High Order Accurate Numerical Simulation of Vortex-Induced Vibrations of a Cooled Circular Cylinder Case using Solution Dependent Weighted Least Square Gradient Calculations

Abstract

In this paper, the fluid-structure interaction problem: vortex-induced vibration of a cooled circular cylinder involving thermal buoyancy is numerically investigated. The elastically mounted cylinder having a temperature lower than the flowing fluid is modelled using mass-spring-damper hence allowed to vibrate in the transverse direction to the flow direction. The gravity is acting opposite to the flow direction. In-house fluid-structure interaction solver is developed based on Harten Lax and van Leer with contact for artificial compressibility Riemann solver. The arbitrarily Lagrangian-Eulerian formulation is employed here, and the mesh is dynamically moved using radial basis function-based interpolation. The solution-dependent weighted least squares based gradient calculations are developed to achieve higher-order accuracy over unstructured meshes. The laminar incompressible flow at Reynolds number, Re = 200, and Prandtl number, Pr = 0.71, is simulated for the mass ratio of 1 and reduced damping coefficient of 0.001. The flow is investigated for Richardson number (-1, 0) and over a wide range of natural frequencies of the cylinder. The heat transfer characteristics from a cylinder are captured and compared with the existing literature results. From the study, it can be observed that in the presence of the thermal boundary layer, the oscillation of the cylinder increases to its maximum amplitude, particularly for values of natural frequencies (0.063 – 0.3).