A numerical model of thermoacoustic heat pumping inside a compact cavity

This paper presents a numerical study of thermoacoustic heat pumping along a stack of solid plates placed inside a compact cavity submitted to an oscillating flow. Velocity and pressure fields are controlled by two acoustic sources: a main “pressure” source monitoring the fluid compression and expansion phases, and a secondary “velocity” source generating the oscillating fluid motion. Numerical simulations are performed with an “in-house” code solving Navier–Stokes equations under a Low Mach number approximation in a two-dimensional geometry. In the linear regime, thermoacoustic heat pumping is correctly described with this model for different sets of parameters such as thermo-physical properties of the stack plates, amplitude of pressure oscillation or of the velocity source, phase shift between both sources. Numerical results on the normalized temperature difference established between the ends of stack plates are in excellent agreement with analytical estimates and experimental results published in the literature. Several configurations corresponding to different thermal conditions applied on the outside wall and an inside separation plate are then considered. If the separation plate is adiabatic, temperature varies linearly along the stack, recovering classical linear theory’s results. If the separation plate is thermally conductive, the model, providing detailed description of local heat and mass transfer, shows that the temperature field becomes fully two-dimensional and thermoacoustic heat pumping is less efficient. The model is well adapted to explore the influence of local heat transfer constraints on the heat pump efficiency and thus well suited for detailed analyses of more complex mechanisms such as buoyancy effects.