CN109540052B - Design method of hyperbolic cosine gap sensor and grid isolator for measuring water film thickness - Google Patents
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Abstract
The invention discloses a hyperbolic cosine gap sensor for measuring the thickness of a water film and a design method of a grid isolator, which comprise a cylindrical cavity with two ends open and a microwave signal transmission interface in the middle, wherein the two ends of the inside of the cylindrical cavity are respectively provided with the grid isolator, the grid isolator consists of a middle linear metal strip and more than 1 pair of hyperbolic cosine metal strips which are symmetrically distributed about the middle linear metal strip, and one end of each of the grid isolator, which is close to a port of the cylindrical cavity, is connected with the cylindrical cavity. The invention is matched with a microwave signal processing circuit, can realize microwave measurement of the thickness of a water film and a liquid film on the inner surface of a cylindrical metal, has the advantages of simple structure, convenient use, low requirement on environment, high measurement precision, larger slit of a grid isolator structure, ensuring good flow characteristics, ensuring accurate sampling and ensuring good electromagnetic performance and radiation performance along the opening of the end surface current density direction of a resonant cavity.
Description
Technical Field
The invention relates to a design method of a resonant cavity sensor and a grid isolator for measuring water film thickness, in particular to a design method of a hyperbolic cosine gap sensor and a grid isolator for measuring water film thickness, and belongs to the technical field of testing.
Background
The last stages of a large condensing steam turbine in a conventional power plant and all stages of the turbine in the plant are operated in a wet steam state. The steam humidity directly influences the safety and economy of the operation of the steam turbine, and on one hand, the steam humidity is increased, so that strong erosion and impact can be generated on the blades of the steam turbine, the blades become rough, pits appear, even the blades are twisted and broken, the safe operation of the steam turbine is seriously threatened, and meanwhile, the thermal efficiency of the steam turbine is reduced. In geothermal power stations and nuclear power stations, the economic and safety hazards of steam turbine generator units due to the presence of saturated steam are particularly significant. Thus, accurate measurement of the humidity of wet steam is of great importance for the long-term stability of the turbine and its life.
Since 2003, a method for measuring steam humidity by using a microwave resonant cavity perturbation technology has been proposed, and the microwave resonant cavity steam humidity measuring technology has been widely studied. Currently, research in this area is mainly focused on steam humidity calibration and measurement accuracy improvement. The microwave perturbation method adopts a microwave cylindrical resonant cavity as a humidity sensor, the working frequency is in a microwave band, the equipment cost is low, and the online measurement can be realized. Compared with humidity measurement methods such as a thermodynamic method and an optical measurement method, the microwave perturbation method is more suitable for online measurement of the humidity of steam in the steam turbine.
Because the humidity sensor adopting the microwave perturbation method must be placed under the wet steam of the steam turbine for a long time, a layer of water film is deposited on the surface of the inner wall of the resonant cavity, if the thickness of the deposited water film on the inner wall of the resonant cavity is 35 mu m, the humidity measurement deviation caused by neglecting the influence of the water film is 1.262%, so that the accurate measurement of the thickness of the water film can improve the humidity measurement precision. In addition, the accurate measurement of the thickness of the water film has important significance for automobile exhaust, sliding shoes, road surface conditions, sliding bearings and the like.
Disclosure of Invention
The invention aims to provide a hyperbolic cosine gap sensor for measuring the thickness of a water film and a design method of a grid isolator.
In order to solve the technical problems, the invention adopts the following technical scheme:
the technical scheme is as follows:
The hyperbolic cosine gap sensor for measuring the thickness of the water film comprises a resonant cavity main body, a left wedge cylinder and a right wedge cylinder, wherein the resonant cavity main body comprises a resonant cavity, a left grid isolator and a right grid isolator, the left end and the right end of the resonant cavity are respectively communicated with the left grid isolator and the right grid isolator, the left grid isolator and the right grid isolator are identical in structure and are composed of more than 1 hyperbolic cosine metal strips which are symmetrically distributed relative to the middle metal strips, the left end of the left isolator is communicated with the left wedge cylinder, the right end isolator is communicated with the right wedge cylinder, a coupling piece mounting hole is formed in the side wall of the resonant cavity main body, and the resonant cavity works in a TE 111 mode.
The radius of the resonant cavity is 20.59mm, the left-end grid isolator and the right-end grid isolator are respectively composed of an intermediate metal strip and 8 hyperbolic cosine-shaped metal strips which are distributed in a bilateral symmetry mode, the widths of the metal strips are 1mm, the x axis is the center point of an over-circle and coincides with the direction of the intermediate metal strip, the y axis is orthogonal with the x axis, 4 hyperbolic cosine-shaped metal strips along the positive direction of the y axis sequentially pass through points (0,4.511), (0,7.855), (0,12.15) and (0,16.9), and corresponding function equations are ：y1＝0.011cosh(x/4)+4.5,y2＝0.055cosh(x/4)+7.8,y3＝0.35cosh(x/4)+11.8,y4＝2.1cosh(x/4)+14.8; units of mm in sequence. Where x is a variable on the x-axis and y 1、y2、y3、y4 is a variable on the y-axis.
The wall surface of the airflow inflow end of the left-end wedge-shaped cylinder and the wall surface of the airflow outflow end of the right-end wedge-shaped cylinder are both in wedge-shaped structures.
The resonant cavity body is coupled in a coaxial line excitation mode.
The second technical scheme is as follows:
The design method of the grid isolator in the hyperbolic cosine slit sensor for measuring the thickness of the water film according to the first design technical scheme is the same as the design method of the left-end grid isolator and the right-end grid isolator, and the left-end grid isolator comprises the following specific steps:
Step 1, calculating the current density direction of the end face of the resonant cavity, namely setting an x-axis in the direction of passing through the center point of the left grid isolator and being overlapped with the middle metal strip, setting a y-axis to be orthogonal with the x-axis, wherein J r is the radial component of the current density of the end face of the resonant cavity, The tangential value of the included angle theta 1 between the current density J of the end face of the resonant cavity and the radial component J r of the current density of the end face of the resonant cavity is as follows:
In the formula (1), J 1 is a first-order Bessel function, and J 1' is a first derivative of the first-order Bessel function;
Step 2, positioning a hyperbolic cosine metal strip, namely determining the position of the hyperbolic cosine metal strip according to the intensity of current density distribution of the end face of the resonant cavity, wherein the distances from the intersection point of the hyperbolic cosine metal strip and a y axis to an origin are respectively 0.22R, 0.38R, 0.59R and 0.82R, and R is the radius of the resonant cavity;
and 3, determining the shape of the hyperbolic cosine metal strips, namely fitting constants a, b and c in a corresponding hyperbolic cosine function y= acosh (x/b) +c through intersection points of the hyperbolic cosine metal strips and a y axis in sequence, so that the slope of any point (x, y) on the hyperbolic cosine function is the same as the current density direction of the corresponding point in the formula (1).
The technical effect obtained by adopting the technical scheme is as follows:
1. The invention is matched with a microwave signal processing circuit, so that the microwave measurement of the thickness of the water film and the liquid film on the inner surface of the cylindrical metal can be realized;
2. the invention has simple structure, low requirement on environment and high measurement precision;
3. The grid isolator has large structural slits, can ensure good flow characteristics and accurate sampling, can ensure good electromagnetic performance and radiation performance along the current density direction of the end face of the resonant cavity, and can reduce the radiation quantity to 0.01w when the input power is 1w.
Drawings
The invention will be described in further detail with reference to the drawings and the detailed description.
FIG. 1 is a schematic diagram of the structure of the present invention;
FIG. 2 is a schematic view of the structure of the left-end wedge cylinder in embodiment 1 of the present invention;
FIG. 3 is a left side view of the left end wedge cylinder of example 1 of the present invention;
FIG. 4 is a schematic view showing the structure of a left end grid separator in embodiment 1 of the present invention;
FIG. 5 is a left side view of the left end grid spacer of embodiment 1 of the present invention;
FIG. 6 is a schematic structural diagram of a main body of a resonant cavity in embodiment 1 of the present invention;
FIG. 7 is a left side view of the main body of the resonator in embodiment 1 of the present invention;
Wherein: 1, a left end wedge-shaped cylinder, 2, a left end grid isolator, 3, a resonant cavity main body, 3-1, a resonant cavity, 4, a coupling piece mounting hole, 5, a right end grid isolator, 6 and a right end wedge-shaped cylinder.
Detailed Description
Example 1:
The hyperbolic cosine gap sensor for measuring the thickness of a water film comprises a resonant cavity main body 3, a left wedge cylinder 1 and a right wedge cylinder 6, wherein the resonant cavity main body consists of a resonant cavity 3-1, a left grid isolator 2 and a right grid isolator 5, the left end and the right end of the resonant cavity 3-1 are respectively communicated with the left grid isolator 2 and the right grid isolator 5, the left grid isolator 2 and the right grid isolator 5 are identical in structure and are composed of 9 metal strips, the middle metal strip of the 9 metal strips is linear, the rest 8 hyperbolic cosine metal strips are symmetrically distributed relative to the middle metal strip, the left end of the left isolator 2 is communicated with the left wedge cylinder 1, the right end of the left isolator is communicated with the right wedge cylinder 6, and a coupling piece mounting hole 4 is formed in the side wall of the resonant cavity main body 3.
The left end grid isolator (2) and the right end grid isolator (5) are respectively composed of a middle metal strip and 4 pairs of hyperbolic cosine-shaped metal strips which are distributed in bilateral symmetry, the widths of the metal strips are 1mm, the x axis is the center point of a circle and coincides with the direction of the middle metal strip, the y axis is orthogonal with the x axis, the 4 hyperbolic cosine-shaped metal strips along the positive direction of the y axis sequentially pass through points (0,4.511), (0,7.855), (0,12.15) and (0,16.9), and the function equations of the two hyperbolic cosine-shaped metal strips are ：y1＝0.011cosh(x/4)+4.5,y2＝0.055cosh(x/4)+7.8,y3＝0.35cosh(x/4)+11.8,y4＝2.1cosh(x/4)+14.8; units which are mm in sequence. Where x is a variable on the x-axis and y 1、y2、y3、y4 is a variable on the y-axis.
The airflow inlet end wall surface of the left wedge-shaped cylinder 1 and the airflow outlet end wall surface of the right wedge-shaped cylinder 6 are both in wedge-shaped structures.
The resonant cavity body 3 is coupled in a coaxial line excitation mode.
The resonant cavity body 3, the left grid isolator 2 and the right grid isolator 5 are all made of the same material with low expansion coefficient.
The resonant cavity 3-1 is generally a cylindrical resonant cavity which is easy to process, and when steam to be tested flows through the resonant cavity 3-1 from the left wedge-shaped cylinder 1 through the left grid isolator 2 at a high speed, a layer of water film is formed on the inner wall of the resonant cavity 3-1 along with the time. If the resonant cavity has a certain structure and size, the thickness of the water film is different, and the resonant frequency is also different. The thickness of the water film of the resonant cavity can be indirectly obtained by monitoring the change of the resonant frequency of the resonant cavity.
At a certain pressure and temperature, the thickness of the water film is a function of the resonant frequency and the dielectric constant of the liquid film.
Since the TE 111 mode has a radial electric field component and the mode is the lowest, the water film thickness has a strong correlation with the resonant frequency. The resonant cavity 3-1 works in TE 111 mode, and the expressions of the components of the end face current density of the resonant cavity 3-1 are as follows:
The resonant cavity works in TE 111 mode, and the radial component J r and tangential component of the current density of the end face of the resonant cavity The expression of (2) is as follows:
Where k c1 = 1.841/R, R is the radius of the resonant cavity, H 111 is the magnitude of the magnetic field strength in the cavity, l is the length of the resonant cavity, R is the radial variable, z is the longitudinal variable, and J 1、J1' is the first order bessel function and the first derivative of the first order bessel function, respectively.
J is the current density of the end face of the resonant cavity, and the included angle between the current density J of the end face of the resonant cavity at a certain point in the electromagnetic field and the radial component J r of the current density of the end face of the resonant cavity is theta 1 The reduced rectangular coordinate system equation is:
Let P (x, y) be any point on the curve y (x), then the slope k=y '=tan (γ) of the point P, y' be the derivative of y, γ be the angle between the tangent of the curve y (x) at the point P (x, y) and the x-axis, Is the included angle between the connecting line of the point P (x, y) and the center of the circle and the positive direction of the x axis. In order to ensure that the electromagnetic field distribution is not affected after the hyperbolic cosine metal strip is added, the tangential direction of any point P (x, y) on the curve y (x) is the same as the current density direction of the end face of the resonant cavity at the point, namely, the current density direction is satisfied,
In the middle ofIn order to install the hyperbolic cosine metal strip, the included angle between the current density of the end face of the resonant cavity and the radial component of the hyperbolic cosine metal strip is equal to the included angle between the current density J of the end face of the resonant cavity and the radial component J r of the current density of the end face of the resonant cavity, which is theta 1.
Since the distribution shape of the current density at the end face of the resonant cavity is very similar to the curve of the hyperbolic cosine function, it is assumed that y= acosh (x/b) +c (a, b, c are constants) and are substituted into the equation (6) and the equation (7), respectively, to obtain:
The functional image of tan (θ 1) with respect to x and the functional image of tan (θ 2) with respect to x are plotted separately with MATLAB. In this embodiment, considering that the radius of the resonant cavity is 20.59mm, b is 4, and when a and c are taken, the function image of tan (θ 1) about x and the function image of tan (θ 2) about x are completely the same within the specified range of x, that is, it is proved that y= acosh (x/4) +c is a curve meeting the requirement, and the tangential direction of any point on the curve is the same as the current density direction of the point. Because there are countless end current density distribution lines of the resonant cavity 3-1, when a and c have different values, the end current density distribution lines of the resonant cavity 3-1 are corresponding to different values.
In this embodiment, four hyperbolic cosine functions are y1＝0.011cosh(x/4)+4.5,y2＝0.055cosh(x/4)+7.8,y3＝0.35cosh(x/4)+11.8,y4＝2.1cosh(x/4)+14.8,, the values of a, b and c are respectively substituted into the formula (6) and the formula (7), and MATLAB is used to respectively draw x images about tan (θ 1) and tan (θ 2), and the function images of the four hyperbolic cosine functions are found to be identical within the specified range of x, so that the distribution line of the current density of the end face of the resonant cavity of the TE 111 mode can be described by the hyperbolic cosine function, and the general formula is y= acosh (x/b) +c.
The simulation proves that the curve drawn by the hyperbolic cosine function can be completely overlapped with the distribution line of the end surface current density of the resonant cavity 3-1, the electromagnetic performance and the radiation performance after slotting are very good, and the radiation quantity can be as small as 0.01w when the input power is 1w, so that the design requirement is completely met.
The invention provides a resonant cavity sensor with a hyperbolic cosine slotted structure for the first time, and combines a microwave perturbation method to enable the resonant cavity sensor to work in a TE 111 mode to measure the thicknesses of a water film and a liquid film of a cylindrical resonant cavity. The grid isolator structure has large slit, good flow characteristic and can ensure accurate sampling, meanwhile, the hyperbolic cosine function is proved to be completely the same as the distribution shape of the current density of the end face of the resonant cavity through theoretical derivation, and the slit along the direction of the current density vector of the end face of the resonant cavity also ensures good electromagnetic performance and radiation performance, and the radiation quantity can be as small as 0.01w when the input power is 1w. The invention has simple structure, convenient use and low requirement on environment, can solve the problem of lacking a cylindrical metal inner surface water film and liquid film thickness measuring method at present, and can accurately measure the water film thickness.
Example 2:
A method for designing a grid isolator in a hyperbolic cosine slit sensor for measuring a water film thickness according to embodiment 1, wherein the method for designing a left-side grid isolator 2 and a right-side grid isolator 5 is the same, and the method for designing the left-side grid isolator 2 comprises the following specific steps:
Step 1, calculating the current density direction of the end face of the resonant cavity, namely setting an x-axis in the direction of passing through the center point of the left grid isolator and being overlapped with the middle metal strip, setting a y-axis to be orthogonal with the x-axis, wherein J r is the radial component of the current density of the end face of the resonant cavity, The tangential value of the included angle theta 1 between the current density J of the end face of the resonant cavity and the radial component J r of the current density of the end face of the resonant cavity is as follows:
In the formula (1), J 1 is a first-order Bessel function, and J 1' is a first derivative of the first-order Bessel function;
Step 2, positioning a hyperbolic cosine metal strip, namely determining the position of the hyperbolic cosine metal strip according to the intensity of current density distribution of the end face of the resonant cavity, wherein the distances from the intersection point of the hyperbolic cosine metal strip and a y axis to an origin are respectively 0.22R, 0.38R, 0.59R and 0.82R, and R is the radius of the resonant cavity;
and 3, determining the shape of the hyperbolic cosine metal strips, namely fitting constants a, b and c in a corresponding hyperbolic cosine function y= acosh (x/b) +c through intersection points of the hyperbolic cosine metal strips and a y axis in sequence, so that the slope of any point (x, y) on the hyperbolic cosine function is the same as the current density direction of the corresponding point in the formula (1).
In this embodiment, since the radius of the resonant cavity is considered to be 20.59mm, b is first determined to be 4. The intersection point of the function and the y axis is a+c, so that 0-20.59 of a+c is satisfied. The simulated current density lines were observed to find that the opening of each hyperbolic cosine line was large to small in the y-axis plus direction, and that the larger a was, the smaller a was for the hyperbolic cosine line near the center and the larger a was for the hyperbolic cosine line near the edge, but none exceeded 2.5. So c can be determined first to determine the approximate position of the hyperbolic cosine line, then the shape of the hyperbolic cosine line is adjusted by adjusting a, and the hyperbolic cosine function is completely overlapped with the simulated current density distribution line by optimization. And finally, obtaining the shape of each hyperbolic cosine-shaped metal strip in the left-end grid isolator 2.
Claims (4)
1. The hyperbolic cosine gap sensor for measuring the thickness of the water film is characterized by comprising a resonant cavity main body (3), a left wedge-shaped cylinder (1) and a right wedge-shaped cylinder (6); the resonant cavity main body (3) consists of a resonant cavity (3-1), a left grid isolator (2) and a right grid isolator (5), wherein the left end and the right end of the resonant cavity (3-1) are respectively communicated with the left grid isolator (2) and the right grid isolator (5), the left grid isolator (2) and the right grid isolator (5) have the same structure and are composed of a straight-line middle metal strip and more than 1 pair of hyperbolic cosine metal strips symmetrically distributed about the middle metal strip; the left end of the left end isolator (2) is communicated with the left end wedge cylinder (1), the right end isolator (5) is communicated with the right end wedge cylinder (6), the side wall of the resonant cavity main body (3) is provided with a coupling piece mounting hole (4), the resonant cavity (3-1) works in a TE 111 mode, the radius of the resonant cavity (3-1) is 20.59mm, the left end grid isolator (2) and the right end grid isolator (5) are composed of an intermediate metal strip and 4 pairs of hyperbolic cosine-shaped metal strips which are symmetrically distributed left and right, the widths of the metal strips are 1mm, the x axis is the center point of a circle and coincides with the direction of the intermediate metal strip, the y axis is orthogonal to the x axis, and 4 hyperbolic cosine-shaped metal strips along the positive direction of the y axis sequentially pass through points (0,4.511), (0,7.855), (0,12.15) and (0,16.9) and the corresponding function equations are ：y1＝0.011cosh(x/4)+4.15,y2＝0.055cosh(x/4)+7.8,y3＝0.35cosh(x/4)+11.8,y4＝2.1cosh(x234/4)+14.8; units of mm in sequence, wherein x is a variable of an x axis and y 1、y2、y3、y4 is a variable of a y axis.
2. The hyperbolic cosine gap sensor for measuring water film thickness according to claim 1, wherein the wall surface of the air inflow end of the left end wedge cylinder (1) and the wall surface of the air outflow end of the right end wedge cylinder (6) are both wedge structures.
3. The hyperbolic cosine gap sensor for measuring water film thickness according to claim 1, wherein the coupling mode of the resonant cavity body (3) is coaxial line excitation.
4. A design method for designing a grid isolator in the hyperbolic cosine slit sensor for measuring a water film thickness according to claim 1, wherein the design method for the left-end grid isolator (2) and the design method for the right-end grid isolator (5) are the same, and the left-end grid isolator (2) comprises the following specific steps:
Step 1, calculating the current density direction of the end face of the resonant cavity, namely setting an x-axis in the direction of passing through the center point of the left grid isolator (2) and overlapping with the middle metal strip, setting a y-axis orthogonal to the x-axis, wherein J r is the radial component of the current r density of the end face of the resonant cavity, The tangential value of the included angle theta 1 between the current density J of the end face of the resonant cavity and the radial component J r of the current density of the end face of the resonant cavity is as follows:
wherein J is a first order Bessel function, and J' is a first derivative of the first order Bessel function;
Step 2, positioning a hyperbolic cosine metal strip, namely determining the position of the hyperbolic cosine metal strip according to the intensity of current density distribution of the end face of the resonant cavity, wherein the distances from the intersection point of the hyperbolic cosine metal strip and a y axis to an origin are respectively 0.22R, 0.38R, 0.59R and 0.82R, and R is the radius of the resonant cavity;
and 3, determining the shape of the hyperbolic cosine metal strips, namely fitting constants a, b and c in a corresponding hyperbolic cosine function y= acosh (x/b) +c through intersection points of the hyperbolic cosine metal strips and a y axis in sequence, so that the slope of any point (x, y) on the hyperbolic cosine function is the same as the current density direction of the corresponding point in the formula (1).
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| WO2015028396A1 (en) * | 2013-09-02 | 2015-03-05 | Siemens Aktiengesellschaft | Microwave resonant cavity humidity sensor |
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| CN201138333Y (en) * | 2007-12-19 | 2008-10-22 | 华北电力大学 | Microwave resonant cavity sensor for on-line detection of steam humidity |
| US9528814B2 (en) * | 2011-05-19 | 2016-12-27 | NeoVision, LLC | Apparatus and method of using impedance resonance sensor for thickness measurement |
| JP2013224871A (en) * | 2012-04-23 | 2013-10-31 | Fujitsu Ltd | Qcm sensor apparatus and corrosive environment evaluation method |
| CN202562453U (en) * | 2012-05-03 | 2012-11-28 | 东南大学 | Water film thickness detecting sensor based on ring-shaped electrical bridge structure |
| CN105716548B (en) * | 2016-04-29 | 2018-05-18 | 华北电力大学（保定） | The system and method that microwave perturbation method measures humidity sensor inner wall water film thickness |
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| CN105548218A (en) * | 2016-01-18 | 2016-05-04 | 华北电力大学（保定） | Pressure compensating microwave resonant cavity for steam on-line humidity measurement |
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