A method for configuring electrode spacing and attenuation frequency band in in-situ calibration of a permanent magnetic sodium flowmeter without vortex generator

Abstract

In the in-situ calibration of a permanent-magnet sodium flowmeter without vortex shedders, a matching method between the electrode spacing and the attenuation frequency band during the in-situ subtraction of multiple pairs of electrodes is presented, providing a better-quality signal for subsequent cross-correlation calculations, thereby improving the accuracy of the in-situ calibration of the permanent-magnet sodium flowmeter without vortex shedders. Specifically, a derivation of multiple pairs of electrodes is presented, linking the electrode spacing to the signal frequency band, and providing a quantitative relationship between the spacing between the cross-correlation electrodes performing in-situ subtraction and the frequency band of the electrode output signal after the in-situ subtraction. In other words, a critical frequency value for attenuating low-frequency signals and enhancing high-frequency signals is provided. This allows the rational configuration of the spacing between the cross-correlation electrodes performing in-situ subtraction to eliminate low-frequency noise, improve the quality of the signal used for cross-correlation calculations, and improve the accuracy of the in-situ calibration of the permanent-magnet sodium flowmeter without vortex shedders.

Description

Technical Field

[0001] The present invention relates to the field of flow detection, in particular to a method for configuring electrode spacing and attenuation frequency band in in-situ calibration of a permanent magnet sodium flowmeter without a vortex generator. Background Art

[0002] The sodium-cooled fast reactor is an advanced fourth-generation nuclear reactor type that can increase the utilization rate of uranium resources to 60%-70%. Sodium-cooled fast reactors often adopt a sodium-sodium-water three-circuit design. Liquid metal sodium with superior performance is used as the coolant and heat transfer agent for the core. In order to ensure the safe operation of the fast reactor, a permanent magnet sodium flowmeter based on Faraday's law of electromagnetic induction is used to monitor the flow of sodium in the primary and secondary circuits. The measuring electrodes of the permanent magnet sodium flowmeter are installed on the pipe cross section at both ends of the diameter perpendicular to the magnetic field, picking up the induced electromotive force generated by the conductive fluid cutting the magnetic flux lines, the amplitude of which is proportional to the flow rate, that is, Where D is the pipe inner diameter, B is the magnetic flux density, and k is the instrument factor. Because the temperature of liquid sodium is constantly between 250°C and 550°C, permanent magnet sodium flowmeters operating in high-temperature environments for extended periods of time can experience demagnetization of their permanent magnets, resulting in a decrease in magnetic flux density and a deviation from the standard flow rate. Therefore, permanent magnet sodium flowmeters must be regularly calibrated to eliminate these deviations. However, permanent magnet sodium flowmeters installed within the stack are not removable, so in-situ calibration is essential. To this end, additional electrodes (called cross-correlation electrodes, or simply correlation electrodes) are added to the permanent magnet sodium flowmeter, and in-situ calibration is achieved using the cross-correlation method.

[0003] The core of the cross-correlation method is signal delay estimation. The cross-correlation electrodes collect the AC signal generated by the fluid velocity fluctuation. The time it takes for the fluid to travel between the front and rear cross-correlation electrodes (two pairs of signal electrodes on the same sensor or two pairs of signal electrodes arranged on the front and rear sensors respectively) is estimated based on the similarity of the signals to reflect the average velocity of the fluid, that is, Where L is the distance between the cross-correlated electrodes, and τ is the signal delay (transit time, or delay time).

[0004] The specific in-situ calibration methods for permanent magnetic sodium flowmeters of different calibers vary. A vortex generator is installed in a permanent magnetic sodium flowmeter with a smaller caliber to enhance the disturbance signal and facilitate the implementation of the cross-correlation method.

[0005] For large-diameter permanent magnetic sodium flowmeters (e.g., DN150, DN200, and DN300), the flow rates within the pipeline are typically high. Adding a barrier to enhance fluid disturbance can cause pressure loss and other issues, and there's also the risk of the barrier falling off. Therefore, in-situ calibration can only be performed using the disturbance within the fluid. However, because the signal intensity is far less than that generated by the barrier and is highly random, large signal repeatability errors can occur, severely impacting measurement accuracy. Furthermore, when the magnetic field of a permanent magnetic sodium flowmeter is short, the Lorentz force distorts the magnetic field, deforming the velocity distribution of the fluid across its cross section and inevitably introducing nonlinearity into its measurement characteristics. This nonlinearity also manifests itself in in-situ calibration using the cross-correlation method.

[0006] In order to better realize the in-situ calibration of large-caliber permanent-magnet sodium flowmeter, it is necessary to solve the problems of serious nonlinear error and large repeatability error. Xinlong Yu et al. disclosed an in-situ calibration of a permanent-magnet sodium flowmeter without a Bluff Body based on multi-pair electrode signal subtraction (Xin-Long Yu, Ke-Jun Xu, In Situ Calibration of a Permanent-Magnet Sodium Flowmeter Without a Bluff Body Based on Multi-Pair Electrode Signal Subtraction, IEEE Transactions on Instrumentation and Measurement, VOL.71, 2022). This document adds multiple pairs of cross-correlated electrodes to the sensor of the permanent-magnet sodium flowmeter without a vortex body, deeply explores the components of the output signal of the cross-correlated electrodes, and proposes to eliminate the basic noise, improve the signal-to-noise ratio and improve the repeatability error by subtracting the electrode pairs in the same direction from the perspective of multi-electrode fusion in the time domain; at the same time, attenuate the low-frequency signal and enhance the high-frequency signal, so that the flow rate reflected by the electrode output signal is closer to the standard flow rate, thereby correcting the nonlinear error. Then, a cross-correlation calculation is performed based on the signals after the same-direction subtraction, achieving in-situ calibration of the permanent magnetic sodium flowmeter. However, the document does not address how to optimize the spacing between the cross-correlation electrodes for subtraction, nor does it provide a relationship between the spacing between two pairs of same-direction subtraction electrodes and the frequency band of the output signal after the same-direction subtraction. Consequently, it is impossible to rationally configure the spacing between the subtraction electrodes to more effectively filter out low-frequency signals. Summary of the Invention

[0007] The technical solution of the present invention is:

[0008] The present invention provides a method for matching the electrode spacing and attenuation frequency band during the multi-pair electrode subtraction phase in the in-situ calibration of a vortex-free permanent magnetic sodium flowmeter. This method provides a better quality signal for subsequent cross-correlation calculations, thereby improving the accuracy of the in-situ calibration of the vortex-free permanent magnetic sodium flowmeter. Specifically, the present invention provides a derivation of multiple pairs of electrodes, links the electrode spacing to the signal frequency band, and provides a quantitative relationship between the spacing between the cross-correlation electrodes performing the in-situ subtraction and the frequency band of the output signal after the in-situ subtraction. This provides a critical frequency value for attenuating low-frequency signals and enhancing high-frequency signals. This allows the rational configuration of the spacing between the cross-correlation electrodes performing the in-situ subtraction to eliminate low-frequency noise, improve the quality of the signal used for cross-correlation calculations, and improve the accuracy of the in-situ calibration of the vortex-free permanent magnetic sodium flowmeter.

[0009] The advantages of the present invention are:

[0010] This patent provides a quantitative relationship between the spacing between the mutually correlated electrodes that are subtracted in the same direction and the frequency band of the electrode output signal after the same direction subtraction, that is, the critical frequency value for attenuating low-frequency signals / enhancing high-frequency signals is provided. In this way, low-frequency noise of different frequencies can be filtered out by configuring (arranging) the electrode spacing, so as to more effectively attenuate low-frequency noise and eliminate the nonlinear error existing in the in-situ calibration of the permanent magnet sodium flowmeter without vortex generator from the source of the signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 The following are the cross-sectional and side views of the sensor of the DN150 permanent magnetic sodium flowmeter without vortex generator;

[0012] Figure 2 It is the signal spectrum diagram under different flow rates;

[0013] Figure 3 It is the actual value and ideal value of the phase difference between the two cross-correlated signals. Specific implementation methods

[0014] The present invention will be further described below in conjunction with the accompanying drawings.

[0015] The sensor of the vortex-free permanent magnetic sodium flowmeter uses a cast aluminum-nickel-cobalt permanent magnet alloy with high magnetic energy, high stability, high temperature resistance, and radiation resistance as the permanent magnet. Electromagnetic pure iron is used for the yoke and magnetic poles, and the surface is treated with anti-oxidation. The length of the permanent magnet pole face is 2D (D is the inner diameter of the pipe). The schematic diagram of the cross-correlation electrode arrangement used for in-situ calibration in the DN150 vortex-free permanent magnetic sodium flow sensor is shown in the figure below. Figure 1 shown.

[0016] Electrodes 1-1 and 1-2 are a pair of cross-correlation electrodes (hereinafter referred to as electrode C1, other electrodes are similar), measuring one signal. The combination of electrode C1 and electrode C2 is used for cross-correlation measurement, hereinafter referred to as electrode group C1&2, other electrode combinations are similar. These cross-correlation electrodes are placed at a 45° angle (with Figure 1 The horizontal line in the center-right image serves as the reference line for the angle. The weld is welded perpendicularly to the pipe wall, primarily due to the higher signal strength at a 45-degree angle. Inside the DN150 pipe, electrode C1 is located 50 mm upstream of the magnetic centerline, while C2 is 75 mm downstream. Electrodes C2, C3, C4, and C5 are evenly spaced, with a spacing of 37.5 mm.

[0017] When performing in-situ calibration on a permanent magnetic sodium flowmeter without a vortex generator, the cross-correlation electrode collects the electrical signal generated by the turbulent pulsation velocity, that is, the voltage fluctuation signal generated by the vortex inside the fluid cutting the magnetic flux lines. Vortices of different sizes will produce signals of different frequencies. Therefore, the electrical signal picked up by the cross-correlation electrode is a broadband signal without a fixed main frequency. Moreover, the energy of signals of different frequencies is different, which is mainly manifested as follows: the energy of the low-frequency signal is large, and the energy of the high-frequency signal is small, such as Figure 2 The signal spectrum at various flow rates is shown in FIG.

[0018] According to Fourier transform, a broadband signal can be expressed as a linear combination of multiple narrowband signals, namely:

[0019]

[0020] Where A i and B i is the signal amplitude of each frequency, f i is the signal frequency, θ i is the corresponding frequency f i The phase difference between the first signal and the

[0021] If the flow velocity is uniformly distributed across the pipe cross section—that is, the fluid velocity across the cross section is assumed to be average—then the time it takes for the fluid at each point on the cross section to reach the next pair of related electrodes is the same. This is reflected in the signal as equal transit times for all frequencies. According to the phase-frequency characteristic of the cross-power spectral density, θ(f) = 2πfτ, when the transit time τ is constant, the phase difference θ(f) is a single-valued function that varies with frequency and is a straight line passing through zero.

[0022] When subtracting sinusoidal signals, the smaller the phase difference between the two, the more likely the signal obtained by subtraction will be attenuated. As the phase difference increases, the attenuation trend will gradually weaken and turn into an enhancement trend. Specifically, according to the properties of sinusoidal signals, when the phase difference between the two signals does not exceed π / 3, that is, when the phase difference is in the range [0, π / 3) ∪ (5π / 3, 2π], the energy of the subtracted signal will be attenuated; when the phase difference exceeds π / 3, that is, when the phase difference is in the range [π / 3, 5π / 3], the energy will be enhanced. This can be demonstrated from the signal range, as shown in Equation (2).

[0023]

[0024] When the phase difference θ∈[0,π / 3)∪(5π / 3,2π], which is equivalent to the phase difference θ∈(-π / 3,π / 3):

[0025]

[0026] According to formula (2), -1<sinx-sin(x-θ)<1. Therefore, when the phase difference between the two signals does not exceed π / 3, the energy of the signal obtained by subtraction will be attenuated.

[0027] When the phase difference θ∈[π / 3,5π / 3]:

[0028]

[0029] Therefore, when the phase difference between the two signals is greater than π / 3, the energy of the signal obtained by subtraction will be enhanced;

[0030] For the in-situ calibration of the permanent magnetic sodium flowmeter without vortex generator, multiple pairs of cross-correlation electrodes (more than two pairs) are arranged in the same direction on the sensor, and the output signals u1, u2…u of multiple cross-correlation electrodes can be collected simultaneously. n , the latter signal is always a delay of the previous signal, and any two cross-correlated electrode output signals u1 and u2 always have a low-frequency phase difference less than π / 3. Therefore, the low-frequency signal of u1(t)-u2(t) is likely to be attenuated, while the high-frequency signal is enhanced.

[0031] Considering the distribution of fluid velocity across the pipe cross section, the velocity of low-frequency signals exceeds the standard value, while the velocity of high-frequency signals approaches the standard value. Therefore, based on the inverse relationship between flow velocity and transit time, the transit time of low-frequency signals is less than the standard value. Based on the relationship between phase difference θ(f), frequency f, and transit time τ (θ(f) = 2πfτ), when the phase difference is π / 3, the smaller the transit time, the larger the corresponding frequency value, meaning the wider the frequency band of the attenuated signal. Furthermore, at a fixed frequency, the smaller the transit time and the smaller the phase difference, the greater the amplitude attenuation.

[0032] In the above example, when the phase difference between the two signals is in [0,π / 3)∪(5π / 3,2π], the signals will be attenuated. The calculation formula for the attenuation band is given below.

[0033] First, we study the attenuation band in the low frequency band, that is, the case when the phase difference is in [0,π / 3].

[0034] According to θ(f)=2πfτ≤π / 3, we can get the attenuation band of the low frequency band as [0,f0], where f0 is the critical frequency, that is, θ(f)=2πf0τ=π / 3, thus we get:

[0035]

[0036] In the formula, the transit time τ can be obtained by performing cross-correlation calculation on the output signals of two pairs of cross-correlated electrodes. Therefore, the formula calculates the actual critical frequency.

[0037] When τ in equation (5) is the ideal transit time τ s (i.e. the standard value of the transit time), according to the relationship τ between the ideal transit time and the spacing L between the two pairs of cross-correlated electrodes and the average flow velocity v of the pipe cross section s =L / v, we can get

[0038]

[0039] Or according to the ideal transit time τ s The distance L between the two pairs of correlated electrodes, the inner diameter of the pipe D and the reference (standard) flow rate Q s The relationship between τ s =πD 2 L / (4Q s ), we can get

[0040]

[0041] The reference flow rate and average flow velocity in equations (6) and (7) are obtained from calibration experiments, that is, the actual average flow rate and flow velocity in the pipeline. Therefore, the ideal critical frequency of the low-frequency attenuation band, or the reference critical frequency, is calculated by equations (6) and (7).

[0042] Next, let's consider the high-frequency attenuation band [f1, f2], where f1 is the lower critical frequency and f2 is the upper critical frequency. This is the case when the phase difference lies within [5π / 3, 2π]. In this case, 5π / 3 ≤ 2πfτ ≤ 2π, and 5 / (6τ) ≤ f ≤ 1 / τ, so the signal within this frequency band is also attenuated.

[0043] According to θ(f) = 2πf1τ = 5π / 3 and θ(f) = 2πf2τ = 2π, the lower and upper critical frequencies f1 and f2 of the high-frequency attenuation band can be determined, thus obtaining

[0044]

[0045]

[0046] Wherein, the transit time τ is obtained by cross-correlating the output signals of two pairs of cross-correlated electrodes. Therefore, f1 and f2 calculated by equations (8) and (9) are the actual critical frequencies.

[0047] According to the ideal transit time τ s The relationship between the distance L between the two pairs of cross-correlated electrodes and the average flow velocity v in the pipe cross section is τ s =L / v, thus we get

[0048]

[0049]

[0050] Or according to the ideal transit time τ s The distance L between the two pairs of correlated electrodes, the inner diameter of the pipe D and the reference (standard) flow rate Q s The relationship between τ s =πD 2 L / (4Q s ), thus we get

[0051]

[0052]

[0053] The reference flow rate and average flow velocity in equations (10), (11), (12), and (13) are obtained from calibration experiments. Therefore, what is calculated by equations (10), (11), (12), and (13) are the ideal critical frequencies of the lower and upper limits of the high frequency band, or the reference critical frequencies.

[0054] The following example illustrates the calculation of the attenuation band.

[0055] For example, the reference flow rate (standard flow rate) of the DN150 vortex-free permanent magnetic sodium flowmeter is 280m 3 / h, the flow rate is 4.4m / s. When the distance between two pairs of cross-correlation electrodes subtracting in the same direction is L = 112.5mm, according to the relationship between the transit time τ, the electrode spacing L and the flow rate v, the ideal value of the transit time is calculated to be: τ s= L / v = 112.5 / 4.4 = 25.57ms. When θ(f) = 2πfτ≤π / 3, we can obtain: f≤f0 = 6.5Hz, and all signals with frequencies below 6.5Hz will be attenuated.

[0056] The reference flow rate is 280m 3 / h signal spectrum, such as Figure 2 As shown in Figure 1, the main frequency band of the signal is around 5 Hz. Therefore, after the collected cross-correlated electrode output signals are subtracted, the low-frequency band signal will be attenuated and the high-frequency band signal will be enhanced.

[0057] In addition, when the phase difference is in [5π / 3, 2π], that is, 5π / 3≤2πfτ≤2π, 5 / (6τ)≤f≤1 / τ, the signal will also be attenuated. Here, the attenuation band of the high frequency band is considered. When the reference flow is 280m 3 / h, τ=25.57ms, and the signal attenuation band is 32.6~39.1Hz. This band is in the higher frequency range, and the signal amplitude is very weak in this frequency range, such as Figure 2 As shown in Figure 2, the signal in this frequency range contributes less to the transit time, and being attenuated does not affect the accuracy of the transit time estimation. Therefore, the present invention focuses on the attenuation band in the low-frequency region.

[0058] Next, we consider the effect of flow rate changes on the critical frequency.

[0059] From formula (7), it can be seen that as the flow rate increases, the ideal value of the transit time gradually decreases and f0 gradually increases, that is, the greater the flow rate, the wider the attenuated low-frequency signal band. For example, when the flow rate is 100m 3 / h, the attenuated signal frequency band after the electrodes are subtracted in the same direction is 0-2.3Hz; when the flow rate is 280m 3 When the flow rate is 0.5 GHz / h, the attenuated signal frequency band after the electrodes are subtracted in the same direction is 0-6.5 Hz, as shown in Table 1. This matches the characteristic that the frequency band where the cross-correlation flow rate is greater than the standard flow rate gradually increases with increasing flow rate, or in other words, the frequency band where the cross-correlation flow rate is close to the standard flow rate gradually shifts to the high frequency band with increasing flow rate.

[0060] More importantly, based on the physical model of the average velocity "M-type" distribution, the cross-correlation flow of the low-frequency signal is greater than the standard flow value, and the cross-correlation flow of the high-frequency signal is close to the standard flow value, that is, the phase difference of the low-frequency signal is smaller than the ideal value (the phase difference is proportional to the transit time, and the transit time is inversely proportional to the flow), such as Figure 3As shown. According to the formula θ(f) = 2πfτ, at this time, the actual transit time calculated is also less than the ideal value. And the larger the flow rate, the more obvious the "M-shaped" distribution, the greater the nonlinearity, the greater the difference between the phase difference of the low-frequency signal and the ideal value, and the smaller the actual transit time. After subtracting the two pairs of cross-correlated electrode signals, the low-frequency band signal is suppressed more. For example, the flow rate is 280m 3 At 1.5 GHz, the actual transit time calculated by cross-correlation is 18.8 ms, and the value of f0 becomes 8.9 Hz. The results at other flow rates are shown in Table 1.

[0061] Next, we consider the effect of the spacing between two pairs of electrodes performing same-direction subtraction on the signal attenuation effect after same-direction subtraction.

[0062] From equations (6) and (7), it can be seen that as the distance L between the cross-correlation electrodes used for in-phase subtraction decreases, the transit time gradually shortens and the f0 value gradually increases, as shown in Table 1. For example, when the distance is 75 mm, the flow rate is 280 m 3 The actual transit time for the flow rate is 11.3 ms, and f0 is approximately 14.8 Hz. This is close to the critical frequency of the correction band of 15.5 Hz calculated in the concurrently filed invention (Xu Kejun and Yu Xinlong, "A Method for Calculating the Correction Band for In-Situ Calibration of a Permanent Magnet Sodium Flowmeter Without a Vortex Generator"). The same is true for other flow rates, as shown in Table 2.

[0063] In other words, by configuring and optimizing the spacing between the electrodes for co-directional subtraction, the signal attenuation band after multi-electrode co-directional subtraction can be aligned with the frequency band causing nonlinearity. This means that the critical value of the attenuation band can be matched to the critical value of the calibration band, thereby completely attenuating the signal causing nonlinearity. Simultaneously, high-frequency signals can be enhanced. Low-frequency signals are the primary cause of nonlinearity and large repeatability errors, while high-frequency signals are more useful. Therefore, the co-directional subtraction method of two pairs of cross-correlated electrode signals is a method for adaptively correcting nonlinearity and improving repeatability, especially for correcting nonlinearity.

[0064] Table 1 Ideal and actual values ​​of critical frequency at different electrode spacings and flow rates

[0065]

[0066] Table 2 Comparison of the critical value of attenuation band for multi-electrode same-direction subtraction and the critical value of cross-correlation signal correction band

[0067]

[0068] Here, it is necessary to compare and explain the correction band and the attenuation band. (1) The difference between the two: The correction band is the signal band used for cross-correlation calculation in order to obtain a more accurate in-situ calibration result, that is, the frequency band from f0 to a certain high frequency; in other words, the correction band is the frequency band where the cross-correlation flow is close to the standard flow; for the specific calculation method, please refer to the invention patent applied for at the same time (Xu Kejun, Yu Xinlong, A method for calculating the correction band in the in-situ calibration of a permanent magnetic sodium flowmeter without a vortex generator). The attenuation band described in the present invention is: if used for cross-correlation calculation, it will cause the accuracy of the in-situ calibration to deteriorate (mainly causing large nonlinear errors). For the low frequency band, it is the frequency band from 0 to f0; in other words, the attenuation band is the frequency band where the cross-correlation flow is greater than the standard flow. (2) The connection between the two: f0 in the correction band is equal to or very close to f0 in the attenuation band. In other words, the correction band critical value gives the target of optimizing the electrode spacing configuration. By configuring the electrode spacing, the attenuation band critical value is matched with it, thereby completely attenuating the nonlinearity.

[0069] The above analysis leads to the following conclusions: by configuring or optimizing the spacing between electrodes for same-direction subtraction, the critical value of the attenuation band can be matched with the critical value of the calibration band (equal or close). In this way, by selecting a suitable spacing between electrodes, the signal causing nonlinear errors can be completely attenuated by same-direction subtraction of multiple pairs of electrodes.

[0070] Furthermore, as shown in Table 1, as the spacing between the in-phase subtraction cross-correlation electrodes decreases, the frequency band of the signal attenuation after subtraction widens, which facilitates nonlinearity correction. However, excessive attenuation of the signal frequency band can also cause signal loss, hindering signal repeatability. Based on the existing experimental conditions and results, a spacing of approximately 75 mm between the two pairs of in-phase subtraction cross-correlation electrodes achieves optimal results, eliminating nonlinearity while minimizing signal attenuation.

Claims

1. A method for configuring the electrode spacing and attenuation band in the in-situ calibration of a permanent magnetic sodium flowmeter without a vortex generator. Multiple pairs of cross-correlation electrodes are arranged in the same direction on the sensor, and the output signals u1, u2, ..., u of multiple cross-correlation electrodes are collected simultaneously. n , the latter signal is the delay of the former signal, and the phase difference of the low-frequency signal of any two cross-correlated electrode output signals u1 and u2 is always less than π / 3; therefore, the low-frequency signal of u1(t)-u2(t) will be attenuated, while the high-frequency signal will be enhanced; the characteristics are: When the phase difference between the two signals is in [0,π / 3)∪(5π / 3,2π], the signal will be attenuated. The calculation formula of the attenuation band is given as follows: First, in the low-frequency attenuation band [0, f0]; that is, when the phase difference is at [0, π / 3]; According to θ(f)=2πfτ≤π / 3, the attenuation band of the low frequency band is [0,f0], where f0 is the critical frequency, that is, θ(f)=2πf0τ=π / 3, thus we get: In the formula, the delay time τ is obtained by cross-correlating the output signals of two pairs of cross-correlated electrodes. The actual critical frequency is calculated by formula (1); When τ in equation (1) is the ideal transit time τ s According to the relationship between the ideal transit time, the distance L between the two pairs of cross-correlated electrodes, and the average flow velocity v in the pipe cross section, τ s =L / v, we get Or according to the ideal transit time τ s The distance L between the two pairs of correlated electrodes, the inner diameter of the pipe D and the reference flow Q s The relationship between τ s =πD 2 L / (4Q s ),get The reference flow rate and average flow velocity in equations (2) and (3) are obtained from calibration experiments. The ideal critical frequency of the low-frequency attenuation band is calculated by equations (2) and (3); Secondly, the attenuation band in the high frequency band is [f1, f2], where f1 is the lower critical frequency of the high frequency band attenuation band, and f2 is the upper critical frequency of the high frequency band attenuation band; that is, when the phase difference is at [5π / 3, 2π]; at this time, 5π / 3≤2πfτ≤2π, 5 / (6τ)≤f≤1 / τ, and the signal in this frequency band will also be attenuated; According to θ(f) = 2πf1τ = 5π / 3 and θ(f) = 2πf2τ = 2π, the lower and upper critical frequencies f1 and f2 of the high-frequency attenuation band are determined, thus obtaining Wherein, the transit time τ is calculated by cross-correlating the output signals of two pairs of cross-correlated electrodes, and f1 and f2 calculated by equations (4) and (5) are the actual critical frequencies; According to the ideal transit time τ s get The reference flow rate and average flow rate in equations (6), (7), (8), and (9) are obtained from calibration experiments. The ideal critical frequencies of the lower and upper limits of the high-frequency band are calculated by equations (6), (7), (8), and (9).

2. The method for configuring the electrode spacing and attenuation frequency band in the in-situ calibration of a vortex-free permanent magnetic sodium flowmeter according to claim 1, characterized in that: The effect of flow rate changes on critical frequency is considered: It can be seen from formula (3) that as the flow rate increases, the ideal value of the transit time gradually decreases and f0 gradually increases, that is, the greater the flow rate, the wider the frequency band of the attenuated low-frequency signal; this just matches the characteristic that the frequency band of the cross-correlation flow close to the standard flow gradually moves to the high frequency band as the flow rate increases; Based on the physical model of the average velocity "M-shaped" distribution, the cross-correlated flow of the low-frequency signal is greater than the standard flow value, while the cross-correlated flow of the high-frequency signal is close to the standard flow value, that is, the phase difference of the low-frequency signal is smaller than the ideal value. According to the formula θ(f) = 2πfτ, the actual transit time calculated is also smaller than the ideal value. Moreover, the greater the flow rate, the more obvious the "M-shaped" distribution and the greater the nonlinearity, the greater the difference between the phase difference of the low-frequency signal and the ideal value, and the shorter the actual transit time. After subtracting the two pairs of cross-correlated electrode signals, the low-frequency band signal is more suppressed.

3. The method for configuring the electrode spacing and attenuation frequency band in the in-situ calibration of a vortex-free permanent magnetic sodium flowmeter according to claim 1, characterized in that: The effect of the distance between two pairs of electrodes performing same-direction subtraction on the signal attenuation after same-direction subtraction is considered: It can be seen from equations (2) and (3) that as the spacing L of the cross-correlation electrodes used for in-phase subtraction decreases, the transit time gradually becomes shorter and the f0 value gradually increases. By configuring and optimizing the spacing of the electrodes for in-phase subtraction, the signal attenuation band after multi-electrode in-phase subtraction corresponds to the frequency band causing nonlinearity, even if the critical value of the attenuation band matches the critical value of the calibration band, thereby completely attenuating the signal causing nonlinearity.

4. The method for configuring the electrode spacing and attenuation frequency band in the in-situ calibration of a vortex-free permanent magnetic sodium flowmeter according to claim 1, characterized in that: As the spacing between the mutually correlated electrodes for same-direction subtraction decreases, the frequency band of the signal attenuation after subtraction becomes wider, which is more conducive to nonlinear correction. Attenuating the signal frequency band too much will also cause signal loss, which is not conducive to improving signal repeatability. According to existing experimental results, the best effect is achieved when the spacing between two pairs of mutually correlated electrodes for same-direction subtraction is about 75mm, which not only eliminates nonlinear errors but also reduces signal attenuation.

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