AME 20213: Fundamentals of Measurements and Data Analysis. LEX-3: Wind Tunnel Pressure Measurement Uncertainty 9 October 2006

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1 AME 20213: Fundamentals of Measurements and Data Analysis LEX-3: Wind Tunnel Pressure Measurement Uncertainty 9 October 2006 TA: John Schmitz Office: B028 Hessert Phone: jschmitz@nd.edu Objective: Pitot-static tubes and static pressure ports interfaced with pressure transducers are wind tunnel measurement devices with long histories and widespread use today. As with any measurement system however, the instruments have basic uncertainties that must be understood and quantified before data interpretation. Objectives of the current exercise are twofold: to demonstrate uncertainties inherent to pressure measurement through the use of imperfect instrumentation and discrete representation of analog signals, as well as to highlight the limiting Pitot-static tube requirement of exact freestream alignment. Background: Often in the experimental study of fluid mechanics, velocities, V, are found by measuring density, ρ, and pressures, P, and implementing the classic Bernoulli expression for total pressure in an incompressible flow (Equation 1). Solving for velocity yields, P T otal = P Static + P Dynamic = P Static ρv 2 (1) V = 2(P T otal P Static ). (2) ρ The value of density in Equation 2 is defined by the equation of state, P = ρrt, (3) where R, P, and T are the universal gas constant, recorded lab ambient pressure, and recorded lab temperature, respectively. One common device to implement the above highlighted relation is the Pitot-static probe. By creating a stagnation point in the flow, a Pitot-static probe measures a total pressure at its tip. Additional pressure ports along the body of the probe are used to measure the static pressure component and, hence, yield velocities according to Equation 2. Other pressure measurement instruments, such as Pitot probes, do not have the capability as single instruments to measure a difference between total and static pressures and hence velocities. Although the Pitot-static probe features an inexpensive and robust design, it requires an exacting alignment to the freestream velocity. Naturally, uncertainty permeates results in 1

2 Figure 1: Pitot-static Tube. the case of Pitot-static probe misalignment. The current exercise seeks to understand the uncertainty trend when Pitot-static probe yaw angle is varied from -80 to 80 degrees to the freestream. The static pressure port is another common measurement device, presented in this exercise to explore uncertainty in the analog-to-digital conversion of data. Static ports are often used to understand pressure forces on bodies submerged in fluids. For example, many static ports arranged along an airfoil body can give a pressure distribution about the airfoil, from which a lift coefficient may be gleaned. In certain applications, such as in the present case of separated flow around a cylinder, highly fluctuating pressure measurements call for the sampling and subsequent averaging of many points to give an accurate pressure reading. The deviation in the measured pressure is given by, 1 S x = (xi x) N 1 2, (4) where N is the number of sampled points, x i is a single sampled point and x is the sample mean of the points. Uncertainty for this case is that for estimating the true mean value, given by, u = ±t ν,p S x N, (5) where t ν,p arises from the Student-t probability distribution, ν is equal to N-1, and P indicates the desired confidence interval. As seen Equations 4 and 5, deviation and hence uncertainty will diminish as the number of sampled points is increased. All data are acquired by groups of two students in the continuous wind tunnel located in the Engineering Learning Center (ELC). The laboratory setup is depicted in Figure 2 2

3 Figure 2: Learning Center Low-Speed Wind Tunnel. and features a Pitot-static probe for Part A of the lab and a cylinder with a static port for the uncertainty measurements in Part B. Procedure: (PART A) To record pressure measurements, a pressure transducer is attached to the Pitot-static probe in order to represent pressures as voltages for data acquisition. Pressures may be converted from the stored voltages according to, P = 0.05 E pt , (6) where E pt1 is the recorded pressure transducer #1 voltage in volts and P is the pressure difference in in. H 2 O. Follow these steps to setup and record data for the Pitot-static tube yaw survey: 1. Record lab ambient temperature [ F] and pressure [in. Hg] using the barometer and thermometer located on the north side of the tunnel. You will need these to solve for density using Equation 3. Be sure to use a consistent system of units. 2. Ensure the Pitot-static probe is oriented upstream of the cylinder in the test section. Also verify that the black plug on the single pressure transducer is set to the port labeled Channel 1 on the acquisition board. 3

4 3. All data will be stored using the Labview package AME located on the computer desktop. First create a folder in the desktop folder ame20213 to save your data files during the procedure. Next, open AME Flip the switch to supply power to the tunnel motor. Set the power to the prescribed tunnel power setting and Pitot-static probe distance from the ceiling according to your group number. Use the meter located on the right side of the tunnel to set the power and the scale attached to the vertical traverse to set the correct probe height for your unique exercise. 5. In the software, verify that the Pitot/Cylinder switch is thrown to the Pitot setting and that data is sampled 1000 times at 500 Hz. 6. In Labview, label Channel 1 Pitot and click into the grey area, checking to make sure a green light switches on. 7. One lab partner must stand on the step stool and set the Pitot-static yaw angle using the available protractor. Start at -80 degrees and click the Start Experiment tab in Labview. Create a file in your folder with a.txt extension. 8. After designating a file and saving the first data point, Labview will ask if you would like to move the traverse and record another data sample. Change the yaw angle by 10 degrees and then click record sample. Continue until you have populated the range of yaw angles from -80 to 80 degrees in increments of 10 degrees. After reaching a positive 80 degrees, record several more points at 0 degrees to help you verify the freestream velocity value in your data analysis. 9. When finished recording data, click No, I m done. (PART B) The pressure transducer equation for cylinder static pressure port measurements is given by, P = (E pt ), (7) where E pt2 is the recorded pressure transducer #2 voltage in volts and P is the pressure difference in in. H 2 O. Follow these steps to setup and record data for the cylinder static port uncertainty: 1. By rotating the handle, position the Pitot-static probe near the tunnel ceiling so as not to disturb flow around the cylinder. 2. Switch the black BNC cable on the pressure transducer from Part A to Channel 2 on the box with two pressure transducers. N.B: A different pressure transducer is used for Part B. It is the larger of the two transducers. 4

5 3. In Labview, erase Pitot and label Channel 1 as Cylinder. 4. In Labview, flip the virtual switch from Pitot to Cylinder. 5. Set number of points sampled to 750 and verify a sampling rate of 1000Hz. 6. Set tunnel power to 50 % and ensure a static tap orientation of 10 degrees counterclockwise from vertical. 7. Start Experiment and save to a.txt file in your group folder, making sure to label clearly which data are for 50 % power and which for 90 %. 8. You only have to take one data point since Labview is now recording 750 raw data points to your.txt file. N.B. Take care not to take more than 1 data set. 9. Repeat the procedure for 90 % power. 10. When finished recording data, click No, I m done. Post-process/Deliverables: Using Equation 2, plot freestream velocity, V, versus yaw angle, θ. Include in your plot y error bars corresponding to measurement uncertainties in dynamic pressure. Take care to account for all pressure transducer measurement uncertainties discussed in the lab introduction. The behavior of the temporal precision error of the cylinder static tap is clearly understood upon plotting standard deviation, S x, versus number of sampled points, N. To make the plots, extract data in cumulative segments of 25 points, and then calculate a mean and standard deviation for every interval (i.e. N=[25,50, ]). Include figures according to the guidelines on p.49 [Dunn 2005]. Remember units on figure axes, a title or caption, and error bars where appropriate. Include three plots, one corresponding to the Pitot-static probe yaw survey, one for cylinder static port data standard deviation, and one for the corresponding temporal precision uncertainty given by expression 5. Include and comment on all results in a technical report as detailed on p [Dunn 2005], with particular focus on the following points: 1. Provide a table of uncertainties present in both parts of the lab. Discuss the sources and meanings of the uncertainties. 2. Include an appendix with a typed sample I.S.O. uncertainty derivation. 3. What is the maximum measurement uncertainty in the Pitot-static tube? Explain the behavior of the uncertainty at its maximum and minimum points. Where should the uncertainty be maximum and minimum? Does this correlate with your data? N.B. Uncertainty due to yaw angle has not been quantified in this exercise, and the maximum measurement uncertainty should correspond to your maximum y error bar value in Part A. 5

6 4. Is the effect of yaw angle on Pitot-static probe pressure measurement negligible? Why/why not? What is the implication for two or three-dimensional flows? Is there any way to correct for this behavior? 5. Explain the mechanism for uncertainty in the cylinder static tap. Why is there a challenge recording digital (discrete) measurements of an analog (continuous) signal in fluctuating conditions? Why is it important to average many samples when using a Pitot-static probe or static tap? Technical Report Due Date: Thursday November 9, 9:30 AM. References: 1. Dunn, P.F Measurement and Data Analysis for Engineering and Science. New York: McGraw-Hill. 6