Numerical investigation of nonlinear effects in a standing wave thermoacoustic engine using the discontinuous Galerkin method

Understanding the nonlinear effects in thermoacoustic heat engines operating under high-pressure amplitude conditions plays a crucial role in improving their operational performance and efficiency. The discontinuous Galerkin (DG) method has several advantages, including high accuracy, adaptability, efficiency, and the ability to handle the coupling of multiple physical fields, making it suitable for accurately simulating the flow and heat transfer characteristics in thermoacoustic engines. The simulation code was developed based on MFEM, an open-source C++ library for modular finite element methods. The fully compressible Navier-Stokes equations and Fourier heat conduction equation were solved to investigate the nonlinear effects, which cannot be captured by the linear theory. To verify the accuracy of the simulation code, the numerical investigation of the thermoa-coustic wave propagations induced by thermal effects in a square enclosure was first conducted. The simulation results presented the details of the generation and propagation of thermoacoustic waves, which were largely consistent with the results obtained using the flux-corrected transport (FCT) algorithm. Second, a quarter-wavelength standing wave thermoacoustic engine was simulated. The simulation results captured the process of pressure wave generation in the thermoacoustic engine, which was consistent with the pressure wave gen-eration process in the enclosure. The results revealed the flow and heat transfer characteristics and nonlinear effects in the thermoacoustic engine under high-pressure amplitudes, which were consistent with the results obtained using finite volume method. The simulation results showed that the DG method is an effective nu-merical method for simulating thermoacoustic engines.