Flow Over A Circular Cylinder Vijay Guvvada,Vidur Paliwal,Vishnu Vardhan,Gaurav Vaibhav,Mofeez Alam B. Tech. Aerospace, Indian Institute of Space Science and Technology
Abstract — — When When a fluid flows around a stationary cylinder or when a cylinder moves through a stationary fluid, the fluid exerts a force on the cylinder. The Component of this force in the direction of free stream velocity is called Drag force. Drag force depends on many factors like shape, orientation etc.In this experiment the drag force on a circular cylinder is found by equating torque on the cylinder and a dead weight connected to it with the help of the deflection of dead weight. This experiment presents the variation of C d with Reynolds Number over the range 1.687*104 -1.04681*105. The Cd decreases with Reynolds number over this range. Keywords-Drag Keywords-Drag force, Reynolds numb er, Torque, Flow seperation, Drag coefficent
I.
INTRODUCTION
Drag, or more specifically air drag, is a phenomenon that occurs as an object passes through a fluid.There are a few factors that determine the drag force that an object experiences. Some of the moreobvious factors are shape, speed, fluid medium, and surface of the object. Thus we have 2 kinds of bodies depending upon the shape- bluff body and streamline body. When the drag force is more due to pressure it is called bluff body and if the contribution of skin friction drag is high-then it is called streamline body. In some instances these factors are manipulated in order to either minimize or maximize drag. The drag coefficient over a cylinder decreases with increase in Reynolds number for the laminar, subcritical and supercritical regimes and in supercritical regime there is a phenomenon called drag crisis-which is an intense decrease in Cd due the movement of the point of separation downstream to 120~130 degree from 80 degree. This phenomenon is seen because the boundary layer becomes turbulent and as it has more kinetic energy -fluid par ticles can travel further in the adverse pressure gradient. After the supercritical regime the Cd increases as the shear forces keeps on increasing due to lage pressure gradient in the normal direction of wall. The parameters such as roughness, freestream turbulence and spanwise flow has not been considered in this experiment. These parameters have an important effect on the flow over the cylinder. In other cases the drag forces must simply be known in order to design for other parameters possibly such as engine horsepower, structural strength, etc. Regardless of the need for finding the drag force, the need for an accurate calculation of this force persists. With this in mind, we experiment with shapes, speeds, and methods in order to draw insight on the ability to predict drag
Figure 1- Ideal flow over a cylinder
Figure 2- Real flow over a cylinder
In this experiment we find the drag force on the cylinder by connecting it to a dead weight and with the help of the deflection on the dead weight we find the drag force on the cylinder. A relation was established between the angle of deflection and the drag force on the body. The body is held by a rod on the top of it so that it is pivoted for free rotation. We got the results for a Reynold number range of of 1.687*104 -1.04681*105
II.
EXPERIMENTAL APPARATUS
The Experiment requires the following equipments Wind Tunnel Cylinder, Dead weight, connecting rods Manometer
Fig.1 (experimental apparatus)
Fig. 2 (experimental apparatus)
III.
THEORY
The sources of this drag are: (a) friction between the fluid and the surface of the cylinder, and (b) a non-uniform pressure distribution. The cylinder in the fluid stream presents a certain area perpendicular to the direction of fluid motion. This is called the planeform area of the cylinder (length x width (diameter)) the fluid moves toward and is deflected around the cylinder, some of its momentum is transferred to the cylinder in the form of pressure on the projected area facing the flow. If the flow follows the contour of the cylinder, the pressure on the side facing the flow is balanced by the pressure on the reverse side in which case the pressure drag is very small or zero. (see Figure 1). This condition is described by potential theory where the fluid is ideal and is realized in real fluids at very low Reynolds numbers. At high Reynolds numbers, the flow does not follow the contour of the cylinder, i.e., the boundary layer grows more rapidly for an adverse pressure gradient and if the pressure gradient is large enough, separation may occur, and turbulent eddies form in the wake of the cylinder.
In this case the pressure on the reverse side fails to recover (see Figure 2) leading to an unbalanced pressure distribution and pressure drag. Ordinarily, it is not practical to separate the viscous and pressure drag forces, and indeed, it is usually their sum in which we are interested. Therefore, the usual practice is to characterize their combined effects with two dimensionless parameters, the drag coefficient
-------- (1)
and the Reynolds number ,
---------(2)
Where, Fd is the drag force, U is the free stream velocity, Ap is the frontal area, and D is the diameter (cylinder).
The drag force on the cylinder is calculated as Fd=6.14tanӨ
IV.
PROCEDURE
The experiment “flow over a cylinder” was performed on a low speed wind tunnel and the following steps were taken. The reference pressure tapping and the tapping inside the test section were connected to the manometer. The blower is switched on and the readings were taken on a varied range of Rotational speed of the blower. Also in each case the angle by which the outer cylinder gets deflected is also noted down. The pressure drop at the outlet of the settling chamber and inlet of the test section was measured which was used to calculate the Free stream velocity. V. SAMPLE CALCULATION
Sample calculation for rpm 1200. h30 = 6.8 h atm=10.4 Similarily, h29=1.8cm P30=Patm+ρm*g*h30 = Patm+791.8*9.81*((10.4-6.22)/100) =101643.47 Pa P29= Patm+ρm*g*h30 =Patm+791.8*9.81*((10.4-1.8)/100) =101643.47 Pa ∆ p=P30-P29 = 388.378 Pa V=(2*∆p/ρa)^0.5 (2*388.378/1.204)^0.5=25.43m/s Re=ρVd/μ 1.204*25.43*0.05/(1.85*10^-5)=8.44*10^4 Fd=6.14tanӨ 6.14*tan12.5=1.36N Fref.=0.5*ρ*V^2
0.5*1.204*(25.43)^2=388.378 Pa Cd=Fd/(Fref *S)=1.42/(388.378*2.25*10^-3)=1.56 VI. OBSERVATIONS
Cd Vs Re
3 2.5 g a r 2 D f o t n 1.5 e i c i f f e o 1 C
Cd Vs Re
0.5 0 0.00E+00
2.00E+04
4.00E+04 6.00E+04 8.00E+04 Reynolds Number, based on Frontal Area
1.00E+05
1.20E+05
Fig 3. (Cd vs Re)
dragVs Reynolds number 2.5
2 g a r D f 1.5 o t e n c i f 1 f e o C
dragVs Reynolds number
0.5
0 0.00E+00 2.00E+04 4.00E+04 6.00E+04 8.00E+04 1.00E+05 1.20E+05 Reynold Number
Fig 4. (Fdvs Re)
VII. R ESULT AND CONCLUSION In the experiment “flow over a cylinder” following points were figured out. 1.
the variation in the Cd is not accurately measured for low reynolds number 1.64*10^4- 5.6*10^4 because the error due to fluctuation of the measurement of Deflection was of the order of the reading itself.
2.
After Re greater than 5.6*10^4 , the amplitude of oscillation was small and we got fairly steady trend of Cd.
3.
On increasing the Reynolds no. in the above mentioned range the drag force increases. The explanation why we got such trend in the plot Re vs Cd is that, If ReD is less than about 100,000 the boundary layer remains laminar from the stagnation point at the front of the cylinder to the point where it separates. The resulting flow pattern shown in fig. termed sub-critical, is associated with a high drag on the cylinder. The laminar boundary layer separates just upstream of the maximum thickness. Separation occurs because the boundary layer anticipates the deceleration of the flow (and therefore positive pressure gradient) that would otherwise occur on the rearward face of the cylinder. Downstream of separation the fl ow quickly becomes turbulent and a broad wake is formed. The wake as a whole is unstable and rolls up into vortices that are shed antisymmetrically at regular intervals from the cylinder. This type of wake is called a von Kármán vortex street. Because of separation the pressure remains low and approximately constant over the rearward face of the cylinder. This causes a net imbalance of pressure forces on the cylinder, usually referred to as the pressure drag. Pressure drag accounts for about 90% of the total drag on the cylinder in this regime. The remaining 10% is due to skin-friction drag - friction between the flow and the cylinder. Most skin-friction drag is produced on the forward-face of the cylinder where the boundary layer is thin and velocity gradients at the cylinder surface are large. As observed in above graphs (fig.4 , 3), as reynols no. increases Cd decreases but Fd increases because the 0.5*ρ*V^2 increases more rapidly than the increase in force with velocity, as reference pressure is i n denominator so it compensate the increase in numerator, overall we get decrease in Cd. The obtained graph can be compared with the available data within the range(50000-100000).
VIII. ACKNOWLEDGEMENT We are very much thankful to all who contributed directly or indirectly in performing the experiment “Flow over a symmetric air foil” on a low speed wind tunnel in aerodynamic lab IIST. We are specially thankful to Dr. Vinoth B.R. and Dr. Satyeesh who gave their maximum in performing this experiment. We are also thankful to all lab assistants and our friends who helped us.
IX. REFERENCES 1. Pope, Alan, Wind Tunnel Testing, John Wiley & Sons, Inc., New York, 1954 2.http://mars.uta.edu/ 3. http://www.eng.fsu.edu 4. https://www.google.co.in/search?q=Cd+vs+Re&source=lnms
X. APENDIX
