Gas Dynamics of the Temperature-Determined Stirling Cycle

Abstract

The Stirling cycle machine is modelled as a number of sections of duct in series, some tapered, some parallel. The working fluid assumes the temperature of the adjacent metal wall. Flow is defined by two conservation equations (mass and momentum) and the equation of state, p = p R T . Friction is taken into account by using the steady-state correlation between friction factor, local instantaneous Reynolds number, and local hydraulic radius. The formulation permits frictional drag and frictional reheating to interact more or less as they do during operation of a Stirling cycle machine at high rotational speeds. The equations are converted to characteristic form and solved numerically with pressure, p , and velocity, u, as state variables rather than the more usual a (acoustic speed) and u. This formulation paves the way for a full characteristics solution incorporating the energy equation but avoiding the entropy gradient term &/ax which is inappropriate to conditions within the Stirling machine. The paper includes a Mach-line net plotted by computer for the first revolutions of the crankshaft after start-up. Indicator diagrams are presented corresponding to different angular speeds. It is found that the indicator diagram for the compression space is not greatly affected by angular speed, while that for the expansion space changes from positive, via figure-ofeight to negative over a relatively narrow speed range. An attempt is made to explain this unexpected finding in terms of the momentum equation for constant area flow with a severe temperature gradient. A comparison is included between the computed results and those predicted for the same operating conditions by the Schmidt isothermal analysis.

Validation of a Simulation Model for a Combined Otto and Stirling Cycle Power Plant

“…Traditional methods of Stirling cycle modeling are elucidated in a number of key texts, for example [23][24][25][26][27][28][29][30][31]. In the literature of Finite Dimensional Optimization Thermodynamics the cycle has perhaps not benefitted from the same attention as other cycles; however, significant progress has been made.…”

Development of a theoretical decoupled Stirling cycle engine

“…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.…”

“…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][3][4][5]. However, being an external combustion engine, it does benefit from an omnivorous fuel or heat source capability and quiet operation.…”

“…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.…”

Operator splitting approach applied to oscillatory flow and heat transfer in a tube

“…Inside the pulse tube, the compression and expansion of the fluid takes place in order to cool down the sample which can be placed at the cold end of the tube. Mathematical descriptions of this system have been developed by several authors as [12,3]. The model focusses on the pulse tube only, so we can analyze its ability to act as a regenerator itself.…”