Computational study of steady flow across a modified semi-circular cylinder in power-law fluids

Abstract

A numerical study was performed to address the viscous flow characteristics of a power-law model fluid across a semi-circular cylinder with a rectangular extension (referred to as Case A), where the curved surface faces upstream. This configuration was compared with a standard semi-circular cylinder (referred to as Case B). The study was focused on the low Reynolds number (Re) spanning from 5 $\le$ Re $\le$ 45, with flow simulations performed for three distinct power-law indices (n = 0.6, 0.8, and 1). Understanding the behavior of non-Newtonian fluids under such configurations is critical for optimizing engineering systems involving flow control, drag reduction, and enhanced performance in food processing industries and biological applications. The study provides a comprehensive analysis of surface parameters, including vorticity and pressure coefficients, along with detailed insights of the separation angle and streamline visualization. The investigation also aimed to determine the critical Reynolds number ($R{e}_c$) for case A for various n, revealing $R{e}_c$ = 34 at n = 0.6, $R{e}_c$ = 39 at n = 0.8, and $R{e}_c$ = 46 at n = 1. Furthermore, the wake generated behind the cylinder in Case A exhibited a reduction of 15.426% for n = 0.6 and 12.229% for n = 1 compared to the wake generated in Case B. The coefficient of drag ($C_D$) was observed to be lower for Pseudo-plastic fluids and higher for Newtonian fluids. The transition from n = 1 to n = 0.6 caused a decline in $C_D$ value of 29.059% for Re = 5 and 28.425% for Re = 45.