מתמר לחץ: כיול באמצעות צינור פיטו-סטטי
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Overview
מקור: שרייאס נרסיספור, הנדסת מכונות וחלל, אוניברסיטת צפון קרוליינה סטייט, ראלי, NC
לחץ נוזלים הוא מאפיין זרימה חשוב הנדרש כדי לקבוע את האווירודינמיקה של מערכת. אחת ממערכות מדידת הלחץ העתיקות והעדיין הקיימות היא מד המנומטר בשל דיוקו ופשטות הפעולה שלו. המנומטר הוא בדרך כלל צינור זכוכית בצורת U, המלא חלקית בנוזל, כפי שמוצג באיור 1. מד הצינורות U אינו דורש כיול מכיוון שאין לו חלקים נעים, והמדידות שלו הן פונקציות של כוח המשיכה וצפיפותהנוזל. לכן, המנומטר הוא מערכת מדידה פשוטה ומדויקת.
איור 1. סכמטי של מד צינור יו.
מדידות לחץ בזמן אמת מתקבלות במטוסים על ידי חיבור יציאות הקיפאון והלחץ הסטטי של גשושית פיטו-סטטית, מכשיר המשמש בדרך כלל למדידת לחץ זרימת נוזלים, לנמלים של התקן מדידת לחץ. הדבר מאפשר לטייסים לקבל תנאי טיסה קיימים ולהזהיר אותם אם מתרחשים שינויים בתנאי הטיסה. בעוד מנומטרים מספקים קריאות לחץ מדויקות מאוד, הם מגושמים מטבעם. יש צורך בפתרון מציאותי יותר כדי למדוד את לחצי המטוסים, שכן אחת ממטרות התכנון העיקריות היא לשמור על משקל המטוס הכולל נמוך ככל האפשר. כיום, מתמרים לחץ אלקטרומכני, הממירים את הלחץ המופעל לאות חשמלי, נמצאים בשימוש נרחב עבור יישומי חישת לחץ במטוס מכיוון שהם קטנים, קלים, וניתן למקם אותם כמעט בכל מקום במסגרת האוויר. המאפיינים לעיל לא רק לעזור להפחית את המשקל, אלא גם להפחית את כמות הצינורות הנדרשים כדי לחבר את הבדיקה pitot-סטטית המתמר, ובכך להקטין את זמן התגובה של הנתונים. בנוסף, בבדיקות טיסה ניסיוניות של מטוסים, מתמרי לחץ זעירים שימושיים מכיוון שהם מאפשרים לחוקרים למקסם את איסוף נתוני הלחץ מבלי להוסיף באופן משמעותי למשקל המטוס. בעוד קיימים סוגים שונים של מתמרים לחץ עם טכניקות מדידה שונות, אחד הסוגים הנפוצים יותר של מתמר הוא מתמר הלחץ הקיבליבי. כמו מתמרים מסוגלים רק לשלוח אותות במונחים של מתח וזרם, כיול של המתמר נדרש לקשר את הכוח של אות מסוים ללחץ שגורם למתמר ליצור את האות. התאמת העקומה הסופית המקשרת את זרם המתמר או המתח למדידה פיזית, במקרה שלנו לחץ, מכונה בדרך כלל עקומת הכיול של המתמר.
בניסוי זה, גשושית פיטו-סטטית ממוקמת במנהרת רוח תת-קולית עם יציאות הקיפאון והלחץ הסטטי המחוברות לנמלים הכוללים והסטטיים של מד הצינור U ומתמר הלחץ. מנהרת הרוח מופעלת לאחר מכן בהגדרות לחץ דינמיות שונות, וקריאת הלחץ המתאימה ממנומטר צינור U, והקריאות הנוכחיות המיוצרות על ידי המתמר נרשמות. נתונים אלה משמשים לאחר מכן ליצירת עקומות כיול עבור מתמר הלחץ.
Principles
Procedure
Results
The following constants were used in the analysis: water density, ρwater: 61.04 lb/ft3; acceleration due to gravity, g: 32.15 ft/s2; and manometer off-set, hoff = 0.8 in. The variation in manometer data for increasing and decreasing dynamic pressures (with and without correcting for the instrument off-set) is shown in Figure 7. Figure 8 shows a plot of the transducer current readings against the manometer pressure, which was calculated using Equation 3.
In order to obtain the calibration curve for the pressure transducer, two linear curves are fitted through the increasing and decreasing data points, respectively. The corresponding linear fit equations are:
(5)
(6)
The equations for the increasing and decreasing curves are almost similar, and the two curves align with each other, as observed in Figure 8. Therefore, it can be deduced that the pressure transducer does not have any hysteresis. A single calibration equation relating the current to the pressure (Equations 5 or 6) can be used for the transducer, thereby removing the necessity of using the bulky U-tube manometer system for all future pressure measurements.
Figure 7. Variation of manometer fluid height with wind tunnel dynamic pressure. Please click here to view a larger version of this figure.
Figure 8. Calibration curves for the pressure transducer. Please click here to view a larger version of this figure.
Applications and Summary
Electromechanical transducers are popular replacements for some of the bulkier measurement systems. However, transducers need to be calibrated regularly using standardized measuring devices in order to be effective experimental tools. In this experiment, an off-the-shelf capacitive type electromechanical pressure transducer was calibrated by comparing the current signals generated by the transducer for a range of dynamic pressure conditions in a subsonic wind tunnel to the pressure measurements from a U-tube manometer. Results showed that a linear relationship exists between the transducer's current signal and pressure with negligible sensor hysteresis. A single calibration equation relating the transducer current output to pressure was obtained.
Modern electromechanical measurement systems provide a path to automating experimental data acquisition and can be used in real-time static and dynamic systems for data monitoring and analysis. However, proper calibration practices, like the one demonstrated in this experiment, are necessary to help users obtain accurate and repeatable data using said sensors.
Transcript
All airplanes use pressure measurements in order to make real-time calculations of wind speed. In an airplane, these pressure measurements are obtained using a pitot-static tube.
A pitot-static tube has openings that measure the stagnation pressure and the static pressure. Recall that stagnation pressure is the sum total of the static pressure and the dynamic pressure, so the pitot-static tube is used to measure the dynamic pressure and therefore the flow velocity.One method to correlate wind speed to pressure using the pitot-static tube is by using a fluid manometer.
A fluid manometer is generally a U-shaped glass tube that is partially filled with liquid. One arm of the manometer is connected to the stagnation pressure port on the pitot-static tube, and the other to the static pressure port. In stagnant air, where this is no difference between the static pressure and stagnation pressure, the manometer fluid height difference is zero.
When the manometer experiences a pressure differential, it is visualized by a change in fluid height. The pressure differential, or dynamic pressure, is calculated from delta H using this equation. Here, rho L is the density of fluid in the manometer and G is gravitational acceleration. This relationship is used to calculate the wind speed by substituting it into the velocity equation. We can then solve for the free-stream velocity, V infinity, using the free-stream density, rho infinity.
However, fluid manometers are bulky, and require manual reading onboard the aircraft. Thus, a more convenient method to measure the pressure differential is to use a pressure transducer in place of the manometer. This enables us to convert the pressure differential into an electrical signal.
A capacitance pressure transducer is based on the working principle of a capacitor, which consists of two conductive plates separated by an insulator. Capacitance is measured by the following equation, where mu is the dielectric constant of the insulator material, A is the area of plates, and D is the spacing between the plates.
To make the capacitance pressure transducer, one of the conductive plates is replaced by a flexible conducting diaphragm. When pressure is applied, the diaphragm deflects causing a change in the spacing between the plates D, resulting in a change in capacitance. The electronics in the transducer are calibrated to generate specific current changes for corresponding deviations in capacitance. Thus, a current reading corresponds to a given applied pressure.
Like the manometer, the pressure transducer is connected to the pitot-tube and is calibrated in a wind tunnel with known wind speeds. This enables us to generate a mathematical relationship between current and pressure, and by extension, current and wind speed.
In this lab demonstration, we will use a pitot-static tube in a wind tunnel connected to a pressure transducer. We will then calibrate the pressure transducer at various wind speeds and determine the relationship between voltage and speed.
For this experiment, you’ll need to use a wind tunnel with its own calibrated pressure transducer and ability to reach a dynamic pressure of 25 psf. You will also use a standard pitot-static tube and a differential U-tube manometer with colored water to calibrate this differential pressure transducer.
To begin, mount the pitot-static tube inside of the wind tunnel on the top of the test section using a vertical sting mount. Ensure that the probe is at the center of the test section. Align the pitot tube with the direction of flow, so that the primary port faces directly into the air flow.
Next, align the top of the manometer fluid to the double O-ring marker on the glass tube. If the reading on the main scale does not correspond to zero, align the fluid to a different reference point, and record the offset height.
Use a T-connector to split the flow from one tube to two, then connect the stagnation and static pressure outlets on the pitot-static tube, to the corresponding ports on the U-tube manometer. Mount the pressure transducer outside of the wind tunnel test section on a vertical surface. Set up a standard voltage supply to power the pressure transducer and a multimeter to read the output current. Then, connect the stagnation and static pressure outlets to the corresponding pressure ports on the transducer.
Now, secure the wind tunnel doors and switch on all of the systems. Then, take readings of the wind tunnel transducer pressure, the manometer height, and the differential pressure transducer current. Record the measurements for the no airflow condition as the base line zero reading. Now turn on the wind tunnel, and set the dynamic pressure in the test section to one psf.
Once the flow has stabilized, record the transducer pressure, the manometer height difference, and transducer current. Increase the dynamic pressure setting in the wind tunnel in steps of one psf, up to a maximum setting of 20 psf, recording the data at each step. In order to check for hysteresis, decrease the dynamic pressure in steps of one psf, back down to zero psf, again recording data at each step. When all of the measurements have been collected, shut down all systems.
Now, lets take a look at the results. First, we look at a plot of the manometer height readings with increasing and decreasing dynamic pressure. Two measurements are shown here for each trace. One is the actual manometer reading, and the other has been corrected with the offset height of 0.8 inches. We can calculate the manometer pressure from the manometer height, using the simple equation shown. Here, we use the density of the liquid in the manometer, which is in this case water, gravitational acceleration, and the manometer offset and height measurements.
Now that we have calculated the pressure from the manometer reading, we’ll plot it against the pressure transducer current readings. To obtain the calibration curve for the pressure transducer, we’ll fit the increasing and decreasing data separately, resulting in two linear best fit equations.
However, we see that the increasing and decreasing data line up. So we can conclude that the pressure transducer does not exhibit hysteresis. Thus, we can simplify to a single calibration equation, thereby enabling us to measure pressure using the current reading from pressure transducer, rather than the bulky fluid manometer. By connecting the pitot-static probe to the calibrated transducer, we can directly measure the dynamic pressure and therefore, wind speeds.
In summary, we learned how pressure differentials measured during flight correlate to flow velocity. We then calibrated a pressure transducer by subjecting a pitot-static tube to varying wind speeds, and determined the relationship between voltage and wind speed.