Aerodynamics Lab 1 – Cylinder Lift and Drag

MAE 449 – Aerospace Laboratory Aerodynamics Lab 1

AERODYNAMICS LAB 1 – CYLINDER LIFT AND DRAG

1 Objective

To determine the aerodynamic lift and drag forces experienced by a circular cylinder placed in a uniform free-stream velocity. Two different methods will be used to determine these forces.

2 Materials and Equipment

• UAH 1-ft x 1-ft open circuit wind tunnel • Smooth, 3/4 inch diameter brass cylinder with one pressure tap at mid-span • Traversing mechanism • Pitot-static probe • Digital pressure transducer • Data Acquisition (DAQ) Box

3 Background

3.1 Aerodynamic Forces The net resultant fluid mechanic force acting on an immersed body is due to the distribution of pressure and viscous shear stresses along the surface of the body. The resultant force is traditionally divided into two components: (1) the lift component, which is normal to the freestream velocity vector; and (2) the drag component, which is parallel to the freestream velocity as shown on Figure 1.

LIFT

U∞ DRAG

Figure 1 - Aerodynamic Forces on an Immersed Body We can express these forces in non-dimensional coefficient form as

F CF = , (1) ⎛⎞1 2 ⎜⎟ρVAREF ⎝⎠2 REF

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where F can be the lift (L) or drag (D) forces, and AREF is a specified reference area. For two-dimensional bodies the force is per unit span (or width), or the area is determined with a unit width.

3.2 Governing Equations Ideal Gas Law At standard conditions, air behaves very much like an ideal gas (the intermolecular forces are negligible). As a result, we can express relation between the pressure, p, the density, ρ, the temperature, T, and a specific gas constant, R ( for air, R = 287 J/(kg K)), as

pRT= ρ . (2)

Sutherland's Viscosity Correlation At standard conditions, an empirical relationship between temperature and viscosity given by the Sutherland correlation

bT 1/2 μ = , (3) 1/+ ST where b = 1.458×10−6 kg /()m ⋅ s and S =110.4 K .

Bernoulli's Equation For a steady, incompressible, inviscid, irrotational fluid flow, a relation between p, the static pressure 1 (due to random molecular motion of the fluid molecules), ρV 2 , the dynamic pressure (due to the 2 directed motion of the fluid), and po, the total/stagnation pressure (pressure you would sense if the fluid flow was isentropically brought to rest), called Bernoulli's equation, can be derived as

1 p=+ pρ V2 = const. (4) o 2

Bernoulli's equation can be used to determine the velocity of an incompressible fluid flow.

3.3 Similarity Parameters The bodies tested in the wind tunnel are generally scale models of a full size prototype. As a result, we must introduce similarity parameters that will allow us to perform a study of dimensional analysis and similitude.

Reynolds Number The Reynolds number is the ratio of inertia forces to viscous forces. 'Low' Reynolds number flows tend to be dominated by viscosity and thus exhibit laminar boundary layers, while 'high' Reynolds number flows tend to exhibit turbulent boundary layers. The Reynolds number can be expressed as

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ρVc Re = , (5) μ where ρ and μ are, respectively, the density and the viscosity of the fluid, V is the flow velocity, and c is a characteristic dimension of the body.

3.4 Pressure Coefficients Consider the pressure and shear stress distributions along the surface of an immersed body. We can divide the surface into small, elemental areas and resolve the contributions to lift and drag on each area (see Figs. 1.11 and 1.12 of Ref. 1). The net lift and drag forces are obtained by summing up these elemental contributions (i.e., integrating). Empirical results indicate that we can generally neglect the shear stress contribution to the lift and only consider the contributions of pressure on the upper and lower body surfaces. Using this approach for a two-dimensional (or infinite span) body, the pressure coefficient can be expressed

pp− REF Cp = . (6) ⎛⎞1 2 ⎜⎟ρV ⎝⎠2 REF

The pressure coefficient is thus the difference in the local pressure and a reference pressure divided by the reference dynamic pressure. Typically, the freestream values far ahead of the body (denoted by the subscript ‘∞’) are used for the reference conditions.

3.5 Lift Coefficient Similarly, a relatively simple equation for the lift coefficient can be derived

xc/1.0= ⎛⎞x CCpCpd=−cosα , (7) l∫ () lower upper ⎜⎟ xc/0= ⎝⎠c where α is the angle of attack, c is the body chord length, and Cp the pressure coefficients are functions of the normalized length x/c. Note that we use a lower case "l" to designate a two-dimensional body or force per unit span. For a two-dimensional, circular cylinder, the surface can be described in cylindrical coordinates: r (the cylinder radius), and θ (the circumferential angle referenced to the forward stagnation point). Using this approach a simple expression for the 2-D cylinder lift coefficient can be obtained,

1 2π CCpd=− ()sinθ θθ. (8) l ∫ 2 0

3.6 Drag Coefficient The calculation of drag by the surface integration technique can be much more complicated when we include the shear stress contributions. For smooth bluff bodies, such as cylinders and spheres, the drag is predominately pressure drag due to boundary layer separation (see body drag handout). A good drag

3/11 MAE 449 – Aerospace Laboratory Aerodynamics Lab 1 estimate for these bodies can be obtained by neglecting the shear stress contribution and only integrating the pressure distribution over the forward and aft body surfaces. Using this approach, a simple expression for the 2-D cylinder drag coefficient can be obtained,

1 2π CCpd= ()cosθ θθ. (9) d ∫ 2 0 For smooth streamlined bodies (such as an airfoil), the drag is predominantly due to shear stress. The surface integration technique requires knowledge of the shear stress distribution along the surface, which may be difficult to obtain experimentally. In this case, we can estimate the drag of the body by comparing the momentum in the air ahead of the body to the momentum behind the body.

The total momentum loss can be equated to the drag of the body by application of a momentum integral analysis (e.g., Chapter 3 of Ref 2). A Pitot-static probe can be traversed along vertical planes ahead and behind the body to determine the profiles of local dynamic pressure and associated flow momentum. In Ref. 3, an equation is derived for the drag of an immersed body based on this dynamic pressure profile in the separated wake. The resultant equation is given by

2 Y2 ⎡ qq⎤ CdYd =−⎢ ⎥ , (10) dqq∫ Y1 ⎣ ∞∞⎦ where q and q∞ are the local and freestream values of dynamic pressure, d is the cylinder diameter, and Y1 and Y2 are the beginning and ending coordinates of the vertical pressure probe traverse. Proper values of q are only obtained if the wake has returned to the tunnel static pressure, p∞, and not the local static pressure near the body. Performing the pressure traverse several chord lengths behind the body rectifies this problem.

4 Procedure

4.1 Determination of the Drag Coefficient From Surface Pressure Measurements The coefficient of lift and drag can be obtained by determining the pressure profile around the cylinder and integrating it using Equations Eqs. (8) and (9). Figure 2 depicts the circumferential locations at which the measurements are taken with an angular displacement of 15°.

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U∞

Figure 2 - Pressure Measurements Around A Cylinder

The following steps are performed to obtain the surface pressure data: 1. Measure the lab static pressure and temperature. 2. Using Eqs. (2) and (3), calculate the room air density ρ and viscosity μ. 3. Determine the dynamic pressure (q) setting for a cylinder Reynolds number of 30,000. 4. Note that the flange of the cylinder plug has a scribed index that relates the circumferential location of the pressure tape to the degree scale surrounding the wall port. Positioning the index to 0° orients the cylinder pressure tap at the forward stagnation point. 5. Set the pressure selector switch to port ‘0’. Do not adjust the Span or Zero on the DAQ box. 6. Place the Pitot-static probe at the farthest upstream position and near the test section roof (but outside the boundary layer). 7. Turn on the wind tunnel and adjust the speed control until the pressure transducer reads the calculated q for ReD = 30,000. 8. Set the port selector to “1”. 9. Using the angle guide on the test section wall, rotate the cylinder pressure tap through 360° in 15° increments. Pause at each angle and record the value of Δpport = pport - p∞. 10. Return the cylinder to the 0° position and the port selector back to 0. Repeat steps as required.

4.2 Determination of the Lift and Drag Coefficients From Wake Pressure Measurements By measuring the velocity profiles in the wake and using conservation of linear momentum, the drag coefficient on the cylinder can be determined using Eq. (10). The experimental set up will be as shown on Figure 3 where wake measurements will be obtained a short distance behind the body.

The following steps are performed to obtain the wake pressure data: 1. Place the Pitot-static probe at an axial location of approximately 3 diameter lengths behind the cylinder. 2. Set the static probe about 10cm above the cylinder

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3. Traverse the probe vertically across the wake, recording the local dynamic pressure (q) at discrete y-locations (every 1cm if no change is noticed on the pressure). 4. When a sudden drop of pressure (20-30Pa) occurs, go back to last Y-position and start taking measurements every 1mm until the pressure is back to approximately 400 and constant 5. At this point, take measurements every 1cm until about 10cm below the cylinder.

U∞

3.d Y2 Figure 3 - Wake Pressure Distribution

5 Laboratory Report

1. Calculate the actual cylinder Reynolds based on the cylinder diameter and freestream velocity. 2. Calculate the cylinder pressure coefficients (Cp) at each circumferential angle with Eq. (6), where the reference values correspond to the freestream conditions. On one plot graph Cp versus θ (in degrees). On the same plot, graph the theoretical Cp distribution derived from potential flow theory (note the 180° phase displacement)

Cp = 14sin180−−2 ( o θ ) (11)

Comment on any differences in the measured and theoretical pressure distributions. 3. Estimate the location of the separation point at the test Reynolds number. Compare this value to the value indicated on Figure 4. 4. Use Equation Eq. (8) and the Cp values from step (2) to calculate the cylinder lift coefficient. What conclusions about the data accuracy and cylinder aerodynamics can you draw from the lift coefficient values? 5. Use Equation Eq. (9) to calculate the cylinder drag coefficient. 6. Plot the dynamic pressure values from the cylinder wake traverse versus y-location. 7. Use Equation Eq. (10) to calculate the cylinder drag coefficient. 8. Compare the two drag coefficients values calculated in steps (4) and (7) to the experimental value shown in Figure 5. Discuss what factors any observed differences might be attributed to.

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Figure 4 - Location of Measured Separation Points on a Circular Cylinder (from Ref. 5). Note that the θ variable is 180° out of phase from the nose reference in this lab.

Figure 5 - Measured Drag Coefficients for a Circular Cylinder (from Ref. 4).

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References

1 Anderson, J. D., Fundamentals of Aerodynamics, 4th ed., McGraw Hill, 2007. 2 Kuethe, A. M., and Chow, C., Foundations of Aerodynamics-Bases of Aerodynamic Design, 5th ed., John Wiley, 1998. 3 Barlow, J. B., Rae, W. H., Jr., and Pope, A., Low-Speed Wind Tunnel Testing, 3rd ed., Wiley- Interscience, 1999, pp. 176-179. 4 Schlichting, H, Boundary Layer Theory, McGraw-Hill, New York, 1968. 5 Achenbach, E., “Distribution of Local Pressure and Skin Friction Around a Circular Cylinder in Cross-Flow up to Re = 5 106,” Journal of Fluid Mechanics, Vol. 34, Part 4, 1968, pp. 625-639.

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MAE 449 – AERODYNAMICS LAB 1 – DATA SHEET

Lab Conditions :

P = ______[Pa]

T = ______[°C]

ρ = ______[kg/m3]

μ = ______[kg/(m⋅s)]

Determination of the Drag Coefficient From Surface Pressure Measurements:

Freestream pressure: q∞ = ______[Pa]

Reference pressure: Pref = ______[Pa]

Static pressure Static pressure θ [°] θ [°] p [Pa] p [Pa] 0° 195° 15° 210° 30° 225° 45° 240° 60° 255° 75° 270° 90° 285° 105° 300° 120° 315° 135° 330° 150° 345° 165° 360° 180°

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Determination of the Drag Coefficient From Wake Pressure Measurements:

Freestream pressure: q∞ = ______[Pa]

Dynamic Pressure Dynamic Pressure Y position [cm] Y position [cm] q [Pa] q [Pa]

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Dynamic Pressure Dynamic Pressure Y position [cm] Y position [cm] q [Pa] q [Pa]

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