Characterisation of Flow Around a Sphere

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. CHAPTER 1 INTRODUCTION 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.

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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 ? ? ???????????? ??????? here ‘d ’ is the sphere diameter and ‘? p ‘ is the pressure difference between front and rear orifices in the sphere. 2 CHAPTER 2 LITERATURE REVIEW 2. 1 DRAG OVER BLUFF BODIES 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 pheres 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 adverse, and a large wake forms. When it is turbulent, separation is delayed and the wake is correspondingly smaller. 2. 2 TURBULENCE IN A WIND TUNNEL Usually turbulence intensity, ’I’ varies from 1-5% for low speed wind tunnel.

For a good quality wind tunnel, turbulence intensity should be less than 1%. ?????? = ?????????????????????????????? ???????????? ???????????????????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????? ???????????????????????????????????????????????? 3 ???????????? = ???????????? (???????????????????????????????????????????????????????????? ) ?????????????????? where, TF is the turbulence factor and ReC is Reynolds number at which the measured drag coefficient passes through 0. during transition from laminar to turbulent boundary layer flow. The turbulence factor is then related to the tunnel turbulence level. Using this correlation, the turbulence level in the wind tunnel may be deduced from the observed Reynolds number at which the drag of a sphere drops due to the transition of the boundary layer. 4 CHAPTER 3 METHODOLOGY 3. 1 EXPERIMENTAL SETUP A Suction-type wind tunnel is used in this experiment. It consists of a converging section, a test section and a subsequent diverging section. A set of 24 blades forms the propeller that sucks in the air.

The propeller is motored to the desired RPM value. The maximum pressure attained in the wind tunnel is the atmospheric pressure, ?????? . There are 3 sets of meshes that ensure a ? smooth streamlined flow at the inlet of the wind tunnel. The each unit of the first mesh is 1” X 1”, the second 1/8” X 1/8”, while the third mesh is the finest with each unit of dimension 1/16” X 1/16”. The test section spans 2 meters horizontally. The cross-sectional area of the test section is 600 X 900 mm2. The convergence ratio is 6:1. The sphere of 4in. iameter is set up in the test section using a hollow pipe, which is used to hold the sphere in its position in the wind tunnel and to help bring out the tubes from the static ports which then are connected to the multi tube manometer. There is an inclined manometer present, one end of which is connected to the inlet of wind tunnel and other end to the test section. The sphere models are made out of wood using two hemispherical shells. The two hemispheres are connected using a sliding wedge mechanism. Radial holes are distributed along equator of the sphere to which static probes are connected.

These tubes are brought out through the hollow steel pipe supporting the sphere and connected to the multi-manometer. 5 FIGURE 3. 1. Models FIGURE 3. 1 represents the two halves of the sphere which uses a sliding mechanism. Small holes on the surface of the sphere represent the static ports. The big hole is to insert the support stand. 6 3. 2 PROCEDURE TO FIND PRESSURE DRAG COEFFICIENT Initially the atmospheric pressure and temperature are noted to determine the density of air. Then, the wind tunnel is switched on and set to a low rpm (300).

Once the flow is fully developed, the inclined manometer reading is noted and is used to calculate the average velocity in the wind tunnel. The static pressure readings from the various probe locations are noted from the multi tube manometer. The experiment is repeated for higher Reynolds numbers by increasing the wind tunnel rpm varying from 300 to 800 rpm. ???????????? (???????????????????????????????????????????????????????????????????????? ) = 1 ? ?????????????????? 2 (?????? ) 9 4 The horizontal force is calculated by multiplying the static pressure by the projected area at each port.

Now sum up all the forces in the horizontal directions to get the drag. Horizontal Force, F = PA Cos? Non-dimentionalise the calculated drag to obtain the coefficient of drag. The graph between the pressure drag coefficient (CDp) and reynolds number (Re) is plotted and studied. FIGURE 3. 2. Distribution of ports 7 FIGURE 3. 2 represents the distribution of ports over which the forces act. The ports are numbered (1,2,3,4,… ). The angle subtended by the ports to the centre can be found out using the relation, ?????? = ?????????????????? ??????????????????????????????? ???????????????????????????????????? here ‘R’ is the radius of the sphere. The perpendicular distance from each port (r1,r2,r3,r4… ) can be found out using simple trigonometric relation. Considering it as various circular cross sections, we can find out the projected area. 3. 3 PROCEDURE TO FIND THE TURBULENCE LEVEL The critical Reynolds number and the Reynolds number during transition are calculated. Using this data, the turbulence factor is calculated for the given spheres. The turbulence factor is then related to the tunnel turbulence level from the FIGURE 3. 3. FIGURE 3. 3. Turbulence factor as a function of turbulence level (Ref. ) 8 CHAPTER 4 RESULTS AND DISCUSSION 4. 1 FLOW VISUALISATION OVER SPHERE FIGURE 4. 1. Flow visualisation over a sphere at 75 RPM 9 FIGURE 4. 2. Flow visualisation over a sphere at 85 RPM FIGURE 4. 3. Flow visualisation over a sphere at 100 RPM 10 FIGURE 4. 1 shows that at very low rpm the flow get detached very early due to in sufficient energy of the streamlines. FIGURE 4. 2 shows that as the rpm increase the energy of the streamline increases and hence flow detachment delays. FIGURE 4. 3 shows that as rpm increases even further the detachment delays to even a higher extent. 4. PRESSURE DRAG COEFFICIENT AS A FUNCTION OF NUMBER REYNOLDS 0. 9 0. 855 0. 8 0. 7 0. 6 0. 5 0. 599 Cd CDp 0. 4 0. 3 0. 2 0. 1 0 0 200000 0. 428 0. 333 0. 272 0. 222 0. 222 0. 181 0. 182 0. 154 0. 13 400000 600000 Re 800000 1000000 1200000 1400000 FIGURE 4. 4. Pressure drag coefficient as a function of Reynolds number (d=4in. ) 11 0. 9 0. 845 0. 8 0. 7 0. 6 0. 5 0. 4 0. 3 0. 2 0. 1 0 0 500000 1000000 1500000 2000000 0. 592 CDp 0. 423 0. 348 0. 269 0. 219 0. 219 0. 18 0. 179 0. 154 0. 129 Re FIGURE 4. 5. Pressure drag coefficient as a function of Reynolds number (d=6in. ) 12 0. 8 0. 748 0. 0. 6 0. 544 0. 5 0. 4 0. 3 0. 2 0. 1 0 CDp 0. 428 0. 333 0. 272 0. 214 0. 214 0. 182 0. 182 0. 154 0. 13 0 500000 1000000 1500000 2000000 2500000 3000000 Re FIGURE 4. 6. Pressure drag coefficient as a function of Reynolds number (d=8in. ) 13 0. 9 0. 8 0. 7 0. 6 0. 5 0. 4 0. 3 0. 2 0. 1 0 0 1000000 CDp 8 Inch 6 Inch 4 Inch Re 2000000 3000000 FIGURE 4. 7. Pressure drag coefficient as a function of Reynolds number for different spheres 14 Flow visualisations for 3 different spheres were carried out and it was found that drag was maximum for the large sphere due to larger projected area.

It was found that as velocity increases the pressure drag decreases and this was due to the increase in energy of each stream line at higher velocity which resulted in delay of flow detachment and hence flow reversal. CDp graphs for the 3 different spheres were drawn separately (FIGURE 4. 4, FIGURE 4. 5, FIGURE 4. 6) and similar trend was observed in all the three graphs but followed an offset (FIGURE 4. 7). The reason for this may be due to the increase in Reynolds number for different spheres even for same free stream velocity which results in shifting of the curve towards the right of the graph with increase in size of the sphere. 5 TABLE 4. 1. Pressure drag coefficient (d=4in. ) Reynolds No. 405872 385110 573991 650844 719535 797118 881247 958017 1040447 1127296 1198135 CDp 0. 855 0. 599 0. 428 0. 333 0. 272 0. 222 0. 182 0. 222 0. 181 0. 154 0. 13 16 TABLE 4. 2. Pressure drag coefficient (d=6in. ) Reynolds No. CDp 608809 727666 860986 948761 1079303 1195678 1321871 1437026 1560670 1675214 1797203 0. 845 0. 592 0. 423 0. 348 0. 269 0. 219 0. 179 0. 219 0. 18 0. 154 0. 129 17 TABLE 4. 3. Pressure drag coefficient (d=8in. ) Reynolds No. CDp 867792 1017577 1147982 1301689 1439071 1623491 1762495 1916034 2080894 2254592 2415833 . 748 0. 544 0. 428 0. 333 0. 272 0. 214 0. 182 0. 214 0. 182 0. 154 0. 13 18 4. 3 TURBULENCE LEVEL IN THE WIND TUNNEL Turbulence Factor (d=4in. ) = 797118 / 650844 = 1. 22 Turbulence Factor (d=6in. ) = 1195678 / 948761 = 1. 26 Turbulence Factor (d=8in. ) = 1623491 / 1301689 = 1. 25 TABLE 4. 4 Turbulence factor Diameter of sphere (inches) 4 6 8 Re (Transition) Rec (At CDp = 0. 3) 650844 948761 1301689 Turbulence Factor 1. 22 1. 26 1. 25 797118 1195678 1623491 Here we approximate the value of turbulent factor to 1. 23. The value for per cent turbulence is obtained from the FIGURE 3. . The per cent turbulence is 0. 23. Clearly, the turbulence level is quite low. These findings are encouraging as low levels of turbulence were found over a large range of operating test-section velocities. 19 CONCLUSION AND FUTURE WORK For a bluff body, the dominant source of drag is pressure drag. Drag basically arises due to difference in pressure at front and rear of the sphere and hence as velocity increases the separation delays and hence pressure at the back increases due to decrease in flow reversal into the wake.

At higher velocities the flow tends to be turbulent and hence more interaction is possible between streamlines and hence separation delays even further and hence drag decreases to even further values. The drag that is been mentioned here is the pressure Drag which depends on the shape of the object and not skin friction drag as skin friction drag which largely depend on the smoothness of the sphere and the flow itself, is not easy to determine under given experimental conditions. The results presented are very encouraging as they demonstrate the low turbulence level of the wind tunnel.

There are some factors, however, that may have been contributors to uncertainty in these findings. The most significant of these was the vibration seen in the mounting structure and sphere. A stiffer mounting solution may yield results with less scatter. Considering the future work, the total drag can be calculated using a strain gauge from which the skin friction drag can be found out. Accurate and reliable methods have to be implemented to find the fluctuation velocities. 20 REFERENCES 1. J. D. Anderson, Jr. ”Fundamentals of Aerodynamics”, McGraw-Hill, 2001. . 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. 21

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