4 th International Conference on Mechanical Engineering, December26-28, 2001, Dhaka, Bangladesh/pp.97-105 Keynote Paper 97 Keynote Paper INTERACTION OF THERMOACOUSTIC WAVES AND BUOYANCY- INDUCED FLOWS IN AN ENCLOSURE Bakhtier Farouk and Murat K. Aktas Department of Mechanical Engineering and Mechanics, Drexel University 3141 Chestnut Street, Philadelphia, PA 19104 USA Abstract The behavior of thermoacoustic waves in a nitrogen-filled two-dimensional cavity is numerically studied. The vertical walls of the cavity are heated or cooled to generate the thermoacoustic waves. Both impulsive and gradual change of the wall temperatures was considered. When a vertical wall is impulsively and nonuniformly heated, the resulting waves induce remarkable two-dimensional flows within the enclosure. The observed thermoacoustic waves oscillate and eventually decay due to the viscosity and thermal conductivity of the fluid. Effects of thermoacoustic wave motion on the developing natural convection process in a compressible gas-filled square enclosure were investigated. In the cases considered, the left wall temperature is raised impulsively or gradually while the right wall is held at a specified temperature. The top and the bottom walls of the enclosure considered are thermally insulated. The numerical solutions were obtained by employing a highly accurate flux corrected transport (FCT) algorithm for the convection terms and by coupling these to the viscous and diffusive terms of the full Navier-Stokes equations. The strength of the pressure waves associated with the thermoacoustic effect and resulting flow patterns are found to be strongly correlated to the rapidity of the wall heating process. Fluid thermal diffusivity was found to affect the strength of the thermoacoustic waves and the resulting interaction with the buoyancy-induced flow. Keywords: Thermoacoustic waves, buoyancy-induced convection, flux-corrected transport algorithm. INTRODUCTION When a compressible fluid is subjected to a rapid temperature increase at a solid wall, part of the fluid in the immediate vicinity of the boundary expands. This gives rise to a fast increase in the local pressure, and leads to the production of pressure waves called thermoacoustic waves. The heat transfer effects of such waves may be very significant when the fluid is close to the thermodynamic critical point or when other modes of convection are weak or absent. This motion may cause unwanted disturbances in otherwise static processes like cryogenic storage or may introduce a convective heat transfer mode to the systems in zero- gravity environment where it is assumed that conduction is the only heat transfer mode. The problem of thermoacoustic waves in a quiescent semi-infinite body of a perfect gas, subjected to a step change in temperature at the solid wall was studied analytically (Trilling, 1955) in order to determine how the sound intensity depends on the wall temperature history. The one-dimensional compressible flow equations were linearized and a closed-form asymptotic solution was obtained using a Laplace transform technique. A simplified model (the hyperbolic equation of conduction) for thermoacoustic motion was compared with one-dimensional Navier-Stokes equations model of the phenomena and limitations of the simplified approach was discussed (Churchill and Brown, 1987). A more general class of solutions for the thermoacoustic waves was obtained by using the Laplace transform method with numerical inversion for equations of the linear wave model for step and gradual changes in the boundary temperature (Huang and Bau, 1995). The equations of the nonlinear wave model were numerically solved using finite differences scheme modified with a Galerkin finite element interpolation in space. A similar analysis for thermoacoustic waves in a confined medium was repeated more recently (Huang and Bau, 1997). In both geometries the medium considered was a gas with Prandtl number of 0.75. Thermoacoustic convection phenomena were experimentally investigated in a cylinder containing air with temperature measurements in normal and reduced gravity environment (Parang and Salah-Eddine, 1984). No pressure measurement was reported. Experimental measurements of pressure waves generated by rapid heating of a surface were reported in a relatively recent paper (Brown and Churchill, 1995).