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Simulation Strategy and Analysis of a Two-Cylinder Two Stroke Engine Using CFD Code Fluent Dalibor Jajcevic, Raimund A. Almbauer Christian Doppler Laboratory “Thermodynamics of Reciprocating Engines”, Graz University of Technology, Austria Stephan P. Schmidt Institute for Internal Combustion Engines and Thermodynamics, Graz University of Technology, Austria Karl Glinsner BRP Rotax Austria

ABSTRACT Successful simulation of processes in a two-cylinder two-stroke engine involves the interaction of various physical models operating in a three-dimensional (3D) geometry and besides, additionally with moving boundaries. The complex physical phenomena inside the engine such as turbulence, phase change, chemical reaction, etc. increase the time of calculation and thus make it impracticable for the development process of a new engine. The time of calculation can be reduced considerably with a smart simulation strategy and therewith the simulation produces successful results within a shorter computational time. This paper discusses the simulation strategy of a two-cylinder two-stroke engine with a gasoline direct injection using the commercial CFD Code Fluent 6.3.26. This code can be used for a spectrum of technical problems, although it has some limitations in the use for the simulation of the internal combustion engine (IC engine). In this paper, the solution to overcome these limitations is shown and the requested settings for the successful simulation of a two-cylinder two-stroke engine are presented, i.e. the specific boundary condition for a two stroke engine such as the reed valve model using user defined functions (UDF), the setting of parameters for the discrete phase model (DPM), the combustion model, etc. A good agreement between the simulation and test bench results indicate the applicability of this simulation strategy and the used settings.

1. INTRODUCTION State of the art for the simulation of two-stoke engines is the restriction to only one or even a half of a cylinder, exhaust, intake ports and crank case using symmetry boundary conditions [4, 5]. The simulation of a two-stroke two-cylinder engine requires the simulation of the complete geometry with both cylinders and the complete exhaust port (see Figure 1). In this engine, the cylinders are coupled a two into one exhaust system. The intake ports and the exhaust ports are open simultaneously over a long period of the cycle and the gas dynamic inside the exhaust system has a dominant influence on the scavenging process and further on the mixture formation inside the cylinders. The simulation of only one cylinder causes an incorrect gas dynamic inside the exhaust pipe and further leads to unrealistic simulation results. Thus, in order to get effective and significant results, the simulation of the complete unaltered geometry design is required. The increase of the investigated domain increases the calculation time and makes it costly and impracticable in the daily work of an engineer. Anyway, with a clever strategy the simulation of the complete geometry can be successfully realized in an acceptable time.

EASC 20094th European Automotive Simulation Conference

Munich, Germany6-7 July 2009

Copyright ANSYS, Inc.

Figure 1: Two-stroke two-cylinder engine

2. SIMULATION STRATEGY In general, CFD simulations consist of following three basic steps: pre-processing, solving, and post-processing (see Figure 2).

Figure 2: Basic steps of a CFD Simulation In the pre-processing step, the geometrical flow model is created. In this steep the aim of the simulation is defined and the primary problems must be analyzed. The next step deals with the generation of the grid. In addition, the injector model has to be calibrated on a spray chamber geometry in order to be able to compare to experimental data. The boundary conditions stem from test bench results and from previous investigations, so that an additional one-dimensional (1D) simulation was not required. The detailed description of the applied boundary conditions can be found in the next chapter of this paper. In this simulation the pre-processing phase takes approximately 15 workdays on a 3333 MHZ 4 core PC, from the start of pre-processing to the start of simulation. This phase of the simulation does not offer a lot of possibilities to reduce its duration. It mainly depends on the engine geometry and the availability of the required data. On the other hand, it is also recommended to carry out a very detailed analysis of the available data and the desired aim of the simulation. A mistake in this phase usually becomes evident not before the post-processing phase. This can cause incorrect results and a considerable increase of the simulation time due to a rerun. The duration of the second phase of the simulation depends on the model size and settings; this means the number of the 3D cells, interaction and selection of physical models etc. The user of the CFD software chooses the models, determines the strategy, and therewith directly influences the success of the simulation. A good example for the importance of the simulation strategy is the investigation of a two-cylinder two-stroke engine. The main challenge is to achieve a unchanging cyclic condition of the gas dynamic inside the exhaust system, which requires the calculation of several revolutions. This has to include all processes inside the two-stroke engine which are: fluid flow, heat transfer, fuel injection, mixture preparation and finally combustion. Some of these processes are a perfect repetition e.g. the simulation of the second cylinder doubles the time consummation without real new




results. Other processes are not in an equilibrium state after one cycle. For instance, the droplet concentration inside the engine accumulates over the cycles and increases nonlinearly the time of calculation (two injections per revolution and additionally the calculation of the several revolutions). Furthermore, to smooth out bad initial conditions is not trivial. The effects are self energizing as in the first several revolutions bad initial conditions lead to wrong values in the combustion process. This incorrect results lead to a wrong pressure difference between cylinder and exhaust pipe during the opening phase, which again leads to improper conditions for the scavenging process and the next combustion. In this case, the time for the calculation increases significantly, to achieve unchanging cyclic conditions in the whole engine. Hence, the straightforward simulation of the two-cylinder two-stroke engine is time consuming and impracticable for the development process of a new engine where fast results are required. The calculation time in this phase of the simulation can be considerably reduced by the use of a smart simulation strategy. This strategy can be divided into two following steps: 1. Simulation of a converged scavenging process 2. Simulation of injection and combustion In the first step of the strategy the discrete phase model (DPM) and the combustion model are switched off. At a selected position of the piston (in this simulation at 30 °CA after TDC) the volumes of the cylinders are every revolution initialized with the pressure, the temperature, and the accordant composition of the exhaust gases. On one hand, this strategy accelerates significantly the time of the calculation, as injection and combustion is missing. On the other hand the condition inside all parts of the engine achieves a steady condition within three or four revolutions. In the second phase, the DPM and the combustion model are switched on to simulate the injection and combustion processes. Using this strategy, the simulation time of the two-stroke two cylinder engine is reduced to about three weeks for the solving. The last phase of the simulation concludes the post-processing and the analysis of the results. This phase can only be accelerated by the use of automatic evaluation procedures. In this case it took a week.

3. MODEL BUILD-UP The grid generation for the real geometry of the two-cylinder two-stroke engine is part of the pre-processing phase. The build-up of the geometry was carried out using the conventional CAD software package CATIA V5R16. The creation of the mesh is heavily dependent on some techniques, such as automatic meshing, multi-block domain and arbitrary mesh interface. Detailed descriptions of these techniques can be found in [1] and [2]. In order to simulate the moving piston, a hexahedral mesh was created inside the cylinder and inside the moving part of the crank case using the software GAMBIT. For the coupling methodology between the multi-block domains the standard arbitrary mesh interface technology of the FLUENT CFD software package was used [1]. All together 20 interface couplings were used for the whole engine. These include the couplings between the 3D domains of the cylinder and the exhaust ports, the cylinder and the intake ports, as well as the couplings between the crank case and the intake ports domains. The grid structure contains approximately 530.000 cells at TDC and is composed of seven main blocks – the cylinder 1 and 2, the crank case 1 and 2, the intake ports 1 and 2 and the exhaust port. The simulation of the two-cylinder two-stroke engine has to deal with two moving cylinders with a time delay of 180 °CA. The piston moving is implemented using a layering moving methodology (a detailed description can be found in [1]). In the window “Dynamic Mesh Parameters” of FLUENT the requested settings for the piston moving can be defined, such as engine speed, crank period, crank angle step size, piston stroke etc. In the window “Dynamic Mesh Zone”, the moving direction is set to 1 respectively to -1 for the z-axis for the two cylinders. Of course, the pistons have two differences TDC-positions, 0 °CA and




180 °CA. The curve of the volume over crank angle is presented in Figure 3. The value of the volume shows a good correlation between the curves in BDC and TDC position of the piston. At 90 and 270 °CA a deviation can be seen, which is erroneous and caused by the standard moving function in FLUENT (further, Standard Moving Function SMF). One possible solution for this problem is the use of the SMF “**piston-full**” model for the first cylinder and a profile for the movement of the second cylinder.

Figure 3: Volume over crank angle for both cylinders However, the value of the volume for both cylinders at 90 and 270 °CA must be equal. In Figure 3 the light blue curve “Cylinder 1 – SMF” and the blue curve “Cylinder 2 – Profile” have the same value at 90 and 270 °CA, what confirms their correctness.

4. SPRAY CALIBRATION The employed injector is a standard automotive high pressure injector, with six streams, capable for injection pressures up to 150 bars. The injector is mounted in the cylinder head coaxial with the cylinder axis. Due to an asymmetric spray axis offset of 54.5°, compared to the injector axis, the fuel spray is directed to the opposite side of the exhaust port, in order to reduce the scavenging losses.

Figure 4: Spray calibration The spray model was chosen and calibrated by the use of experimental data. The injection into a simple shaped cylindrical spray chamber was simulated for different spray settings and parameters. The measurements included timing of the spray, angle and penetration of the injected fuel. This calibration of the injector in advance for a simple geometry without initial air flow is essential for the accuracy of the spray model. After this analysis the spray model can be implemented in the complete engine simulation. The injector calibration in the CFD

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simulation consists of the three basic steps: spray classification, model settings, and analysis. The first step comprises the spray classification and the calculation of the dimensionless Reynolds and Weber numbers. For the better understanding of the spray behaviour and for the subsequent choice of the correct model, a spray classification is recommended. The requested data for the injector calibration are presented in Table 1. In the simulation n-Heptan is used as medium as well as in the measurement. The first step consists of the calculation of the mean velocity, applying the Bernoulli equation (1) with cq=0.7 (flow coefficient according to [9]), the pressure difference, and the density of the fuel. The flow coefficient depends on the Reynolds number which is calculated according to equation (2). In [9] can be found that for a Re number greater then 250 the flow coefficient remains constant with the value of 0.7. In this simulation, the Re number is 45525, calculated with the pressure difference of 100 bars and fuel data.

smdpcv

T

q 119

21 ==ρ

(1)

455252

==ρ

ρμ

dpdR Te (2)

Table 1: Data for injector calibration

Data for Injector Calibration – Medium n-Heptan C7H16 Density fuel ρT[kg/m³] 684 Density gas ρG[kg/m³] 1 Viscosity μT[kg/m-s] 0.000409 Surface tension σT[Nm] 0.0198263 Diameter bore dA[mm] 0.4 Diameter droplet dT[mm] 0.16 Rail pressure prail[bar] 100 Injection time tinj[ms] 1.5 Flow static Qstat[g/min] 615.5 Flow dynamic qdyn[mg/hub] 14.8

Using the calculated mean velocity the Weber number (equation 3) results in the value of 115.

1152

=⋅⋅

=T

TTG wdWeσ

ρ (3)

The Weber number is a reliable indicator for the atomization of the spray and it is helpful for the choice of the atomization models. We > 100 indicates a catastrophic atomization of the droplets. Further information about the classification of the droplets atomization in dependence on the Weber number can be found in [10, 11]. The catastrophic atomization appears in the flow where the aerodynamic forces dominate and essentially influence the breakup of the droplets. This means that the breakup of the droplet is induced by the relative velocity between the gas and the liquid phase of the injected fuel. As the actual Weber number was above 100, the WAVE breakup model was chosen and the standard constants were kept. An alternative to the WAVE model is the TAB model, which is appropriate for low-Weber number flows (We < 100). This model is based upon Taylor’s analogy between an oscillating and distorting droplet and a spring mass system. A detailed description about these models can be found in [1].




During the injection of a GDI system the mass flow and the velocity of the injected droplets are not constant. For a realistic simulation of an injection process a injection rate for the mass flow and velocity is required, as the change of the velocity gradients has an important influence on the penetration of the spray and therewith directly on the results of the simulation.

Figure 5: Injection rate over time Figure 5 shows the used simplified injection rate distribution for the simulation of the spray. The x-axis shows the standardized duration of the injection, the y-axis represents the standardized injection rate. From the start of the injection to approximately 10% of the total injection time the injection rate increases up to 140% of the mean value. This implies that during the opening phase of the needle, the droplet velocity achieves its maximum. This is realistic as during this phase the flow area is still reduced and only a very high rail pressure can cause the peak mass flow. After this phase, the rail pressure decreases and therewith the values of velocity and mass flow. In Figure 5 the five blocks defined for FLUENT can be seen, which should represent the injection. As the injector consists of six streams and as each stream is modelled by five injections the total number of 30 injections has to be simulated for each cylinder and each cycle.

On the one hand an increasing number of defined injections would increase the accuracy of the results but on the other hand it is time consuming in the pre-processing and the solving phases of the simulation. Namely, in the pre-processing phase the 30 injections for only one cylinder have to be defined consisting of position, start, and stop of the injections. After the first injection, the user has to define the same data for the second cylinder. As the simulation must be carried out for several revolutions, the injection positions occur alternating between the two cylinders and additionally for the start and stop of each injection. It is necessary as FLUENT does not allow the automatic periodical repeating of the injection every 360 °CA. However, the simulation of the injection process with FLUENT is possible, but requests additional time losses in the solving process. A possible solution of this problem would be an option for a profile definition for mass flow, velocity, droplet diameter, and cone angle. Additionally, an option for the automatic periodic repeating of the injections every 360/720 °CA is required as well. With these changes a continuous simulation would be possible, wherewith the duration of the solving process can be seriously reduced.




Figure 6: Comparison of the injector simulation with test bench results Figure 6 shows the results of the simulation of the injection phase and the comparison with the experimental data (last phase of the injector calibration). The results show a good agreement from the point of view of spray angle and penetration. The necessary data for the injector calibration are taken from Table 1.

5. REED VALVE MODEL AS A BOUNDARY CONDITION The simulation of a two-stroke engine requires a reed valve representation at the inlet boundary or a complete simulation of the moving reed valve together with the intake port. A complete 3D modelling of a reed valve is time-consuming, as it needs the coupling of the CFD code with a finite element code (FEM code) for the deformation calculation of the valve in combination with a moving grid in the CFD code. The simulation of the exact movement of the valves of a two-stroke engine can often be replaced by a reed valve model, especially when the influence of the reed valve on the flow situation inside the cylinder can be neglected. Usually the read valve boundary conditions stem from a 1D simulation and they are implemented into the 3D code as an unchangeable profile. The disadvantage of this method is that the boundary conditions are constant and the transfer of information between 3D domain and the boundary condition is missing. To overcome this disadvantage an adaptive boundary condition was generated. The basic idea is to change mass flow during the simulation depending on the pressure difference between the crank case and the section upstream of the reed valve. This leads to a quasi self-control of the sucked mass and solves the above-mentioned problem. The disadvantage of this methodology is a constant pressure outside of the 3D domain, upstream of the reed valve. The basic investigation of this reed valve model can be found in [12]. For this simulation the model was changed and optimized. The aim is that the mass flow is calculated in dependence of the pressure difference applying the mass flow equation (4).

(4)

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+κκ

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κκ

ρρ

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12

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in

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in

out

outoutflowarea p

ppppAcm

areac … correction factor flowA … flow area




outρ … density outside inp … pressure crank case outp … pressure outside

κ … ratio of specific heat

The correction factor areac is the ratio between the flow area and theoretical flow area and it can be calculated from equation (5) based on the experimental data.

theo

sideflowwidthpvalvelift

theo

flowarea A

cbhAA

c⋅⋅

== Δ )( (5)

theoA … theoretical flow area )( pvalvelifth Δ … height of valve lift

widthb … width of valve sideflowc … side flow coefficient

6. COMBUSTION SETTINGS In order to get fast and significant simulation results a minimum number of transported species and therewith reactions has to be used. The used finite-rate model is an approach based on the solution of transport equations for species mass fractions. The reaction rate that appears as a source term is calculated using the Arrhenius rate expression. The influence of the turbulent flow and the interaction with the combustion is modelled using the eddy dissipation concept (EDC) based on the work of [13]. In this work the kinetic mechanism consists of only five main reactions. Detailed kinetic mechanisms demand a large number of species and therewith typically over hundred several reactions, which causes a large increase in the computational time. Concurrently, the results of the simulation with the used mechanism (Eq. 6) offer an array of detailed information about the combustion. As the simulation of a two-stroke engine has to cover several revolutions, the use of detailed mechanisms is impracticable and consumes a lot of the computational time. Equation (6) shows the five global reactions used in this work. In order to reduce an unrealistic high combustion temperature adjusted polynomials of the heat capacity are used, wherewith the dissociation processes can be partially included. The spark ignition is a very short event compared to the main combustion in the engine. The spark model in FLUENT is based on the work of Lipatnikov (see [1]). For the definition of the spark the following data are required: position of the spark, initial radius, energy, start time, duration time and diffusion time. The spark model in FLUENT allows only one position of the spark and therewith of the ignition. That means that the investigation of the several spark definitions in one cylinder is impossible applying the standard options.

(6)

NOONCONOCOON

OCOCOCOOCO

OHCOOHC

225.0

5.0875.7

22

22

22

22

22167

→++→++

+→→+

+→+

For the simulation of the two-cylinder two-stroke engine two spark positions are required. The spark ignitions of both cylinders are shifted by 180 °CA. In this work, the spark position




had to be transferred after the end of each ignition process to the other cylinder, what additionally increases the simulation time, and prohibits the automatic simulation of several cycles. The energy input into the domain was taken constant so that the total energy was evenly distributed over the duration of the ignition events. Further, the energy input is only a model parameter and it is not equal to the typical energy input of an automotive ignition system, which ranges between 25 and 150 millijoules (see [1, 11]).

7. RESULTS OF THE SIMULATION After achieving a converged result of the scavenging process, the simulation including injection and combustion was carried out. The DPM and the reaction models were simultaneous started and applied for three revolutions. Figure 8 and Figure 9 show the comparison of the pressure in the measurement points inside the exhaust port (see Figure 7) with and without injection, and the measurement for the third revolution, respectively after three injections per cylinder. The comparison shows that the simulation of the engine with injection and combustion are very similar to the converged status of the scavenging process concerning the gas dynamic inside the exhaust pipe.

Figure 7: Measurement points in the exhaust port

Figure 8: Pressure trend in the exhaust port P-EXH-C1, simulation with injection and combustion

Figure 9: Pressure trend in the exhaust port P-EXH-C2, simulation with injection and combustion

Figure 10 shows the fuel distribution in different regions of the engine. The green curve shows the fuel mass in cylinder 1 and the yellow curve in cylinder 2 over the crank angle, for three revolutions respectively three fuel injections. The red curve represents the fuel mass inside the exhaust pipe and the blue curve the total mass of the injected fuel. The fuel mass inside the cylinders shows an almost periodically steady behaviour without big changes. This confirms the correctness of the simulation strategy, namely that the only initialization of the cylinder volume with the corresponding condition values leads to the faster convergence of

Pressure Trend in Exhaust Port - WOT 7900 1/min - Manifold Cylinder 1

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the simulation in a shorter calculation time. Besides, in Figure 10 there can also be seen that already the first cycle shows almost the same fuel distribution inside the engine as the following do. This means further that for an evaluation of different injection strategies in a development process already the first injection can be used for a suitable estimation. After the selection of the best variants further investigations can be carried out.

Figure 10: Fuel distribution inside the engine after three revolutions, respectively three injections pro cylinder

Figure 11: Equivalence ratio at 350 °CA, comparison of the 1st and the 3rd cycle of cylinder 1

Figure 11 shows the comparison of the equivalence ratio in the cylinder after the 1st (left) and 3rd (right) injection at 350 °CA (start of the ignition). The blue colour represents a pure air and the red colour a rich fuel concentration with an equivalence ratio of 2. The scale is limited in the region between 0 and 2, so that the values over 2 are also represented by the red colour. The figures show a very small deviation between the results what again confirms the correctness of the used simulation strategy.

Figure 12: Pressure trend in cylinder 1

Figure 13: Burn rate cylinder 1

Figure 12 shows the pressure trend in cylinder 1 for 3rd cycle of the combustion process . The start of ignition is 11 °CA before TDC. In the first phase of the ignition up to approximately 20 °CA after TDC a good agreement between the simulation and the test bench results can be seen. After 20 °CA after TDC a deviation and a lower pressure value in the simulation is visible. At approximately 80 °CA after TDC (opening phase of the exhaust port) this difference is 0.6 bars, which also explains the deviation between the results in

Fuel Distribution inside the Engine - WOT 7900 1/min

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Figure 8 and Figure 9 in the extreme points of the curves and after opening phase of the exhaust port. This pressure difference can be well explained with the deviation in the burn rate curve (see Figure 13). It is visible that the after burning in the simulation is clearly shorter as the after burning in the test bench results. Therefore additional work has to be carried out for the calibration of the entire model.

8. CONCLUSION This paper discuses the methodology for an efficient simulation of a two-stroke two-cylinder high-performance engine. The simulation was carried out using the commercial CFD Code Fluent 6.3.26. The applied settings for the simulation, like injection settings, combustion model and reaction are presented. The results of the scavenging process, internal mixture preparation and combustion are presented and are discussed as well. Test bench results of the fired engine were used for the validation of this simulation.

A simulation strategy for an efficient and significant simulation of a two-cylinder two-stoke engine was developed, which needs only a small number of revolutions.. The strategy leads to a faster convergence of the simulation, especially for the simulation of the injection, the mixture formation, and the combustion. Besides, the presented results show that the first fuel injection generates almost the same fuel distribution inside the engine as the following injections of the subsequent revolutions. This means further that for the analysis of different injection strategies in a development process of a new engine already the first injection can be used for a suitable evaluation. After the selection of the best variants further investigations can be realized.

9. REFERENCES [1] ANSYS Fluent: “Fluent 6.3 User’s Guide”; Fluent Inc, 2005 [2] ANSYS Fluent: “Gambit User’s Guide”; Fluent Inc, 2005 [3] ANSYS Fluent: “UDF Manual”; Fluent Inc, 2005 [4] Jajcevic D., Almbauer R.A., Schmidt R.A., Glinser K., “CFD Simulation of a Real

World High-Performance Two Stroke Engine with Use of a Multidimensional Coupling Methodology”; 2004742(JSAE), 2008-32-0042(SAE), 2008

[5] Schmidt St., Winkler F., Schoegl O., France M.M., „Development of a Combustion Process for a High Performance 2-Stroke Engine with High Pressure Direct Injection”; 2004-01-2942(SAE), 2004

[6] Johnson J., Braven K.R.D., “Comparison of Homogeneous, Stratified and High-Squish Stratified Combustion in a Direct-Injected Two-Stroke Engine”; 2008-32-0030(SAE), 2008

[7] Harker N., Braven K.R.D., Johnson J., Findlay A.: “University of Idaho’s Clean Snowmobile Design Using a Direct-Injection Two-Stroke Engine”; 2008-32-0031 (SAE), 2008

[8] Basshuysen R., “Ottomotor mit Direkeinspritzung”; ATZ/MTZ-Fachbuch, Vieweg 2007 [9] Stanciu A.S.: „Gekoppelter Einsatz von Verfahren zur Berechnung von

Einspritzhydraulik, Gemischbildung und Verbrennung von Ottomotoren mit Kraftstoff-Direkteinspritzung“, Dissertation, TU Berlin, 2005

[10] Petermeier L., „Simulation der Gemischbildung wandgeführter Otto – DE Brennverfahren unter besonderer Berücksichtigung der Strahl-Wandinteraktion“, Dissertation, TU Graz, 2001

[11] Eichlseder H., Klüting M., Piok W.F., „Grundlagen und Technologien des Ottomotors“, Springer, 2008

[12] Schmidt St., Schoegl O., Rothbauer R.J., Eichlseder H., Kirchberger R., „An Integrated 3D CFD Simulation Methodology for the Optimization of the Mixture Preparation of 2-Stroke DI Engines” ”; 2007-32-0029 (SAE), 2008




[13] Magnussen B. F., “On the structure of turbulence and a generalized eddy dissipation concept for chemical reaction in turbulent flow”, 1981

[14] Toro E., “Riemann Solvers and Numerical Methods for Fluid Dynamics”; Springer, ISBN 3-540-61676-4,1997




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