Design of a Thermoacoustic Engine Using Vanishing Perturbation and Genetic Algorithm

• Determination of a robust range for the damping coefficients of the thermoacoustic Stirling engine using the vanishing perturbation method and nonlinear mechanical modeling. • Investigation of the sufficient condition of thermoacoustic Stirling engine using error dynamic and vanishing perturbation method (in two conditions: considering and not considering the uncertainty damping coefficients). • Presentation of a design method using the concept of energy changes and genetic algorithm. In this study, the robustness of the dynamic equations of a thermoacoustic Stirling engine (TASE) against disruptive variations in the damping coefficients of the mechanical model is studied based on the vanishing perturbation theory. The objective of this work is to determine a permissible range for the damping coefficients that guarantees the occurrence of stable oscillations in the nonlinear dynamics of the TASE, and to predict the key engine design parameters within this permissible range. Furthermore, after determining the allowable range of the uncertain components of the damping coefficients, important engine parameters, including Rq, the diaphragm cross-sectional area (A), and the hot temperature (Th) are calculated using energy-based concepts and a genetic algorithm (GA). To this aim, the dynamic error equations of the TASE are first derived based on the expected steady oscillation of the pistons. Then, employing the vanishing perturbation technique, the permissible range of the damping coefficients is obtained such that stable fluctuations in the nonlinear engine dynamics are ensured. The evaluation of the engine dynamics is also performed both in the absence and presence of these uncertain components. The outcomes show that the dynamics of the TASE can sustain oscillations within the identified permissible range of the damping coefficients. Moreover, by defining two pseudo-energy functions for the two dynamic equations of the engine and applying the GA, the design parameters are determined based on given design objectives. Finally, the obtained design parameters are compared with the parameters of the experimental engine. This comparison demonstrates that the proposed technique can both satisfy the sufficient condition and predict the engine design parameters prior to engine fabrication. The main outcome of this work is that the presented method provides a reliable pre-fabrication framework for achieving stable oscillations while accurately estimating the key design parameters, thereby reducing development cost and time.