AE 460 Laboratory Note for Experiment 1

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AE 460 Laboratory Note for Experiment 1 Wind Tunnel Calibration Lab by Ani Saini, Margarita Kuzmanova, Andrew Beusse, Srinu Rayudu TA: Derrick Wiberg Section AB6, Group B, Tuesday, 5:00 - 7:00 pm Date of submission {placed at the bottom of the title page}

1 1. INTRODUCTION For this experiment, students were acquainted with the use of the Aerolab low-speed wind tunnel, which was calibrated to gather accurate data for future experiments. Using the static pressure ring, the rake of pressure probes, and the Dwyer inclined manometer, data was collected for a range of RPM from 400 to 1400 in increments of 100 RPM. To determine the differential pressure at the tunnel inlet, pressure measurements were obtained from the wall static pressure taps. The rake of pressure probes was used to calculate the average dynamic pressure and speed. The Dwyer inclined manometer and the input motor RPM for the tunnel fan were used to determine the average test-section dynamic pressure. Each data point (measurement) was then recorded in NI LabView software to be accessed later. 2. APPARATUS This lab utilized a static pressure ring, rake of pressure probes, Omega PX653 Pressure Transmitter, Pressure Systems Incorporated (PSI) NetScanner pressure system, and Model 4195 Compact Digital Barometer to calibrate the Dwyer inclined manometer attached to the Aerolab low-speed wind tunnel using the tunnel fan frequency controller to control the speed of the tunnel. The static pressure ring was used to measure the static pressure in the system which was then used as the reference for the PSI NetScanner pressure system to calculate the difference in pressure of each tap on the pressure rake in the tunnel. This can be seen in the figure below depicting the laboratory set up with one line entering the pressure system coming from the ring and the other from the test section with

2 the rake inside. The Dwyer manometer was used to determine the difference in static pressure and atmospheric pressure. This was also the function of the pressure transducer located under the control panel. Figure 1. Schematic of the experimental apparatus to measure the static and total pressure through the wind tunnel test section. Table. 1. List of Laboratory Equipment and their accuracy as used in the experiment No. Item Size/Range/ Capacity Accuracy Use in experiment 1 The Aerolab Low-Speed 9.5:1 contraction ratio / Test … Used as the wind tunnel that Flo w In Flow Conditi oning Section Contr action Sectio n Test Sectio n Fa n Diffus er Flow out Static Press ure Ring Pressure Rake Dwyer Manometer Test Section Zoomed In Con trol Pan el PSI NetScann er Pressure System 1. 5”

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3 Wind Tunnel section dimensions: 24” x 12” x 12” was being calibrated 2 Static Pressure Ring … … Used as reference which rake measurements were compared to 3 Rake of 13 Pressure Probes each arm is 4.5”/ each tap is 1.5” apart … measure pressures at various locations in the test section 4 Dwyer Inclined Manometer 0”-6” of water 1% of measureme nt measure the difference between the atmospheric pressure and static pressure 5 Omega PX653 Pressure Transmitter 0”-10” of water ± 0.25% of the measureme nt measure the difference between the atmospheric pressure and static pressure 6 PSI NetScanner Pressure System Maximum pressure differential of 1 Psid 0.1% of the measureme nt Used to find the differential pressure of the rake and the static pressure 7 Compact Digital Manometer …. ± 0.148 in Hg and ± 1.8 ̊F Used to get atmospheric pressure and temperature in the lab

4 3. RESULTS AND DISCUSSION All the following experiments are derived as part of procedures laid out in the laboratory manual. 3.1. Average Total, Static, and Dynamic Pressures The dynamic pressure was a key element to collect in this lab. The data included nine total pressure probes (T1-T9), and five static pressure probes (S1-S5) for individual runs conducted with a 100 RPM increment from 400-1400 RPM. The values from the probes were averaged and the average dynamic pressure was calculated using the difference between the Average Total Pressure vs Average Static Pressure at each point. This data is provided for reference in Table. 2. Table. 2. Data and Specifications for Dynamic Pressure Data Point Motor Speed [RPM] Average Total Pressure [psi] Average Static Pressure [psi] Average Dynamic Pressure [psi] 1 400 4.62E-03 4.77E-05 4.58E-03 2 500 7.60E-03 8.50E-05 7.52E-03 3 600 1.15E-02 1.22E-04 1.13E-02 4 700 1.63E-02 2.46E-04 1.60E-02 5 800 2.16E-02 2.39E-04 2.14E-02 6 900 2.81E-02 2.75E-04 2.78E-02 7 1000 3.51E-02 4.30E-04 3.47E-02 8 1100 4.28E-02 4.96E-04 4.23E-02 9 1200 5.17E-02 3.81E-04 5.13E-02 10 1300 5.95E-02 9.74E-04 5.85E-02 11 1400 6.94E-02 4.20E-04 6.90E-02

5 The table above presents the average dynamic pressure as derived from the other given quantities. One thing to notice is that the data for all the quantities are not linear, in fact they increase as a quadratic as the motor speed increases linearly. 3.2 Actual Velocity, Reynolds Number per unit Length, and Mach Number Since the dynamic pressure is calculated, other quantities such as the true velocity, Mach number, and Reynolds number can be computed. Modifying Bernoulli's equation with assumptions such as steady, inviscid, and incompressible allows for the usage of the equation (1): , (1),(2) where V is the flow velocity, q is the average dynamic pressure, ⍴ is the computed average density of air, P ambient is the ambient pressure, R is gas constant, and T is the ambient temperature. With the flow velocity calculated, equation (3), and (4) will be used to get the Mach number and equation (5) will be used to get the Reynolds number. , (3),(4) (5)

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6 Table. 3. Data Calculated for Various Attributes from Varying RPM in the Wind Tunnel Data Point Motor Speed [RPM] Average Dynamic Pressure [psi] Velocity [ft/s] Reynolds Number per Unit Length [1/ft] Mach Number 1 400 0.00457672 2.01634741 1.19E+04 1.78E-03 2 500 0.00751837 2.58434163 1.52E+04 2.28E-03 3 600 0.01134455 3.17454547 1.87E+04 2.81E-03 4 700 0.01603178 3.77379949 2.22E+04 3.33E-03 5 800 0.0213614 4.3561501 2.57E+04 3.85E-03 6 900 0.02780254 4.9697003 2.93E+04 4.39E-03 7 1000 0.03469222 5.5514194 3.27E+04 4.91E-03 8 1100 0.04229269 6.1294376 3.61E+04 5.42E-03 9 1200 0.05129694 6.75046515 3.98E+04 5.97E-03 10 1300 0.05849267 7.20839688 4.25E+04 6.37E-03 11 1400 0.06901303 7.82985172 4.61E+04 6.92E-03 Based on this data, a comparison was made between the properties and the varying RPM. The findings are shown in the graphs below.

7 Figure 2. 2-Dimensional Graphs for Computed Quantities against increasing Motor Speed. Plot 1 (top left), Plot 2 (top right), Plot 3 (Bottom left), Plot 4 (Bottom right) depicting Dynamic Pressure, Flow Velocity, Reynolds number per unit length, and Mach number against increasing Motor Speed. As a general trend, as the RPM increases the specific attribute also increases. The increase is linear for all attributes except dynamic pressure where the increase is exponential. Also, these graphs can only give an approximation for a given motor speed setting. This is because of many reasons. One such reason is that these values are computed using quantities that are user (pressure values) and environment (temperature values) dependent that will provide inconsistent results even when the same test is repeated. Another reason that the collected data is an approximation can be seen from the plots as the data measured shows some deviation from the true linear data one can expect to see. This could be due to several factors such as a sudden change in the room pressure, and such as someone walking in front of the intake tunnel.

8 3.3. Static and Total Pressure Variation To compare the variation in the static pressure from the different probe locations, the percent difference of each static pressure from the average static pressure with the difference normalized by the average dynamic pressure was calculated. This static pressure variation ( SPV i ) for each static pressure probe is given by SPV i [ % ] = 100% ∗( PS i − PS avg )/ q actual where PS i is the static pressure of the i th static probe on the rake (i.e., S1 to S5) and SPV i is the static pressure variation for the i th static pressure tap. The graph below shows the static pressure variation on the static pressure probes. Figure 2. Scatterplot Depicting the Trends from the Static Pressure Probes. (description)

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9 Figure 3. Scatterplot Depicting the Trends from the Total Pressure Probes As dynamic pressure increased the SPV values had a normal distribution on the scatterplot, whereas as on the TPV scatterplot, the points stayed towards the lower limit but did not increase with dynamic pressure. 3.4. Variation of the Total and Dynamic Pressures Aside from the slight pressure losses through the converging section, the pressure measured using the manometer and the pressure measured using the Omega transducer should be approximately equal to the actual dynamic pressure in the test section of the tunnel. The table below shows the values of the percent differences between different pressure data attributes. Table. 4. Percent Differences between Different types of Pressures

10 Data Point Motor Speed [RPM] Actual Dynamic Pressure [psi] Omega Transmitter delta P [dpsi] % Difference (Dynamic and Omega Pressure) Manome ter delta P [dpsi] % Difference (Dynamic, Manometer Pressure) 1 400 4.58E-03 5.49E-03 1.81E+01 5.78E-03 2.32E+01 2 500 7.52E-03 9.02E-03 1.82E+01 9.39E-03 2.21E+01 3 600 1.13E-02 1.33E-02 1.59E+01 1.30E-02 1.36E+01 4 700 1.60E-02 1.84E-02 1.38E+01 1.88E-02 1.59E+01 5 800 2.14E-02 2.45E-02 1.37E+01 2.46E-02 1.41E+01 6 900 2.78E-02 3.14E-02 1.22E+01 3.18E-02 1.34E+01 7 1000 3.47E-02 3.90E-02 1.17E+01 3.97E-02 1.35E+01 8 1100 4.23E-02 4.74E-02 1.14E+01 4.77E-02 1.20E+01 9 1200 5.13E-02 5.69E-02 1.04E+01 5.71E-02 1.07E+01 10 1300 5.85E-02 6.57E-02 1.16E+01 6.65E-02 1.28E+01 11 1400 6.90E-02 7.66E-02 1.04E+01 7.80E-02 1.22E+01

11 0.00E+00 2.00E-02 4.00E-02 6.00E-02 8.00E-02 1.00E-01 0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 7.00E-02 8.00E-02 f(x) = 0.91 x − 0 Linear fit for dynamic pressure and Omega Transducer Omega Pressure Transmitter P [dpsi] Dynamic Pressure (lbf/ft2) Figure 3. This graph depicts how dynamic pressure changes as omega pressure transmitter is increased. The equation for the linear fit is also given above. When the actual dynamic pressure to the omega transmitter delta pressure was compared, it was found that the omega transmitter delta pressure was greater than the actual dynamic pressure for each data point. This might be due to various elements in the wind tunnel room disturbing the flow slightly, therefore altering the readings slightly. Also, the % Difference (Dynamic and Omega Pressure) generally tended to decrease as RPM increased which highlights that error decreases as RPM increases. When the manometer delta pressure and the actual dynamic pressure were compared, it was found that % difference also decreased as RPM increased but as seen with the omega transmitter delta pressure, the manometer delta pressure was greater than the actual dynamic pressure for each data point.

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12 4. CONCLUSIONS The average total and static pressure were successfully discovered through experimentation methods, using a pressure rake in a subsonic wind tunnel. Average dynamic pressure was then calculated, using the collected data. A modified Bernoulli’s equation was used to calculate actual velocity, Mach, and inverse Reynolds numbers with ease. These quantities appeared to be linear. The variations of static and total pressure were calculated with a significant difference of 10 to 23%. Future tests should include more stable conditions with minimized flow disruption and a predetermined wait-time to record measurements. Standard conditions would ensure that the error is minimized from the outside factors. Additionally, it will be of benefit to record more points, either in smaller increments or in a wider range. The former would provide more precise data for the current range, while an expanded range would provide insight into the behavior of the pressure measurements at lower or higher RPM. Regardless, more data would result in a more accurate analysis, but would consume more time to implement. Alternatively, different devices for pressure data collection can be used to check which one yields less error. In the future, that can be a significant source of error, if a pressure rake is used, instead of a more sophisticated and error-resistant device.

13 5. REFERENCES [1] “Experiment #1: Wind Tunnel Calibration,” Laboratory Writeup for AE 460, University of Illinois at Urbana-Champaign, 2022. 6. APPENDIX APPENDIX A: SAMPLE CALCULATIONS ALL THE EQUATIONS USED 1. Actual Velocity Calculation V = Actual velocity [ft/s] q = Dynamic pressure [psi] ρ = Density [lbf/ft 3 ] V = (2*3.47E-02 psi)/() 2. Density Calculation ρ = Density [lbf/ft 3 ] P ambient = Ambient pressure [psi] R = Gas constant [ft*lbf / (slug*(°R))] T = Temperature [°R] 3. Reynolds Number Calculation Re = Reynolds number

14 ρ = Density [lbf/ft 3 ] V = Actual velocity [ft/s] μ = Atmospheric viscosity [lbf*s/ft 2 ] Re = (? lbf/ft 3 )*(5.5514194 ft/s)/(3.737E-07 lbf*s/ft 2 ) = 4. Mach Number Calculation M = Mach number V = Actual velocity [ft/s] a = Atmosphere speed of sound [ft/s] M = (5.5514194 ft/s) / (1125.33 ft/s) = 4.91E-03 5. Atmosphere Speed of Sound Calculation a = Atmosphere speed of sound [ft/s] γ = Heat capacity ratio R = Gas constant [ft*lbf / (slug*(°R))] T = Temperature [°R] 6. Total Pressure Variation for the i th Static Pressure Probe TPV i = Total pressure variation for the i th static pressure probe P 0, i = Total pressure of the i th total probe on the rake [psi] P 0, avg = Average total pressure of a total probe on the rake [psi] q avg = Actual dynamic pressure from the rake [psi]

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15 7. Static Pressure Variation for the i th Static Pressure Tap SPV i = Static pressure variation for the i th static pressure tap P S, i = Static pressure of the i th static probe on the rake [psi] P S, avg = Average static pressure of a static probe on the rake [psi] q avg = Actual dynamic pressure from the rake [psi] 8. The Uncertainty in the Actual Velocity U V = Uncertainty of actual velocity ∂V ∂ p 0 = Partial derivative of actual velocity with respect to total pressure U p0 = Uncertainty of total pressure ∂V ∂ p s = Partial derivative of actual velocity with respect to static pressure U ps = Uncertainty of static pressure ∂V ∂ ρ = Partial derivative of actual velocity with respect to density U ρ = Uncertainty of density 9. The Uncertainty in the Density U ρ = Uncertainty of density

16 ∂ ρ ∂ pamb = Partial derivative of density with respect to ambient pressure U p amb = Uncertainty of ambient pressure ∂ ρ ∂R = Partial derivative of density with respect to gas constant U R = Uncertainty of gas constant ∂ ρ ∂T amb = Partial derivative of density with respect to ambient temperature U T amb = Uncertainty of ambient temperature 10. The Uncertainty in the Pressure U p = Uncertainty of pressure U p single = Uncertainty of pressure from a single source n = Number of pressures APPENDIX B: RAW DATA Motor Speed [RPM] Actual Velocity [ft/s] Actual Velocity Uncertainty [ft/s] Percent Uncertainty (%) 400 2.01634741 ±1.4762796936638 73.2155424 500 2.58434163 ±1.15426206841032 44.6636798 600 3.17454547 ±0.94368662259631 29.7266689 700 3.77379949 ±0.79981581780645 21.193914 800 4.3561501 ±0.70086305174509 16.0890474 900 4.9697003 ±0.62527646501277 12.5817741 1000 5.5514194 ±0.57280369805835 10.3181485 1100 6.1294376 ±0.53442834072577 8.71904366 1200 6.75046515 ±0.50501513644787 7.48119019 1300 7.20839688 ±0.48964009481017 6.79263508

17 1400 7.82985172 ±0.47575633960346 6.07618582 APPENDIX C: GROUP MEMBER CONTRIBUTIONS Laboratory Note #1 Group Member Contribution to Technical Note Ani Saini Completed all the analysis to prepare plots and tables and implemented them in the report. Also completed the handwritten uncertainty analysis and created a formula in excel to get each uncertainty (1-6). Srinu Rayudu Authored introduction as well as authored results section; Authored data analysis and discussion. Margarita Kuzmanova Prepared conclusions and all appendices

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