Numerical Simulation of Fluid-Structure Interaction in Undulated Cavity

This study presents a numerical exploration into the phenomenon of natural convection within a cavity, characterized by a straight (cold) right wall and a wavy (hot) left wall. The focus lies in the dynamic interaction between the working fluid (air) and a sinusoidally moving solid structure (the fin). The Arbitrary Lagrangian-Eulerian (ALE) methodology is employed to handle the moving mesh, and the Galerkin weighted residual finite element method is utilized to solve the nonlinear equations and boundary conditions. A mesh validation test is undertaken, and a comparative analysis against numerical reference is included. In a novel approach, a mathematical formulation incorporating the geometric aspect ratio Ar (defined as the fundamental wavelength relative to its wavy width) is introduced into the fundamental equations. Numerical results, including isotherms, streamlines, temperature profiles, horizontal velocity, and local heat flux coefficient, are presented under specific conditions: a geometry ratio Ar=0.3, a Rayleigh number spanning from 103 to 107, and a dimensionless time t ranging from 10-5 to 3. These results are based on three distinct positions of the oscillating elastic. The findings elucidate the combined effect of convection and the vibration of the flexible oscillating fin, particularly at high Rayleigh numbers. This study contributes novel insights into the complex interplay between fluid dynamics and vibrating structures in the context of natural convection.