654 >135 INTERNAL FACE ANGLES 0 180 3940 17747 <45 OR > 135 NEGATIVE VOLUME CELLS 0 0 0 0 CELLS SEEM TO RESIDE IN 0 0 0 0 OTHER CELLS CELL CENTROIDS IN OTHER 0 0 0 0 CELLS CRACKS 0 47 0 1484 COLLAPSE 0 1344 0 0 CELL CONNECTIVITY ALL ALL ALL 3 groups RATIO OF SMALL TO 23436 12096 2 58 LARGEST FACE AREA <0.2 TETRAHEDRAL QUALITY NONE NONE NONE NONE NOTE: SUZUKI 100cc is a complete model with ports. Cracks are due to the ports not being "ATTACHED". Few non-severe errors not affecting the geometry in the SUZUKI model are due to the skew in the ports.