This study focuses on natural convection flows within a cylindrical guide partly filled with a porous medium. Such configurations are found in thermoacoustic devices, usually composed of an acoustic resonator where a stack (or porous medium) is inserted. Under usual functioning conditions, with acoustic energy converted into heat or reciprocally, horizontal temperature gradients are present across the stack, and natural convection can be triggered. Apart from some recent experimental studies, these effects are usually neglected in thermoacoustics : gravity is neglected in all commercial codes used to design thermoacoustic devices.

We focus here on a simplified standing-wave thermoacoustic engine, composed of a horizontal cylindrical tube filled with gaz. The tube wall is either insulated or in simple thermal contact with the outside air. A short porous medium is positioned close to one of the tube ends. One of its ends is maintained hot by thermal contact with a hot heat-exchanger (which can be realized by attaching a spiral-shaped resistive wire to the porous medium). We perform a 3D numerical study using a finite volume code for solving Navier-Stokes equations under Boussinesq approximation. A penalisation method is used to account for natural convection within the porous medium, which is considered to be macroscopically homogeneous. Its physical characteristics are permeability, porosity, thermal conductivity, anisotropy. We study the influence of these physical characteristics on the flow and temperature fields. We show that such flows are fully three-dimensional and that the temperature distribution can be significantly different from simple heat conduction. Therefore they can influence the starting conditions of the thermoacoustic engine, as well as steady operating conditions.