Measurement method of coaxial capacitive liquid level sensor considering fringe effect

Abstract

The invention discloses a measurement method of a coaxial capacitive liquid level sensor considering an edge effect. The method comprises the following steps: S1, designing a calculation formula of the capacitance above a liquid level by taking air as a medium and a calculation formula of the capacitance between the lower part of the liquid level and the bottom of an inner electrode of a coaxial capacitive liquid level sensor model by taking to-be-measured liquid as a medium when the coaxial capacitive liquid level sensor measures the liquid level; s2, a finite element method is used for designing a capacitance calculation formula considering the fringe effect between the bottom of an inner electrode and the bottom of an outer electrode of the coaxial capacitive liquid level sensor model when the coaxial capacitive liquid level sensor measures the liquid level; s3, total output capacitance is measured through a coaxial capacitive liquid level sensor; and S4, calculating based on the total output capacitance and the calculation formulas in S1 and S2 to obtain a liquid level result. The method can be realized on the basis of the existing coaxial capacitive liquid level sensor, and the liquid level measurement result is more accurate while the simple structure of the sensor is kept.

Description

Technical Field

[0001] The present invention relates to the technical field of liquid level sensor detection, and in particular to a measurement method of a coaxial capacitive liquid level sensor taking edge effect into consideration. Background Art

[0002] Capacitive liquid level sensors sense the height change of the current liquid level according to the change of capacitance. They have the advantages of simple structure, easy reading, and no contamination of the liquid to be measured during operation. Nowadays, capacitive liquid level sensors have been widely used in the fields of electricity, chemical industry, machinery and other industries. At present, many in-depth studies have been conducted on the structure and measurement methods of capacitive liquid level sensors at home and abroad. In terms of structure, the application of a new type of non-contact edge field capacitance sensor not only solves the problem that the contact sensor electrode is easily contaminated, but also has high sensitivity and accuracy; a capacitive liquid level sensor with a flexible plate is designed, so that the capacitor plate can be bent and fits tightly with the outer wall of the liquid storage container to achieve continuous water level detection with high sensitivity; three identical capacitive sensors are combined into a whole, and the internal media are no liquid to be measured, full of liquid to be measured, and liquid whose level needs to be measured, respectively, eliminating the error caused by temperature drift and parasitic capacitance to the measurement result; the capacitive sensor adopts a segmented structure, and a reference plate is added to the bottom, which can maintain high-precision and reliable measurement when the dielectric constant of the measured medium changes due to temperature changes. In terms of measurement methods, the capacitance-to-digital converter AD7147 is used as a liquid level collector to achieve segmented capacitance measurement and improve measurement accuracy. For eccentric capacitance sensors, the conformal transformation method is used to achieve the transformation from eccentric circles to concentric circles, so that the analysis method of coaxial liquid level sensors can be used. Most studies ignore the edge effect between the inner and outer electrodes of the sensor. However, for coaxial liquid level sensors, this edge effect has a greater impact on the measurement accuracy of the sensor, so it is necessary to study the additional capacitance caused by the edge effect.

[0003] There are two main countermeasures for edge effects in the prior art. One is to directly change the structure of the sensor, such as adding two identical sensors, that is, using three sensors for measurement. Some also add a plate at the bottom and do corresponding calculations to offset the edge effect. These increase the volume of the original sensor, increase production costs, and also make the operation more complicated. The second is to use the conformal transformation method to calculate the additional capacitance caused by the edge effect. This method transforms the complex capacitive sensor model into an easily calculated field model, and then lists the Poisson equation that the field satisfies to solve the additional capacitance of the edge effect. However, this method needs to find a suitable transformation function when performing the conformal transformation, and the transformation process and solving the Poisson equation are relatively complicated. Summary of the invention

[0004] The invention provides a measurement method of a coaxial capacitive liquid level sensor taking edge effect into consideration, so as to overcome the technical problem.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A measurement method of a coaxial capacitive liquid level sensor considering edge effect, the specific steps comprising:

[0007] S1: Design a calculation formula for the capacitance above the liquid surface with air as the medium when measuring the liquid level using a coaxial capacitive liquid level sensor, and a calculation formula for the capacitance between the bottom of the liquid surface and the bottom of the inner electrode of the coaxial capacitive liquid level sensor model with the liquid to be measured as the medium;

[0008] S2: Using the finite element method, design a calculation formula for the capacitance between the bottom of the inner electrode and the bottom of the outer electrode of the coaxial capacitive liquid level sensor model considering the edge effect when measuring the liquid level;

[0009] S3: The total output capacitance is measured by the coaxial capacitive liquid level sensor;

[0010] S4: Calculate the liquid level result based on the total output capacitance and the calculation formulas in S1 and S2.

[0011] Furthermore, in S2, the process of designing a calculation formula for the capacitance between the bottom of the inner electrode and the bottom of the outer electrode of the coaxial capacitive liquid level sensor model considering the edge effect is as follows:

[0012] S21: dividing the bottom of the outer electrode of the coaxial capacitive liquid level sensor model to obtain a finite element discrete model composed of a number of finite elements;

[0013] S22: Calculate the capacitance of one of the finite elements, and then integrate it to obtain the capacitance between the bottom of the inner electrode and the bottom of the outer electrode of the coaxial capacitive liquid level sensor model considering the edge effect.

[0014] Furthermore, in S22, the capacitance of one of the finite elements is calculated and then integrated to obtain the capacitance between the bottom of the inner electrode and the bottom of the outer electrode of the coaxial capacitive liquid level sensor model considering the edge effect.

[0015] Assume that the bottom of the outer electrode is a circle with a radius of R2, take a distance dr from the center of the circle with a length of r, take the corresponding central angle dθ, and calculate the area S′ at a distance of r from the center of the circle based on dr and dθ, which can be expressed as:

[0016] S′=rdθ·dr (5)

[0017] Calculate the distance d from the outer electrode finite element to the bottom of the inner electrode, expressed as:

[0018]

[0019] Based on the angle α between the electric field line and the bottom of the outer electrode, S′ is corrected so that the corrected finite element of the outer electrode is perpendicular to the electric field line. The corrected finite element area S is:

[0020]

[0021] Where H is the distance between the bottom of the inner electrode and the bottom of the outer electrode;

[0022] Substituting formula (5) into formula (7), we get:

[0023]

[0024] According to the formula of parallel plate capacitor and equations (6) and (8), the capacitance of a single finite element is obtained as:

[0025]

[0026] The capacitance C′ of a single finite element is integrated over the entire edge space, including:

[0027] First, integrate r to obtain the size of the edge effect additional capacitance C″ in the area with an angle of dθ, expressed as:

[0028]

[0029] Then, by integrating θ from 0 to 2π, the capacitance C0 between the bottom of the inner electrode and the bottom of the outer electrode considering the edge effect is obtained, which is expressed as:

[0030]

[0031] Where ε0 is the dielectric constant of vacuum; ε w is the relative dielectric constant of water; H is the distance between the bottom of the inner electrode and the bottom of the outer electrode; R1 is the radius of the inner electrode; R2 is the radius of the outer electrode.

[0032] Furthermore, in S1, the calculation formula for the capacitance above the liquid surface with air as the medium is:

[0033]

[0034] The calculation formula for the capacitance between the bottom of the liquid surface and the bottom of the inner electrode with the liquid to be measured as the medium is:

[0035]

[0036] Where ε0 is the dielectric constant of vacuum; ε a is the relative dielectric constant of air; H1 is the length of the inner electrode immersed in the liquid to be measured; h1 is the height of the inner electrode in the air part above the liquid surface, and h1=h0-h, h0 is the total length of the outer electrode, and h is the liquid level height in the outer electrode.

[0037] Further, in S3, the total output capacitance measured by the coaxial capacitive liquid level sensor is expressed as:

[0038] C=C a +C w +C0 (4)

[0039] In the formula, C a C is the capacitance above the liquid surface with air as the medium; w It is the capacitance between the bottom of the liquid surface and the bottom of the inner electrode with the liquid to be measured as the medium; C0 is the capacitance between the bottom of the inner electrode and the bottom of the outer electrode considering the edge effect.

[0040] Beneficial effect: The present invention uses the finite element method to design a calculation formula for the capacitance between the bottom of the inner electrode and the bottom of the outer electrode of the coaxial capacitive liquid level sensor model considering the edge effect. Since the capacitance considering the edge effect can be calculated, a more accurate liquid level result can be obtained based on the calculation formula for the capacitance with air as the medium above the liquid surface and the calculation formula for the capacitance between the bottom of the inner electrode of the coaxial capacitive liquid level sensor model and the liquid to be measured as the medium below the liquid surface. This method can be implemented based on the existing coaxial capacitive liquid level sensor, which maintains the simple structure of the sensor while making the liquid level measurement result more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0042] Figure 1 It is a flow chart of a measurement method of a coaxial capacitive liquid level sensor taking edge effect into consideration in the present invention;

[0043] Figure 2 Schematic diagram of the structure of a coaxial capacitive liquid level sensor in an embodiment of the present invention;

[0044] Figure 3 is an equivalent circuit diagram of a coaxial capacitive liquid level sensor in an embodiment of the present invention;

[0045] Figure 4Schematic diagram of the finite element of the bottom of the outer electrode of the coaxial capacitive liquid level sensor according to an embodiment of the present invention;

[0046] Figure 5 A schematic longitudinal section diagram of the edge space of the coaxial capacitive liquid level sensor in an embodiment of the present invention;

[0047] Figure 6 Graph showing energy distribution at the bottom of the outer electrode of the coaxial capacitive liquid level sensor in an embodiment of the present invention.

[0048] In the figure: 1. inner electrode; 2. container; 3. liquid to be tested. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] This embodiment provides a measurement method of a coaxial capacitive liquid level sensor taking edge effect into consideration, such as Figure 1 As shown, the specific steps include:

[0051] S1: Design a calculation formula for the capacitance above the liquid surface with air as the medium when measuring the liquid level using a coaxial capacitive liquid level sensor, and a calculation formula for the capacitance between the bottom of the liquid surface and the bottom of the inner electrode of the coaxial capacitive liquid level sensor model with the liquid to be measured as the medium;

[0052] In a specific embodiment, in S1, a calculation formula for the capacitance above the liquid surface with air as the medium is designed based on the calculation formula for the output capacitance of the coaxial cylindrical capacitor, which is expressed as:

[0053]

[0054] The calculation formula for the capacitance between the bottom of the liquid surface and the bottom of the inner electrode of the coaxial capacitive liquid level sensor with the liquid to be measured as the medium is:

[0055]

[0056] Where ε0 is the dielectric constant of vacuum; ε a is the relative dielectric constant of air; H1 is the length of the inner electrode immersed in the liquid to be measured, and H1=h0-H-h1; h1 is the height of the inner electrode in the air part above the liquid surface, and h1=h0-h, h0 is the total length of the outer electrode, and h is the liquid level height in the outer electrode.

[0057] Specifically, Figure 1 As shown, the effective measurement liquid level range of the coaxial capacitive liquid level sensor is H~h0.

[0058] S2: Using the finite element method, design a calculation formula for the capacitance between the bottom of the inner electrode and the bottom of the outer electrode of the coaxial capacitive liquid level sensor when measuring the liquid level, taking into account the edge effect;

[0059] S3: The total output capacitance is measured by the coaxial capacitive liquid level sensor;

[0060] In a specific embodiment, in S3, the total output capacitance measured by the coaxial capacitive liquid level sensor is expressed as:

[0061] C=C a +C w +C0 (4)

[0062] In the formula, C a C is the capacitance above the liquid surface with air as the medium; w It is the capacitance between the bottom of the liquid surface and the bottom of the inner electrode with the liquid to be measured as the medium; C0 is the capacitance between the bottom of the inner electrode and the bottom of the outer electrode considering the edge effect.

[0063] Specifically, the equivalent circuit of the coaxial capacitive liquid level sensor considering the edge effect is as follows: Figure 3 As shown in the figure, it can be seen that C a , C w and C0 are connected in parallel, J and K represent the inner electrode and outer electrode of the coaxial capacitive liquid level sensor respectively. When the liquid level gradually rises, the immersion depth H1 of the inner electrode in the water will increase accordingly, and the height h1 of the inner electrode in the air above the liquid surface will decrease accordingly, resulting in a change in the capacitance between the J and K plates.

[0064] In a specific embodiment, in S2, the process of designing a calculation formula for the capacitance between the bottom of the inner electrode and the bottom of the outer electrode taking into account the edge effect using the finite element method is:

[0065] S21: dividing the bottom of the outer electrode of the coaxial capacitive liquid level sensor to obtain a finite element discrete model composed of a number of finite elements;

[0066] S22: Calculate the capacitance of one of the finite elements, and integrate it to obtain the capacitance between the bottom of the inner electrode and the bottom of the outer electrode taking the edge effect into consideration.

[0067] Specifically, C a and C wIt can be obtained according to formula (2) and formula (3), and the capacitance C0 considering the edge effect cannot be directly obtained by using the calculation formula of the output capacitance of the coaxial cylindrical capacitor because it is not a coaxial cylindrical capacitor model. In this embodiment, since the bottom of the inner electrode is parallel to the bottom of the outer electrode, C0 is calculated based on the calculation idea of ​​the parallel plate capacitor. However, the relative area difference between the bottom of the inner electrode and the bottom of the outer electrode is very large, and it cannot be simply calculated using the formula of the parallel plate capacitor. Therefore, the finite element method is used to decompose the bottom of the outer electrode into a discrete model composed of several small finite elements, and then the capacitance calculation formula of each finite element is improved based on the parallel plate capacitor. Then, by integrating it, the capacitance C0 considering the edge effect can be obtained. One of the finite elements is as follows: Figure 4 Shown as shaded area.

[0068] Specifically, the finite element method is a numerical calculation method based on mathematical analysis, which is mainly used to solve physical problems under various boundary conditions. It simplifies complex actual physical problems into discrete models composed of a large number of small finite elements. In this way, the entire problem is converted into a large-scale set of algebraic equations, and the results are obtained by solving this set of algebraic equations.

[0069] In a specific embodiment, in S22, the capacitance of one of the finite elements is calculated and then integrated to obtain the capacitance between the bottom of the inner electrode and the bottom of the outer electrode of the coaxial capacitive liquid level sensor taking the edge effect into consideration as follows:

[0070] like Figure 4 As shown, the bottom of the outer electrode is assumed to be a circle with a radius of R2, a distance dr from the center of the circle is taken as r, and the corresponding central angle is taken as dθ. Based on dr and dθ, the area S′ at the distance r from the center of the circle is calculated, which is expressed as:

[0071] S′=rdθ·dr (5)

[0072] like Figure 5 As shown, it is a schematic diagram of the longitudinal section along the axis of the inner and outer electrodes in the edge space. Figure 5 In the figure, the arrows are approximate electric field lines, J is the bottom of the inner electrode, K is the bottom of the outer electrode, and S′ is Figure 4 The shaded area is Figure 5 It is known that the distance d from the outer electrode finite element to the bottom of the inner electrode can be calculated as:

[0073]

[0074] Specifically, the distance d can be approximated as the distance between the two planes facing each other. In addition, since the two parallel plates are perpendicular to the electric field lines when using the parallel plate capacitor formula for calculation, D in the formula is the length of the electric field line between the two plates. For this model, the line connecting the two planes can be approximated as the electric field line, that is, d in formula (6) is the length of the electric field line. However, S′ needs to be corrected based on the angle α between the electric field line and the bottom of the outer electrode, as follows: Figure 5 As shown, the modified external electrode finite element is made perpendicular to the electric field line, and the modified finite element area S is:

[0075]

[0076] Where H is the distance between the bottom of the inner electrode and the bottom of the outer electrode;

[0077] Substituting formula (5) into formula (7), we get:

[0078]

[0079] According to the formula of parallel plate capacitor and equations (6) and (8), the capacitance of a single finite element is obtained. The formula of parallel plate capacitor is:

[0080]

[0081] Where D is the length of the electric field lines between the two plates, ε is the dielectric constant of the dielectric between the inner and outer electrodes; S is the facing area of ​​the two plates.

[0082] The capacitance of a single finite element is expressed as:

[0083]

[0084] The capacitance C′ of a single finite element is integrated over the entire edge space, including:

[0085] First, integrate r to obtain the size of the edge effect additional capacitance C″ in the area with an angle of dθ, expressed as:

[0086]

[0087] Specifically, for the upper and lower limits of the r integral, after a large number of finite element simulations, it is found that in the edge space, on any horizontal plane, the energy is mainly concentrated on the radius In the circle, such as Figure 6 As shown, when When the energy is almost zero, and because the radius R1 of the inner electrode is very small relative to R2 (R2>>R1), the upper and lower limits of the integral of r can be determined as R1 and

[0088] Then integrate θ. Since the edge space is a complete cylinder, we only need to integrate θ from 0 to 2π to obtain the capacitance C0 between the bottom of the inner electrode and the bottom of the outer electrode considering the edge effect, which is expressed as:

[0089]

[0090] Where ε0 is the dielectric constant of vacuum; ε w is the relative dielectric constant of the liquid to be measured; H is the distance between the bottom of the inner electrode and the bottom of the outer electrode; R1 is the radius of the inner electrode; R2 is the radius of the outer electrode.

[0091] Specifically, since the minimum measurement value of the liquid level sensor is H, that is, the liquid must submerge the bottom of the inner electrode for the sensor to work properly, the additional capacitance caused by the edge effect has nothing to do with the liquid level, and the medium of the capacitance is liquid.

[0092] S4: Calculate the liquid level result based on the total output capacitance and the calculation formulas in S1 and S2.

[0093] Specifically, in this embodiment, Figure 2 As shown in FIG. 1 , the coaxial capacitive liquid level sensor includes a container 2 as an outer electrode, an inner electrode 1 and a peripheral circuit (not shown in the figure). The container 2 is filled with a liquid 3 to be measured. The inner electrode is a solid stainless steel round tube and is suspended in the container. The axis is coaxial with the axis of the container. The space between the inner and outer electrodes is filled with the liquid to be measured. The total output capacitance C can be directly measured by the peripheral circuit. According to formulas (2), (3), (4) and (11), C0 can be obtained by formula (11), and C a h1 in the figure is the liquid level result to be obtained, C w Substituting H1=h0-H-h1 into formula (3), there is only one unknown variable, h1, and the other parameters can be obtained through measurement. Therefore, it is only necessary to solve the linear equation to obtain h1. Since h=h0-h1, the final liquid level result can be obtained.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A measurement method of a coaxial capacitive liquid level sensor considering edge effect, characterized in that: The specific steps include: S1: Design a calculation formula for the capacitance above the liquid surface with air as the medium when measuring the liquid level using a coaxial capacitive liquid level sensor, and a calculation formula for the capacitance between the bottom of the liquid surface and the bottom of the inner electrode of the coaxial capacitive liquid level sensor model with the liquid to be measured as the medium; S2: Using the finite element method, design a calculation formula for the capacitance between the bottom of the inner electrode and the bottom of the outer electrode of the coaxial capacitive liquid level sensor model considering the edge effect when measuring the liquid level; S3: The total output capacitance is measured by the coaxial capacitive liquid level sensor; S4: Calculate the liquid level result based on the total output capacitance and the calculation formulas in S1 and S2.

2. The measurement method of the coaxial capacitive liquid level sensor considering the edge effect according to claim 1 is characterized in that: In S2, the process of designing the calculation formula of the capacitance between the bottom of the inner electrode and the bottom of the outer electrode of the coaxial capacitive liquid level sensor model considering the edge effect using the finite element method is as follows: S21: dividing the bottom of the outer electrode of the coaxial capacitive liquid level sensor model to obtain a finite element discrete model composed of a number of finite elements; S22: Calculate the capacitance of one of the finite elements, and then integrate it to obtain the capacitance between the bottom of the inner electrode and the bottom of the outer electrode of the coaxial capacitive liquid level sensor model considering the edge effect.

3. The measurement method of the coaxial capacitive liquid level sensor considering the edge effect according to claim 2 is characterized in that: In S22, the capacitance of one of the finite elements is calculated and then integrated to obtain the capacitance between the bottom of the inner electrode and the bottom of the outer electrode of the coaxial capacitive liquid level sensor model considering the edge effect. The process is: Assume that the bottom of the outer electrode is a circle with a radius of R2, take a distance dr from the center of the circle with a length of r, take the corresponding central angle dθ, and calculate the area S′ at a distance of r from the center of the circle based on dr and dθ, which can be expressed as: S′=rdθ·dr (5) Calculate the distance d from the outer electrode finite element to the bottom of the inner electrode, expressed as: Based on the angle α between the electric field line and the bottom of the outer electrode, S′ is corrected so that the corrected finite element of the outer electrode is perpendicular to the electric field line. The corrected finite element area S is: Where H is the distance between the bottom of the inner electrode and the bottom of the outer electrode; Substituting formula (5) into formula (7), we get: According to the formula of parallel plate capacitor and equations (6) and (8), the capacitance of a single finite element is obtained as: The capacitance C′ of a single finite element is integrated over the entire edge space, including: First, integrate r to obtain the size of the edge effect additional capacitance C″ in the area with an angle of dθ, expressed as: Then, by integrating θ from 0 to 2π, the capacitance C0 between the bottom of the inner electrode and the bottom of the outer electrode considering the edge effect is obtained, which is expressed as: Where ε0 is the dielectric constant of vacuum; ε w is the relative dielectric constant of water; H is the distance between the bottom of the inner electrode and the bottom of the outer electrode; R1 is the radius of the inner electrode; R2 is the radius of the outer electrode.

4. The measurement method of the coaxial capacitive liquid level sensor considering the edge effect according to claim 1, characterized in that: In S1, the calculation formula for the capacitance above the liquid surface with air as the medium is: The calculation formula for the capacitance between the bottom of the liquid surface and the bottom of the inner electrode with the liquid to be measured as the medium is: Where ε0 is the dielectric constant of vacuum; ε a is the relative dielectric constant of air; H1 is the length of the inner electrode immersed in the liquid to be measured; h1 is the height of the inner electrode in the air part above the liquid surface, and h1=h0-h, h0 is the total length of the outer electrode, and h is the liquid level height in the outer electrode.

5. The measurement method of the coaxial capacitive liquid level sensor considering the edge effect according to claim 4 is characterized in that: In S3, the total output capacitance measured by the coaxial capacitive liquid level sensor is expressed as: C=C a +C w +C0 (4) In the formula, C a C is the capacitance above the liquid surface with air as the medium; w It is the capacitance between the bottom of the liquid surface and the bottom of the inner electrode with the liquid to be measured as the medium; C0 is the capacitance between the bottom of the inner electrode and the bottom of the outer electrode considering the edge effect.

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