A numerical study on unsteadiness of vertical flow around a horizontal heated square cylinder with variable thermal buoyancy

Abstract

Analyzing the unsteadiness of flow is crucial due to its significant influence on flow characteristics, and at times, it can even alter the flow pattern entirely. In this research, the effects of two distinct types of unsteadiness—thermal buoyancy and vortex shedding—were examined in the context of laminar flow around a square cylinder. Initially, the impact of each unsteady phenomenon on the flow was studied independently. Subsequently, the combined influence of both unsteady factors on the flow was assessed. The Navier–Stokes equations are solved using a finite-volume approach, which discretizes the computational domain into small control volumes. This technique integrated a pressure-based method with a symmetry-preserving technique, which minimizes numerical diffusion, making it well-suited for accurately capturing flow instabilities. An in-house solver was developed specifically for this purpose. The calculations were conducted for Richardson numbers (Ri) ranging from 0 to 0.35 and for three different Prandtl numbers (Pr) of 0.2, 0.7, and 2.5, all at a Reynolds number (Re) of 100. Vortex shedding, referred to as type 1 unsteadiness, occurs naturally at Re = 100. To induce type 2 unsteadiness, Richardson numbers were varied according to a sinusoidal equation. The findings revealed that the drag coefficient of the cylinder is significantly affected by the frequency of Richardson numbers' variation. As the variation frequency decreased, the difference in drag coefficients during the increasing and decreasing phases of Ri also diminished.