**4.3 CFD calculation cases**

284 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

dimensional commercial CFD software AVL\_Fire was used to evaluate the effects of

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

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.

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

model was employed to capture turbulence. As the engine operates on a two

translator ignition position with different effective stroke length to bore ratio.

piston.

Fig. 7. Computational mesh of cylinder

standard *k-*

**4.2 Boundary conditions and combustion model** 

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 parameters are the same with the base case mentioned before.

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 the combustion process required by the CFD software.

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 their maximum value.


Table 4. CFD calculation cases

The piston motion profiles with different operating conditions listed in Tab.4 are shown in Fig.8.

Dimensionless Parametric Analysis of Spark Ignited Free-Piston Linear Alternator 287

Fig. 9. Comparation of experimental and numerical simulated pressure data

Fig. 10. Dimensionless velocity vs. dimensionless displacement with different effective

stroke length to bore ratio

Fig. 8. Piston dynamics with different operating conditions
