Numerical simulation of performance of a double-acting alpha-type stirling engine

October 16th, 2015) ABSTRACT Computational Fluid Dynamics (CFD) analysis is one of the most important powerful processes in commercial engine project, which is going to give the engineers the overall vision that a simulator may want to know about. It could save lots of time and costs before people actually manufacture the engine. This paper deals with numerical simulation of a double acting alpha-type Stirling engine (DASE), which has four cylinders with four pistons moving respectively. In the engine, double actions of the four pistons take place in two opposite chambers in each of four cylinders. For each cycle, the piston alternately moves back-and-forth in a cylinder by the connecting expansion chamber of a cylinder to the compression chamber of the next cylinder with a channel, the pressure difference between the expansion and compression chambers is increased and the power capacity of the engine is improved. In this paper, the numerical module is built based on the frame of commercial CFD software (FLUENT). The user-defined functions (UDFs) of the software are adapted so that the movement of those pistons in those cylinders can be simulated. Periodic changes in temperature, pressure and velocity fields in the engine are predicted and the power output of


INTRODUCTION
The idea of double acting alpha-type Stirling engine which original created with four cylinders but in one cylinder have two chambers, expansion room (hot space) and compression room (cold space). The adjacent cylinders would be connected to the behind cylinders after throughout the regenerators. Each cylinder has only one piston which can move from the top dead center (TDC) point to bottom dead center (BDC) point to create the swept volume in other room. The four pistons can be driven by apply any mechanism systems, whichever can make the sinusoidal motions of multi-pistons by the phase angle differences of adjacent pistons in the engine, for example the crankshaft system and swash-plate system…etc.
The models are designed with the exact fluids occupied by the volumes inside the engine. TAÏ P CHÍ PHAÙ T TRIEÅ N KH&CN, TAÄ P 18, SOÁ K7-2015

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The primer design has 4 modules within hot chamber (fluid in the expansion chamber), cold chamber (fluid in the compression chamber), and regenerator (fluid in the regenerator) and pipes (fluid occupied in the pipes which connected hot chamber and cold chamber to regenerator).
Each module has the same structure and working principles but the phase angle is 90 degree difference between these modules (shown on Figure 1), so that total volume of each module is not the same at the start point. At the beginning, two modules are at the smallest volume (pressing) and two other modules are at the biggest volume (stretching).

Piston displacement
For the determination of sinusoidal motion of those 4 pistons in simulation, the analysis trajectories of those pistons are a necessary process. The displacements of four pistons in alternate cylinders can be seen in Figure 1, it can be written following as bellow: (3) where, α is the phase angle; r is the radius; L is the length of connecting rod; 1 S , 2 S , 3 S , 4 S are the straight trajectory of these 4 pistons.

Volume variation
In a DASE model there are 4 modules, one module consisting of compression chamber, expansion chamber and regenerator. Those theoretical thermodynamics model of each module are the same as sinusoidal variation so that in this section, theoretical study of one unit module analytical studied model as others. These total expansions space and total compressions space can be calculated as equations below: Thermodynamic of this model calculated by the consideration on three main spaces are hot chamber (CV-hot), cold chamber (CV-cold) and regenerator space [1]. The volumes of hot chamber and cold chamber are not stationary; its variable due to piston's displacements all the time but the volume of regenerator is constant.

A control volume of DASE
In the Figure 2 shows a control volume (CV) in a DASE which called one module. The CV design includes hot chamber (fluid in the expansion chamber), cold chamber (fluid in the compression chamber), and regenerator (fluid in the regenerator) and pipes (fluid occupied in the pipes which connected hot chamber and cold chamber to regenerator), which are the exact fluids occupied by the volumes inside the engine.

Working condition
The operation of Stirling engine [2] can be controlled by the different levels of heat sources from both of expansion room and compression room. The net work done can be adjusted by many ways such as initial pressure in charge, variation of volume including dead volume in each room, variation of temperature of heat sources, etc.   Besides, the working fluid used inside those chambers is considered as air, hydrogen and nitrogen; they have almost the same thermodynamic proprieties [3] so that the performance in a Stirling cycle [4] also must be similar. The advantages of nitrogen is reduces the explosion factor under working and the hydrogen can creates high engine's efficiency but the main purpose that we had used air as working fluid because it is likely as the normal environment and during the time life cycle of engine it is not only reduce the maintenance fee but also can make the longer life time for the engine.

RESULT AND DISCUSSION
In this paper, the results obtained at primer design which can be seen in Table 1. The design of engine cylinder diameter and stroke are fixed. We do investigate the effects of power output and energy to improve the performance of engine. The work done per cycle can be calculated as the following formula:  At high charged pressure and low rotation speed of engine, the performance of engine is increased as the difference in pressure between the lowest and the highest point in the PV diagram is larger. Morever, the area enclosed by PV diagram also becomes bigger. The effect of charged pressure also influences to obtain better indicated work. By the ideal gas equation PV mRT  , while the specific gas R is constant, the initial volume and the initial temperature are the same;the change of initial pressure will directly affect the quality of the initial mass. By that mean, the variation of pressure will change the quality of initial mass so if the power output per unit mass fixed, more quality of initial mass charged which will create more power output of Stirling engine. Figure 7 is the influence of charged pressure to work done and power output, which shows the greater of the charged pressure, will create the higher result of power output and work done.
To know about the performances of engine, the investigation effect of speed engine is necessary, in this paper the performance of engine bases on the affection of speeds engine have shown on. The best performance of this engine given at rotation speed of engine around point 1500rpm, even though the indicated work done at this speed does not perfect. Its indicated work is smaller than the one created by the lower of speed engine and higher speed engine. The important issue has also explored is the negative work will be created when the rotation speed of engine increases too high. So that, to reach the highest engine efficiency, the operation engine at this point is possible.