**1. Introduction**

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The decreasing crude oil sources, the increasing concern about greenhouse gas pollution, and the strict emission standards force researchers into never-ending effort to design less polluting and more fuel efficient vehicles. Free-piston linear alternator (FPLA) which is a free-piston engine coupled to a linear alternator, converting piston's kinetic energy into electricity directly, has attracted considerable research interests recently by a number of research groups worldwide due to its potential advantages listed bellow:


In the recent two decades, some literatures have already been published about the design and numerical simulation of FPLA. Martin Goertz and Lixin Peng evaluated several feasible hybrid power-train concepts and the results indicated that free-piston linear generator was one of the most promising candidates of the future power-train configuration [3]. West Virginia University had already demonstrated stable operation of a spark ignited FPLA prototype with bore of 36.5mm, maximum possible stroke of 50mm and 316W output power was produced at 79V working at full load [4]. Ehab Shoukry did some research about parametric study of a two-stroke direct injection linear engine using zero dimensional single zone models [5].The European Union has been doing a subject of

Dimensionless Parametric Analysis of Spark Ignited Free-Piston Linear Alternator 273

The Modeling of FPLA and numerical simulation of its performance have already been done by a lot of researchers. Usually the model consists of a dynamic calculation of the piston motion and a thermodynamic calculation of the engine's thermodynamic events. The piston motion is governed by the interaction of forces that act on the piston simultaneously, which are in-cylinder pressure force from each cylinder, electromagnetic force, friction force and

Since the FPLA doesn't have a crankshaft, it is free of the dynamic friction caused by the crankshaft mechanism and the friction force is caused mainly by the interactions between cylinder and piston rings, cylinder and piston skirt, which is small compared with the load of the linear alternator. Therefore, the friction force is considered to be constant during the

The linear alternator consists of two main components, a stator and a translator. The permanent magnets are mounted on the stator and the translator is the moving portion of the machine which is made up of coils. A schematic of a three-phase, "U" shaped linear

The FPLA operates on the same basic physical principles as conventional rotary alternators. The principle that governs the voltage generating operation of the alternator is Faraday's

> *ind coil d d <sup>N</sup> dt dt*

The permanent magnets create a magneto motive force (MMF) in the air gap between the stator and the winding coils as shown in Fig.4, and it can be described by the following

 (2)

2 *L R f e*

*d x m p p AF F dt* (1)

2

alternator with permanent magnet (PM) excitation is shown in Fig.3.

**2. System modeling 2.1 Dynamic modeling** 

inertia force, as is shown in Fig.2.

Fig. 2. Free body diagram for FPLA The Newton's second law is applied:

whole cycle in the calculation [13].

law expressed as [14]:

mathematic equation:

**2.2 Modeling of the linear alternator** 

Free-piston Energy Converter (FPEC) since 2002 aimed to develop an efficient new technology suitable for vehicle propulsion, auxiliary power unit and distributed power generation. The design and optimization of linear alternator and crankless engine, control strategy, numerical simulation and power management have been carried out systemically [6]. Dr. Peter Van Blarigan at Sandia National Laboratory presented the design of a dual piston free-piston engine generator with 40kW electric power output and the engine employed homogeneous charge compression ignition (HCCI) operating on a variety of hydrogen-containing fuels [7, 8]. Jakob Fredriksson and Ingemar Denbratt at Chalmers University of Technology investigated a two-stroke free-piston engine with different fuels using BOOST and SENKIN [9]. Czech Technical University had successfully developed a direct injection FPLA prototype recently, and steady operation had been realized based on precise motion control. When the prototype was running with frequency of 27Hz and compression of 9, the average power output was approximately 350W, but the efficiency had not been reported [10]. Mikalsen and Roskilly proposed a design of a single cylinder free-piston engine generator with gas-filled bounce chamber, simulated its working process and discussed the effects of parameters in a wide operating range to the engine's performance [11]. A novel approach of modeling the free-piston engines through the introduction of solution-dependent mesh motion in an engine CFD toolkit OpenFOAM was also presented [12].

Dimensionless analysis using Buckingham's theory was performed base on the parameters of a spark ignited FPLA prototype (as can be seen in Fig.1) in the following contents. The objectives of this work are:


Fig. 1. FPLA configuration
