CN113125103A - Data processing method for elliptical cross-section flow meter with 41 measuring points equidistantly distributed - Google Patents

Data processing method for elliptical cross-section flow meter with 41 measuring points equidistantly distributed Download PDF

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CN113125103A
CN113125103A CN202110314172.6A CN202110314172A CN113125103A CN 113125103 A CN113125103 A CN 113125103A CN 202110314172 A CN202110314172 A CN 202110314172A CN 113125103 A CN113125103 A CN 113125103A
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pressure
section
pitot
measuring point
pressure measuring
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CN113125103B (en
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李一鸣
余安远
乔文友
杨大伟
杨辉
张胜
曲俐鹏
秦思
张小庆
贺元元
陈锐杰
贺佳佳
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Institute of Aerospace Technology of China Aerodynamics Research and Development Center
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Institute of Aerospace Technology of China Aerodynamics Research and Development Center
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    • G01MEASURING; TESTING
    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M9/00Aerodynamic testing; Arrangements in or on wind tunnels
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Abstract

The invention discloses a data processing method of an elliptic section flowmeter with 41 measuring points equidistantly distributed, which comprises the steps of measuring the pitot pressure of each measuring point of an elliptic section of an outlet of an air inlet channel and the static pressure of the section position through a flowmeter positioned at the downstream of the outlet of the elliptic section of the air inlet channel, obtaining the static pressure of each measuring point by utilizing a linear interpolation method, obtaining the specific flow density, the airflow Mach number and the total pressure recovery coefficient of each measuring point through calculation, respectively integrating and superposing the specific flow density, the airflow Mach number and the total pressure recovery coefficient of each measuring point in the elliptic section to obtain the flow, the superposed Mach number and the superposed total pressure recovery coefficient in the elliptic section, and respectively dividing the superposed Mach number and the superposed total pressure recovery coefficient in the elliptic section by the area of the elliptic section to obtain the average Mach number and the total pressure recovery coefficient in the elliptic section. The invention fills the blank of the post-processing method when the measuring points of the elliptical cross-section flow meter are distributed at equal intervals, and can more comprehensively obtain the performance parameters of the air inlet channel.

Description

Data processing method for elliptical cross-section flow meter with 41 measuring points equidistantly distributed
Technical Field
The invention belongs to the technical field of experimental aerodynamics, and particularly relates to an elliptic section flowmeter with 41 measuring points distributed equidistantly and a data processing method thereof.
Background
The air inlet channel is positioned at the foremost end of the engine, captures incoming flow, decelerates and pressurizes the incoming flow, and provides airflow for a downstream combustion chamber, and the working capacity of the air inlet channel is directly related to the working efficiency of the whole air suction type propulsion system.
Parameters such as outlet flow of the air inlet, Mach number, total pressure recovery coefficient and the like are key parameters influencing the design of the air inlet, the Mach number is the ratio of local airflow speed to sound velocity, and the total pressure recovery coefficient is the ratio of local airflow total pressure to incoming flow total pressure. The total pressure of the airflow is measured by installing a pressure measuring rake on the outlet section, the positions of measuring points on the leather supporting rake are limited by the size of a sensor and are usually distributed at equal intervals, pressure measuring holes are formed in the wall surface where the measuring section is located to measure the static pressure of the airflow, and parameters of the outlet section are obtained through data processing.
However, the current cross-sectional parameter measurement is directed at the air inlet with a rectangular cross section or a circular cross section, and with the development of the air inlet design technology, the air inlet with an elliptical outlet also becomes another common air inlet. For a rectangular cross-section air inlet channel, a measurement method of grid uniform distribution is often adopted; for a circular-section air inlet channel, the symmetry of a circle is utilized, and the average flow of an outlet is usually obtained by simply averaging pressure data of each measuring point. In the traditional method, by averaging the pressure data of each measuring point, the data of the outlet section cannot be represented, and the parameter distribution rule on the section cannot be obtained.
Disclosure of Invention
The invention aims to provide an elliptic section flowmeter with 41 measuring points distributed equidistantly and a data processing method thereof, so as to solve the technical problem that the flow, the Mach number and the total pressure recovery coefficient of an elliptic outlet of an air inlet channel are difficult to measure.
In order to achieve the purpose, the invention provides the following technical scheme:
an elliptic cross section flowmeter with 41 measuring points distributed at equal intervals comprises an elliptic shell, wherein the elliptic shell is connected with an elliptic cross section outlet at the downstream of an air inlet, the elliptical shell is used for mounting a leather supporting harrow and a static pressure measuring device, the leather supporting harrow is circumferentially provided with 8 harrow positions, the 8 harrow positions divide the cross section area of an elliptical outlet into 8 parts, the central intersection point of the 8 harrow positions is provided with 1 leather supporting pressure measuring point, each harrow position is uniformly provided with 5 leather supporting pressure measuring points along the radial direction, the pitot pressure measuring point is provided with a pitot pressure sensor, the static pressure measuring device comprises 8 wall surface pressure sensors which are uniformly arranged on the elliptical shell along the circumferential direction, the position distribution of the wall surface pressure sensors corresponds to the rake positions, the pitot pressure sensors are used for acquiring pitot pressure of corresponding pitot pressure measuring points, and the wall surface pressure sensors are used for measuring flow field static pressure of corresponding positions.
Another object of the present invention is to provide a data processing method for an elliptical cross-section flowmeter with equidistantly distributed 41 measuring points, which is applied to the elliptical cross-section flowmeter with equidistantly distributed 41 measuring points, and includes:
step 1: averaging the measurement results of the 8 wall surface pressure sensors to obtain the static pressure of the center of the elliptical section, and obtaining the static pressure of each pitot pressure measurement point by using a linear interpolation method along the radial direction according to the static pressure of the center of the elliptical section and the wall surface static pressure corresponding to the corresponding rake position;
step 2: calculating the Mach number of the airflow of each pitot pressure measuring point according to the pitot pressure and the static pressure of each pitot pressure measuring point;
and step 3: calculating to obtain the total airflow pressure of each pitot pressure measuring point according to the static pressure and the airflow Mach number of each pitot pressure measuring point;
and 4, step 4: calculating the specific flow density of each pitot pressure measuring point according to the airflow Mach number and the airflow total pressure of each pitot pressure measuring point;
and 5: calculating to obtain a total pressure recovery coefficient of each pitot pressure measuring point according to the total airflow pressure and the total incoming flow pressure of each pitot pressure measuring point;
step 6: respectively integrating and superposing the specific flow density, the airflow Mach number and the total pressure recovery coefficient of each pitot pressure measuring point in the elliptical section to obtain the flow, the superposed Mach number and the superposed total pressure recovery coefficient in the elliptical section;
and 7: and respectively dividing the superposed Mach number and the superposed total pressure recovery coefficient in the elliptical section by the area of the elliptical section to obtain the average Mach number and the total pressure recovery coefficient in the elliptical section.
Preferably, the integrating and superposing the specific flow density, the airflow mach number and the total pressure recovery coefficient of each pitot pressure measuring point in the elliptical cross section to obtain the flow, the superposed mach number and the superposed total pressure recovery coefficient in the elliptical cross section includes:
step 61, a sector area is formed by the center of the elliptical section and two adjacent pitot pressure measurement points on the innermost layer, the specific flow density of each pitot pressure measurement point is interpolated by utilizing a linear interpolation method to obtain a specific flow density interpolation function of each sector area, and the interpolation function of the compared flow density is integrated in the sector area to obtain the flow in each sector area; the calculation formula of the interpolation function of the specific flow density in the sector area is as follows:
Figure BDA0002990436520000031
the calculation formula of the flow in the sector area is as follows:
Figure BDA0002990436520000032
and 62, interpolating the specific flow density of each pitot pressure measuring point by using a linear interpolation method in a first arc-shaped area consisting of two pitot pressure measuring points adjacent to the innermost layer and two pitot pressure measuring points adjacent to the corresponding outermost layer to obtain a specific flow density interpolation function of each first arc-shaped area, and integrating the interpolation function of the specific flow density in the first arc-shaped area to obtain the flow in each first arc-shaped area. Wherein the calculation formula of the interpolation function of the specific flow density in the first circular arc-shaped area is as follows:
Figure BDA0002990436520000033
the calculation formula of the flow in the first arc-shaped area is as follows:
Figure BDA0002990436520000034
and 63, approximating a second arc-shaped area consisting of two adjacent pitot pressure measuring points on the outermost layer and the corresponding elliptical shell by adopting the measuring points on the outermost layer along the radial direction, interpolating the specific flow density of each pitot pressure measuring point by adopting linear interpolation values along the circumferential direction to obtain a specific flow density interpolation function of each second arc-shaped area, and integrating the interpolation function of the specific flow density in the second arc-shaped area to obtain the flow in each second arc-shaped area. Wherein the calculation formula of the interpolation function of the specific flow density in the second circular arc-shaped area is as follows:
Figure BDA0002990436520000041
the calculation formula of the flow in the second arc-shaped area is as follows:
Figure BDA0002990436520000042
and step 64, superposing the flow in each sector area, the flow in each first circular arc area and the flow in each second circular arc area to obtain the flow in the elliptical section. Wherein, the calculation formula of the flow in the elliptical section is as follows:
Figure BDA0002990436520000043
step 65, replacing the specific flow density in the formulas (1), (3) and (5) with the Mach number of each pitot pressure measuring point, and repeating the steps 61-64 to obtain the superposed Mach number in the elliptical section;
and 66, replacing the specific flow density in the formulas (1), (3) and (5) with the total pressure recovery coefficient of each pitot pressure measuring point, and repeating the steps 61 to 64 to obtain the total pressure recovery coefficient superposed in the elliptical section.
By utilizing the technical scheme, the invention has the following beneficial technical effects:
the elliptical cross-section flowmeter and the data processing method thereof can obtain the flow, the Mach number and the total pressure recovery coefficient of the outlet of the elliptical cross section of the air inlet channel, fill the blank of the post-processing method when measuring points of the elliptical cross-section flowmeter are distributed at equal intervals so as to more comprehensively obtain the performance parameters of the air inlet channel, and provide scientific basis for the flow calculation of the elliptical cross section and the further post-processing of the distribution of the Mach number and the total pressure recovery coefficient, the average Mach number and the average total pressure recovery coefficient of the elliptical cross section.
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FIG. 1 is a schematic structural diagram of an elliptical cross-section flowmeter with equidistantly distributed 41 measuring points according to an embodiment of the present invention;
fig. 2 is a flowchart of a data processing method of an elliptic cross section flowmeter with equidistantly distributed 41 measuring points according to an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and embodiments:
as shown in figure 1, the elliptical cross-section flow meter with the 41 measuring points distributed equidistantly comprises an elliptical shell, wherein the elliptical shell is connected to an elliptical cross-section outlet at the downstream of an air inlet, and the elliptical shell is used for mounting a pitot-harrow and a static pressure measuring device.
For convenient calculation, a coordinate system is established by taking the center of the ellipse as the origin, the major axis of the ellipse as the x axis, the length of the ellipse as the 2a, the minor axis of the ellipse as the y axis and the length of the ellipse as the 2b, and the elliptic equation is
Figure BDA0002990436520000051
Let DijThe pitot pressure measuring points (shown by solid dots in fig. 1) are represented by i, the position i of the sensor measuring point on each rake position is 1, 2 and … … 5 and increases from inside to outside along the radial direction, j is the rake position number j is 1, 2 and … … 8 and increases from the x axis along the circumferential direction in a counterclockwise manner, and D is the index of the sensor measuring point on each rake position00Is a pitot pressure measuring point at the center of the ellipse. Let EjThe static wall pressure measurement points (shown as the triangular dots in fig. 1) are set to j 1, 2, … … 8, which increases counterclockwise from the x axis in the circumferential direction and corresponds to the pitot rake number.
The leather-supporting rake comprises 8 rake positions, the 8 rake positions divide the cross section area of the elliptic outlet into 8 equal parts, wherein 4 forward rake positions are distributed in a cross shape and coincide with the coordinate axis, and the included angle between the other 4 oblique rake positions and the elliptic major axis is theta0Arctan (b/a); 1 pitot pressure measuring point is arranged at the center intersection point of 8 rake positions, 5 pitot pressure measuring points are uniformly arranged on each rake position along the radial direction, and the total number of the pitot pressure measuring points is 41; and each pitot pressure measuring point is provided with a pitot pressure sensor, the static pressure measuring device comprises 8 wall surface pressure sensors which are uniformly arranged on the elliptical shell along the circumferential direction, the position distribution of the wall surface pressure sensors corresponds to the rake positions, the pitot pressure sensors are used for acquiring the pitot pressure of the corresponding pitot pressure measuring point, and the wall surface pressure sensors are used for measuring the static pressure of the flow field at the corresponding position.
Referring to fig. 2, a data processing method for an elliptic cross section flowmeter with equidistantly distributed 41 measuring points is applied to the elliptic cross section flowmeter with equidistantly distributed 41 measuring points, and includes:
step 1: averaging the measurement results of the 8 wall surface pressure sensors to obtain the static pressure of the center of the elliptical section, and obtaining the static pressure of each pitot pressure measurement point by using a linear interpolation method along the radial direction according to the static pressure of the center of the elliptical section and the wall surface static pressure corresponding to the corresponding rake position;
in particular, through 8 measuring points EjThe static pressure of (2) is averaged to calculate the center D of the ellipse00Static pressure p of00(ii) a For the measuring point Dij on the jth rake position, use D00At static pressure p00And EjAt static pressure pE jObtaining D by linear interpolation in the radial directionijStatic pressure p at (i ═ 1, 2, … 5)ijAs shown in the formula (8),
Figure BDA0002990436520000061
step 2: calculating the Mach number of the airflow of each pitot pressure measuring point according to the pitot pressure and the static pressure of each pitot pressure measuring point;
in particular, D is obtained by means of a Pitot-rake measurementijPressure p for skint ijCalculating the ratio p of the skin pressure to the static pressuret ij/pijAnd further calculating D by the formula (2)ijMach number M of treated air flowij
Figure BDA0002990436520000062
Wherein γ is a gas specific heat ratio, and γ is 1.4 for air.
And step 3: calculating to obtain the total airflow pressure of each pitot pressure measuring point according to the static pressure and the airflow Mach number of each pitot pressure measuring point;
in particular, by means of DijAt static pressure pijAnd DijMach number M of treated air flowijCalculating D by equation (3)ijTotal pressure p of the gas flow0 ij
Figure BDA0002990436520000063
And 4, step 4: calculating the specific flow density of each pitot pressure measuring point according to the airflow Mach number and the airflow total pressure of each pitot pressure measuring point;
specifically, the specific flow density m is calculatedA ijRho, the product of the gas density rho and the velocity u,
Figure BDA0002990436520000064
in the formula T0 ijThe total temperature of the gas flow can be approximated or measured by a thermocouple or the like.
And 5: calculating to obtain a total pressure recovery coefficient of each pitot pressure measuring point according to the total airflow pressure and the total incoming flow pressure of each pitot pressure measuring point;
specifically, the total pressure recovery coefficient σijIs the total pressure p0 ijAnd total pressure p of incoming flow0 Ratio of σij=p0 ij/p0
Step 6: respectively integrating and superposing the specific flow density, the airflow Mach number and the airflow total pressure of each pitot pressure measuring point in the elliptical section to obtain the flow, the superposed Mach number and the superposed total pressure recovery coefficient in the elliptical section;
preferably, the step of integrating and superposing the specific flow density, the airflow mach number and the airflow total pressure of each pitot pressure measuring point in the elliptical cross section to obtain the flow, the superposed mach number and the superposed total pressure recovery coefficient in the elliptical cross section includes:
step 61, a sector area is formed by the center of the elliptical section and two adjacent pitot pressure measurement points on the innermost layer, the specific flow density of each pitot pressure measurement point is interpolated by utilizing a linear interpolation method to obtain a specific flow density interpolation function of each sector area, and the interpolation function of the compared flow density is integrated in the sector area to obtain the flow in each sector area;
step 62, interpolating the specific flow density of each pitot pressure measuring point by using a linear interpolation method in a first arc-shaped area consisting of two pitot pressure measuring points adjacent to the innermost layer and two pitot pressure measuring points adjacent to the corresponding outermost layer to obtain a specific flow density interpolation function of each first arc-shaped area, and integrating the interpolation function of the specific flow density in the first arc-shaped area to obtain the flow in each first arc-shaped area;
step 63, approximating a second arc-shaped area composed of two adjacent pitot pressure measuring points on the outermost layer and a corresponding elliptical shell by adopting the measuring points on the outermost layer along the radial direction, interpolating the specific flow density of each pitot pressure measuring point by adopting linear interpolation values along the circumferential direction to obtain a specific flow density interpolation function of each second arc-shaped area, and integrating the interpolation function of the specific flow density in the second arc-shaped area to obtain the flow in each second arc-shaped area;
step 64, superposing the flow in each sector area, the flow in each first arc-shaped area and the flow in each second arc-shaped area to obtain the flow in the oval cross section;
step 65, replacing the specific flow density with the Mach number of each pitot pressure measuring point, and repeating the step 61 to the step 64 to obtain the superposed Mach number in the elliptical section;
and 66, replacing the specific flow density with the total pressure recovery coefficient of each pitot pressure measuring point, and repeating the steps 61-64 to obtain the total pressure recovery coefficient superposed in the elliptical section.
Specifically, for ease of calculation, standard equations are aimed at
Figure BDA0002990436520000071
Can be represented by the following parametric equation (12)
Figure BDA0002990436520000072
In the formula, t is a radial parameter, t is more than or equal to 0 and less than or equal to 1, alpha is a circumferential angle parameter, and alpha is more than or equal to 0 and less than or equal to 2 pi.
In the parametric equation, measure point DijHas the coordinates of (t)ij) In the invention, the measuring points are distributed at equal intervalsThe coordinate of the measuring point can be represented by the distance delta t and delta alpha, ti=iΔt,Δt=1/6,αjJ Δ α, Δ α ═ pi/4, the elliptical area S can be calculated according to equation (6),
S=∫∫abtdtdα (13)
however, specific flow density mA ijAre discrete points, in order to achieve a specific flow density mAijIntegration in the elliptical cross section requires interpolation using discrete points to obtain a continuous interpolation function, and then integration is performed on the interpolation function. The interpolation function is divided into three parts according to the discrete measurement point distribution positions in the ellipse.
The first part is a sector area (t is more than or equal to 0 and less than or equal to t) consisting of the ellipse center and the innermost adjacent measuring point1) Within each sector, for the center D of the ellipse00And a first layer measuring point D1j、D1,j+1Linear interpolation is carried out on the data to obtain an interpolation function m of specific flow densityA(t,α)
Figure BDA0002990436520000081
The flow q in each sector can be obtained by integrating the interpolation function of the specific flow densitym 0j
Figure BDA0002990436520000082
Second, an annular region (t) surrounded by the innermost measuring point and the outermost measuring point1≤t≤t5) In a first circular arc area consisting of 4 adjacent measuring points, pair Dij、Di,j+1、Di+1,j、Di+1,j+1Linear interpolation is carried out on the data to obtain an interpolation function mA(t,α)
Figure BDA0002990436520000083
By applying an interpolation function of specific flow densityIntegrating to obtain the flow q in each sectorm ij
Figure BDA0002990436520000084
Third part, part t between the outermost measuring point and the elliptical shell5≤t≤t6I.e. a second circular arc-shaped zone, which is only the zone inner side D5jIf the data of the measuring points are interpolated outwards, larger deviation can occur, so that the measuring points at the outermost layer are adopted to approximate along the radial direction, linear interpolation is adopted along the circumferential direction, and the data are interpolated according to the D5j、D5,j+1、Ej、Ej+1Fractional flow density interpolation function m in composed regionA(t,α)
Figure BDA0002990436520000085
The flow q in each sector can be obtained by integrating the interpolation function of the specific flow densitym 5j
Figure BDA0002990436520000091
Finally, the flow rates of all parts are superposed, and the flow rate q in the elliptic section is calculatedm
Figure BDA0002990436520000092
According to the periodicity of the ellipse along the circumferential direction, when j is 8, mA i,j+1=mA i1
The specific flow density in the interpolation formulas (1), (3) and (5) is replaced by the Mach number or the total pressure recovery coefficient of each pitot pressure measuring point, and the distribution of the Mach number or the total pressure recovery coefficient in the elliptical section can be obtained; and (3) replacing the specific flow density in the flow formula (7) with a Mach number and a total pressure recovery coefficient to obtain a superposed Mach number and a superposed total pressure recovery coefficient.
And 7: and respectively dividing the superposed Mach number and the superposed total pressure recovery coefficient in the elliptical section by the area of the elliptical section to obtain the average Mach number and the total pressure recovery coefficient in the elliptical section.
Specifically, the average mach number and the total pressure recovery coefficient in the cross section can be obtained by dividing the superposed mach number and the total pressure recovery coefficient by the elliptical area pi ab.
In the embodiment, the description of the relevant symbols in the formula is shown in table 1:
Figure BDA0002990436520000093
Figure BDA0002990436520000101
TABLE 1
The foregoing is merely an example of the present invention and common general knowledge in the art of designing and/or characterizing particular aspects and/or features is not described in any greater detail herein. It should be noted that, for those skilled in the art, without departing from the technical solution of the present invention, several variations and modifications can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicability of the patent. The scope of the claims of the present application shall be determined by the contents of the claims, and the description of the embodiments and the like in the specification shall be used to explain the contents of the claims.

Claims (3)

1. The utility model provides an oval cross-section flowmeter that 41 measurement stations equidistance distributes which characterized in that: the device comprises an elliptical shell, the elliptical shell is connected with an elliptical cross-section outlet at the downstream of an air inlet, the elliptical shell is used for mounting a leather-supporting rake and a static pressure measuring device, 8 rake positions are arranged on the leather-supporting rake along the circumferential direction, the cross-section area of the elliptical outlet is divided into 8 equal parts by the 8 rake positions, 1 leather-supporting pressure measuring point is arranged at the central intersection point of the 8 rake positions, 5 leather-supporting pressure measuring points are uniformly arranged on each rake position along the radial direction, a leather-supporting pressure sensor is mounted at each leather-supporting pressure measuring point, the static pressure measuring device comprises 8 wall surface pressure sensors uniformly arranged on the elliptical shell along the circumferential direction, the position distribution of the wall surface pressure sensors corresponds to the rake positions, the leather-supporting pressure sensors are used for acquiring the leather-supporting pressure of the corresponding leather-supporting pressure measuring points, and the wall surface pressure sensors.
2. A data processing method of an elliptic cross section flowmeter with equidistantly distributed 41 measuring points is applied to the elliptic cross section flowmeter with equidistantly distributed 41 measuring points in claim 1, and is characterized by comprising the following steps of:
step 1: averaging the measurement results of the 8 wall surface pressure sensors to obtain the static pressure of the center of the elliptical section, and obtaining the static pressure of each pitot pressure measurement point by using a linear interpolation method along the radial direction according to the static pressure of the center of the elliptical section and the wall surface static pressure corresponding to the corresponding rake position;
step 2: calculating the Mach number of the airflow of each pitot pressure measuring point according to the pitot pressure and the static pressure of each pitot pressure measuring point;
and step 3: calculating to obtain the total airflow pressure of each pitot pressure measuring point according to the static pressure and the airflow Mach number of each pitot pressure measuring point;
and 4, step 4: calculating the specific flow density of each pitot pressure measuring point according to the airflow Mach number and the airflow total pressure of each pitot pressure measuring point;
and 5: calculating to obtain a total pressure recovery coefficient of each pitot pressure measuring point according to the total airflow pressure and the total incoming flow pressure of each pitot pressure measuring point;
step 6: respectively integrating and superposing the specific flow density, the airflow Mach number and the total pressure recovery coefficient of each pitot pressure measuring point in the elliptical section to obtain the flow, the superposed Mach number and the superposed total pressure recovery coefficient in the elliptical section;
and 7: and respectively dividing the superposed Mach number and the superposed total pressure recovery coefficient in the elliptical section by the area of the elliptical section to obtain the average Mach number and the total pressure recovery coefficient in the elliptical section.
3. The data processing method of the elliptic cross section flowmeter with the 41 measuring points equidistantly distributed as claimed in claim 2, wherein the step of integrating and superposing the specific flow density, the airflow mach number and the total pressure recovery coefficient of each pitot pressure measuring point in the elliptic cross section to obtain the flow, the superposed mach number and the superposed total pressure recovery coefficient in the elliptic cross section comprises the following steps:
step 61, a sector area is formed by the center of the elliptical section and two adjacent pitot pressure measurement points on the innermost layer, the specific flow density of each pitot pressure measurement point is interpolated by utilizing a linear interpolation method to obtain a specific flow density interpolation function of each sector area, and the interpolation function of the compared flow density is integrated in the sector area to obtain the flow in each sector area; the calculation formula of the interpolation function of the specific flow density in the sector area is as follows:
Figure FDA0002990436510000021
the calculation formula of the flow in the sector area is as follows:
Figure FDA0002990436510000022
and 62, interpolating the specific flow density of each pitot pressure measuring point by using a linear interpolation method in a first arc-shaped area consisting of two pitot pressure measuring points adjacent to the innermost layer and two pitot pressure measuring points adjacent to the outermost layer corresponding to the two adjacent pitot pressure measuring points to obtain a specific flow density interpolation function of each first arc-shaped area, and integrating the interpolation function of the specific flow density in the first arc-shaped area to obtain the flow in each first arc-shaped area. Wherein the calculation formula of the interpolation function of the specific flow density in the first circular arc-shaped area is as follows:
Figure FDA0002990436510000023
the calculation formula of the flow in the first arc-shaped area is as follows:
Figure FDA0002990436510000024
and 63, approximating a second arc-shaped area consisting of two adjacent pitot pressure measuring points on the outermost layer and the corresponding elliptical shell by adopting the measuring points on the outermost layer along the radial direction, interpolating the specific flow density of each pitot pressure measuring point by adopting linear interpolation values along the circumferential direction to obtain a specific flow density interpolation function of each second arc-shaped area, and integrating the interpolation function of the specific flow density in the second arc-shaped area to obtain the flow in each second arc-shaped area. Wherein the calculation formula of the interpolation function of the specific flow density in the second circular arc-shaped area is as follows:
Figure FDA0002990436510000031
the calculation formula of the flow in the second arc-shaped area is as follows:
Figure FDA0002990436510000032
and step 64, superposing the flow in each sector area, the flow in each first circular arc area and the flow in each second circular arc area to obtain the flow in the elliptical section. Wherein, the calculation formula of the flow in the elliptical section is as follows:
Figure FDA0002990436510000033
step 65, replacing the specific flow density in the formulas (1), (3) and (5) with the Mach number of each pitot pressure measuring point, and repeating the steps 61-64 to obtain the superposed Mach number in the elliptical section;
and 66, replacing the specific flow density in the formulas (1), (3) and (5) with the total pressure recovery coefficient of each pitot pressure measuring point, and repeating the steps 61 to 64 to obtain the total pressure recovery coefficient superposed in the elliptical section.
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CN114200091A (en) * 2022-02-18 2022-03-18 中国矿业大学(北京) Method for measuring spatial distribution data of concentration of harmful substances in underground roadway
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