EGR 365 Laboratory 4a Drag On Cylinders Using Wake Momentum Balance Performed on June 15th 1999 Performed by Lee C Groeneweg Professor Dr Fleischmann OUTLINE I II III IV Background Experiment Description Process Description V VI Purpose Results Post Lab Remarks VII Design Considerations Purpose The purpose of this laboratory experiment is to experimentally determine the drag on a cylinder in crossflow using a momentum balance in the wake of the cylinder Background When a bluff body is placed into a viscous flowing fluid it experiences forces caused by fluid action The component of such forces in the streamwise direction is called the drag force Due to the no slip boundary condition a boundary forms on the body causing viscous shear stresses at the surface Due to viscous effects a region of separated flow also forms behind the body This region is known as the wake Pressures in the wake are lower than pressures on the front of the body causing what is known as form drag Drag can be determined experimentally using multiple methods For this lab experiment the method used to determine drag uses a momentum balance on a control volume which contains the model This momentum balance would require velocity measurements both upstream and downstream from the model Undisturbed flow enters the control volume containing the bluff body When only the flow disturbance in the control volume is the bluff body any loss of fluid momentum is realized as a force on the body Drag measurements are generally presented in non dimensional form The drag coefficient CD is defined as CD Drag 0 5 AV2 1 where A is the projected frontal area of the bluff body and V is the undisturbed fluid speed Flow speed can be non dimensionalized as the Reynolds number Red Vd 2 where d is the diameter of the cylinder and and are the absolute viscosity and density respectively Figure 1 below shows a model of the control volume of interest Figure 1 Control volume used for purpose of analysis Using the control volume approach an equation for the drag force D can be developed D LV2 1 u2 v2 dy 3 This result can be non dimensionalized to create an expression for the drag coefficient CD CD Drag 0 5 LdV2 2 d 1 u2 v2 dy 4 It is important to note that the region of disturbed wake is between 0 and H Outside of this region u V and the quantity in the integral is equal to zero The derivations for the above equations are attached as Appendix A4 For this experiment the wind tunnel measures pressures which are converted to wind speeds using the following equation Flow speed ft sec 67 28 z 5 where z is the pressure measured in inches of water Experiment Description In this experiment we collected data that would help us to determine the drag force on the vertical cylinder in the wind tunnel The data that was collected is as follows the initial undisturbed velocity the projected frontal area of the cylinder the disturbed velocity the density and absolute viscosity of the test fluid Once we knew what data had to be collected we ran the experiment as described in the Process Description section following Process Description The specimen was placed vertically in wind tunnel with a rake of total pressure tubes placed behind the cylinder in the wake The tubes were connected in such a way that were able to determine the pressure at finite points across the wake in terms of inches of water These values would then be calculated into a velocity value using equation 5 These values then allowed us to create a plot of the momentum defect by plotting the ratio of the square of the disturbed velocity u and the square of the undisturbed velocity v versus the transverse wake position This plot is attached as Appendix A1 along with the data used to create the plot attached as Appendix A2 The area between the plotted line and the u2 v2 1 line is the value for the integral portion of Equation 3 This value was determined to be 0 611 in This value was obtained by summing all individual areas in this region This value along with the values shown in Table 1 were used to determine the Drag Force D and the Drag Coefficient CD using Equations 3 and 4 respectively Density slug ft3 Undisturbed velocity V ft sec Absolute viscosity 10 6 lbf s ft2 Cylinder Diameter d in Cylinder Length L in 0 0023 115 0 3758 0 503 11 25 Table 1 Values used in determining Drag Force and Drag Coefficient Results After collecting all the necessary data the values were substituted into the appropriate equations above to get the results for the Reynolds Number Drag Force and Drag Coefficient Table 2 contains these values Reynolds Number dimensionless 29 502 3 Drag Force lbf 1 45 Drag Coefficient dimensionless 2 426 Table 2 Values calculated from experimental data The calculations for these values are attached as Appendix A3 Post Lab Remarks The results for this lab are only valid for the tested wind tunnel speed of 115 ft sec Other wind tunnel speeds will produce different values Since drag is calculated experimentally there is no theoretical base to determine a error for this experiment Before the data was to be collected a determination of the fixed variables and changing variables had to be determined That is which variables will change with position across the wake It was noted that the disturbed velocity would change since the pressure changes in the wake Since the flow was mechanically produced using a wind tunnel an assumption of steady flow was made which results in all partial derivatives in the conservation of mass momentum and energy equations go to zero The use of dimensionless quantities in the calculations helped to ease the calculations to get the final results The observed velocity profiles in the cylinder wake are different that the upstream velocity profiles because of viscous interactions at the stationary cylinder surface If viscosity was zero for this experiment there would be no wake since there would be no viscous stresses in theory Design Considerations For the wind tunnel the highest acceptable speed is attained when the pressure is equal to 5 inches of water 150 44 ft sec Higher speeds cause deflection and vibration in the rake Proposing a cylinder with a diameter of 0 375 inches and length of 8 inches the Reynolds number calculates to be 28 772 95 Comparing this value to range of constant drag coefficients this value would provide acceptable results since it is just slightly less than the value for the lab experiment The length to diameter ratio L D calculates to be 21