Background_Flow_Visualization_Boundary_Layers_Wakes1 - Lab...

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Lab 1: Flow Visualization, Boundary Layers and Wakes Background 1. Objectives At the completion of this experiment you will be able to: 1. Understand basic concepts of viscosity, boundary layers, and boundary-layer separation. 1. Measure the Karman vortex shedding frequency behind a circular cylinder. 2. Measure the boundary layer growth on a flat plate. 2. Specific Applications Both channel flows and "bluff-body" flows (like the cylinder wake) are common. Bluff-body flows have large separated wakes and high drag coefficients. Examples include trucks, cars, buildings, oil platforms, and many bombs. Airfoils are used as wings, propellers, rotors, turbines, compressors, etc. 3. Introduction This experiment is designed to demonstrate various flow phenomena that occur in nature and which will be discussed in the fluid mechanics courses. Boundary layers, separation, and the formation of Karman vortices will be discussed in an introductory manner. 3.1 Boundary Layers The boundary-layer concept was introduced at the turn of the century by L. Prandtl to treat the effect of viscosity in a flow along the surface of a body. Viscosity is the effect of friction between fluid elements, or fluid elements and surfaces. Prandtl considered the flow to be composed of two regions: 1. A very thin region in the neighborhood of the body where the viscous (friction) effects cannot be neglected. This region is called the boundary layer. 1. The region outside the boundary layer where the viscous forces can be neglected. Usually the inviscid region is irrotational. One of the first cases in which the boundary layer theory was tested is that of the flow along the horizontal flat plate. Figure 1 shows the viscous boundary layer region and the inviscid region. 3.1.1 Boundary Layer Region This region is a very thin layer along the surface of the body in which the fluid speed changes very rapidly, from zero at the surface, to the freestream speed, U , at the edge of the boundary layer. This is shown in Figure 1. The condition of zero relative velocity at a surface is called the no-slip condition, and the "edge" of the boundary layer is commonly defined as the location in the fluid where the fluid speed parallel to the body 1
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2 is equal to 0.99 U . The boundary layer thickness, δ (x), is the distance normal from the body to this edge. The boundary layer thickness increases along the plate due to the diffusion of vorticity as the fluid travels along the body. Friction between the layers of fluid gradually slows down fluid that is farther and farther from the wall. The velocity gradient is greatest near the wall. It decreases as the edge of the boundary layer is approached and the fluid speed approaches that of the free stream. A shear stress is present as a result of viscosity and the velocity gradient. Newton's law of friction, generally valid for flows of gases and water, gives: where τ is shear stress, μ is viscosity, u is velocity in the direction parallel to the flow,
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Background_Flow_Visualization_Boundary_Layers_Wakes1 - Lab...

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