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Wind Tunnel - Pressure
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This experiment is done on a wind tunnel. For general information of this windtunnel and the data that can be obtained from it, pl. go through the Wind Tunnel fundamentals (first tab)

• Verify the negative suction pressures on the top surface ( measurement station 1 to 5, X- axis) , and low positive/low negative pressures on the bottom surface ( measurement station 6 to 10, X -axis) , as in Fig above.

PRESSURE DISTRIBUTION OVER AN AIRFOIL

In this lab the generation of Lift and Drag from the overall pressure distribution surrounding a streamlined body will be investigated. The investigation described herein applies to many fluid dynamic scenarios like wind turbine blades, wings on F1 cars, helicopter blades, propeller blades and hydrofoils. An Airfoil is a body designed to produce lift from the movement of the fluid around it. Specifically lift is a result of circulation in the flow produced by the airfoil.

Figure 1: Pressure distribution of an airfoil and generation of lift and drag

INTEGRATION OF PRESSURES TO OBTAIN LIFT AND DRAG

The pressures over an airfoil are generally integrated over the surface to produce the resultant Normal and Axial forces. These forces are then converted to Lift and Drag by taking the angle of attack into account. The pressures are first converted into dimensionless coefficients,

and integrated.

Lift and drag forces are related to stress distributions on a body through integration. Consider the stress acting on the airfoil. There is a pressure distribution and a shear stress distribution. To relate the stress to force, select a differential area as shown in figure below. The magnitude of the pressure force is dFp = pdA and the magnitude of the viscous force is dFv = ΓdA. The differential lift force is normal to the free stream direction

dFL =  - p dAsinθ – Γ dAcosθ

and the differential drag is parallel to the free stream direction

dFD = -p dAcosθ + Γ dA sin θ

Integration over the surface of the airfoil gives the lift force (FL) and drag force (fD)

FL = ∫ (-p sinθ – Γ cosθ) dA

FD = ∫ (-p cosθ + Γ sinθ) dA

This equations of FD and FL show that the lift and drag are related to pressure distributions through integration.

The Lift Coefficient

The lift coefficient is a number that aerodynamicists use to model all of the complex dependencies of shape, inclination, and some flow conditions on lift. The lift coefficient expresses the ratio of the lift force to the force produced by the dynamic pressure (q∞) times the area. By knowing the lift coefficient, we can predict the lift that will be produced under a different set of velocity, density (altitude), and area conditions using the lift equation. For given air conditions, shape, and inclination of the object, we have to determine a value for CL to determine the lift.

Where L is the lift force, ρ is air density, Ʋ is the true air speed, A is the planform area (projected area of the wing) and CL is the lift coefficient.

The Drag Coefficient

The drag coefficient is a number used to model all of the complex dependencies of shape, inclination, and flow conditions on aircraft drag. The drag coefficient expresses the ratio of the drag force to the force produced by the dynamic pressure times the area.  In a controlled environment (wind tunnel) we can set the velocity, density, and area and measure the drag produced. Through division we arrive at a value for the drag coefficient. As pointed out on the drag equation slide, the choice of reference area (wing area) will affect the actual numerical value of the drag coefficient that is calculated.  We can predict the drag that will be produced under a different set of velocity, density (altitude), and area conditions using the drag equation.

For given air conditions, shape, and inclination of the object, we must determine a value for CD to determine drag. Determining the value of the drag coefficient is more difficult than determining the lift coefficient because of the multiple sources of drag. The drag coefficient given above includes form drag, skin friction drag, wave drag, and induced drag components.

Where FD is the drag force, [ ho]  is the mass density of the fluid [v]  is the velocity of the object relative to the fluid, A is the reference area, and CD is the drag coefficient.

Cite this Simulator:

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