CN114528778B - Air flow measuring method based on bell mouth flow tube speed distribution model - Google Patents
Air flow measuring method based on bell mouth flow tube speed distribution model Download PDFInfo
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Abstract
The invention discloses an air flow measuring method based on a bell-mouth flow tube speed distribution model, and belongs to the field of measurement of air inflow of an aero-engine. The implementation method of the invention comprises the following steps: and determining the distribution range of the pressure measurement rake on the measurement section in the test according to the velocity distribution model in the pipe, measuring data of a few points on the measurement section to obtain a complete velocity distribution model in the pipe, and performing integral calculation on the obtained complete velocity distribution model in the pipe to obtain the air flow in the pipe and realize the measurement of the air inlet flow of the aero-engine. The invention divides the velocity distribution model in the pipe into a constant section, a linear section and a logarithmic section, and selects the distribution range and the distribution quantity of the pressure measurement rake on the measurement section for calibrating the velocity distribution model in the pipe in sections according to the velocity distribution characteristics of each section, thereby realizing the accurate distribution of the measurement points, reducing the quantity of the measurement points, and improving the flow measurement precision and the measurement efficiency on the premise of ensuring the measurement precision of the air intake flow of the aero-engine.
Description
Technical Field
The invention belongs to the field of measurement of air inflow of an aircraft engine, and relates to an air flow measurement method based on a bell-mouth flow tube speed distribution model.
Background
The measurement result of the air intake flow of an aeroengine is commonly used for performance evaluation and condition monitoring of the whole engine and parts, the most common measurement scheme at present is to measure by means of a bell-mouth flow tube equipped with a total static pressure probe, and the following two embodiments exist in the measurement method.
One is to obtain the flow in the pipe by the average condition of a few measuring points, wherein the measuring points are arranged in a small number for simple measurement. This solution does not reflect the true pressure and velocity distribution in the pipe, resulting in inaccurate measurement results.
The other is to obtain the air flow in the tube by the annular area method. This method is to divide the cross section of the pipe into a central circle and a plurality of rings, using the center of the circle of the cross section of the pipe as the center, as shown in fig. 2. The velocity value measured in each ring is multiplied by the area of the ring, and all the results are added to obtain the volume flow in the pipe (see fig. 3). Theoretically, in the measuring method, accurate flow value in the pipe can be obtained only by arranging the measuring points densely enough. Therefore, in this scheme, for accurate measurement, the number of measurement points is increased to obtain the true velocity distribution in the pipe. It is often necessary to make more pressure measurement rakes with more densely packed stations or to manually remove the in-line measurement probe. Both of these cases can greatly increase labor, time, and process fabrication costs, which are difficult to achieve in actual field measurements.
Therefore, the invention provides a method for obtaining the complete velocity distribution in the pipe by measuring a few points in the pipe, and can conveniently and quickly obtain the accurate flow in the pipe.
Disclosure of Invention
In order to solve the problems of more measuring point arrangement and higher cost of labor, time, process and the like, the invention mainly aims to provide a flow measuring method based on a bell-mouth flow tube speed distribution model.
The purpose of the invention is realized by the following technical scheme.
The invention discloses an air flow measuring method based on a velocity distribution model in a bell-mouth flow pipe, which comprises the following steps:
step one, aiming at the bell-mouth flow tube, an in-tube velocity distribution model is established, and measuring point arrangement ranges on all sections of the velocity distribution model are determined according to the established three-section in-tube velocity distribution model, namely the pressure measurement rake measuring point arrangement range and the number of measuring points in a test are determined.
Step 1.1: velocity in the tubeThe distribution model is as the following formula (1), wherein D is the diameter of the pipeline of the straight pipe section of the flow pipe; v. of ave 、k 1 、k 2 A and b are undetermined function coefficients; r 1 、R 2 And R 3 The boundary location points of the different function segment intervals.
Step 1.2: the in-pipe speed distribution model is a three-section speed distribution model, and the arrangement range of pressure measurement rake measuring points and the number of the measuring points in the test are determined according to the three-section speed distribution model as follows: two measuring points are respectively arranged on the constant section (core area), the linear section (transition section) and the logarithmic section. The constant segment is 0-0.39D-0.45D, the linear segment is 0.39D-0.45D-0.4625D-0.465D, and the logarithmic segment is 0.4625D-0.465D-0.5D.
And step two, numbering the measuring point arrangement range and the number of the measuring points determined in the step one, measuring the pressure distribution in the pipe in any flowing state, and measuring the atmospheric pressure and the absolute temperature in the test environment by an atmospheric pressure and temperature measuring device.
Step 2.1: setting measuring points according to the measuring point arrangement range determined in the step one, and installing a total pressure measuring device on a measuring section 1.5D away from the tail end of the inlet profile section of the flow tube, wherein: the total pressure measuring point numbers of the core area are i =1 and 2, the total pressure measuring point numbers of the transition section are i =3 and 4, and the total pressure measuring point numbers of the logarithmic section are i =5 and 6.
Step 2.2: measuring the pressure distribution in the pipe in any flow state, wherein the acquisition time is at least 1min, and obtaining a total pressure measurement value on each measurement point: the core region measures two sets of data as (r) 1 ,p 1 *)、(r 2 ,p 2 * ) The two sets of data measured at the transition section are (r) 3 ,p 3 *)、(r 4 ,p 4 * ) Two sets of data measured logarithmically are (r) 5 ,p 5 *)、(r 6 ,p 6 * ) (ii) a Meanwhile, on the measuring section, a static pressure value p on the section is obtained by a static pressure measuring device t 。
Step 2.3: measuring the atmospheric pressure p in the test environment by means of an atmospheric pressure and temperature measuring device 0 And the absolute temperature T.
And step three, processing the measured data to obtain the air density, the average total pressure value of each measuring point, the average static pressure value on the measuring section and the speed value of each measuring point under the test condition.
Step 3.1: the air density under the test conditions was calculated:
wherein the content of the first and second substances,
p 0 atmospheric pressure, pa;
n is the molar mass of air, 28.965294g/mol;
r is a gas constant, 8.3144621J/(mol. K);
t is the absolute temperature, K.
Step 3.2: calculating the average value of the total pressure of each measuring point:
wherein the content of the first and second substances,
m is the group number of total pressure data measured in the acquisition time;
n is the group number of total pressure data measured in the acquisition time and is an integer of 1-m;
Step 3.3: calculating the average static pressure value on the measuring section:
wherein the content of the first and second substances,
p t-ave is the static pressure average, pa;
m' is the number of groups of static pressure data measured in the acquisition time;
n 'is the serial number of the groups of the static pressure data measured in the acquisition time, and the value is an integer between 1 and m';
p t-n' is the measurement of the n' th group of data of static pressure, pa.
Step 3.4: calculating to obtain speed values at each measuring point:
wherein v is i The velocity value at the test point number i in the test is m/s.
And step four, substituting the data of the measuring points processed in the step three into the velocity distribution model in the pipe established in the step one, and calculating the undetermined coefficient.
Step 4.1: aiming at the constant segment part of the core area in the pipe, the speed distribution model is
Wherein R is 1 The boundary of the core area is obtained by solving the intersection point of the core area and the transition section speed distribution model.
Step 4.2: for the transitional linear segment portion, (r) is 3 ,v 3 ) And (r) 4 ,v 4 ) Two sets of data are substituted into a velocity distribution model v (r, theta) = k 1 r+k 2 ,r∈[R 1 ,R 2 ) Solving the undetermined coefficient k 1 And k is 2 A value of (b), wherein R 2 The boundary of the logarithmic section is obtained by solving the intersection point of the velocity distribution model of the linear transition section and the logarithmic section.
Step 4.3: for the pair of log segments, will (r) 5 ,v 5 ) And (r) 6 ,v 6 ) Two sets of data are brought into a velocity distribution model
Solving the values of undetermined coefficients a and b; the integral boundary R is obtained by setting the speed value of the fitting function to 0 according to the nature of the logarithmic function 3 The position coordinates of (a).
And step five, establishing a complete velocity distribution model in the pipe for the undetermined coefficient obtained in the step four, and performing integral calculation on the complete velocity distribution model in the pipe to obtain the air flow in the pipe, so that the measurement of the air inlet flow of the aircraft engine is realized, and the flow measurement precision and the measurement efficiency are improved.
Step 5.1: according to the calculated undetermined coefficient obtained by calculation in the fourth step, the complete velocity distribution in the pipe is modeled as a formula (6):
step 5.2: according to the complete velocity distribution model in the pipe, the mass air flow in the pipe is obtained through the integration of the formula (7), so that the measurement of the air inlet flow of the aero-engine is realized, and the flow measurement precision and the measurement efficiency are improved.
Wherein, B is an integral interval, namely a measuring section on the pipeline.
Has the beneficial effects that:
1. the invention discloses a flow measurement method based on a bell-mouth flow tube speed distribution model, which comprises the steps of determining the distribution range of a pressure measurement rake on a measurement section in a test according to the in-tube speed distribution model, carrying out data measurement on a few points on the measurement section to obtain an in-tube complete speed distribution model, carrying out integral calculation on the obtained in-tube complete speed distribution model to obtain the air flow in a tube, realizing the measurement of the air inlet flow of an aero-engine, and improving the flow measurement precision and the measurement efficiency.
2. The invention discloses a flow measuring method based on a bell-mouth flow pipe speed distribution model, which divides the pipe speed distribution model into a constant section, a linear section and a logarithmic section through a large number of tests and data analysis, and selects a point distribution range and a point distribution number for calibrating a pressure measuring rake on a measuring section of the pipe speed distribution model in a subsection mode aiming at the constant section (core area), the linear section (transition section) and the logarithmic section speed distribution characteristic points of the speed distribution model, thereby realizing accurate distribution of measuring points, reducing the number of the measuring points and improving the flow measuring precision and the measuring efficiency on the premise of ensuring the measuring precision of the air inlet flow of an aeroengine.
Drawings
FIG. 1 is a schematic flow diagram of a flow measurement method based on a bell-mouth flow tube velocity distribution model according to the present disclosure;
FIG. 2 is a schematic view of a measurement cross-sectional area segmentation;
FIG. 3 is a schematic diagram of measuring the flow rate in a pipe by a circular area method.
Detailed Description
The present invention will be further described with reference to the following examples.
Example 1:
in order to solve the problem of more measuring points when the bell-mouth flow tube is used for accurately measuring the air flow, the diameter D =400mm of the pipeline, the section of the molded surface is a twisted-pair molded surface, and the polar coordinate formula rho of the twisted-pair is adopted 2 ＝r 2 The process of using the bell-mouth flow tube to measure the field air flow is described by taking 0.637D as r in cos 2 theta and taking a bell-mouth flow tube with a 40mm flanging structure as an example. Meanwhile, an annular area method is used, the air flow is measured under the same flow state, and the two results are compared and analyzed.
As shown in fig. 1, the flow measurement method based on the bell mouth flow tube velocity distribution model disclosed in this embodiment specifically includes the following steps:
step one, aiming at the used bell-mouth flow tube, establishing a velocity distribution model in the tube, and determining the arrangement range of the measuring points on each section of the velocity distribution model, namely determining the arrangement range of the pressure difference measuring rake measuring points and the number of the measuring points in the test.
1. The velocity distribution in the pipe is modeled as follows (8), where v ave 、k 1 、k 2 A and b are undetermined function coefficients; r 1 、R 2 And R 3 The boundary location points of the different function segment intervals.
2. Aiming at the three-section velocity distribution model, determining the arrangement range of the measuring points on the pressure measuring rake and the number of the measuring points in the test as follows: the point distribution range of the constant section (core area) is 0-0.178 m, and the positions of 2 measuring points are set to be 0.0688m and 0.1562m; the distribution range of the linear section (transition section) is 0.178-0.185 m, and the positions of 2 measuring points are set to be 0.1805m and 0.1845m; the range of the point distribution of the logarithmic section is 0.185 m-0.2 m, and the positions of 2 measuring points are set to be 0.1865m and 0.1985m.
And secondly, numbering the measuring point arrangement range and the number of the measuring points determined in the step one, measuring the pressure distribution in the pipe in any flowing state, and measuring the atmospheric pressure and the absolute temperature in the test environment by an atmospheric pressure and temperature measuring device.
1. Setting measuring points according to the measuring point arrangement range determined in the step one, and installing a total pressure measuring device on a measuring section 1.5D (0.6 m) away from the tail end of the molded surface section of the inlet section of the flow pipe, wherein: the total pressure measuring point numbers i =1 and 2 in the core area, the total pressure measuring point numbers i =3 and 4 in the transition section, and the total pressure measuring point numbers i =5 and 6 in the logarithmic section.
2. The pressure distribution in the pipe under the flowing state with the main flow speed of about 50m/s is measured, the acquisition time is 99s, the acquisition frequency is 1Hz, and the total pressure measurement value on each measurement point is obtained: the core region measures two sets of data as (r) 1 ,p 1 *)、(r2,p 2 * ) The linear segment measures two sets of data as (r) 3 ,p 3 *)、(r 4 ,p 4 * ) Two sets of data measured logarithmically are (r) 5 ,p 5 *)、(r 6 ,p 6 * ) (ii) a At the same time, on the measuring cross sectionObtaining a static pressure value p on the section by a static pressure measuring device t 。
3. Measuring the atmospheric pressure p in the test environment by means of an atmospheric pressure and temperature measuring device 0 =101150Pa and absolute temperature T =284.5K.
And step three, processing the measured data to obtain the air density, the average total pressure value of each measuring point, the average static pressure value on the measuring section and the speed value of each measuring point under the test condition.
1. The air density under experimental conditions was calculated:
2. calculating the average total pressure value of each measuring point:
the average total pressure at each measurement point is calculated as shown in the following table.
| Total pressure measuring |
1 | 2 | 3 | 4 | 5 | 6 |
| Measurement point position/m | 0.0688 | 0.1562 | 0.1805 | 0.1845 | 0.1865 | 0.1985 |
| Average total pressure/Pa | 101166 | 101154 | 101102 | 101075 | 101054 | 100605 |
3. Calculating the average static pressure value on the measuring section:
4. and calculating to obtain speed values at each measuring point:
| total pressure measurement |
1 | 2 | 3 | 4 | 5 | 6 |
| Measurement point position/m | 0.0688 | 0.1562 | 0.1805 | 0.1845 | 0.1865 | 0.1985 |
| Velocity value/(m/s) | 46.9 | 46.7 | 45.8 | 45.3 | 45.0 | 36.0 |
Step four, substituting the data of each measuring point processed in the step three into the velocity distribution model formula (8) in the tube established in the step one, and calculating undetermined coefficients;
1. aiming at the constant segment part of the core area in the pipe, the speed distribution model is
2. For the transitional linear segment portion, (r) is 3 ,v 3 ) And (r) 4 ,v 4 ) Two sets of data are substituted into a velocity distribution model v (r, theta) = k 1 r+k 2 ,r∈[R 1 ,R 2 ) Solving the undetermined coefficient k 1 = -125 and k 2 =68.3625. At this time, R can be solved 1 ＝0.1725m。
3. For the pair of log segments, will (r) 5 ,v 5 ) And (r) 6 ,v 6 ) Two-group data-in velocity distribution model
And solving the undetermined coefficients of a =4.0961 and b =62.6339. At this time, R can be solved 2 ＝0.1862m，R 3 ＝0.19999977m。
And step five, establishing a complete velocity distribution model in the pipe for the undetermined coefficient obtained in the step four, and performing integral calculation on the complete velocity distribution model in the pipe to obtain the air flow in the pipe, so that the measurement of the air inlet flow of the aircraft engine is realized, and the flow measurement precision and the measurement efficiency are improved.
1. According to the calculation result in the fourth step, the velocity distribution can be expressed as the following formula:
2. the mass air flow in the tube is calculated by:
the calculation result is q m ＝7.152kg/s。
Meanwhile, the air flow rate is measured by the annular area method for the same flow state. Here, 14 measuring points are arranged in the pipe, and the obtained calculation result is as follows: q. q.s m ' =7.120kg/s. With q of m ' for standard flow, the relative error between the measurement and the standard flow value that can be obtained with the present invention is: 0.44 percent. The invention can obtain the flow measurement result with the relative error with the standard flow within 0.5 percent by using 6 measuring points, and solves the problems of more measuring points and more measuring points in the existing aeroengine air intake flow measurementHigh cost of labor, time, process and the like.
The above detailed description is further intended to illustrate the objects, technical solutions and advantages of the present invention, and it should be understood that the above detailed description is only an example of the present invention and should not be used to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (6)
1. The air flow measuring method based on the velocity distribution model in the bell-mouth flow pipe is characterized in that: comprises the following steps of (a) carrying out,
step one, aiming at a bell-mouth flow pipe, establishing a pipe inner velocity distribution model, and determining a measuring point arrangement range on each section of the velocity distribution model according to the established three-section pipe inner velocity distribution model, namely determining a pressure measurement rake measuring point arrangement range and the number of measuring points in a test;
step two, numbering the measuring point arrangement range and the number of the measuring points determined in the step one, measuring the pressure distribution in the pipe in any flowing state, and measuring the atmospheric pressure and the absolute temperature in the test environment by an atmospheric pressure and temperature measuring device;
processing the measured data to obtain the air density, the total pressure average value of each measuring point, the static pressure average value on the measuring section and the speed value of each measuring point under the test condition;
step four, substituting the data of each measuring point processed in the step three into the velocity distribution model in the pipe established in the step one, and calculating undetermined coefficients;
and step five, establishing a complete velocity distribution model in the pipe for the undetermined coefficient obtained in the step four, and performing integral calculation on the complete velocity distribution model in the pipe to obtain the air flow in the pipe so as to realize the measurement of the air inlet flow of the aircraft engine.
2. The method of air flow measurement based on a model of velocity distribution in a bellmouth flow tube of claim 1, wherein: the first implementation method of the method is that,
step 1.1: the velocity distribution model in the pipe is as the following formula (1), wherein D is the pipe diameter of the straight pipe section of the flow pipe; v. of ave 、k 1 、k 2 A and b are undetermined function coefficients; r is 1 、R 2 And R 3 Then the boundary position points of different function segment intervals are obtained;
step 1.2: the in-pipe speed distribution model is a three-section speed distribution model, and the arrangement range and the number of the measuring points of the pressure measurement rake in the test are determined as follows according to the three-section speed distribution model: two measuring points are respectively arranged on the constant section, the linear section and the logarithmic section; the constant segment is 0-0.39D-0.45D, the linear segment is 0.39D-0.45D-0.4625D-0.465D, and the logarithmic segment is 0.4625D-0.465D-0.5D.
3. The method of air flow measurement based on a model of velocity distribution in a bell-mouth flow tube of claim 2, wherein: the second step is realized by the method that,
step 2.1: setting measuring points according to the measuring point arrangement range determined in the step one, and installing a total pressure measuring device on a measuring section 1.5D away from the tail end of the inlet profile section of the flow tube, wherein: the total pressure measuring points of the constant section are numbered i =1 and 2, the total pressure measuring points of the linear section are numbered i =3 and 4, and the total pressure measuring points of the logarithmic section are numbered i =5 and 6;
step 2.2: measuring the pressure distribution in the pipe in any flow state, wherein the acquisition time is at least 1min, and obtaining a total pressure measurement value at each measurement point: two sets of data measured in constant section are (r) 1 ,p 1 *)、(r 2 ,p 2 * ) The linear segment measures two sets of data as (r) 3 ,p 3 *)、(r 4 ,p 4 * ) Two sets of data measured logarithmically are (r) 5 ,p 5 *)、(r 6 ,p 6 * ) (ii) a At the same time, on the measuring section, the static pressure measuring device obtains the sectionStatic pressure value p of t ；
Step 2.3: measuring the atmospheric pressure p in the test environment by means of an atmospheric pressure and temperature measuring device 0 And the absolute temperature T.
4. A method of air flow measurement based on a model of velocity distribution in a bell-mouth flow tube as set forth in claim 3 wherein: the third step is to realize the method as follows,
step 3.1: the air density under the test conditions was calculated:
wherein the content of the first and second substances,
p 0 atmospheric pressure, pa;
n is the molar mass of air, g/mol;
r is a gas constant, J/(mol. K);
t is absolute temperature, K;
step 3.2: calculating the average total pressure value of each measuring point:
wherein the content of the first and second substances,
m is the group number of total pressure data measured in the acquisition time;
n is the group number of the total pressure data measured in the acquisition time, and the value is an integer of 1-m;
step 3.3: calculating the average static pressure value on the measuring section:
wherein the content of the first and second substances,
p t-ave is the static pressure average, pa;
m' is the number of groups of static pressure data measured in the acquisition time;
n 'is the serial number of the groups of the static pressure data measured in the acquisition time, and the value is an integer between 1 and m';
p t-n' pa, the measured value of the nth data of the static pressure;
step 3.4: calculating to obtain speed values at each measuring point:
wherein v is i Is the speed value at the test point number i in the test, m/s.
5. The method of air flow measurement based on a model of velocity distribution in a bell-mouth flow tube of claim 4, wherein: the implementation method of the fourth step is that,
step 4.1: for the constant segment part in the pipe, the velocity distribution model is
Wherein R is 1 The boundary of the constant section is obtained by solving the intersection point of the constant section and the linear section speed distribution model;
step 4.2: for the linear segment portion, (r) is 3 ,v 3 ) And (r) 4 ,v 4 ) Two sets of data are substituted into a velocity distribution model v (r, theta) = k 1 r+k 2 ,r∈[R 1 ,R 2 ) Solving the undetermined coefficient k 1 And k 2 A value of (1), wherein R 2 Is the boundary of the log segment and is,obtaining the speed distribution model by solving the intersection point of the linear section and the logarithmic section;
step 4.3: for the pair of log segments, will (r) 5 ,v 5 ) And (r) 6 ,v 6 ) Two sets of data are brought into a velocity distribution model
Solving the values of undetermined coefficients a and b; according to the property of the logarithm function, the integral boundary R is obtained by making the speed value of the logarithm section speed distribution model be 0 3 The position coordinates of (a).
6. The method of air flow measurement based on a model of velocity distribution in a bellmouth flow tube of claim 5, wherein: the fifth step is to realize that the method is that,
step 5.1: according to the calculated undetermined coefficient obtained by calculation in the fourth step, the complete velocity distribution in the pipe is modeled as a formula (6):
step 5.2: according to the complete velocity distribution model in the pipe, the mass air flow in the pipe is obtained through the integration of the formula (7), namely the measurement of the air inlet flow of the aircraft engine is realized, and the flow measurement precision and the measurement efficiency are improved;
wherein, B is an integral interval, namely a measuring section on the pipeline.
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