Development of a theoretical decoupled Stirling cycle engine

The Stirling cycle engine is gaining increasing attention in the current energy market as a clean, quiet and versatile prime mover for use in such situations as solar thermal generation, micro cogeneration and other micro distributed generation situations. A theoretical Stirling cycle engine model is developed. Using a theoretical decoupled engine configuration in which working space swept volume, volume variation, phase angle and dead space ratio are controlled via a black-box electronic controller, a model is developed that is to be used as a tool for analysis of the ideal Stirling cycle engine and the limits on its real world realisation. The theoretical configuration approximates the five–space configuration common in Stirling cycle analysis. It comprises two working spaces and three heat exchangers: hot side, cold side and the regenerator between. The kinematic crank mechanism is replaced with an electronically controlled motor/generator system, with one motor/generator controlling each of the working pistons. Use of stop valves permits flow and non-flow processes inherent in the ideal cycle to be realised. The engine configuration considered here is not intended as a viable prime mover but rather a tool for study of the limitations of the cycle. 1.0 INTRODUCTION The Stirling engine is a closed cycle, regenerative, external combustion reciprocating engine that relies for its power conversion on the cyclic heating and cooling of a fixed mass of gas within the engine. At the time of its invention, steam engines were the dominant power generation technology, and although it offered a competitive and, importantly, safer alternative to such engines, it never seriously challenged their market share [1]. Similarly, although it predated the Otto and Diesel cycle engines by some fifty years, it has struggled to maintain market presence in competition with these Internal Combustion engines since their introduction in the late nineteenth century. The reasons for this are numerous but are generally held to stem from its relatively sluggish response characteristics, its low power-toweight ratio and its comparatively expensive manufacturing requirements [2-5]. However, being an external combustion engine, it does benefit from an omnivorous fuel or heat source capability and quiet operation. It was these characteristics that reinvigorated interest in the engine in the nineteen thirties in the Philips Electric Company, Eindhoven, and have continued to drive its development in the modern day for applications in distributed generation, particularly solar thermal generation and micro cogeneration applications[6-10]. The practical Stirling cycle always departs significantly from the ideal cycle. There are several reasons for this, corresponding particularly to the performance of the heat exchangers and the regenerator and the achievement of volume variations through the use of crank-and-connecting-rod or other mechanisms. The latter is of relevance in the current work. A decoupled arrangement is proposed that utilises four separate motor/generator units for the achievement of volumetric variations of the working fluid, thereby permitting more complete control over the volume changes in the cycle. This paper presents an initial conceptual treatment of the proposed mechanism and a discussion of its possible merits. The concept is not intended as a viable prime mover at this preliminary stage but rather a conceptual device useful for consideration of the ideal cycle and its practical realisation. 2.0 THE STIRLING CYCLE ENGINE 2.1 Ideal Cycle Figure 1 (a) shows the ideal Stirling thermodynamic cycle. The air standard cycle comprises the following four processes [5, 11]: 1-2: Isothermal compression: heat rejection to external sink 2-3: Isochoric regeneration: internal heat transfer from the working fluid to the regenerator 3-4: Isothermal expansion: heat addition from external source 4-1: Isochoric regeneration: internal heat transfer from the regenerator to the working fluid The realisation of this cycle is usually described in terms of a 5-space configuration, as seen in Fig. 1(b) [4, 12]. The expansion and compression working spaces are complemented by three heat exchange devices: a hot side heat exchanger, which admits heat to the system; a cold side heat exchanger which rejects heat from the system; and a regenerator linking the two heat exchangers. 2.2 Stirling Engines – State of the Art and Limitations The modern Stirling engine is a versatile and technologically developed device. The engines can broadly be divided according to their attributes into Kinematic or Free Piston machines. Kinematic engines use kinematic drive mechanisms to regulate the volume variations in the working spaces. Free Piston machines use gas pressure variations in the cycle to control the movement of the displacer piston [13-15]. These engines were pioneered in the 1960’s by William Beale and offer their own set of advantages, particularly in relation to reduction of friction losses in the drive. They find use in solar thermal plant and in remote generation in space [8, 16]. Kinematic engines are of interest in the present work, however. A number of variations exist on the kinematic mechanisms used in the Stirling engine. The traditional modelling of the cycle, as first offered by Schmidt, treats the volume variations as being harmonic sinusoidal [4]. This is a significant departure from the ideal case and has the effect of reducing the cycle work. Narasimhan and Adinarayan present an evaluation of the displacement-time characteristics of various Stirling engine drive mechanisms in terms of optimum specific work of the engine [17, 18]. Crank/connecting rod, Crank/connecting rod/cross head, Ross yoke, wobble yoke and rhombic drive are all examples of kinematic mechanisms previously deployed [5, 12]. Such mechanical mechanisms offer a harmonic or near harmonic variation in system working volumes. Fang et al describe an elliptical drive that more closely approximates the ideal non harmonic volume variations [19]. (a) (b) Figure 1. The Stirling cycle (a) air standard cycle (b) five space ideal Stirling engine circuit 3.0 PROPOSED ENGINE CONFIGURATION Figure 2 shows the proposed engine configuration for the present work. The two working spaces (heated/expansion space and cooled/compression space) are shown as operating with two pistons each. The working spaces are isolated from each other through the use of cut-off valves 1 and 2 in the line on either side of the regenerator, R. The pistons are each actuated by a motor/generator via a rack and pinion gear and are controlled by a black-box electronic controller. Power storage is represented in the diagram as being from a battery, although grid connection is also feasible. As the realisation of the thermodynamic circuit is the issue of concern for this study, technical considerations relating to the electronic control and power storage are not elaborated on. 4.0 THERMODYNAMIC ANALYSIS 4.1 Description of Operation Assumptions Heat Exchange Volumes Ideally the hot and cold side heat exchangers and the regenerator would have negligible internal volume but very large internal surface area. They would also, ideally, present negligible resistance to the flow of the working gas. These ideals cannot be attained in practice, but the volumes, areas and flowresistance characteristics are amenable to modeling and engineering optimization. The regenerator ideally has no internal thermal conductivity that would allow heat transfer through the thermal gradient that it contains (ideally from the source temperature to the sink temperature), but departures from the ideal can be modeled. Ideally, all volume of the working fluid is contained within the four working spaces that are swept by the four pistons shown in Fig. 2. Ideally, the fluid temperature in each working space is uniform and the working space boundaries are adiabatic. Departures from this could be modeled and quantified. Process 1-2 Sawtooth Approximation of Isothermal Compression Figure 3 (a) shows how the compression process is achieved by reduction of the total