A transient one-dimensional numerical model for kinetic Stirling engine

Abstract

A third-order numerical model based on one-dimensional computational fluid dynamics is developed for kinetic Stirling engines. Various loss mechanisms in Stirling engines, including gas spring hysteresis loss, shuttle loss, appendix displacer gap loss, gas leakage loss, finite speed loss, piston friction loss, pressure drop loss, heat conduction loss, mechanical loss and imperfect heat transfer, are considered and embedded into the basic control equations. The non-equilibrium thermal model is adopted for the regenerator to capture the oscillating features of the gas and solid temperatures. To improve the numerical stability and accuracy, the implicit second-order time difference scheme and the second-order upwind scheme are adopted for discretizing the time differential terms and convective terms, respectively. Experimental validations are then conducted on a beta-type Stirling engine with the extensive experimental data for diverse working conditions. The results show that the developed model has better accuracies over previous second-order models. Good agreements are achieved for predicting various critical system parameters, including pressure-volume diagram, indicated power, brake power, indicated efficiency, brake efficiency and mechanical efficiency. In particular, both the experiments and simulations show that the Stirling engine charged with helium tends to have much lower optimal working frequencies and poorer performances compared to the hydrogen system. Based on the analyses of the losses, it reveals that the pressure drop in the flow channels plays a critical role in shaping the different behaviors. The pressure drop in the helium system is much larger and more sensitive to the frequency increase due to the much larger viscosity of gaseous helium. Hydrogen is a superior working gas for a Stirling engine. The transient characteristics of the oscillating flow and the associated thermal interactions between gas and solid in the regenerator are finally analyzed in order to have an insight of the complex thermodynamic process. The study provides a promising numerical approach in simulating Stirling engines for further understandings of their operating characteristics and the underling mechanisms.

Parameter sensitivity analysis of duplex Stirling coolers

“…The free-piston Stirling concept was introduced by Beal in 1969 [11]. In recent years, it has drawn worldwide attentions due to the urgent need for renewable energy technologies [12][13][14][15][16][17][18]. In the 1980s, several duplex Stirling machines were developed by Sunpower Inc. and while experimental results demonstrated their feasibility, detailed parameters of these machines and quantitative results were not presented [19][20][21].…”

Theoretical investigations of Stirling engine performances for different filling gas properties

“…The material used in SE's regenerators, the exchange surface with hot and cold sources, the exchanger design, and the oscillatory flow characteristics all have an impact on their efficiency. These efficiencies were determined using Equation (30) given in Table 1, for the three heat exchangers. The pressure drop Δp across the three heat exchangers significantly reduces the SE efficiency and power.…”

“…The heat transfer coefficients of Helium, nitrogen, and carbon dioxide inside a heater were studied by Ni et al 29 They determined that Helium had the best heat transmission capabilities. Wang et al 30 investigated the effect of using Helium and Hydrogen on the GPU-3 Stirling engine output power. When Helium is used, the output power is 2.31 kW, while when hydrogen is used, the output power is 3.47 kW.…”

“…The most widely documented fluids used in the Stirling cycle are Air, H 2 , He, Ne, N 2 , CO, O 2 , and Ar. [26][27][28][29][30][31] These fluids can be grouped into monoatomic and diatomic gases. Hydrogen is thermodynamically a better choice; however, it is not safe to work with this it is not considered in this study.…”

The examination of performance characteristics of a beta‐type Stirling engine with a rhombic mechanism: The influence of various working fluids and displacer piston materials

“…The researchers stated that the Stirling engine, which used helium as the working fluid, had much lower optimum operating frequencies and lower engine performances compared to the engine using hydrogen and showed both experimental and theoretical results. 32 Abuelyamen et al carried out a numerical study on a betatype Stirling engine with a rhombic mechanism using the ANSYS fluent 14.5 analysis program. In that study, basic information on engine performance, such as P-V diagrams, heat transfer occurring in the engine, heater, and coolant temperature, was determined theoretically and graphically in comparison with air, helium, and hydrogen working fluids.…”