Objective

        The objective of this experiment is to determine the aerodynamic lift and drag forces, F_l and F_d, respectively, experienced by a circular cylinder placed in a uniform free-stream velocity, U_¥. Two different methods will be used to determine these forces.

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Theoretical Background

        The total drag on any body consists of skin friction drag and form drag. The former arises due to the viscous forces acting on the body while the latter is due to the unbalanced pressure forces on the body. The sum of the two is called total or profile drag. There are several methods that can be used to determine the drag forces. These are discussed in detail below.
 

Prediction of Drag from Wake Measurements

        From the measured velocity profiles in the wake, the drag can be determined by means of the law of conservation of linear momentum, providing the flow is steady. With reference to Figure 1, a control surface around the body is selected as shown. The cross section II in which measurements will be taken is located behind the body at a short distance; the static pressure at this station is different from the free-stream pressure, p_¥. Hence, there will be therefore a net contribution to the momentum balance due to this pressure difference. In order to account for and minimize this effect another section, Section I (an imaginary section), is chosen far behind the body such that the pressure is equal to the free-stream pressure. Therefore, the pressure forces acting on this newly-defined control surface will be canceled. The general conservation law can be written, without considering the effects contributed by pressure, as:

where W is the width of the body and u₁ denotes the velocity profile in the wake measured at Section I. Unfortunately, the flow cannot achieve the required relation p₁ = p_¥unless the measuring station is placed very far downstream, usually more than 100 diameters, from the cylinder. It is therefore not realistic to take measurement at section I. Nevertheless, it is possible to establish relation between the flow quantities measured at section I and those measured at section II which is located close to the cylinder. The procedure is described as follows:

        In order to find the relation between F_d and the velocity profile at the designated measuring station II, we apply the equation of continuity along a stream tube.

Hence,

                (3)

Furthermore, we make the assumption that the flow moves from Section II to I without pressure losses, i.e., the total pressure remains constant along each streamline between I and II:

Introducing the total pressure as

We can rewrite Equation 3 by using Equations 4 and 5. Hence, we have:

where the integral extends over cross-section II.

            Introducing a dimensionless drag coefficient, C_D, as follows :

                                           (7)

   (8)

where

Measurement of the Normal Pressure distribution on the body

        When the Reynolds number is sufficiently large, Re > 10³, the skin friction drag of a bluff body is relatively negligible compared to its form drag. Then the measurement of the drag forces due to normal pressures around the body will be a good approximation to the total drag.

        For a cylinder, the body lift and drag per unit length due to normal pressure only are given by

where the integrations are taken around the contour of the cylinder. A cylindrical coordinate will be used instead, and we can rewrite Equation 11 as:

                       (12)

Similarly, the lift force can be estimated to be:

Apparatus

The following components will be used:

                    1. Wind Tunnel.
                    2. Pitot static tube.
                    3. A cylindrical test section with circumferential pressure ports.
                    4. Scanivalve and scanivalve digital interface unit.
                    5. ADC Card on a Pentium-based PC.
                    6. Computer-operated vertical drive.

Click here to see apparatus

        A pitot tube can be used in the wind tunnel to measure the velocity of the tunnel. The assumption we have to make is that the static pressure is constant everywhere in a uniform free-stream inside the wind tunnel. It is a reasonable assumption considering that there is no pressure loss, therefore, no pressure gradient, in the system. However, the situation will be totally different for measurement taken inside a wake behind a bluff body, that is, a significant amount of pressure variation exists across the wake profile. In order to accurately determine the velocity profile in the wake, a pitot- static tube should be used. The pitot-static tube is a combination of the static tube and the pitot tube, see Figure 2. Let us assume that the tube is properly aligned with the flow direction. Assuming steady one-dimensional flow of an incompressible inviscid fluid, we can derive the following result,

where V is flow velocity, p is the density of the fluid, p_stag is the stagnation pressure of the free-stream and p_stag is the static pressure.

        It is usually more difficult to accurately measure the static pressure. The difference between the true p_stag and measured p_stag may be due to one or all of the following:

1. Misalignment of the tube axis and velocity vector.
2. Nonzero tube diameter. Streamlines next to the tube must be different from those in undisturbed flow, indicating a difference in velocity, also making the static taps read different from what should be.
3. Influence of the tube-support leading edge.

Click here to see apparatus

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Experimental Procedure

WARNING: Start the wind tunnel at a counter setting of 100 to 200 only. Do not start it at higher counter settings

1.  Wake Measurement:

        For the wake measurement, select two downstream locations, x/D = 5 and x/D=10 for the measuring section II. Set the wind tunnel speed counter at 550.

1. Insert the pitot, or pitot-static, tube into the windtunnel upstream of the bluff body. Measure and record the dynamic pressure upstream of the body.
2. Remove the pitot tube from the upstream.
3. Move the pitot-static tube to the x/D=5 location. Center it at the center of the cylinder.
4. Using the computer, measure the ADC output. Record this value.
5. Switch reference to P₂.
6. Using the computer, move the pitot-static tube vertically upwards by 1 step. Each step moved by the pitot-static tube using the computer constitutes a movement of 4 mm.
7. Measure and record the ADC output at this point.
8. Repeat the measurement procedure for a total of 26 steps, i.e. a total travel distance of 100 mm.
9. Move the pitot-static tube to the x/D=10 location. Center it at the center of the cylinder.
10. Repeat the measurement procedure followed for the x/D=5 location.

2.     Normal Pressure distribution:

        Two different Reynolds numbers shall be used for this part of the experiment. Wind tunnel speed counter settings of 550 and 350 will be used to obtain the two different Reynolds number.

1. Set the wind tunnel speed counter at 550.
2. Using the scanivalve, select the port # 2 on the scanivalve digital interface unit (SDIU). This corresponds to the port # 1 on the Figure 3.
3. Using the computer, measure and record the ADC output
4. Step through to the next port on the SDIU.
5. Repeat Step 2c.
6. Go through this process for all the ports, i.e., up to port 16 on the SDIU.
7. Set the wind tunnel speed counter at 350.
8. Repeat Step 2b through to Step 2f

Report Specifications

        Present all of your data in a dimensionless form, that is, use C_D and C_L, instead of drag and lift forces respectively. Also indicate the Reynolds number of the flow when presenting the values for C_D and C_L.

1. Plot the non-dimensional vertical distance versus the non-dimensional velocity at the locations x/D=5 and x/D=10. Use D and U_¥ as the non-dimensionalizing parameters. Discuss the wake profiles obtained at the two locations.
2. Calculate C_D from the wake profiles, compare to values obtained from Fig. 4. Discuss reasons for discrepancies, if any.
3. Plot the variation of C_p as a function of the angular location and compare it to the theoretical profile for the cylinder in an inviscid flow (Refer to any Fluid Mechanics book). Explain the difference.
4. Calculate the values of C_D and C_L from surface pressure measurements? Compare C_D values to those obtained from Figure 4.
5. Compare the results obtained by the two different measuring methods and discuss reasons for any differences. Which method is more accurate ?
6. Does the pitot-static tube read steady inside the wake? How about, outside the wake? Can pitot-static tubes measure turbulent fluctuations? Why?

Figure 4. Drag coefficient of a circular cylinder

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Note: Please note the units of the quantities which are being measured, when recording data. For example, when measuring voltage, if the voltmeter reads 16 mV, then write down 16 mV instead of just 16.

1. Double-click on the LabVIEW icon to start the program.

2. Double click on the eml4304l folder, and select Exp4trucontrol.vi. Double click on it to start the virtual
    instrument.

Notes on the Virtual Instrument:

The Exp4trucontrol.vi VI is an expansion of the oscilloscope.vi used by you in Experiment 3. The main modifications in this program are :

a). Velmex Control: This controls the movement of the pitot-static probe in the vertical direction.

b). Scanivalve Control: This controls the scanivalve port setting remotely. This has four selections:

1. Home: This selects the home (port 0) port of the scanivalve unit.
2. Step: This steps the scanivalve forward through one port.
3. Pitot port: This steps the scanivalve to the port reading the pitot tube pressure (port 16).
4. Step to: When you type in a port number, this will allow you to step directly to that particular port.

d). The Output Center gives the output of the VI in two different forms:

1. ADC output: This is the basic signal output seen by the ADC, in volt.
2. DPressure (psi): This is the actual output pressure value, obtained by applying the calibration equation to the ADC output value. The calibration equation should be obtained from the TA and recorded below.

     You can record either value. If you record the ADC output, you will need to use the above equation to
     obtain the pressure values.

e). Unlike the other labs, the data will not be written to file (since it is difficult to tag the data vis-a-vis the
      pitot probe position and the scanivalve position, while keeping the program fool-proof). You need to
      record the data, obtained in Step d above, in your lab book.
 

I.     Prediction of Drag from Wake Measurement

Case A: Probe at x/D = 5
Velocity = 30.68 m/s (Counter 550). pt- p= _________
 

Position	Distance from center (mm)	pt2-p2 (D/A #)	pt2-p (D/A #)
1	0
2	4
3	8
4	12
5	16
6	20
7	24
8	28
9	32
10	36
11	40
12	44
13	48
14	52
15	56
16	60
17	64
18	68
19	72
20	76
21	80
22	84
23	88
24	92
25	96
26	100

                        Case B: Probe at x/D = 10

                        Velocity = 30.68 m/s (Counter 550). pt - p=_________

Position	Distance from center (mm)	pt2-p2 (D/A #)	pt2-p (D/A #)
1	0
2	4
3	8
4	12
5	16
6	20
7	24
8	28
9	32
10	36
11	40
12	44
13	48
14	52
15	56
16	60
17	64
18	68
19	72
20	76
21	80
22	84
23	88
24	92
25	96
26	100

                        II. Normal Pressure Distribution
 

Tap	p-p(D/A #)
Number	V = 17.83 m/s (SCR=350)	V = 30.68 m/s (SCR=550)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

                        Scanivalve operation:

Port	Pressure tap
0	Total pressure probe (pt2)
1 till 15	Cylinder static ports (see Handbook)
16	Total pressure probe (pt)

                        Pressure Tap Selector (Reference Pressure):

Port	Pressure tap
1	p
2	p2

Cylinder Geometry: Diameter: 3 cm; Length: 30 cm.
 

YOU NEED TO GET THE LAB INSTRUCTOR'S SIGNATURE BEFORE LEAVING.

The student has performed the experiment satisfactorily and has cleaned the work area.

___________________________ _______________

(Lab assistant's signature)                          Date

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