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Laboratory 2 Drag Measurements in a Subsonic Wind Tunnel OBJECTIVES This experiment illustrates several concepts and principles concerning drag forces acting upon bodies. These concepts will be demonstrated by the measurement of drag for two sizes of smooth spheres at various wind speeds in a subsonic wind tunnel. The results will be presented in both dimensional and nondimensional terms. This experiment will allow the observation of the effects of boundary layer transition on drag for flow over a sphere and determination of the critical Reynolds number. REQUIRED READING Section 9.1 in your fluid mechanics text [1] should be studied before undertaking this laboratory exercise. BACKGROUND DRAG A body immersed in a flowing fluid is acted upon by both pressure and viscous forces from the flow. The sum of the forces (pressure and viscous) that acts parallel to the free-stream direction is termed drag. Body forces, such as buoyancy or weight may also act on the body; however, drag forces are limited by definition to those forces produced by the dynamic action of the flowing fluid. The pressure forces are a function of the form or shape or the body and contribute to the "form drag." The viscous resistance contributes to the viscous drag or "skin-friction" drag. Our intuition would tell us that the drag force should increase with increasing fluid velocity. One purpose of the present experiment is to measure these changes over a range of wind speeds. TRANSITION EFFECTS (Note: The assigned background reading is essential here!) The drag force on a sphere experiences a marked reduction when the flow in the boundary layer upstream of the separation point undergoes transition from laminar to turbulent flow (see Figure 2.1). This boundary layer transition causes a delay in the separation point resulting in a reduction of the form drag. Figure 2.1 shows the pressure coefficient for the case of a laminar boundary layer (a) and for the case where the boundary layer experiences transition to turbulence 2-1 upstream of the separation point (b). The Reynolds number associated with this transition is known as the critical Reynolds number. 2-2 cp 0 cp 0 U P P P c p 2 U / 2 Figure (a)3 .1:Flow of Viscous Fluid Past a Cylinde r Show ing Laminar Bounda ry La yer Sepa ration from the F ront Portion: A) Pa ttern of Streamlines , B) Pressure Distribution cp 0 cp 0 cp 0 U cp 0 P U P P P 2 U /2 c p (b) P P c 2 Figure 3.2:Flow of Visc ous F luid Pas pt a C yl inde Showing / 2r U Turbu le nt Bounda ry Layer Sepa rat ion from t he R ear Po rt ioof n:Viscous A ) Patt ern ofcoefficient Stream lines, Pr es su Figure 3 .1:Flow Fluid Past a Cylinde r Show ingre Figure 2.1 Streamlines and pressure for B) flow over a sphere. D is trib ut ion Laminar Bounda ry La yer Sepa ration from the F ront Portion: A) Pa ttern of Streamlines , B) Pressure Distribution 2-3 To measure Vo a Pitot tube is used in conjunction with a digital manometer. By determining the difference between the total and static pressures, the free-stream velocity may be determined using equation (2.3). Vo 2gh w (2.3) where, g acceleration due to gravity (32.174 ft/sec2 ) h pressure difference ( ft of air) w density of water (62.4 lb/ft 3 ) density of air (lb/ft 3 ) PROCEDURE: An AEROLAB subsonic wind tunnel, 2 smooth spheres (diameter 2.92in and 3.70in) , a digital manometer and a pitot tube will be available for use in this laboratory exercise. To perform the exercise, follow the following steps. 1. Calculate the nominal pressure drop associated with a given wind speed. Record these values in the worksheet provided. 2. Turn control panel on. 3. Install 0.75 inch diameter calibration barrel on the sting balance. 4. Adjust angle of attack of sting assembly to 30, and zero the value of the axial force readout. 5. Hang a 0.5 and 1 kg weight on the calibration barrel, and record the new axial force readout value for both inputs. This data may then be used to establish the calibration for the axial force measurement. 6. Remove calibration barrel from the sting balance, readjust angle of attack to 0o, and install first sphere (NOTE: Do not over-tighten the set-screw). 7. Remove all tools and loose objects from the test section and close the viewing window. 2-4 8. Turn on wind tunnel, and adjust air speed to the maximum value. Reduce air speed to zero, and again zero the axial force readout. 9. Now it is time to take data. Set the wind speed to 45 MPH and record axial force readout. 10. Repeat step 8 for air speeds of 60, 80, 100, 120, and 130 (or maximum wind tunnel velocity) mph. If the critical Reynolds number, where the transition to turbulence in the boundary layer is reached, you will observe a decrease in the drag force for increasing wind speed. Through careful observation of the sphere you should be able to determine an accurate value of the critical Reynolds number. Comment on the stability of the flow at this Reynolds number. 11. Repeats steps 7 through 9 for the second sphere. 12. Shut off wind tunnel. Fl ow St r ai ght ener s 1 f t . by 1 f t . Tes t Sec t i on Fan Out l et I nl et Cont r ol Figure 2.2 Box Schematic of AEROLAB apparatus. 2-5 ASSIGNMENT Write a formal lab report-due in one (1) week at the beginning of the lab period. Make sure to address the following topics in your report. 1. Plot the drag force as a function of wind speed for each sphere. Explore various plot formats (log-log, etc.) to see if a functional relationship between drag and wind speed can be discerned. 2. Plot the drag coefficient as a function of Reynolds number for the two spheres on the same plot. Comment on the results. 3. Estimate the drag force on a 17.5 mm sphere at a wind speed of 90 m/sec. 4. Evaluate the accuracy of the drag coefficient by comparison with published values. 5. Discuss the significance of the critical Reynolds number. REFERENCE 1. Munson, B.R., Young, D.F., and T.H. Okiishi, Fundamentals of Fluid Mechanics, 4th Ed. 2002, John Wiley and Sons, Inc. NOMENCLATURE Ap = area of the test shape projected in the free-stream [ft2] direction Cd = Drag coefficient [dimensionless] d = cross-sectional width of object [ft] Fd = axial force [lbf] g = Gravitational acceleration constant [ft/s2] h = Manometer reading [in h20] Red = Reynolds number [dimensionless] Recrit = Reynolds number associated with boundary layer [dimensionless] transition Vo = Free-stream velocity [ft/s] = free-stream density of air [lbm/ft3] 2-6 w = free-stream density of water [lbm/ft3] = kinematic viscosity [ft2/s2] 2-7 DATA SHEETS FOR DRAG EXPERIMENT Speed MPH Air Density (lb/ft3) Pitot Tube Pressure Difference (in.H2O) 45 60 80 100 120 130 Sphere Axial Force, counts 45 MPH 60 MPH 80 MPH 100 MPH 1 2 2-8 120 MPH 130 MPH Max Acheivable Velocity inches H20