Four-port network method for obtaining initial approximations in the problems of the thermoacoustic devices designing

Today, the parameters of thermoacoustic devices are calculated by linearized equations of the dynamics of viscous heat-conducting gas. Such programs require precise initial approximations for the system of equations to be solved. Therefore, an engineer spends tens of hours to get the convergence of a solution for a complex model. To facilitate this, the Rott-Swift acoustic equations are reduced to the four-port element equation for pressure and volume flow rate. The technique is based on the approximation of the elements included in the acoustic tract in the form of typical four-port network of acoustic circuits. Then the numerical integration of the acoustic equations along the tract length is replaced by the matrix product.The authors obtained matrices of tipical four-port elements for the device modeling: a channel section, a heat exchanger, a regenerator, etc. As an example, a diagram of a toroidal thermoacoustic engine (TAE) with a resonator is considered. The authors carried out modeling of acoustic branches using four-port networks, calculated the operating frequency of the TAE by the developed algorithm, determined the distribution of pressure and volume flow rate along the axis of the device, and energy estimates were made.The calculation results of this approximation were compared with the results obtained by the special DeltaEC software. Comparison of the results showed satisfactory compliance. Using the approximation allowed to halve the time spent by an engineer to obtain an initial solution. This method is recommended for calculating thermoacoustic engines and refrigerators.