Development and validation of a thermodynamic model for the performance analysis of a gamma Stirling engine prototype

Abstract

h i g h l i g h t sA numerical model for a Stirling engine was developed. A mechanical efficiency analysis was included in the model. The model was validated with experimental data of a novel prototype. The model results permit a deeper insight into the engine operation. a b s t r a c tThis work presents the development and validation of a numerical model that represents the performance of a gamma Stirling engine prototype. The model follows a modular approach considering ideal adiabatic working spaces; limited internal and external heat transfer through the heat exchangers; and mechanical and thermal losses during the cycle. In addition, it includes the calculation of the mechanical efficiency taking into account the crank mechanism effectiveness and the forced work during the cycle. Consequently, the model aims to predict the work that can be effectively taken from the shaft. The model was compared with experimental data obtained in an experimental rig built for the engine prototype. The results showed an acceptable degree of accuracy when comparing with the experimental data, with errors ranging from ±1% to ±8% for the temperature in the heater side, less than ±1% error for the cooler temperatures, and ±1 to ±8% for the brake power calculations. Therefore, the model was probed adequate for study of the prototype performance. In addition, the results of the simulation reflected the limited performance obtained during the prototype experiments, and a first analysis of the results attributed this to the forced work during the cycle. The implemented model is the basis for a subsequent parametric analysis that will complement the results presented.

Thermodynamic Model for Performance Analysis of a Stirling Engine Prototype

“…For an ideal gas, enthalpy and internal energy depend only on the temperature, then specific enthalpy and specific internal energy can be expressed as h = c p T and u = c v T, respectively. Then the energy balance [28] is represented by:…”

Numerical simulation for the design analysis of kinematic Stirling engines

“…These equations were grouped in the blocks shown in Figure 1. The detailed derivation of these equations can be found in Araoz [47,48]. The ideal adiabatic module contains the equations that describe the thermodynamics of the working fluid inside the engine.…”

“…These are shown in Figure 2. Further details of the engine are shown in Appendix C. Figure 2: Genoa Stirling engine scheme [48] According to the manufacturer specifications, the electrical output for the engine is close to 1 kW when air is used as working fluid, at 600 rpm rotational speed, heater temperature around 750 C and water at 20 C as cooling fluid [34]. Furthermore, the heat exchangers materials allows to stand higher temperatures and makes the engine suitable for coupling to systems such as a boilers based on biomass combustion.…”

“…The model was calibrated for the experimental conditions of the actual prototype [48]. The details of the experimental measurements can be found in Cardozo [35].…”

A transient one-dimensional numerical model for kinetic Stirling engine

“…Though the accuracies were still low, these models laid a good foundation for the follow-up developments of second-order methods. More studies were then conducted by either directly adopting Urieli and Berchowitz's models [21,22] or modifying the ideal adiabatic model [23][24][25][26][27][28][29][30], quasi-steady model [31] or simple analysis model [32][33][34][35][36][37]. These models were improved by considering more internal or external losses [23][24][25][26][27][28][29][30][31][32][33][34][35], introducing the concept of finite speed thermodynamics [28,35], or changing the treatments of compression/expansion processes in working spaces [36,37].…”