Characteristic-based non-linear simulation of large-scale standing-wave thermoacoustic engine

Abstract

A few linear theories [Swift, J. Acoust. Soc. Am. 84(4), 1145-1180 (1988); Swift, J. Acoust. Soc. Am. 92(3), 1551-1563 (1992); Olson and Swift, J. Acoust. Soc. Am. 95(3), 1405-1412 (1994)] and numerical models, based on low-Mach number analysis [Worlikar and Knio, J. Comput. Phys. 127(2), 424-451 (1996); Worlikar et al., J. Comput. Phys. 144(2), 199-324 (1996); Hireche et al., Canadian Acoust. 36(3), 164-165 (2008)], describe the flow dynamics of standing-wave thermoacoustic engines, but almost no simulation results are available that enable the prediction of the behavior of practical engines experiencing significant temperature gradient between the stack ends and thus producing large-amplitude oscillations. Here, a one-dimensional non-linear numerical simulation based on the method of characteristics to solve the unsteady compressible Euler equations is reported. Formulation of the governing equations, implementation of the numerical method, and application of the appropriate boundary conditions are presented. The calculation uses explicit time integration along with deduced relationships, expressing the friction coefficient and the Stanton number for oscillating flow inside circular ducts. Helium, a mixture of Helium and Argon, and Neon are used for system operation at mean pressures of 13.8, 9.9, and 7.0 bars, respectively. The self-induced pressure oscillations are accurately captured in the time domain, and then transferred into the frequency domain, distinguishing the pressure signals into fundamental and harmonic responses. The results obtained are compared with reported experimental works [Swift, J. Acoust. Soc. Am. 92(3), 1551-1563 (1992); Olson and Swift, J. Acoust. Soc. Am. 95(3), 1405-1412 (1994)] and the linear theory, showing better agreement with the measured values, particularly in the non-linear regime of the dynamic pressure response.

Modeling of thermoacoustic systems using the nonlinear frequency domain method

“…Typical solution times range from 1 to 5 min, which is fast compared to computation times of $10 h when using the method of characteristics. 10…”

“…A more recent work discusses the application of the method of characteristics 10 to model the experimental standing wave thermoacoustic engine of Swift. 11 Here, heat transfer and viscous resistance is computed using semi-empirical models.…”