Research on Three-dimensional Pitot Tube Nulling-calibration based on Numerical Methods

ObjectiveObtaining the pitch angle calibration coefficient(<italic>F</italic><sub>1</sub>) and dynamic pressure calibration coefficient(<italic>F</italic><sub>2</sub>) of a Three-dimensional pitot tube is a prerequisite for accurately measuring the gas flow velocity of a stationary pollution source. The traditional offline real-flow calibration method based on the equipment of low-speed wind tunnels have problems such as high resource consumption, difficulty in calibration of unavailable-offline tubes, and significant differences between calibration conditions and actual usage conditions. This paper proposes a technical solution for non real-flow nulling-calibration for Three-dimensional pitot tube based on finite element numerical calculation method which aims at reducing the resource consumption and workload of traditional method and can be used as an effective supplement to the traditional real-flow calibration method.MethodsFirstly, the principle of velocity measurement of Three-dimensional pitot tube was analyzed. On this basis, the method, process and equipment conditions of traditional real-flow calibration for Three-dimensional pitot tube were introduced. Secondly, with reference to the real-flow calibration method and combined with the finite element calculation idea, a non-real-flow calibration for Three-dimensional pitot tube method based on numerical method was proposed. In this process, the following steps were completed sequentially: a) Establishment of a simplified typical wind tunnel model that could provide an approximately equivalent flow field compared to that in real wind tunnel ; b) Establishment of a basic model of the combination of a Three-dimensional pitot tube with the pitch angle of 0° and a typical simplified wind tunnel; c) Mesh generation and mesh independence check; d) Setting of boundary conditions and selection of the <italic>k</italic>-<italic>e</italic> two-equation turbulence model; e) Grid calculation; f) Acquisition of the pitch angle calibration coefficient <italic>F</italic><sub>1(0)</sub> and the dynamic pressure calibration coefficient <italic>F</italic><sub>2(0)</sub> under the basic model and visualization the flow field in the wind tunnel model. Thirdly, a method of changing the pitch angle of the pitot tube in the basic model was proposed, and the numerical calculation model of the combination of the Three-dimensional pitot tube with the pitch angles of ±15°, ±30° and ±45° were obtained. The variable pitch angle model were numerically calculated, then the <italic>F</italic><sub>1</sub> and <italic>F</italic><sub>2</sub> calibration coefficients, the vector streamline of velocity, the contour of static pressure of probe shell, the dynamic pressure-position curve on the central axis, the <italic>F</italic><sub>1</sub>-pitch angle calibration coefficient curve (after a fourth-order fit) and the <italic>F</italic><sub>2</sub> -dynamic pressure calibration coefficient curve of the Three-dimensional pitot tube under different pitch angles were obtained. Based on the numerical result, the overall flow field of the wind tunnel including the Three-dimensional pitot tube and the spherical shell were analyzed. Finally, the real-flow calibration test for comparison purposes was carried out under the conditions at flow velocity of 15m/s, and pitch angles of 0°, ±15°, ±30° and ±45°.Results and Discussions Analysis of the flow field in the process of Three-dimensional pitot tube nulling-calibration: a) the flow conformed to the Bernoulli principle followed by the kind of pitot tube instrument; 2) Due to the complex change of flow field in the area above the top of the spherical shell, it is not suitable to place the flow velocity standard device-standard <italic>L</italic>-shaped pitot tube in this area during the real flow calibration test; 3) If multiple pitot tubes are calibrated at one time, the spacing between tubes with a relatively small pitch angle needs to be longer. Analysis of the calibration curves mentioned in the methods: 1) With a relatively small pitch angle, the decrease in velocity of the gas flow before reaching the spherical shell of the tube (before the flow stagnation) occurred continuously with no fluctuation; however the pitch angle increased to a certain extent, there would be a "spike-shaped" rebound of flow velocity and dynamic pressure before stagnation. The flow velocity (dynamic pressure) of the central axis would recover quickly after the stagnation. When the pitch angle was small, the dynamic pressure and flow velocity would return to the "high value" before the stagnation, but the degree of this recovery would decrease with the increase of the pitch angle, and the worst case of the recovery of occurred at the pitch angle of -45°. The result also suggested the placement of the standard <italic>L</italic>-shaped pitot tube used in real flow calibration needed to be selected where was before the flow velocity and dynamic pressure beginning to decrease. 2) The slope of the <italic>F</italic><sub>2</sub>-pitch angle curve was very small when the absolute value of the pitch angle was lower than 15°, then the absolute value of the slope of the curve increased continuously with the increase of the pitch angle, while the steepest part of the curve appeared in the stage when the absolute value of the pitch angle was between 30° and 45°. The results of the comparison of the calibration coefficients curves between the real flow calibration test and the numerical calculation were as follows: 1) The <italic>F</italic><sub>1</sub> curve and <italic>F</italic><sub>2</sub> curve obtained by the numerical calculation were basically consistent with shape of the curves obtained by the real flow calibration test. 2)At the range of -15°≤<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M003.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M003c.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic></alternatives></inline-formula>≤15°U30°≤<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M004.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M004c.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic></alternatives></inline-formula>≤45°,the differences between the calibration results obtained by the two methods were <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></mrow></mfenced></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M005.jpg"><?fx-imagestate width="5.50333309" height="4.74133301"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M005c.jpg"><?fx-imagestate width="5.50333309" height="4.74133301"?></graphic></alternatives></inline-formula>≤1.7%,<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub></mrow></mfenced></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M006.jpg"><?fx-imagestate width="5.50333309" height="4.74133301"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M006c.jpg"><?fx-imagestate width="5.50333309" height="4.74133301"?></graphic></alternatives></inline-formula>≤1.5%; while, at the range of -45°≤<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M007.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M007c.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic></alternatives></inline-formula>≤-30°, the differences rapidly became larger, which were <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></mrow></mfenced></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M008.jpg"><?fx-imagestate width="5.50333309" height="4.74133301"?></graphic><graphic specific-use="sma

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SHILAP Revista de lepidopterología
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2025-01-01
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Reproductive biology and impacts on aquatic species
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article

Research on Three-dimensional Pitot Tube Nulling-calibration based on Numerical Methods

SHILAP Revista de lepidopterología
Reproductive biology and impacts on aquatic species
article

Research on Three-dimensional Pitot Tube Nulling-calibration based on Numerical Methods

article en

Abstract

ObjectiveObtaining the pitch angle calibration coefficient(<italic>F</italic><sub>1</sub>) and dynamic pressure calibration coefficient(<italic>F</italic><sub>2</sub>) of a Three-dimensional pitot tube is a prerequisite for accurately measuring the gas flow velocity of a stationary pollution source. The traditional offline real-flow calibration method based on the equipment of low-speed wind tunnels have problems such as high resource consumption, difficulty in calibration of unavailable-offline tubes, and significant differences between calibration conditions and actual usage conditions. This paper proposes a technical solution for non real-flow nulling-calibration for Three-dimensional pitot tube based on finite element numerical calculation method which aims at reducing the resource consumption and workload of traditional method and can be used as an effective supplement to the traditional real-flow calibration method.MethodsFirstly, the principle of velocity measurement of Three-dimensional pitot tube was analyzed. On this basis, the method, process and equipment conditions of traditional real-flow calibration for Three-dimensional pitot tube were introduced. Secondly, with reference to the real-flow calibration method and combined with the finite element calculation idea, a non-real-flow calibration for Three-dimensional pitot tube method based on numerical method was proposed. In this process, the following steps were completed sequentially: a) Establishment of a simplified typical wind tunnel model that could provide an approximately equivalent flow field compared to that in real wind tunnel ; b) Establishment of a basic model of the combination of a Three-dimensional pitot tube with the pitch angle of 0° and a typical simplified wind tunnel; c) Mesh generation and mesh independence check; d) Setting of boundary conditions and selection of the <italic>k</italic>-<italic>e</italic> two-equation turbulence model; e) Grid calculation; f) Acquisition of the pitch angle calibration coefficient <italic>F</italic><sub>1(0)</sub> and the dynamic pressure calibration coefficient <italic>F</italic><sub>2(0)</sub> under the basic model and visualization the flow field in the wind tunnel model. Thirdly, a method of changing the pitch angle of the pitot tube in the basic model was proposed, and the numerical calculation model of the combination of the Three-dimensional pitot tube with the pitch angles of ±15°, ±30° and ±45° were obtained. The variable pitch angle model were numerically calculated, then the <italic>F</italic><sub>1</sub> and <italic>F</italic><sub>2</sub> calibration coefficients, the vector streamline of velocity, the contour of static pressure of probe shell, the dynamic pressure-position curve on the central axis, the <italic>F</italic><sub>1</sub>-pitch angle calibration coefficient curve (after a fourth-order fit) and the <italic>F</italic><sub>2</sub> -dynamic pressure calibration coefficient curve of the Three-dimensional pitot tube under different pitch angles were obtained. Based on the numerical result, the overall flow field of the wind tunnel including the Three-dimensional pitot tube and the spherical shell were analyzed. Finally, the real-flow calibration test for comparison purposes was carried out under the conditions at flow velocity of 15m/s, and pitch angles of 0°, ±15°, ±30° and ±45°.Results and Discussions Analysis of the flow field in the process of Three-dimensional pitot tube nulling-calibration: a) the flow conformed to the Bernoulli principle followed by the kind of pitot tube instrument; 2) Due to the complex change of flow field in the area above the top of the spherical shell, it is not suitable to place the flow velocity standard device-standard <italic>L</italic>-shaped pitot tube in this area during the real flow calibration test; 3) If multiple pitot tubes are calibrated at one time, the spacing between tubes with a relatively small pitch angle needs to be longer. Analysis of the calibration curves mentioned in the methods: 1) With a relatively small pitch angle, the decrease in velocity of the gas flow before reaching the spherical shell of the tube (before the flow stagnation) occurred continuously with no fluctuation; however the pitch angle increased to a certain extent, there would be a "spike-shaped" rebound of flow velocity and dynamic pressure before stagnation. The flow velocity (dynamic pressure) of the central axis would recover quickly after the stagnation. When the pitch angle was small, the dynamic pressure and flow velocity would return to the "high value" before the stagnation, but the degree of this recovery would decrease with the increase of the pitch angle, and the worst case of the recovery of occurred at the pitch angle of -45°. The result also suggested the placement of the standard <italic>L</italic>-shaped pitot tube used in real flow calibration needed to be selected where was before the flow velocity and dynamic pressure beginning to decrease. 2) The slope of the <italic>F</italic><sub>2</sub>-pitch angle curve was very small when the absolute value of the pitch angle was lower than 15°, then the absolute value of the slope of the curve increased continuously with the increase of the pitch angle, while the steepest part of the curve appeared in the stage when the absolute value of the pitch angle was between 30° and 45°. The results of the comparison of the calibration coefficients curves between the real flow calibration test and the numerical calculation were as follows: 1) The <italic>F</italic><sub>1</sub> curve and <italic>F</italic><sub>2</sub> curve obtained by the numerical calculation were basically consistent with shape of the curves obtained by the real flow calibration test. 2)At the range of -15°≤<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M003.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M003c.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic></alternatives></inline-formula>≤15°U30°≤<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M004.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M004c.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic></alternatives></inline-formula>≤45°,the differences between the calibration results obtained by the two methods were <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></mrow></mfenced></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M005.jpg"><?fx-imagestate width="5.50333309" height="4.74133301"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M005c.jpg"><?fx-imagestate width="5.50333309" height="4.74133301"?></graphic></alternatives></inline-formula>≤1.7%,<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub></mrow></mfenced></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M006.jpg"><?fx-imagestate width="5.50333309" height="4.74133301"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M006c.jpg"><?fx-imagestate width="5.50333309" height="4.74133301"?></graphic></alternatives></inline-formula>≤1.5%; while, at the range of -45°≤<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M007.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M007c.jpg"><?fx-imagestate width="2.53999996" height="2.96333337"?></graphic></alternatives></inline-formula>≤-30°, the differences rapidly became larger, which were <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></mrow></mfenced></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1DDA9011-B759-40be-85C5-3F8B632FA727-M008.jpg"><?fx-imagestate width="5.50333309" height="4.74133301"?></graphic><graphic specific-use="sma

SHILAP Revista de lepidopterología
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Reproductive biology and impacts on aquatic species
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