Characterisation of Flow Around a Sphere

Topics: Aerodynamics, Fluid dynamics, Reynolds number Pages: 12 (2473 words) Published: August 21, 2013

One of the most widely used methodologies in characterising the quality of a wind tunnel is to study the flow over a sphere.The flow around the bluff body was characterised using smoke test, and the region of flow separation was analysed. The drag characteristics of 3 spheres of different diameters were studied for a wide range of Reynolds number. The Reynolds number at which the transition occurs is strongly dependent on the degree of turbulence in the wind tunnel. Based on the following tests, the quality of the wind tunnel was determined. The turbulence level in the wind tunnel was experimentally studied. The sphere test results were in good agreement with the literature and the quality of the wind tunnel was found to be fairly good.


FIGURE 1.1. Flow around a sphere

FIGURE 1.1 shows that whenever a flow encounters a body, the flow tends to curve around that body. As air flows around the sphere, the flow gets deflected due to the shape and there is a difference in pressure at various points on the sphere. Pressure decreases as we move from front to the top point and increases as we move from top to the rear. For the latter part there is a chance for flow separation due to adverse pressure gradient. Spheres are known to have a distinct critical Reynolds number above which the flow on the upstream face of the sphere is fully turbulent causing the drag coefficient to drop dramatically. This is because the turbulent boundary layer results in separation further aft than a laminar boundary layer, thus producing a smaller wake. The critical Reynolds number for the three spheres was determined by examining the measured drag coefficient CDp as a function of Reynolds number. To understand the quality of flow in the test section, turbulence level is the flow quality parameter. In this experiment, the level of turbulence and resultant turbulence factor for the wind tunnel was determined. ������������������������ ������������������������������������������������������������������, ������������ = 1

������������������������ ������������������������������ ������∞ ������

������������������������������������������������ ������������������������������������������������������������������, In which, ������∞ = 1

������������ 2 ������ = 4

������ ������ 2 2 ∞ ∞

������������ ������∞

where ‘d ’ is the sphere diameter and ‘Δp ‘ is the pressure difference between front and rear orifices in the sphere.


A body moving through a fluid experiences a drag force, which is usually divided into two components: frictional drag and pressure drag. Frictional drag comes from friction between the fluid and the surfaces over which it is flowing. This friction is associated with the development of boundary layers. Frictional drag is important for attached flows (that is, there is no separation), and it is related to the surface area exposed to the flow. Pressure drag comes from the eddying motions that are set up in the fluid by the passage of the body. This drag is associated with the formation of a wake. Pressure drag is important for separated flows, and it is related to the cross-sectional area of the body. When the drag is dominated by viscous drag, we say the body is streamlined, and when it is dominated by pressure drag, we say the body is bluff. Whether the flow is viscous-drag dominated or pressure-drag dominated depends entirely on the shape of the body. For a bluff body, the dominant source of drag is pressure drag. Cylinders and spheres are considered bluff bodies because at large Reynolds numbers the drag is dominated by the pressure losses in the wake. The boundary layer over the front face of a sphere or cylinder is laminar at lower Reynolds numbers, and turbulent at higher Reynolds numbers. When it is laminar, separation starts almost as soon as the pressure gradient becomes...

References: 1. J.D. Anderson, Jr.”Fundamentals of Aerodynamics”, McGraw-Hill, 2001. 2. E.L .Houghton and P.W. Carpenter “Aerodynamics for Engineering Students” Fifth Edition, Butterworth-Heinemann publications, 2003. 3. B.R Munson, P.F Young, T.H Okiishi, ”Fundamentals of Fluid Dynamics” John Wiley & Sons, 2002. 4. Barlow, J.B., Rae Jr., W.H., Pope, A., Low-Speed Wind Tunnel Testing Wiley & Sons, Inc., New York, 1999. pp 147-150. 5. Robert C. Platt,”Turbulence Factors of NACA Wind Tunnels As Determined Sphere Tests”1937. 6. Dryden, H.L., Keuthe, A.M., “Effect of Turbulence in Wind Tunnel Measurements” NACA Report 342, 1929.
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