Eur. Phys. J. Plus (2015) 130: 9
https://doi.org/10.1140/epjp/i2015-15009-5

Regular Article

Lattice Boltzmann study on thermoacoustic onset in a Rijke tube

¹ Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi’an Jiaotong University, 710049, Shaanxi, China
² Department of Mechanical and Aerospace Engineering, University of California, 92697, Irvine, CA, USA
³ Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, School of Mechanical Engineering, Southeast University, 211189, Nanjing, China

^* e-mail: ywangcam@gmail.com

Received: 9 July 2014
Revised: 14 November 2014
Accepted: 19 December 2014
Published online: 23 January 2015

Abstract

Nonlinear thermoacoustic self-excited onset was numerically studied in this work. A lattice Boltzmann model for viscous compressible flow and the implicit-explicit finite difference method were used to develop a solver. Nonlinear onset in an open-open Rijke tube with a constant-temperature stack was simulated with the solver. Based on the numerical results, overall onset process and self-excited standing wave in the Rijke tube are observed. The length of the Rijke tube along the x -direction covers a 1/4 wavelength of the standing wave and the main component of this standing wave is 171.2Hz. These results agree well with the theoretical prediction. Instantaneous velocity and temperature fields at several phases under the limit cycle are presented and discussed. The maximal Mach number is about 0.035, indicating that the flow in the Rijke tube is a low Mach number compressible flow. This solver can also be applied for simulations of some other complex flows, such as the flow in porous media stack in thermoacoustic engine.