압력 변환기: 피트 정압관을 사용한 보정
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Overview
출처: 슈레야스 나르시푸르, 기계 및 항공 우주 공학, 노스 캐롤라이나 주립 대학, 롤리, NC
유체 압력은 시스템의 공기 역학을 결정하는 데 필요한 중요한 유동 특성입니다. 가장 오래되고 여전히 기존의 압력 측정 시스템 중 하나는 작동의 정확성과 단순성으로 인해 기마계입니다. 기마계는 일반적으로 그림 1에도시된 바와 같이 부분적으로 액체로 채워진 U자 형 유리 튜브입니다. U-튜브 기마계는 움직이는 부품이 없기 때문에 교정이 필요하지 않으며 측정은 중력의 기능과액체밀도입니다. 따라서, 기마계는 간단하고 정확한 측정 시스템입니다.
그림 1. U-튜브 기마계의 회로도.
유체 유압을 측정하는 데 일반적으로 사용되는 장치인 피토 정적 프로브의 정체 및 정적 압력 포트를 압력 측정 장치의 포트에 연결하여 항공기에서 실시간 압력 측정을 얻을 수 있습니다. 이를 통해 조종사는 기존 비행 조건을 확보하고 비행 조건이 변경될 경우 경고할 수 있습니다. 기마계는 매우 정확한 압력 판독값을 제공하지만 본질적으로 부피가 큽합니다. 항공기 압력을 측정하기 위해서는 보다 현실적인 솔루션이 필요하며, 주요 설계 목표 중 하나는 전체 항공기 중량을 가능한 한 낮게 유지하는 것입니다. 오늘날, 가압을 전기 신호로 변환하는 전기 기계 압력 트랜스듀서는 작고 가볍고 기체의 거의 모든 곳에 배치 할 수 있기 때문에 항공기의 압력 감지 응용 분야에 널리 사용됩니다. 위의 특성은 무게를 줄이는 데 도움이 될 뿐만 아니라 피토 정적 프로브를 트랜스듀서에 연결하는 데 필요한 튜브의 양을 줄여 데이터 응답 시간을 줄입니다. 또한 실험적인 항공기 비행 테스트에서 소형 압력 트랜스듀서는 연구원이 항공기의 무게를 크게 증가하지 않고 압력 데이터 수집을 최대화할 수 있도록 유용합니다. 다양한 측정 기술을 가진 다양한 유형의 압력 트랜스듀서가 존재하지만, 더 일반적인 유형의 트랜스듀서 중 하나는 정전용량 압력 변환기입니다. 트랜스듀서는 전압 및 전류 측면에서만 신호를 전송할 수 있기 때문에 트랜스듀서의 교정은 특정 신호의 강도를 트랜스듀서가 신호를 생성하는 원인이 되는 압력과 관련이 있습니다. 트랜스듀서 전류 또는 전압과 물리적 측정과 관련된 최종 곡선 피팅은 당사의 경우 압력에서 일반적으로 트랜스듀서 교정 곡선이라고 합니다.
이 실험에서 피토 정적 프로브는 U-튜브 기마계와 압력 변환기의 총 및 정적 포트에 연결된 침체 및 정적 압력 포트가 있는 아음속 풍동에 배치됩니다. 그런 다음 풍동은 다른 동적 압력 설정에서 실행되며 U-튜브 기마계에서 해당 압력 판독값과 트랜스듀서에 의해 생성된 전류 판독값이 기록됩니다. 그런 다음 이 데이터는 압력 변환기의 교정 곡선을 생성하는 데 사용됩니다.
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.