FLOWS PAST A CIRCULAR CYLINDER

Flows Past a Circular Cylinder

Flows past a circular cylinder

Chapter 1: Introduction

External flows past objects have been studied extensively because of their many practical applications.  For example, airfoils are made into streamline shapes in order to increase the lifts, and at the same time, reducing the aerodynamic drags exerted on the wings.  On the other hand, flow past a blunt body, such as a circular cylinder, usually experiences boundary layer separation and very strong flow oscillations in the wake region behind the body.  In certain Reynolds number range, a periodic flow motion will develop in the wake as a result of boundary layer vortice being shed alternatively from either side of the cylinder.  This regular pattern of vortices in the wake is called a Karman vortex street (Bertin, 2002: 69).  It creates an oscillating flow at a discrete frequency that is correlated to the Reynolds number of the flow. The periodic nature of the vortex shedding phenomenon can sometimes lead to unwanted structural vibrations, especially when the shedding frequency matches one of the resonant frequencies of the structure.  One example is the famous Tacoma Narrow bridge incident and this topic has been discussed in great details in the Tacoma bridge link. 

In this presentation, we are going to investigate the flow past a circular cylinder and study the turbulent wake flow field using the Particle Image Velocimetry (PIV) technique.  Based on the PIV velocity field measurements and other reference information, a comprehensive discussion about many important flow concepts such as: boundary layer flow separation, wake flow, vortex shedding, vortex-induced oscillations, aerodynamic loading, momentum balance, and the lift and drag forces on an immerse body, will be given in the following section.

Chapter 2: Theory

Flow Separation: The presence of the fluid viscosity slows down the fluid particles very close to the solid surface and forms a thin slow-moving fluid layer called a boundary layer.  The flow velocity is zero at the surface to satisfy the no-slip boundary condition.  Inside the boundary layer, flow momentum is quite low since it experiences a strong viscous flow resistance. Therefore, the boundary layer flow is sensitive to the external pressure gradient (as the form of a pressure force acting upon fluid particles).  If the pressure decreases in the direction of the flow, the pressure gradient is said to be favorable. In this case, the pressure force can assist the fluid movement and there is no flow retardation (Williamson & Roshko, 1990: 38).  However, if the pressure is increasing in the direction of the flow, an adverse pressure gradient condition as so it is called exist.  In addition to the presence of a strong viscous force, the fluid particles now have to move against the increasing pressure force.  Therefore, the fluid particles could be stopped or reversed, causing the neighboring particles to move away from the surface.  This phenomenon is called the boundary layer separation.

Wake: Consider a fluid particle flows within the boundary layer around the circular cylinder.  From the pressure distribution measured in an earlier experiment, the pressure is a maximum at the stagnation point ...