2D Flow Past a Confined Circular Cylinder with Sinusoidal Ridges Kieran Cavanagh 1* Dr. Rachmadian Wulandana 2 1,2 Mechanical Engineering Program, State University of New York at New Paltz, New Paltz, NY, USA. * Dept. of Mathematics, State University of New York at New Paltz 1. Introduction Flow past a circular cylinder is a classical problem in fluid mechanics. Cylindrical structures immersed in viscous flow, such as smokestacks, bridge struts, measurement instruments, medical devices, etc., are common in engineering applications, so understanding the flow physics in these situations is of prime importance. While a significant amount of work has been done analyzing viscous flow past an unconfined circular cylinder, there is significantly less work studying the same problem with a confined cylinder. These situations arise in applications such as pipe flow, blood flow through arteries, or in situations where the scaling of a particular experiment requires wall effects to be taken into consideration. There are various effects imposed on the flow in the confined case, particularly when the cylinder is confined to a plane channel. For example, when no-slip conditions on the walls are assumed, the velocity profile becomes parabolic as opposed to uniform. The von Kármán vortex street that appears at the onset of the laminar periodic shedding regime exhibits different behavior when confined to a plane channel, as the walls limit the motion of vortices moving perpendicular to the flow [1]. Furthermore, a variety of effects have been noted when the ratio of cylinder diameter to channel width (also known as blocking ratio) changes. For instance, evidence suggests that the critical Reynolds number marking the start of the periodic shedding regime increases with increasing blocking ratio [2]. This is likely because the walls inhibit the oscillation of the near-wake tail, hence enhancing the stability of the near-wake region and postponing the transition to the periodic shedding regime [3]. Surface roughness can have a considerable effect on the flow physics, as well, most notably at high Reynolds numbers. While most surface roughness has a relatively random pattern, predictable forms of roughness can appear in certain contexts. For example, consistent waviness resembling sinusoidal waves can appear on the surface of 3D printed solids (see Figure 1) due to vibrations caused by the 3D printing process or external events. The effect of surface roughness is primarily studied at high Reynolds numbers [4], but in the present study we study the flow effects at Reynolds numbers in the steady laminar and periodic shedding regimes. Figure 1: Waviness on 3D printed solid We use the CFD Module of COMSOL Multiphysics 5.4 to simulate two-dimensional flow past a circular cylinder with consistent sinusoidal ridges confined to a plane channel with fixed blocking ratio. Flow effects are studied at Reynolds numbers of 20, 50, 200, and 500. We perform steady and time-dependent simulations to measure a variety of quantities of interest, such as the recirculation zone length and drag coefficient in the laminar regime (corresponding to Re = 20 and 50), and the Strouhal number, peak-to-peak lift coefficient amplitude, and mean drag coefficient in the periodic shedding regime (corresponding to Re = 200 and 500). 2. Problem Formulation To model the sinusoidal ridges, we parametrically define the cylinder boundary in polar coordinates by () =  2 +  ⋅ cos() , 0 ≤  ≤ 2 Where L is the base cylinder diameter,  is the amplitude of the ridges, and  is the total number of ridges. For all simulations, we select  = 0.15m. Motivated by the size of the observation chamber utilized in a closed loop water flow tank available in Mechanical Engineering Program of our campus, the two-dimensional computational domain is selected to have channel length and width of 20 and 3, respectively. Following Schäfer 5 , the center of the cylinder is positioned in the center of the channel, a Excerpt from the Proceedings of the 2019 COMSOL Conference in Boston