Advancements in mathematical modeling and numerical simulation: Immersed boundary method for Navier-Stokes equations applied to stationary and rotating isothermal cylinders

Résumé

This study investigates the growing scientific and industrial interest in the dynamics of fluids around bodies, with a particular focus on thermal fluctuations. These phenomena are prevalent in various scenarios, such as oil extraction platforms, power transmission lines, and fluid-structure interactions, necessitating a comprehensive understanding of vortex generation, heat transfer, and fluid dynamic forces. We employ the Immersed Boundary Method (IBM) to simulate two-dimensional, incompressible flows around stationary and rotating heated (isothermal) cylinders. Using a computational framework developed in C/C++, we analyze the effects of variations in cylinder rotation rates on flow dynamics and thermal distributions. This study involves multiple simulations to evaluate the stability of the method and extract relevant parameters, including drag, lift coefficients and Nusselt numbers, along with velocity, pressure, vorticity, and temperature fields. Through systematic comparison with existing literature, we aim to validate our findings and contribute to the continuous improvement of numerical accuracy in this domain. By elucidating these complex phenomena, our research aims to provide valuable insights for practical applications in industrial and engineering contexts. The objective of this work is to analyze the combination of heat transfer phenomena with rotation in isothermal cylinders and their thermofluid-structure interaction. To achieve this, a low computational cost C/C++ code (in terms of memory and computational resources) was developed. Furthermore, numerical simulations indicated that with an increase in the Reynolds number, there is an increase in the drag coefficient, highlighting the significant influence of the pressure distribution downstream of the cylinder. This pressure distribution is strongly affected by vortex formation and detachment, thereby validating the methodology.