Laboratory #3 - Manual (1)

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ME 4312 - Thermal and Fluids Laboratory | Page 1 of 10 The University of Texas at San Antonio (UTSA) Klesse College of Engineering and Integrated Design Department of Mechanical Engineering ME 4312 - Thermal and Fluids Laboratory Laboratory Assignment #3 - Analysis of Two-Dimensional Airfoil Aerodynamics Manual and Supplementary Materials The objective of this laboratory assignment is to determine the experimental and theoretical/simulation lift force (and the pressure and lift force coefficients) experienced by an airfoil (a National Advisory Committee for Aeronautics , NACA 4415), that is subject to different free-stream wind speeds and angles of attack. For such purpose, a wind tunnel and a set of manometers installed on both the wind tunnel and a model NACA 4415 will be considered. In general, the two-dimensional aerodynamics of a body consist of three different forces: the lift force (which always acts perpendicular to the direction of the free stream flow), the drag force (which always acts in the direction of the free stream flow), and a moment force (torque), which acts clockwise or counterclockwise and with respect to a reference position on the airfoil (usually at the aerodynamic center). Each of these forces has two components: (1) a viscous component, and (2) a pressure-based component. On the one hand, the viscous component results from the shear stresses developed between the free-stream flow and the surface of the object, and require detailed descriptions of the near-wall velocity profile and the flow condition (e.g., laminar vs turbulent). On the other hand, the pressure component depends on the pressure distribution around the surface of the object. In this laboratory assignment, only the pressure component will be investigated. It is worth nothing that, viscous contributions to the lift force are usually small and, thus, often neglected. However, the viscous component is usually important when analyzing drag and moment forces. In this laboratory assignment, only the pressure component of the lift force will be analyzed for different free-stream flow speeds (Reynolds numbers) and angles of attack. Experimental Procedures: The wind tunnel has two 8-tube manometers (16 tubes total) that are used to measure the pressure at different points along the surface of the NACA 4415 airfoil (Figure 1 shows one 8-tube manometer to measure pressure along the upper surface of the airfoil, the other 8-tube manometer is to measure pressure along the lower surface of the airfoil). Each tube has a black ring on it that can slide up and down. Use these rings to mark the baseline water level on each tube (when the airfoil is at an angle of attack of 0 degrees and the wind tunnel is turned off) to later measure pressure changes on the surface due to changes in flow speed or the angle of attack. The baseline water levels are shown in Figure 2. The water is dyed to make it easier to read, and the dye has a negligible effect on the water’s density. Figure 1. Airfoil Manometers. Figure 2. Slide Black Ring to Baseline Water Level. The angle of attack (AOA) is shown by a black arrow attached to the airfoil (Figures 3 and 4) and a protractor taped to the back window (Figure 4). The AOA is controlled by turning an orange handle located beneath the wind tunnel, as shown in Figure 5.

ME 4312 - Thermal and Fluids Laboratory | Page 2 of 10 Figure 3. NACA 4415 Airfoil. Figure 4. Protractor. Figure 5. Orange Handle. The key on the control unit should be turned to RUN (see Figure 6). The green button labeled FAN ENABLE will turn on the wind tunnel when pressed. The red button above it will stop it. The black dial below the display controls fan speed, and the display shows the wind tunnel’s fan rotational speed in RPM. The rotational speed of the fan is NOT an appropriate measurement of the wind tunnel’s wind speed and should not be referred to as such in your report. Instead, you need to determine the wind tunnel wind speed using the measurements of a Pitot tube that is installed in the upwind section of the tunnel (before the airfoil). The Pitot tube is connected to a “red” manometer located on top of the wind tunnel and shown in Figure 7. The manometer reads the dynamic pressure in the wind tunnel in “inches of water”. This pressure can later be converted into wind speed using equations presented later in this document (make sure to conduct appropriate review of how manometers work, using your lecture notes of the class fluid mechanics, and measurements and instrumentation). The wind speed (for a fixed fan speed in RPM) should always be recorded at an AOA of 0° to prevent blockage effects between the airfoil and the Pitot tube. Figure 6. Wind Tunnel Controls. Figure 7. Manometer to Measure Wind Speed (Pressure Readings Collected from Pitot Tube). Using the supplied ruler, measure the change in pressure (i.e., the change in water level with respect to the baseline water level marked with the black rings) for each of the 16 tubes (8 tubes are for measuring the change in pressure along the upper surface of the airfoil, and 8 tubes are for measuring the change in pressure along the lower surface of the airfoil, see figure 8). The manometer tubes start at #1 on the far right and increase from right to left to tube #16. Note that if the water is sucked up the tube it indicates a vacuum pressure (negative gage pressure). Once all 16 measurements are taken, change the AOA and repeat the measurements. The sixteen pressure measurements will be taken for 9 AOA (-15°, -10°, -6°, -4°, 0°, 4°, 6°, 10°, and 15°) values and at 4 different wind speeds (defined by the instructor in terms of the fan’s RPM) for a total of 576 measurements.

ME 4312 - Thermal and Fluids Laboratory | Page 3 of 10 Figure 8. Measuring Manometer Water Levels. Airfoil Physical Dimensions Using a measuring device, record the chord length and airfoil width (wingspan, which is perpendicular to the chord length). From the leading edge of the airfoil, make precise measurements to each of the pressure sensing ports for both the upper and lower surfaces of the airfoil. Use a flexible tape for measuring the distances along the surface of the airfoil. Denote each dimension of the upper surface as X U and subscript each of the X U dimensions with respect to pressure sensing ports starting with the port nearest to the leading edge. X U1 , X U2 , X U3 , and so on are examples of the subscripting process (see Figure 9 for example). The dimensions for the lower surface shall be identified the same as described for the upper surface except the symbol shall be X L in place of X U . The table shown in page 6 reports the results of such measurements. Figure 9. Example of Model Airfoil Dimensions (Upper Surface Only). Figure 10. Pressure Port Distribution Along the Surface of the Airfoil.

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ME 4312 - Thermal and Fluids Laboratory | Page 4 of 10 Theoretical Analysis: The airfoil used in this laboratory assignment is the NACA 4415 (normally used on the Lake Amphibious aircraft). The NACA 4415 is a very high lift airfoil designed to lift aircraft out of water quickly. Nomenclature C Chord Lengh L Lift Force S Scale 𝐶𝐶 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 Model Chrod Length 𝐶𝐶 𝑃𝑃𝑃𝑃𝑀𝑀𝑃𝑃𝑀𝑀𝑃𝑃𝑃𝑃𝑃𝑃𝑀𝑀 Prototype Chrod Length A Surface Area 𝐴𝐴 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 Model Surface Area 𝐴𝐴 𝑃𝑃𝑃𝑃𝑀𝑀𝑃𝑃𝑀𝑀𝑃𝑃𝑃𝑃𝑃𝑃𝑀𝑀 Prototype Surface Area 𝐿𝐿 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 Model Lift 𝐿𝐿 𝑃𝑃𝑃𝑃𝑀𝑀𝑃𝑃𝑀𝑀𝑃𝑃𝑃𝑃𝑃𝑃𝑀𝑀 Prototype Lift 𝑉𝑉 ∞ Relative (Freestream) Wind Velocity 𝜌𝜌 ∞ Frestream Fluid Density 𝐶𝐶 𝐿𝐿 Lift Coefficient 𝐶𝐶 𝑃𝑃 Pressure Coefficient 𝑃𝑃 Pressure at Evaluation Point 𝑃𝑃 ∞ Freestream Pressure Due to the high cost of testing full size prototype airfoils in a wind tunnel, such testing is usually accomplished by use of scale models of the prototype. In scaling an airfoil, the parameters scaled from the prototype are its chord, its surface area, and its “lift force”. Figure 11 provides the basic dimensional nomenclature of the airfoil, i.e., the chord, the chord line, the mean camber line, the camber, the thickness, the leading edge, and the trailing edge. Figure 11. Airfoil Nomenclature. The scale factor for a model is determined by dividing the chord length of the model by the chord length of the full-sized airfoil (often referred to as the prototype). This relation is shown in equation 1. 𝑆𝑆 = 𝐶𝐶 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶 𝑃𝑃𝑃𝑃𝑀𝑀𝑃𝑃𝑀𝑀𝑃𝑃𝑃𝑃𝑃𝑃𝑀𝑀 (1) Model scale typically ranges from 1/5 scale to as small as 1/48 scale. The aerodynamic area of the model is also related to the aerodynamic area of the prototype by use of the scale factor, as shown in equation 2. 𝐴𝐴 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 = 𝐴𝐴 𝑃𝑃𝑃𝑃𝑀𝑀𝑃𝑃𝑀𝑀𝑃𝑃𝑃𝑃𝑃𝑃𝑀𝑀 ∗ 𝑆𝑆 (2) And finally, the lift force of the prototype can be estimated by using the scale factor and the lift force of the model as shown in equation 3. 𝐿𝐿 𝑃𝑃𝑃𝑃𝑀𝑀𝑃𝑃𝑀𝑀𝑃𝑃𝑃𝑃𝑃𝑃𝑀𝑀 = 𝐿𝐿 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑆𝑆 (3)

ME 4312 - Thermal and Fluids Laboratory | Page 5 of 10 The air speed in a wind tunnel (also known as freestream wind speed) acts as a simulation of the speed of a moving airfoil. The velocity of the tunnel air speed is referred to as the relative wind speed or freestream wind speed (V ∞ ). The airfoil reacts to the V ∞ by experiencing lift force (L), a drag force (D), and a moment force (M), the magnitude of such being also highly dependent on the angle of attack. A sketch showing the definitions of lift, drag, relative wind velocity V ∞ , and angle of attack is provided in Figure 12. Figure 12. Two-Dimensional Airfoil Aerodynamics. The equation used for determining the lift force on an airfoil is shown in equation 4. 𝐿𝐿 = 1 2 𝜌𝜌 ∞ 𝐴𝐴𝑉𝑉 ∞ 2 𝐶𝐶 𝐿𝐿 (4) The lift coefficient ( C L ) can be considered a function of all the simple and complex factors such as: (1) body shape, (2) inclination (e.g., angle of attack), (3) surface roughness, and (4) flow conditions (flow velocity, fluid viscosity, etc.), among others. This value is usually determined experimentally for different airfoils, and is correlated with the angle of attack and the Reynolds number Re = 𝜌𝜌 ∞ 𝑉𝑉 ∞ 𝐶𝐶 / 𝜇𝜇 , where 𝜌𝜌 ∞ is the air density, 𝑉𝑉 ∞ is the wind tunnel air speed, 𝐶𝐶 is the chord length of the airfoil, and 𝜇𝜇 is the dynamic viscosity of air. Since the air velocity varies in magnitude over the surface of the airfoil, so does the pressure. Thus, to establish the pressure component of the lift force of the airfoil, a measure of the dynamic pressure at many locations over the top and bottom surfaces of the airfoil is required. The air stream velocity profile can be assumed constant over the wingspan (i.e., direction perpendicular to the airfoil), the flow stream will essentially be two- dimensional. Therefore, the pressure distribution over the airfoil can be established by way of multiple pressure sensors aligned along the top and bottom surface of the airfoil in a direction tangential to the direction of airflow. It is common practice to express pressure distribution measurements in terms of a pressure coefficient defined by the dimensionless ratio, as indicated in Equation 5. 𝐶𝐶 𝑃𝑃 = 𝑃𝑃 − 𝑃𝑃 ∞ 1 2 ( 𝜌𝜌 ∞ 𝑉𝑉 ∞ 2 ) (5) It should be noted that, for each different air stream velocity, the pressure coefficient profile over the airfoil surface should not substantially change. To establish the magnitude of the pressure-based lift force from model test data (i.e., from pressure measurements along the airfoil surface), the product of measured pressure times the airfoil segment area A n (i.e., the segment of area where the pressure is exerted by the freestream air) must be calculated for both the upper surface of the airfoil and for the lower surface of the airfoil. The absolute difference between the absolute force in the lower section ( 𝐿𝐿 𝑀𝑀𝑙𝑙 ) and the absolute force in the upper section ( 𝐿𝐿 𝑢𝑢𝑙𝑙 ) leads to the magnitude of the pressure-based lift force. Since there are many pressure measurements along the airfoil surface, the total airfoil surface area has to be apportioned into a number of areas A n associated with the location of each pressure sensing port. The boundaries of each area shall be the length of the wingspan and the half way distances along the curve between each pressure sensing port . The magnitude of the pressure-based lift force shall then be established as indicated in Equations 6, 7, and 8. 𝐿𝐿 𝑀𝑀𝑙𝑙 = | 𝑝𝑝 9 𝐴𝐴 9 + 𝑝𝑝 10 𝐴𝐴 10 + 𝑝𝑝 11 𝐴𝐴 11 + 𝑝𝑝 12 𝐴𝐴 12 + 𝑝𝑝 13 𝐴𝐴 13 + 𝑝𝑝 14 𝐴𝐴 14 + 𝑝𝑝 15 𝐴𝐴 15 + 𝑝𝑝 16 𝐴𝐴 16 | (6) 𝐿𝐿 𝑢𝑢𝑙𝑙 = | 𝑝𝑝 1 𝐴𝐴 1 + 𝑝𝑝 2 𝐴𝐴 2 + 𝑝𝑝 3 𝐴𝐴 3 + 𝑝𝑝 4 𝐴𝐴 4 + 𝑝𝑝 5 𝐴𝐴 5 + 𝑝𝑝 6 𝐴𝐴 6 + 𝑝𝑝 7 𝐴𝐴 7 + 𝑝𝑝 8 𝐴𝐴 8 | (7) 𝐿𝐿 = | 𝐿𝐿 𝑀𝑀𝑙𝑙 − 𝐿𝐿 𝑢𝑢𝑙𝑙 | (8)

ME 4312 - Thermal and Fluids Laboratory | Page 6 of 10 Note that the direction of the lift force can be upwards (when 𝐿𝐿 𝑀𝑀𝑙𝑙 > 𝐿𝐿 𝑢𝑢𝑙𝑙 ) or downwards (when 𝐿𝐿 𝑀𝑀𝑙𝑙 < 𝐿𝐿 𝑢𝑢𝑙𝑙 ). Analysis and Summary of Findings: 1. Starting from the leading edge of the airfoil to each of the pressure sensing ports, divide the X U and X L dimensions by the chord length C . Below a summary of the results: Chord Length: 6 inches Wingspan (perpendicular to chord length c): 11.75 inches Refer to Figures 9 and 10 for a visual representation of the data provided in the next tables: Upper Airfoil Surface Pressure Port # X u /C (Normalized Distance Along Chord Line) Starting Point to Ending Point Distance along curve (inches) 1 0.04 Leading edge to port 1 0.4 2 0.09 Port 1 to 2 0.33 3 0.16 2 to 3 0.44 4 0.25 3 to 4 0.55 5 0.34 4 to 5 0.54 6 0.48 5 to 6 0.84 7 0.64 6 to 7 0.97 8 0.8 7 to 8 0.98 Distance from port 8 to trailing edge along the curve of the airfoil is 1.25 inches Lower Airfoil Surface Pressure Port # X L /C (Normalized Distance Along Chord Line) Starting Point to Ending Point Distance along curve (inches) 9 0.01 Leading edge to port 9 0.1 10 0.06 Port 9 to 10 0.39 11 0.13 10 to 11 0.47 12 0.21 11 to 12 0.51 13 0.31 12 to 13 0.55 14 0.45 13 to 14 0.87 15 0.62 14 to 15 0.98 16 0.79 15 to 16 0.98 Distance from port 16 to trailing edge along the curve of the airfoil is 1.25 inches

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ME 4312 - Thermal and Fluids Laboratory | Page 7 of 10 2. Calculate the airfoil surface area A n associated with each pressure sensing port. Boundaries of each area shall be the length of the wingspan and the halfway distances between each pressure sensing port (see image below for an example). The areas can be obtained by taking the product of the wingspan and the length “along the curve” (use the data provided in the previous table to find the appropriate length along the curve). 3. Calculate the total surface area of the airfoil and check to see if the sum of the areas determined in step 2 equals the total surface area (calculated as wing span times distance along the curve from leading edge to trailing edge for both upper and lower surfaces). 4. Procedures to calculate the air velocity in the wind tunnel using experimental data from red manometer: https://en.wikipedia.org/wiki/Pitot_tube Note that: • Stagnation (or total) pressure (pt) = static pressure (ps) + dynamic pressure (pd). The manometer reads dynamic pressure, which can be expressed as pd = (pt-ps). • 1 in of H2O equals 248.84 Pa. So, for example, if the dynamic pressure read by the manometer is 0.36 in of H2O, then, the value (pt-ps) is equal to 89.5824 Pa. • Estimate the air density at a height of 200 m above the sea level (altitude of the city of san Antonio) and for a temperature of about 22 degrees Celsius. Alternatively, assume the sea level value 1.2254 kg/m 3 . • The wind tunnel air speed is v = sqrt(2*(pt-ps)/rho_air). 5. Calculate the pressure coefficient C p (equation 5) for each of the recorded airfoil pressures 𝑝𝑝 . Remember that p-p ∞ is obtained from the height difference measured from the green tube manometers (measured displacement minus baseline). https://en.wikipedia.org/wiki/Pressure_coefficient 6. Prepare two sets of tables for each of the four wind velocities 𝑉𝑉 ∞ ( specified by your instructor in terms of fan RPM) . The tables shall consist of the non-dimensional tap locations X U /C and X L /C as the first column of data followed by columns of their corresponding (1) airfoil pressures 𝑝𝑝 , (2) surface areas A n established in Step 2 above, and (3) the lift forces L ls and L us for each angle of attack. One table set shall apply to data corresponding to the airfoil upper surface and the second table set shall apply to the lower surface. The total airfoil surface area A and the total lift force L shall be included at the bottom of each of their respective columns. The column headings shall appear as denoted in the following example: X U /C Airfoil Pressure p (Units) at Various AOA A U 2 Lift Force L U -15 o -10 o -6 o -4 o 0 o +4 o +6 o +10 o +15 o • There will be a total of 8 tables for this step (lower surface and upper surface for each of the three wind velocities). • Refer to Equations 6 and 7. • Calculate pressure values. Multiply each pressure value by corresponding area. Add down the column for a lift

ME 4312 - Thermal and Fluids Laboratory | Page 8 of 10 force per angle of attack. The values in the table below are not the correct values for the data provided to you; only use the table as an example. 7. Prepare two tables consisting of tap locations X U /C and X L /C as the first column of data followed by columns Wind Velocity 𝑉𝑉 ∞ and pressure coefficients C p . One table shall apply to data corresponding to the airfoil upper surface and the second table shall apply to the lower surface. The “average” C p shall be established for each Angle of Attack (AOA) as indicated in the following table. Cite what you observe from this data, especially regarding the significance of C p. For each angle of attack, establish the “average” C p over the range of wind velocity. Column headings should appear as in the following example: X U/C Wind Velocity (ft/sec) Pressure Coefficient (C p ) at Various AOA -15 o -10 o -6 o -4 o 0 o +4 o +6 o +10 o -15 o (1) (2) (3) (4) AVERAGE C P The values in the table below are not the correct values ; only use the table as an example. 8. Prepare a plot of the “average” pressure coefficient C p versus the chord position X/C for each angle of attack. Differentiate which C p applies to the top surface and that of the lower surface. Apply the chord position X/C as the abscissa.

ME 4312 - Thermal and Fluids Laboratory | Page 9 of 10 Note: To make the data easier to interpret, it would be best for the ordinate to include negative C p ’s above the abscissa and positive C p ’s below the abscissa as illustrated below. A sample plot is shown below: • For the upper and lower surface, you will plot the average pressure coefficients obtained for each angle of attack. • You can switch the negative and positive numbers as in the plot above if it helps to interpret the data. 9. Prepare tables and Compute the total lift L = |L l - L u | for each Angle of attack and for each wind velocity. Prepare a plot of L versus angle of attack, with angle of attack as the abscissa. All four wind velocities should be included on a single plot (overlay). Comment on your observations in your data analysis, especially with regard to “stalling”. A useful reference of 2D steady-state airfoil aerodynamics is: https://www.hindawi.com/journals/mpe/2015/854308/ A sample plot is shown below: 10. Discuss all tables and plots as they are presented in the report. Questions to guide discussion: • What is the significance of the pressure coefficient and lift force? • What is the relationship to angle of attack? • What effects occur on the upper and lower surface of the airfoil? • What effects occur at the leading edge vs. the trailing edge? • Does the data make sense? Why or why not? • What sources of error could affect the data collected?

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ME 4312 - Thermal and Fluids Laboratory | Page 10 of 10 Simulation Data: Below information for the simulation data component of this laboratory assignment: 1. Using the coordinate data provided, recreate the NACA 4415 airfoil in your desired simulation software (For S olid W orks tutorial : https://www.youtube.com/watch?v=6kXwoe6KMR0 ) . 2. For the simulation boundary condition, you will need to choose one of the four (4) velocities considered during the experiment and for all angles of attack calculate the lift force. For this you will need to set an external flow simulation with the chosen velocity boundary condition and adjust the airfoil orientation towards the airflow for each angle of attack. (For S olid W orks tutorial : https://www.youtube.com/watch?v=4ltTTYbmQkY ) 3. Calculate the simulation lift force for the chosen velocity and all angles of attack and compare with the lift force calculated for those conditions with experimental data. 4. During the experiment it is not possible to visualize the conditions of the flow surrounding the airfoil and identify any areas of stagnated flow, flow separation, etc. Please include in your flow analysis the differences in the flow for the different angles of attack and what happens when the angle of attack is +/- 15 degrees. (For this analysis you should create velocity cut plots and using contours or isolines for each angle of attack. The velocity condition chosen should be in the direction of the flow you set for your simulation).