**4.1 Combustion modeling of FPLA**

Since the combustion model used in the numerical program is zero dimensional Wiebe function and some parameters like combustion duration are of great uncertainty, the accuracy of the numerical calculated results is suspectable. Nowadays, multi-dimensional CFD computational tools have become an integral part of the engine design process due mainly to advances in computing capabilities and improvements in the modeling techniques utilized. In this study, in order to validate the results of dimensionless analysis, a multi-

Dimensionless Parametric Analysis of Spark Ignited Free-Piston Linear Alternator 285

stroke cycle, the simulations run from the point of exhaust port closing to the point of

The initial conditions in the cylinder, such as pressure, temperature, EGR ratio and kinetic energy were defined based on the results of multi-dimensional scavenging calculation using CFD tools. In order to investigate the effects of ignition timings, the initial conditions were the same with base case. The input energy in the cylinder had just the same value as it is in

Probability Density Function (PDF) model which takes into account the simultaneous effects of both finite rate chemistry and turbulence was chosen to describe the combustion process. The benefits of the PDF approach lie in the fact that it provides a complete statistical description of the scalar quantities under consideration. Thus, it allows first (mean values), second (variance), and even higher (skewness) order moments to be easily extracted, and that the term expressing the rate of chemical reaction appears in closed

Based on the basic geometry of the FPLA, two kinds of effective stroke length to bore ratio and four ignition compression ratios were chosen in the CFD calculation. The other

As the piston dynamics is changing with different operating conditions, the piston motion profiles have to be defined first in the numerical simulation program, and then the required data in the CFD calculation can be derived, which are listed in Tab.4. The other parameters are based on the FPLA prototype. The revolution of the engine doesn't has real meanings as the free piston engine does not have a crankshaft, and it is bring forward just to complete

Practically, the maximum compression ratio is confined by the geometry of the chamber since the roof of cylinder and piston is not flat, as is shown in Fig.7. Thus, we have to make sure that the compression ratios of the typical effective stroke length chosen do not exceed

*L*eff/mm D/mm *L*eff /D *ε*ign *t*ign/ECA *ε f*/Hz EGR *Qin*/J Revolution/rpm 23 34 0.6765 3 319.5 21.0 46.7 20% 17.84 2803.7 23 34 0.6765 4 328.5 22.2 45.0 20% 17.84 2697.8 23 34 0.6765 5 333.6 21.6 43.4 20% 17.84 2606.4 23 34 0.6765 6 337.4 20.7 42.2 20% 17.84 2531.6 35 34 1.0294 3 320.7 11.4 34.1 20% 27.15 2046.4 35 34 1.0294 4 328.6 13.8 33.7 20% 27.15 2025.0 35 34 1.0294 5 333.7 14.6 33.0 20% 27.15 1980.2 35 34 1.0294 6 335.4 14.5 32.1 20% 27.15 1928.0

The piston motion profiles with different operating conditions listed in Tab.4 are shown in

parameters are the same with the base case mentioned before.

the combustion process required by the CFD software.

exhaust port opening.

form.

the numerical simulation program.

**4.3 CFD calculation cases** 

their maximum value.

Table 4. CFD calculation cases

Fig.8.

dimensional commercial CFD software AVL\_Fire was used to evaluate the effects of translator ignition position with different effective stroke length to bore ratio.

As the FPLA doesn't have a crankshaft mechanism, the dynamics of the piston is totally different from conventional engine. The dynamics were defined based on the results of a zero dimensional FPLA modeling mentioned in the former paragraphs. The dynamics and thermodynamics equations of FPLA in section 2 were solved using a numerical simulating program in Matlab, and some of the parameters were defined according to the experimental data measured. Then the dynamics of the FPLA were incorporated into AVL\_Fire to define the movement of the piston. The piston motion profile was described with two arrays of numbers, one of which represented the ECA (Here ECA is equivalent crank angle which is used to note the port timings. However, it is only a time notation since the free-piston engine does not have a crankshaft to define the piston's motion and *ECA*= *t*·*f*·360 [23, 24, 25]) and the other represented the displacement of the piston, and then the file was imported into the CFD code directly. Since there was no coupling between CFD code and free piston's motion, the dynamics was adjusted depending on the desired operating frequency and the stroke of the free-piston engine in the zero-dimensional FPLA simulating program. The dynamic mesh tool *Fame Engine* in AVL\_Fire was used to create the moving mesh according to the numerical simulated free-piston motion profile. The update of the volume was handled automatically at each time step based on the new positions of the piston.

Only compression, combustion and expansion processes of the free-piston engine were calculated in order to minimize the number of computational cells (intake port, scavenging ports, exhaust port and scavenging case were not included in the combustion process). The computational model of the cylinder is shown in Fig.7, and the basic geometry is defined based on the FPLA prototype. Due to the symmetry of the cylinder ports layout, it is only necessary to model half of the geometry in order to minimize the computational cost.

Fig. 7. Computational mesh of cylinder

### **4.2 Boundary conditions and combustion model**

The boundary conditions were chosen to reflect the physical conditions which exist in the validation model and the prototype engine. Constant wall temperatures were also used. The standard *k-*model was employed to capture turbulence. As the engine operates on a two stroke cycle, the simulations run from the point of exhaust port closing to the point of exhaust port opening.

The initial conditions in the cylinder, such as pressure, temperature, EGR ratio and kinetic energy were defined based on the results of multi-dimensional scavenging calculation using CFD tools. In order to investigate the effects of ignition timings, the initial conditions were the same with base case. The input energy in the cylinder had just the same value as it is in the numerical simulation program.

Probability Density Function (PDF) model which takes into account the simultaneous effects of both finite rate chemistry and turbulence was chosen to describe the combustion process. The benefits of the PDF approach lie in the fact that it provides a complete statistical description of the scalar quantities under consideration. Thus, it allows first (mean values), second (variance), and even higher (skewness) order moments to be easily extracted, and that the term expressing the rate of chemical reaction appears in closed form.
