In this paper, the Lattice Boltzmann Method (LBM) is used to study the acoustic waves propagation inside a differentially heated square enclosure filled with air. The waves are generated by a point sound source located at the center of this cavity. The main aim of this simulation is to simulate the interaction between the thermal convection and the propagation of these acoustic waves. The results have been validated with those obtained in the literature and show that the effect of natural convection on the acoustic waves propagation is almost negligible for low Rayleigh numbers (Ra ≤ 10 4 ), begins to appear when the Rayleigh number begins to become important (Ra ≥ 10 5 ) and it becomes considerable for large Rayleigh numbers (Ra ≥ 10 6 ) where the thermal convection is important.
The present paper implements the lattice Boltzmann method (LBM) to simulate the emission and propagation of sound waves in three-dimensional (3D) situations, with the point source technique used for wave emission. The 3D numerical model is exercised on a benchmark problem, which is the simulation of the lid-driven cavity flow. Tests are then proposed on acoustic situations. The numerical results are first confronted with analytical solutions in the case of spherical waves emitted by a single point source at the center of a cavity. In view of acoustic streaming applications, we then study the case where the waves are emitted from a circular sound source placed at the center of the left boundary of a three-dimensional cavity filled with water. With the circular source discretized as a set of point sources, we can simulate the wave propagation in 3D and calculate the sound pressure amplitude in the cavity. Tests using different emission conditions and LBM relaxation times finally allow us to get good comparisons with analytical expressions of the pressure amplitude along the source axis, highlighting the performance of the lattice Boltzmann simulations in acoustics.
In this paper, a three‐dimensional (3D) numerical study of thermal convection and acoustic waves is presented using a hybrid method. This method consists of two computational approaches: the lattice Boltzmann method (LBM) with multiple relaxation times for the study of the fluid behavior and the finite difference method (FDM) for the description of the thermal exchange. The two approaches have been validated by studying two benchmark problems reported in the literature. The LBM was validated by simulating the flow induced by a lid‐driven cavity. The FDM was checked by simulating natural convection in a differentially heated cubic cavity filled with air. After this validation, the main focus was on the study of enhancement of the heat transfer in a 3D cavity using a vibrating acoustic source. The numerical study is performed for different values of the wave amplitude, the Rayleigh number (
italicRa ${Ra}$), and the sound source size. It shows that the heat transfer is significantly improved for a low
italicRa ${Ra}$. However, for high
italicRa ${Ra}$ values, natural convection cannot be neglected in front of forced convection. The transfer is also influenced by the variation of the source size. This allows obtaining the optimal size corresponding to the maximum heat exchange.
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