PRESSURE MEASUREMENT IN A TWO DIMENSIONAL UNSTEADY FLOW

Transcription

1 PRESSURE MEASUREMENT IN A TWO DIMENSIONAL UNSTEADY FLOW William Walker Virginia Polytechnic Institute and State University, Blacksburg, Virginia, This project is aimed at developing a system to obtain unsteady aerodynamic data from a two dimensional wing, and analyzing the pressure variations with time over the wing surface. The data was gathered by using electronic pressure transducers. The transducers were placed inside a wing model along the surface around the wing; to allow for a two dimensional section of the wing to be analyzed. The output of the transducers is too small to be used for data analysis, only in millivolts. This problem was solved by designing an amplifier circuit for each transducer to produce a gain of 1000, making the output into Volts. The unsteady flow is created by rotating the wing about the quarter chord axis in the wing tunnel in a sinusoidal manner. This rotation, if rapid enough, could appear to be a low frequency vibration, which testing has shown affects the transducer due to its own inertia. This problem was solved by adding a low pass filter to the amplifier circuit. The low pass filter and amplifier circuit was used in conjunction with the pressure transducers to obtain pressure measurements in an unsteady flow. C G F f g h Ω P o P R R G ρ ρ air ρ water V V V ω Nomenclature = Capacitance = Gain = Farad, unit of Capacitance = Frequency = Gravitational constant for Earth = Water column height = Ohm, unit of Resistance = Total Pressure = Free Stream Pressure = Resistance = Resistance of amplifier resistor = Density = Density of air = Density of Water = Velocity = Free Stream Velocity = Volts = Oscillating frequency 1

2 I. INTRODUCTION The main goal of this research project was to find a successful way to measure pressures on a wing in an unsteady flow, and use this pressure data to see how lift and drag on the wing changes in an unsteady flow. The unsteady flow primarily to be looked at would be simulating an aircraft in a pitch up or pitch down motion by rotating the airfoil in a wind tunnel about the span wise axis. Other unsteady flows would include responses such as phugoid motion response and short period responses, as well as changes the lateral directional axes such as a roll and yaw movements. In order to achieve an analysis of these flows, instantaneous values of lift and drag need to be found during the motions. The calculation of lift and drag can be found from the pressure distribution over the wing. For an airplane in an unsteady flow, the pressures over the wing are not constant, but are changing. This makes it difficult to measure the pressures. For a wing in a steady flow simple setups using Tygon tubes and manometers could be used. For unsteady flows this is not an accurate due to a time lag in the tubes. There also needs to be a way of recording these pressures. In order to achieve this goal the use of pressure sensors was required. II. APPARATUS FOR THE EXPERIMENT A. Pressure Sensors There are many types of pressure sensors available on the market. The key was choosing the right pressure sensor for the project. Several Companies make the pressure sensors required for this research such as Honeywell and All Sensors. The dynamic pressure of a low speed flow is not very large; therefore the pressure sensor chosen will need to measure very small pressures. The main types of pressure sensors available are gage sensors, absolute sensors, and differential sensors. The gage pressure sensor measures pressures relative to the atmospheric pressure like a tire gage. Absolute pressure sensors measure the absolute pressure of the system, and differential pressure sensors measure pressure difference between two areas. Absolute pressure sensors were not desired for this project because the dynamic pressure relative to the total pressure was very small, almost an order of magnitude different. Therefore measuring changes with an absolute pressure would be very inaccurate. Gage pressure sensors measure the pressure relative to a set atmospheric pressure; for this project that would just complicate things and make computations harder because the atmospheric pressure is always changing. The differential pressure sensors measure a pressure difference between two areas. This would be prefect in that the pressure difference could be the surface of the wing and a place outside the flow. Therefore, the dynamic pressure could be directly measured in this way. Due to this, a differential pressure sensor was required. B. Open Jet Wind Tunnel The Virginia Tech Open Jet wind tunnel, which is shown in figure 1 below, was used for this experiment. The wind tunnel is a closed circuit tunnel with a three foot diameter test section. The top speed of the tunnel is roughly 100 mph (Aerospace and Ocean Engineering Department 2005). 2

3 C. Choosing the Right Pressure Sensor Differential Pressure sensors can be made for use in a large range of pressures. Some can measure very large pressures, while some a very sensitive to even the slightest pressure change. The first step in choosing the right pressure sensor was to find out what range of pressures were to be measured. In order to find the pressure range, the wind tunnel speed was needed. The experiments were to be preformed in the Virginia Tech Open Jet Wind Tunnel shown in Figure 1. To find the dynamic pressure this equates to, Bernoulli s Equation was used. The general form of Bernoulli s equation is shown in equation 1. P + 1/2ρV 2 = P o This equation ignores the effects of compressibility, which is a good assumption for low speed flows. To find how this relates to the tunnel measuring system, or inches of a water column, equation 2 was used. (1) P = ρgh (2) Since a differential pressure sensor is going to be used to measure the dynamic pressure, the pressure range needs to be found in a common unit of measurement, which for the wind tunnel is inches of a water column. To find out the largest pressures to be seen, a combination of equations 1 and 2 needs to be used. The dynamic pressure in Bernoulli s equation can be set equal to the dynamic pressure in equation 2. ½ ρv 2 = ρgh (3) Solving for the height of the water column equation 4 can be used. h = ½ ρ air * V 2 / ρ water * g (4) Substituting in the values of ρ air = slugs/ft 3, V = 100 ft/s, ρ water = slugs/ft 3, g = 32.2 ft/s 2, and the maximum velocity for the tunnel, the maximum values of h could be found for the free stream. These values yielded h = inches of water. This value was for the free stream dynamic pressure. As the flow moves over the wing, larger velocities and in turn larger pressures will be seen. Therefore slightly more than this value could be measured. There are many different types of differential pressure sensors on the market. Some sensors have ports on the side, on the top and bottom and no port at all, just a hole. There is no way of telling which pressure sensor will work the best without testing them. Therefore two pressure sensors were ordered that would fulfill the requirements previously calculated. The result was a Differential H Grade minisensor which measures up to 4 inches of water. Four sensors were purchased, two with two ports, and two with no ports. These pressure sensors are shown in figure 2. Each sensor required a +/- 16 V input and would output up to +/- 24 mv. This is a relatively small output, and with electronic noise and noise from mechanical vibration of the test structure, this could be a problem. The noise could be so large that it may completely nullify the signal from the pressure reading. One possible solution to this is to attach a differential amplifier between the sensor and the multimeter outputting the voltage. The only way to find out is to test the setup. 3

4 D. Testing the Pressure Sensors The two port pressure sensor was the first to be tested. The no port sensor would need to be integrated into some type of test setup before it could be tested. For the testing of the two port pressure sensor a small wind tunnel test was run. The wind tunnel was ran at different velocities and measured with a pitot-static tube hooked up to a digital manometer and another pitot-static tube hooked up to the pressure sensor itself. The pressure sensor was placed on a breadboard with four wires coming off it. These four wires are the inputs and outputs of the Wheatstone bridge circuit which the sensor is made from. Figure 3 shows the test setup for the sensor and the breadboard. The two Tygon tubes coming from the Pitot - static tube were attached to the two ports on the pressure sensor. The input voltage was 15 V DC. The results from this test are tabulated in appendix 2 and a plot of the calibration is given in figure 4. It appears that the pressure sensor calibration is very linear. The equation of the best it line through the data is shown on the plot. Also the R 2 value is This is very close to 1, meaning that the data fits very well to the line. The slope of the line is Therefore it can be assumed that the calibration turns out to be in of water per mv. This is good because it will make the testing much easier to perform. Also from performing this, it appears that electronic and mechanical noise was not a very big problem. Now that the sensor has been calibrated, the next test ran was a vibration test. This was done because the sensor will more than likely experience some vibration in the wind tunnel just from trailing vortices and separation alone. Also, vibration may occur due to a high frequency rotation during a test. The main reason this could be a problem is because the sensor has a small membrane which measures the differential pressure between the two ports. This membrane has some inertia and with vibration is could have an inertial response which would give false pressure data. Therefore it was important to know how this sensor responds to vibration. The sensor was placed on the tip of a vibrating beam used for dynamic testing. The setup consists of two small thin beams attached by a cross member at the tip. The beam has an electromagnet which changes the current going through the coil to move the beam back and fourth (a test setup used for another experiment, but would work just fine to perform this test). The frequency of this can be varied. The sensor was placed on the tip of the beam, shown in figure 5. The leads from the sensor are hooked up to a power supply, which inputs 15 V DC to the sensor. The output from the sensor went through BNC cables to an oscilloscope so that the response may be viewed. The output then went to the National Instruments Data acquisition system and into the computer running LabView. This allowed for the data to be recorded to a file for a given period of testing at a given sampling rate. The test was run for a sampling period of 1 second at a sampling rate of 1000 Hz. Therefore 1000 samples were taken. Figure 6 shows the results from the test. The top plot is the plot with no vibration showing the noise in the setup. The bottom plot has two lines on it, the white line is the response from the sensor and the red line is the excitation. The excitation frequency was 15 Hz. As can be seen in figure 6 there is some amount of frequency response. This could be due to the sensor moving and air going in the sensor ports causing small pressure readings. Therefore a second test was done with the same setup, same sampling rate and sampling period. These results are shown in figure 7. The plot has 3 lines on it. The white line is the response, the red line is the excitation, and the green line was the response data filtered in LabView, which helps show the trend a little better. This data even with the pressure ports covered still appeared to have a frequency response. To help find out what the response frequency was, a Fast Fourier Transform was done on the data. Figure 8 4

5 shows a fast Fourier transform for the data, showing a spike at around 18 Hz and 60 Hz. The 60 Hz spike is the response from the electrical equipment, but the 18 Hz response appears to be due to the vibration of the membrane in the sensor. The excitation frequency was roughly the same as the response frequency from vibration. This shows that it is a first order system; so nothing out of the ordinary is going on, and this inertial response of the sensors can be taken into account in testing. E. Filtering Methods These vibration tests led to the conclusion that some method of getting rid of the undesired response was needed. The first method thought of was a low pass filter to filter out all of the frequency response above 18 Hz. In this case each transducer will require a low pass filter which the output signal goes through. A low pass filter simply requires a capacitor and a resistor. Equation 5 shows the method to solving for the filtering frequency. ω = 2πf = 1/RC Using a common capacitor size of 0.15 µf, solving the equation for 18 Hz, results in a resistor size of kω. The closest size resistor available was a 53.6 kω. This solution would get rid of the inertial response if a vibration in the test was below 18 Hz, but the change in pressure may be sinusoidal in some tests, and the pressure change may be less than an 18 Hz frequency response, in which case the filter is worthless. This led to the conclusion that the best way to solve this problem was to perform two runs for each test done with the final model. The first test would be performed in the wind tunnel with all the pressure ports covered. This would record the changes in the output from the transducers due to their inertia. The second test would be the test with the sensors uncovered. The test with the sensors covered could be subtracted from the test with the sensors uncovered to get the pressures from that particular test. F. Amplifying Equipment The output from the pressure sensor is very small, in mv. Therefore an amplifier needs to be used to make the output signal larger. There are many types of amplifiers that could be used, varying from one, two, and three op-amp amplifiers. The single op-amp amplifier would not be the best because they have a lot of noise from the electrical equipment, and work well on a DC battery power. The double and triple op-amp amplifiers would work much better. These amplifiers would be very tedious to build because they require many more resistors and op-amps. Therefore, another method was looked at. The AD622 is a type of op-amp made for instrumentation amplifiers. The entire amplifier is one op-amp and one resistor. This type of amplifier was chosen. Therefore, an amplifier would have to be built for each transducer. One could not be used because these sensors are to be read all at the same time, and using a multiplexer with a large number of channels would be useless because we want pressure data for every sensor at the same time. The AD622 op-amp uses only one resistor. The resistor for the op-amp depends on the desired gain. This value of resistance can be found by using equation 6 (Analog Devices). (5) R G = 50.5 kω / G-1 (6) 5

6 The desired gain for this project was 1000, mainly to turn the mv signal up to Volts. Therefore, the resistor to get this gain is close to 51.1 Ω. With the 51.1 Ω resistors, the actual gain is Using this system with the low pass filter, a small circuit board can be constructed for each transducer. These boards need to be very small, and therefore they will be constructed with surface mount parts. The output signal goes from the pressure sensor to the amplifier and out to the data acquisition system. The amplifier circuit was developed by drawing the circuit board in AutoCAD and then printing the circuit board backwards onto a transparency sheet with a laser printer. With this, the transparency sheet was ironed onto the copper topped PC board, to transfer the toner from the transparency sheet to the copper topped board. This made a nice clean circuit drawing. With this, PC board etchant was used to eat the remaining copper away, and the toner was then scraped off yielding the copper lines for the circuit. These lines were covered with Liquid Tin to cover the copper and protect it from corrosion. Holes were drilled in the board for the pressure transducer pads, and then the amplifier circuit and transducer were soldered to the board. With the completed amplifier circuit, the same test was performed in the wind tunnel for calibrating the sensor with the amplifier. The results are shown in figure 4 below, and the tabulated data is in appendix 2. The slope of this line is about This compared with the first calibration, shows that the output has been amplified by about It is not exactly 1000 because the actual gain is only G. Wing Model Now that the pressure sensor and amplifier system has been decided on, the next step was to design and build a model. A simple symmetric NACA 0012 was chosen for the wing. The wing model was designed to fit in the Virginia Tech Open Jet wind tunnel. The wing needed to be large enough to fit the sensors on the upper surface and the lower surface of the wing. Therefore a chord of 18 inches was chosen, with a 24 inch span. This gave the thickness needed to fit the pressure sensors in the wing. The model wing spar is a 7/8 inch diameter wooden dowel, the ribs are 1/8 inch thick plywood, and the skin is 1/32 inch balsa wood sheeting. The balsa wood was chosen because it is very easy to sand and shape to the airfoil. The center of the wing is where the sensors are placed. These sensors were placed every 1.5 inches along the surface all the way around the airfoil. The surface sheeting contains holes which were drilled just wide enough for a small piece of plastic tubing to fit into the hole, and the plastic tubing was placed flush against the wing surface. These pieces of tubing are only 0.5 inches long; their main purpose was to give a stiff region to plug the port of the sensor into, and does not make the effective port length any longer, which could cause error in the data from time lag in the tubes. Under the balsa wood sheeting, there is 1/8 inch foam, which just serves as something to help hold the plastic tubes in place. The pressure sensor port plugs into the tube and therefore is on the wing surface. The ports from the pressure sensors will be soldered directly to each amplifier circuit board. The completed wing model is shown in figure 9 below. 6

7 III. RESULTS OF EXPERIMENT A. Steady Testing The first wind tunnel test was a steady flow test to validate the pressure sensors in the wing model. Therefore two sensors were placed in the wing and a steady test was run at a tunnel Q of 0.5 inches of water. The model was placed in the open jet wind tunnel, figure 9, and the leads from the sensors which run out the side of the wing were attached to a 15 V DC power supply, and the output signal to a multimeter. This test was mostly a quantitative test, in that not much data was actually recorded. The sensors were on the upper surface of the wing. As the angle of attack was increased, the velocity over the top will increase, yielding a drop in the static pressure, which is what the transducer measures. The output from the transducer decreased in voltage and became negative when the angle of attack was increased. This was expected. As the angle of attack is decreased, the static pressure will get larger with the decrease in velocity on the upper surface. When this was tested in the wind tunnel, the voltage increased showing an increase in the static pressure. Therefore the sensors to work as they should in the wind model. B. Future research Now that a working amplifier/transducer system has been developed, more of them will be built and placed into the wing model. A data acquisition system will be used to record the pressure data for the wing in a steady test. Once this has proved to work properly, a motor driven device which can rotate the airfoil in the wind tunnel will be designed and finally and unsteady test will be performed. IV. CONCLUSIONS It appears that the dual port differential pressure sensors will be perfect for this application in unsteady aerodynamics. These pressure sensors can directly read the dynamic pressure and output it as a voltage. Due to the fact that the pressure sensors have an inertial response, two runs will be performed for each test, one with the sensors covered to take into account inertial responses. The output from the pressure transducer is in mv, and therefore an instrumentation amplifier was built to amplify the output signal. Finally, the pressure transducers have proven to work properly with the amplifier and in testing in the wing model. V. REFERENCES 1 Virginia Tech Department of Aerospace and Ocean Engineering, 2005, available. 2 Analog Devices, 2005, available. 7

8 APPENDIX 1. FIGURES Figure 1. Virginia Tech Open Jet Wind Tunnel Figure 2. Pressure Sensors Figure 3. Setup for Pressure Sensor Testing. 8

9 Pressure Sensor Calibration y = x R 2 = in H2O Sensor Output (mv) Pressure sensor Calibration with Amplifier 8 6 y = x R 2 = output, Voltage in H20 Figure 4. Pressure Sensor Calibration 9

10 Figure 5. Vibration test setup. Figure 6. First Vibration Test. Figure 7. Second Vibration Test. 10

11 Figure 8. Fast Fourier Transform Figure 9. Wing Model in Wind Tunnel. APPENDIX 2. TABULATED DATA Calibration without amplifier Calibration with amplifier Inches of water Sensor output(mv) Inches of Water Sensor Output (V)