Design Method of Ultrasonic Phased Array Sensor for Gas-Liquid Two-Phase Flow Holdup Measurement

Abstract

The present invention relates to a design method of an ultrasonic phased array sensor for measuring the holdup of gas-liquid two-phase flow. The ultrasonic phased array sensor is a fan-shaped scanning circular ultrasonic phased array sensor, and comprises the following steps: establishing an arc ultrasonic array sound field constructed by the superposition of the sound fields of all array elements; after delay control, the sound waves excited by all array elements are in the peak state when reaching a preset focal point, so that the energy at this point is the highest in the sound field, enabling the arc ultrasonic array to have the scanning measurement ability of deflection and focusing, and obtaining the normalized far-field solution of the arc phased array sound wave after delay control; performing multi-angle and multi-parameter optimization design on the actual pipe diameter; obtaining the physical parameters of the array elements comprehensively considering various optimization indexes, and obtaining the corresponding far-field solution and sound field distribution map of the array element delay scan. The present invention also provides a fan-shaped scanning circular ultrasonic phased array sensor obtained by the above optimization design method.

Description

Technical Field

[0001] The present invention belongs to the technical field of fluid measurement, and relates to an ultrasonic phased array sensor for measuring the holdup of gas-liquid two-phase flow. Background Art

[0002] In the fields of petroleum industry and chemical engineering, etc., the accurate measurement of the gas holdup in gas-liquid two-phase flow is a current difficult problem; the classical flow patterns in a vertical pipe of gas-liquid two-phase flow include bubbly flow, slug flow, churn flow, etc. Among them, bubbly flow is the state when the gas phase is broken up at high water cut, and slug flow and churn flow are the most common intermittent flow patterns in vertical gas-liquid flow. The gas phase exists in various forms, including bubbles, large bubbles formed by coalescence, and gas plugs. The unstable gas phase structure and complex gas phase distribution characteristics make the measurement of local gas content and the establishment of models of great significance.

[0003] Modern methods for measuring holdup mainly include conductivity method, capacitance method, ultrasonic method, optical method, differential pressure method, ray method, etc. Among them, the transmission ultrasonic method is a non-contact measurement means, so it has unique advantages in fluid detection and is widely used in the field of two-phase flow. Especially during the flow process, the ultrasonic detection element is located on the outer wall of the pipe, which can avoid direct contact with the flowing medium, does not disturb the flow field, has no pressure loss, and is suitable for application in relatively harsh industrial sites. It is an important means for detecting flow parameters.

[0004] However, in traditional ultrasonic measurement, whether single transmit and single receive or single transmit and multiple receive are adopted, the problem of the concentration profile anisotropy of holdup in the plane cannot be completely solved. Improvements have been made in the fields of conductivity and optical fiber to solve the anisotropy problem. The unstable gas phase structure and complex gas phase distribution characteristics pose great challenges to the measurement of local gas content and the establishment of models by traditional transmission ultrasonic measurement methods. Therefore, the present invention proposes to use a fan-shaped scanning circular arc ultrasonic array sensor to obtain the local concentration of different measurement paths on the pipe cross-section, and gives a design method for an ultrasonic phased array sensor suitable for pipeline fluid measurement, providing an effective way to obtain the local flow parameters of the gas phase in gas-liquid two-phase flow. Summary of the Invention

[0005] The purpose of the present invention is to provide a fan-shaped scanning circular arc ultrasonic array sensor and its sound field design optimization method that can solve the problem that the traditional ultrasonic transmission measurement method cannot reflect the anisotropic concentration profile, and based on this method, a fan-shaped scanning circular arc ultrasonic array sensor for a 20-mm pipe diameter pipeline environment is designed. The technical solution of the present invention is as follows:

[0006] A design method for an ultrasonic phased array sensor for measuring the holdup of gas-liquid two-phase flow, the ultrasonic phased array sensor being a fan-shaped scanning circular ring ultrasonic phased array sensor, comprising the following steps:

[0007] (1) According to the actual pipeline shape and size, a calculation model of the fan-shaped scanning arc ultrasonic array sound field is established through physical parameters such as the number of array elements, the natural frequency of the array elements, and the aperture of the array elements. The fan-shaped scanning arc ultrasonic array elements are segmented to obtain multiple tiny point sources. After representing the position of each tiny point source with angle and radius of curvature parameters, according to Huygens' principle, the sound fields excited by each tiny point source in space are superimposed to obtain the sound field of a single array element, and the sound field of the arc ultrasonic array is constructed by superimposing the sound fields of all array elements;

[0008] (2) After delay control, the sound waves excited by all array elements are in the peak state when reaching the preset focus point, so that the energy at this point is the highest in the sound field, enabling the arc ultrasonic array to have the scanning measurement ability of deflection and focusing, and obtaining the normalized far-field solution of the arc phased array sound wave after delay control:

[0009]

[0010] Among them, P is the sound field intensity, ρ is the medium density, c is the sound wave velocity in the medium, v0 is the starting vibration velocity of the transducer, M is the number of array elements, i is the imaginary unit, k is the wave number, Δt m is the emission delay of the m-th array element, m = 1, 2,..., M, Δs is the length of the point source after array element cutting, N is the number of point sources after array element cutting, r mn , Θ mn are respectively the distance between a certain point source n on the m-th array element and a certain point in the sound field, and the angle between a certain point in the sound field to any point source n on the m-th array element and to the centroid m of the array element, n = 1, 2,..., N; among them, as the position of the array element centroid changes, three geometric parameters change: the distance between a certain point source on the array element and a point in the sound field; the angle between any point in the sound field to any point source on a certain array element and to the centroid of the array element; and the relative delay time of each array element. These three determine the delay time table of each array element in each state, that is: the geometric acoustic path difference between the distance r m from each array element m to the preset focus point and the distance from the array element closest to the current preset focus point to this point min(r m ) and the ratio of the wave velocity c:

[0011] Δt m =Δr m / c=(r m -min(r m )) / c

[0012] The delay time of each array element is preset through the delay time table so that the sound waves excited by all array elements are in the peak state when reaching the preset focus point, so that the energy at this point is the highest in the sound field;

[0013] (3) Use the normalized far-field solution of the circular arc phased array acoustic wave obtained in the foregoing steps as the basis for physical field simulation analysis, and perform multi-angle and multi-parameter optimization design on the actual pipe diameter, including the number of transmitting probes, the natural frequency of the transmitting probes, the aperture size of the transmitting probes, and the actual deflection angle. The aperture size of the transmitting probes includes the actual size of the array elements and the element spacing; the optimization indicators include: whether the focal length F, the radius a of the transmitting array, and the acoustic wavelength λ satisfy the near-field condition: a 2 / λ < F ≤ 20 mm, whether the sound field energy is strong enough at the receiving end after focusing, and whether there are no side lobes in the measurement area when the sound field is deflected; if the above optimization indicators are not satisfied, adjust the physical parameters of the array elements and draw the sound field according to the normalized far-field solution obtained in step (2) until an ideal sound field state is achieved;

[0014] (4) Obtain the physical parameters of the array elements that comprehensively consider various optimization indicators, and obtain the corresponding far-field solution of the array element delay scan and the sound field distribution map.

[0015] The present invention also provides a fan-shaped scanning circular ultrasonic phased array sensor, which is suitable for measuring the gas-liquid two-phase flow holdup in a pipeline with an inner diameter D = 20 mm. Its characteristics are that the array parameters include the number of transmitting array elements N = 16, the natural frequency of the ultrasonic waves generated by the transmitting array elements is f = 3 MHz, the arc length of the element width d = 0.2 mm, the central angle subtended is 1.15°, the arc length of the element spacing g = 0.1 mm, and the central angle subtended is 0.573°; the total arc length of the transmitting array is 5.3 mm, and the central angle subtended by the total arc length of the transmitting array is 30.37°; the receiving array parameters include 13 receiving array elements, namely R1 to R13. The arrangement method is based on the transmitting array element passing through the center of the pipeline to the 7th element on the opposite side as the baseline, and one receiving array element is arranged every 7.5° on both sides until 45°. The centroids of the transmitting array and the receiving array are opposite to each other and are in the same measurement channel cross-section.

[0016] Due to the adoption of the above technical solutions, the present invention has the following advantages:

[0017] (1) There are complex interaction and relative motion phenomena at the interface between the gas and liquid phases in the gas-liquid two-phase flow. Its flow behavior exhibits characteristics such as high irregularity, randomness, and instability of the flow structure. Existing ultrasonic measurement methods are all "linear gas holdup", which cannot reflect in detail the distribution (anisotropy) of the complex gas holdup in the pipe diameter profile; due to the measurement method of the fan-shaped scanning circular ultrasonic phased array sensor adopted by the present invention, it can realize the measurement of the local gas concentration distribution of the gas-liquid two-phase flow under non-uniform flow conditions in the pipe cross-section, greatly reducing the measurement blind area of the ultrasonic sensor, and thus realizing the measurement of the average gas holdup and the instantaneous gas holdup profile of the gas-liquid two-phase flow.

[0018] (2) In the past, many researchers have optimized the design of ultrasonic phased array sensors mostly by combining actual requirements with theoretical models. For the existing experiments on gas-liquid two-phase fluids in small-diameter pipes, a specific design is carried out for the structure of the receiving and transmitting probe arrays of the ultrasonic phased array, including the consideration of near-field interference. The parameter design of the circular arc array is the key advantage of the present invention, that is, the acoustic field calculation method is used to guide the parameter optimization design of the fan-shaped scanning circular arc ultrasonic array;

[0019] (3) Since the present invention gives the acoustic field regulation method and the influence of structural parameters for the ultrasonic phased array distributed in a circular arc, it has good adaptability to various application scenarios such as the monitoring of gas-liquid two-phase flow phase interfaces and the detection of concentration profiles suitable for ultrasonic sensors in various pipes. Brief Description of the Drawings

[0020] Figure 1 It is a detailed explanation of the steps of the overall design method of the fan-shaped scanning circular arc ultrasonic array sensor.

[0021] Figure 2 It is a three-dimensional schematic diagram of the fan-shaped scanning circular arc ultrasonic array sensor.

[0022] Figure 3 It is a two-dimensional top view of the fan-shaped scanning circular arc ultrasonic array sensor.

[0023] Figure 4 It is a schematic diagram of the deflection range that the phased array should satisfy in this design and 13 states of the fan-shaped scanning circular arc ultrasonic array sensor.

[0024] Figure 5 It is a schematic diagram of the one-dimensional model principle of the piston sound source fluctuation in a medium with a medium density and propagation speed of ρ and c respectively.

[0025] Figure 6 It is a schematic diagram of the principle of the acoustic field model formed at any point Q in the acoustic field formed by the arc-shaped array element array.

[0026] Figure 7 The near-field constraint relationship between the number of array elements M, the center frequency f of the array element and the aperture A of the array element, and the influence of the normalized sound pressure of the acoustic field at the receiving end of the pipe wall (taking the focus on the 7th array element, that is, the deflection angle is 0° as an example): (a) The curve relationship between the number of array elements within 20 mm in the near-field range and the array aperture size; (b) The influence of different numbers of array elements and frequencies on the normalized acoustic field at the receiving end of the pipe wall when the array element size is 0.3 mm; (c) The influence of different array element sizes and frequencies on the normalized acoustic field at the receiving end of the pipe wall when the number of array elements is 16; (d) The influence of different array element center frequencies and array element sizes on the normalized acoustic field at the receiving end of the pipe wall when the number of array elements is 16.

[0027] Figure 8It is the normalized sound intensity distribution of the sound field when the natural frequency f = 3 MHz and the array element aperture A = 0.3 mm: (a) The number of array elements M = 14 (b) The number of array elements M = 16 (c) The number of array elements M = 18

[0028] Figure 9 It is the sound field distribution under the condition that the natural frequency f = 3 MHz, the array element width d = 0.2 mm, and the array element spacing g = 0 mm: (a) The main lobe deflection angle in the sound field is 0°; (b) The main lobe deflection angle in the sound field is 15°; (c) The main lobe deflection angle in the sound field is 30°; (d) The main lobe deflection angle in the sound field is 45°

[0029] Figure 10 It is the sound field distribution under the condition that the natural frequency f = 3 MHz, the array element width d = 0.2 mm, and the array element spacing g = 0.1 mm: (a) The main lobe deflection angle in the sound field is 0°; (b) The main lobe deflection angle in the sound field is 15°; (c) The main lobe deflection angle in the sound field is 30°; (d) The main lobe deflection angle in the sound field is 45°.

[0030] Figure 11 It is the sound field distribution under the condition that the natural frequency f = 3 MHz, the array element width d = 0.3 mm, and the array element spacing g = 0 mm: (a) The main lobe deflection angle in the sound field is 0°; (b) The main lobe deflection angle in the sound field is 15°; (c) The main lobe deflection angle in the sound field is 30°; (d) The main lobe deflection angle in the sound field is 45°.

[0031] Description of the attached figure labels:

[0032] Figure 1 In, 1 is the receiving array element array, and 2 is the transmitting array element array.

[0033] Figure 2 In, 1 to 13 are respectively 13 receiving transducers of the receiving array element array. The included angle between every two sensors and the centroid of the transmitting array is 7.5°. Among them, the 7th array element to the centroid of the transmitting array is the 0° deflection angle, and the 1st and 13th array elements to the centroid of the transmitting array are the -45° and 45° deflection angles respectively.

[0034] Figure 3Among them, A1 deflects and focuses to the left, and the central angle of the main lobe of the sound beam deflects by -45°; A2 deflects and focuses to the left, and the central angle of the main lobe of the sound beam deflects by -37.5°; A3 deflects and focuses to the left, and the central angle of the main lobe of the sound beam deflects by -30°; A4 deflects and focuses to the left, and the central angle of the main lobe of the sound beam deflects by -22.5°; A5 deflects and focuses to the left, and the central angle of the main lobe of the sound beam deflects by -15°; B1 deflects and focuses to the left, and the central angle of the main lobe of the sound beam deflects by -7.5°; B2 focuses on the opposite side center, and the central angle of the main lobe of the sound beam deflects by 0°; B3 deflects and focuses to the right, and the central angle of the main lobe of the sound beam deflects by 7.5°; B4 deflects and focuses to the right, and the central angle of the main lobe of the sound beam deflects by 15°; B5 deflects and focuses to the right, and the central angle of the main lobe of the sound beam deflects by 22.5°; C1 deflects and focuses to the right, and the central angle of the main lobe of the sound beam deflects by 30°; C2 deflects and focuses to the right, and the central angle of the main lobe of the sound beam deflects by 37.5°; C3 deflects and focuses to the right, and the central angle of the main lobe of the sound beam deflects by 45°. Detailed implementation mode

[0035] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0036] In the present invention, in order not to interfere with the normal flow of the fluid through the pipeline and to measure a larger cross-sectional area of the pipeline through soft focus scanning, a combined Figure 2 geometric structure is proposed to design a fan-shaped scanning arc ultrasonic array sensor, the cross-sectional schematic diagram of which is as Figure 3 shown, including the schematic diagram of the main geometric parameters, combined with Figure 4 , the receiving end and the phased array scanning measurement state are scanned and measured from A1 to C3.

[0037] To establish the sound field model, first, the influence of a tiny point source in the sound field is deduced. Combined with Figure 5 , it is assumed that there is a tiny transducer as a velocity source at the position z = 0, and its initial vibration velocity v z in the z-axis direction is a function of the x-axis coordinate and time t. This function is defined within the range [-b, b] in the x direction, and the starting vibration velocity of this velocity source is v z = 0 outside this range.

[0038] Applying Newton's law of motion in a micro liquid particle medium gives the motion equation:

[0039]

[0040] In the formula: ρ is the liquid density, and u(x, z, t) is the displacement vector; is the two-dimensional gradient operator; for an ideal compressible liquid, the basic relationship between liquid pressure and liquid motion is:

[0041]

[0042] Among them, λ B is the bulk modulus of the liquid, For the expansion degree.

[0043] Find the divergence on both sides of the equation of motion, substitute the basic relationship between liquid pressure and liquid motion, and obtain the wave equation of micro-perturbation under ideal conditions:

[0044]

[0045] Where c is the wave propagation speed in the medium:

[0046]

[0047] For the wave equation of micro-perturbation under ideal conditions, the acoustic field waveform should be in the form of a harmonic solution, that is:

[0048]

[0049] Substituting the above formula into the wave equation, we can get The Helmholtz formula should be satisfied:

[0050]

[0051] Where k = ω / c is the wave number.

[0052] May wish to and p(x,z,ω) are considered as Fourier transform pairs, namely:

[0053]

[0054]

[0055] It should also satisfy the Helmholtz formula. First, it is clear that the Helmholtz formula has a harmonic solution, namely:

[0056] p=exp(ik x x+ik z z)

[0057] in:

[0058]

[0059] For k z In terms of the real part of the harmonic solution, it represents a plane wave propagating at an angle θ with the z-axis, where k x =ksinθ,k z = kcosθ. And k z The imaginary part of represents a non-homogeneous wave in the positive or negative x direction and whose amplitude decays exponentially along the z-axis. Since the waveform shown in the harmonic solution is a solution to the Helmholtz formula, it can be obtained by superimposing these waves with kx The general solution of the waveform varying with the change is obtained, that is

[0060]

[0061] The above solution is called the angular spectrum of plane waves. And it is actually a combination of plane waves and inhomogeneous waves.

[0062] Use the above solution to describe the array element model: Let v z (x, 0, ω) be the Fourier transform of v z (x, 0, t) (in the plane z = 0):

[0063]

[0064] In the formula

[0065]

[0066] The motion equation gives

[0067]

[0068] Therefore

[0069]

[0070] In this way, substituting the general solution of the waveform into the above formula gives

[0071]

[0072] In the formula

[0073]

[0074] Therefore, v z (x, 0, ω) can be regarded as the inverse spatial Fourier transform of V(k x ). Through the corresponding forward transform, we get

[0075]

[0076] Therefore, the pressure at any point in the liquid medium can be obtained through the general solution and V(k x ), that is

[0077]

[0078] In this way, the above formula can be transformed into the inverse spatial Fourier transform of the product of the functions G(k z , z, ω) and H(k x , ω), that is

[0079]

[0080] wherein

[0081]

[0082] According to the convolution theory, i.e.,

[0083] p(x,z,ω) = ∫h(x',ω)g(x - x',z,ω)dx'

[0084]

[0085]

[0086] Since V(k x ) is the spatial Fourier transform of v z (x,0,ω), thus

[0087] h(x,ω) = ρωv z (x,0,ω)

[0088] g(x,z,ω) is the inverse Fourier transform of the characteristic equation and is proportional to the zeroth-order first-kind Hankel equation, i.e.,

[0089]

[0090] Then the sound intensity at any point in the sound field represented by the Hankel function can be obtained

[0091]

[0092] where: r is the distance from the point (x’,0) to the point (x,z) on the z = 0 plane in the liquid medium,

[0093] For the piston waveform, this function is only defined within the range [-b,b] in the x direction, then there is the following formula:

[0094]

[0095] where ρ is the density of the sound wave propagation medium, c is the wave speed, k is the wave number, k = ω / c, H0 (1) (·) is the zeroth-order first-kind Hankel function. When the distance from a certain point in the liquid medium to the point source is far enough, i.e., kr >> 1, the Hankel equation has an asymptotic value:

[0096]

[0097] For the arc-shaped array element m embedded in the pipe wall, as Figure 6 shown, then the point source model can be extended to the line integral of the arc-shaped array element curve, and this line integral shows that the influence of the sound field is equivalent to the line integral of the influence from the starting point s1 to the end point s N of the infinitesimal array element:

[0098]

[0099] Based on the above micro point source model, an arc array sound field model is established. Combining Figure 6 , assuming that the centroid of a certain arc-shaped element m in the XOZ plane is located at point m, the central angle corresponding to its arc length is θ0, and the central angle corresponding to the distance between this arc-shaped element m and the adjacent element O is β, then the distance length g can be approximately expressed as g = Rβ. The center of the arc is located at O', the length of its radius of curvature OO' is R, and the angle between the line connecting its centroid and the corresponding center O' and the negative z-axis direction is θ m , then its arc length d can be approximately expressed as d = Rθ0. Now, the element m is cut into N equal-length unit arcs, and the angle between the line connecting any unit arc n and the center O' of the element and the negative z-axis direction is φ mn . For any point Q in the far field region of the sound field, the distance between the centroid O of the emission array and this point is the focal length F, the angle between OQ and the positive z-axis direction is α, and the distance between the centroid m of the element and this point is r m , and the distance between any unit arc on the element and Q is r mn .

[0100] Then the influence of the element m (m = 1, 2,..., M) on any point of the normalized sound field can be equivalently considered as the cumulative influence of the N unit point sources Δs obtained by cutting the element along the arc length, where the central angle corresponding to the unit arc length Δs is θ0 / N. Therefore, Δs = Rθ0 / N. Then the normalized and discretized expression of the above formula is obtained:

[0101]

[0102] In the formula, the point source Δs is the length of the point source after segmentation, that is, Δs = d / N, and r can be expressed as a function of known quantities. Here, it is written in the form of an exponential expansion:

[0103]

[0104] Since the point source Δs is small enough, the high-order terms in the expansion are ignored for the convenience of calculation. Among them, |np| is the distance from a point p on the point source n to its centroid n. When any point Q in the sound field is far enough away, this distance is approximately the same as the arc length between these two points on the element, that is:

[0105]

[0106] The physical meaning of the above approximation is that when the point Q is in the far field region, combining Figure 6 , the difference between the distances of q and n from the point Q can be approximately the difference between the projection of pQ on mQ and mQ. According to the cosine theorem, the distance r between the centroid of the element m and a certain point Q in the sound field m can be expressed as:

[0107]

[0108] The Q point is within the far-field range, and np can be regarded as the element arc length from the point source n on the element to the centroid m of the element. Since the point source Δs is small enough, it may be assumed that within the point source Δs range, the connection line np from any point p on the point source n to the centroid of the point source is perpendicular to the connection line nO' from the centroid to the center O' of the element. Then the included angle Θ between np and nQ mn is expressed as:

[0109]

[0110] φ mn is the included angle between the connection line of the nth unit arc (n = 1, 2,..., N) in the mth element and the center O' of the element and the negative z-axis direction:

[0111]

[0112] where θ m is the included angle between the connection line of the centroid of the mth element (m = 1, 2,..., M) and the corresponding center O' and the negative z-axis direction, and can be expressed in terms of the central angle corresponding to the element as:

[0113]

[0114] After neglecting the high-order terms and substituting them into the integral term, the normalized sound field integral model of the element m (m = 1, 2,..., M) is obtained:

[0115]

[0116] When the divided unit arc length is small enough, cosΘ can be approximately regarded as a constant value during the line integral along the unit arc path, and it is only related to the position of the centroid of the unit arc. In addition, |mn| in the formula is approximately equal to the arc length between the two points on the element, that is, |mn| = s'. Therefore, the integral part in the above formula can be solved, that is: mn

[0117]

[0118] Then the normalized sound field discrete model of the element m (m = 1, 2,..., M) can be expressed as:

[0119]

[0120] Figure 4 is the information of the cross-section of the maximum range detection tube. The array structure enables the sound field formed by the transmitting array in the tube to reach the strongest sound intensity at each element of the receiving array by adjusting the excitation delay time of each element in the transmitting array, that is, to form a focusing effect. Combining Figure 4, 13 detection states from A1 to C3 are achieved by sequentially changing the focused receiving array elements, that is, the main lobe focusing deflection angle ranges from -45° to 45°.

[0121] Combined with Figure 2 , a single arc-shaped array element is arranged along the pipe wall as an array, and each arc-shaped array element is driven with a time delay and accumulated respectively to obtain a normalized phased sound field model formed by the array:

[0122]

[0123] Among them, as the centroid position of the array element changes from 1 to M, a total of three parameters change accordingly: the distance r between a certain point source n (n = 1, 2,..., N) on the array element m (m = 1, 2,..., M) and a point Q in the sound field mn , and the angle Θ between any point Q in the sound field and the upper arbitrary point source n (n = 1, 2,..., N) of the array element m (m = 1, 2,..., M) and the centroid m of the array element mn . And the relative time delay Δt of each array element m can be expressed as:

[0124] Δt m = Δr m / c = (r m - min(r m )) / c

[0125] Δr m is the difference between the distance from the centroid of the m-th array element to Q and the shortest distance from the centroid to Q among all array elements. By presetting the relative time delay Δt of each array element m m different scanning states are achieved, and all scanning states are combined to form Figure 4 the soft focusing effect shown in

[0126] Using the above time-delay far-field solution as the basis for physical field simulation analysis, multi-angle and multi-parameter optimization design is carried out for a 20-mm pipe diameter in actual tests, including optimization research on the number of transmitting and receiving probes, the central angle, the actual spacing, the actual deflection angle, the sound beam focusing position, etc. The optimization indicators mainly include three points: whether there is a suitable near-field range, whether the sound field energy is strong enough at the receiving end after focusing, and whether there will be side lobes in the measurement area when the sound field deflects.

[0127] Parameter declaration: the number of transmitting array elements M, the array element size d, the array element spacing g, the aperture A (the distance between the centroids of the array elements), where A = d + g, the array radius a, the ultrasonic wavelength λ, the inherent ultrasonic frequency f of the transducer, the deflection angle θ, the ultrasonic velocity c in pure water medium, the inner diameter D of the pipe, and the distance F from any point in the pipe to the centroid of the array element.

[0128] The limiting size factors mainly include: the relationship between the distance required to maintain the far field and the element size, the size range to be designed to prevent the influence of grating lobes, and the final simulation steering effect. To enable the phased array to have a larger detection range, the acoustic field focusing deflection angle should be as large as possible. Combining with Figure 4 , the design requirements should at least meet the -45° to 45° deflection range from state A1 to state C3, and ensure that no side lobes appear in the interface when the main lobe scans within this range.

[0129] Delayed excitation of each element in the transmitting array can theoretically achieve the required acoustic field focusing effect. The array structure parameters, including the number of elements M, the natural frequency f of the element transducer (included in the beam k), the element size d and the spacing g, directly or indirectly determine the deflection ability of the acoustic field, indicators such as the energy of acoustic field focusing, and thus affect the effect of acoustic field scanning.

[0130] To make the effective measurement area of the acoustic field (i.e., the far field area) cover the measurement area (i.e., the area where the fluid flows through the pipe cross-section) as much as possible, that is, the effective detection range of the acoustic source soft focus is as large as possible, that is, the near field area of the acoustic field should be reduced as much as possible. Then the array size of the elements and the focal length F from any point in the acoustic field to the element array should first meet the near field conditions and meet the pipe detection requirements:

[0131]

[0132] Among them, λ is the acoustic wave wavelength, λ = c / f. a is the radius of the array, which can be expressed by the total arc length of the elements, that is:

[0133]

[0134] Among them, A is the aperture size, that is, A = d + g, λ is the acoustic wave wavelength and is the quotient of the sound speed c and the natural frequency f. In the above formula, g can be ignored relative to the total size. Since the pipe cross-section diameter D = 20mm, that is, F is at most 20mm. Therefore, when designing the structure parameters, the selection of the number of elements M and the element aperture A in the formula should ensure that the near field range is as small as possible than the wavelength to ensure the point source approximation. However, currently, it is difficult to make the element size d of the commercial acoustic wave phased array less than 0.2mm. Then the minimum element spacing should be 0.1mm to prevent errors. Therefore, the size of the aperture A should be at least 0.3mm. That is, the design range of the element size can be obtained: 0.3mm ≤ A < c / f.

[0135] According to the above conditions, the relationship between the number of elements and the element aperture that meets the near field requirements can be obtained. According to Figure 7 (a), taking several typical frequencies as examples, the trade-off strategy between the number of elements and the frequency should be: when the frequency f is 2MHz, 3MHz, 4MHz, 5MHz, the number of elements M should not be greater than 26, 21, 18, 16 respectively. According to Figure 7(b), with the same number of array elements and the same aperture size (especially when the array element aperture A is in the range of 0.3 mm to 0.6 mm), the increase in frequency can more efficiently improve the normalized sound pressure of the 7th array element at the receiving end of the pipe wall obtained from the sound field model, that is, increasing the ultrasonic frequency can save the cost of the number of array elements and the array element aperture. When the natural frequency is increased to above 3 MHz, according to Figure 7 (c), the cost savings brought about by the increase in frequency decrease significantly.

[0136] In fact, increasing the aperture size A and increasing the number of array elements N can both enhance the sound pressure at the receiving end, but both of them will also lead to an increase in the near-field region. When the center frequency of the array element is 3 MHz, the total size A of the array element should satisfy 0.3 mm ≤ A < 0.5 mm. It is worth noting that according to Figure 7 (b), at frequencies of 3 MHz and above, increasing the array element size beyond 0.5 mm does not significantly improve the sound pressure at the receiving end. Based on the above array element size range, according to Figure 7 (a), the range of the number of array elements M should be: 13 < M < 21. It is not difficult to see that the smaller the array element size, the larger the range of the number of array elements that can be selected. That is, only when A = 0.3 mm, 13 < M < 21, which provides the possibility of significantly reducing the near-field region under the above conditions. As the number of array elements increases, after M is greater than 18, increasing the number of array elements does not significantly improve the sound pressure at the receiving end. However, the increase in the near-field range caused by increasing the number of array elements is very obvious. Combining Figure 8 (a)(b)(c), in the case of the natural frequency f = 3 MHz and A = 0.3 mm, the sound field conditions in three cases where the number of array elements M = 14, 16, 18. Among them, M = 16 takes into account a larger sound pressure at the receiving end and a smaller near-field range compared to other cases.

[0137] Therefore, when f = 3 MHz, the scheme with the array element aperture A = 0.3 mm and the number of array elements M = 16 is more superior. At this time, the wavelength λ = 0.5 mm. The array element size d mainly determines the main lobe width and the main lobe energy, while the array element spacing g affects the deflection ability of the phased array, that is, when the main lobe of the sound beam deflects by a certain angle, whether grating lobes will be generated in the main body of the pipeline.

[0138] According to the simulation of the ultrasonic phased array multi-point source circular arc array model, the sound field effects under three schemes can be obtained. Combining Figure 9 , when d = 0.2 mm and the array element spacing is cancelled, it can be observed that as the array element deflects, the aperture of this scheme is the smallest among the three schemes. Therefore, the near-field range of its sound field radiation is smaller, and it has a higher detectable range of the main body of the pipeline. However, since the width of its array element is small, the energy remaining when the sound wave propagates to the pipe wall decreases. Therefore, the sensitivity of this scheme is relatively weak.

[0139] Combined with Figure 10 , when the element spacing d = 0.2 mm and the element pitch g = 0.1 mm, the near-field region is larger than that without element pitch. And due to the increased element pitch, the element deflection ability decreases. As shown in Figure 10 (d), when the deflection angle reaches 45°, grating lobe leakage appears in the main pipeline. However, when the sound waves at all deflection angles propagate to the pipe wall in this scheme, the energy distribution is more ideal than in the middle effect.

[0140] Combined with Figure 9 and Figure 11 , as the element width increases, the remaining energy reaching the opposite side of the pipe wall also increases. At the same time, the size of the near-field region also increases, and the energy of the side lobes beside the main lobe also increases. When the deflection angle rises to 45°, there is energy leakage in the main pipeline. Combined with Figure 10 and Figure 11 , it can be observed that although the element width of Scheme 3 increases, the energy reaching the opposite side of the pipe wall does not increase significantly compared to Scheme 2, but instead decreases with the deflection of the sound field, as shown in Figure 10 (d) and 11(d). This is related to the increase in element pitch. When the element pitch increases, as the deflection angle rises, the energy reaching the opposite pipe wall shows a significant attenuation.

[0141] In summary, for a 16-element phased array with a natural frequency of the sound wave of 3 MHz and an aperture-to-wavelength ratio A / λ = 0.5, the energy distribution and deflection performance reach the best. By changing the proportions of the element width d and the element pitch g that occupy the aperture A, different main lobe and grating lobe energy distributions can be obtained. As d increases and g decreases, the main lobe energy will gradually leak to the grating lobes. It should be noted that in the actual processing and manufacturing of phased array probes, it is very difficult to process phased array probes with A / λ < 0.3. Therefore, the actual ratio of the element width d to the element pitch g should be weighed as needed. Finally, this design combines Figure 1 the design scheme in Figure 2, which is arranged evenly on the opposite side of the transmitting array elements and has a coverage range of half the perimeter of the measurement channel. By delaying to synthesize the sound field, a fan-shaped scanning ultrasonic phased circular array sensor based on phased deflection focusing for measuring the holdup of gas-liquid two-phase flow is designed.

Claims

1. A design method for an ultrasonic phased array sensor used for measuring the holdup of gas-liquid two-phase flow. The ultrasonic phased array sensor is a fan-shaped scanning circular ultrasonic phased array sensor, and the method includes the following steps: (1) According to the actual pipeline shape and size, establish a calculation model for the sound field of the fan-shaped scanning circular ultrasonic array by using physical parameters such as the number of array elements, the natural frequency of the array elements, and the aperture of the array elements. Divide the elements of the fan-shaped scanning circular ultrasonic array into multiple tiny point sources. After representing the position of each tiny point source with angle and radius of curvature parameters, superpose the sound fields excited by each tiny point source in space according to Huygens' principle to obtain the sound field of a single array element, and construct the sound field of the circular ultrasonic array by superposing the sound fields of all array elements. (2) After delay control, the sound waves excited by all array elements are in the peak state when reaching the preset focal point, so that the energy at this point is the highest in the sound field, enabling the circular ultrasonic array to have the scanning measurement ability of deflection and focusing, and obtaining the normalized far-field solution of the circular phased array sound wave after delay control: Among them, P is the sound field intensity, ρ is the medium density, c is the sound wave velocity in the medium, v0 is the starting vibration velocity of the transducer, M is the number of array elements, i is the imaginary unit, k is the wave number, and Δt m is the emission delay of the m-th array element, where m = 1, 2, …, M, Δs is the point source length after the array element is cut, N is the number of point sources after the array element is cut, and r mn , Θ mn are respectively the distance between a certain point source n on the m-th array element and a certain point in the sound field, and the angle between a certain point in the sound field to any point source n on the m-th array element and to the centroid m of the array element, where n = 1, 2, …, N; among them, with the change of the centroid position of the array element, three geometric parameters change: the distance between a certain point source on the array element and a point in the sound field; the angle between any point in the sound field to any point source on a certain array element and to the centroid of the array element; and the relative delay time of each array element. These three determine the delay time table of each array element in each state, that is: the distance r m from each array element m to the preset focal point and the geometric acoustic path difference between the array element closest to the current preset focal point and the distance from this point to the ratio of the wave velocity c: m ) Δt m = Δr m / c = (r m - min(r m )) / c Preset the delay time of each array element through a delay time table so that the sound waves excited by all array elements are in the peak state when reaching the preset focal point, so that the energy at this point is the highest in the sound field. (3) Use the normalized far-field solution of the circular arc phased array acoustic wave obtained in the foregoing steps as the basis for physical field simulation analysis, and perform multi-angle and multi-parameter optimization design on the actual pipe diameter, including the number of transmitting probes, the natural frequency of the transmitting probes, the aperture size of the transmitting probes, and the actual deflection angle. The aperture size of the transmitting probes includes the actual size of the array elements and the element spacing; the optimization indicators include: whether the focal length F, the radius a of the transmitting array, and the acoustic wave wavelength λ satisfy the near-field condition: a 2 / λ < F ≤ 20 mm, whether the sound field energy is strong enough at the receiving end after focusing, and whether there are no side lobes in the measurement area when the sound field deflection is achieved; if the above optimization indicators are not satisfied, adjust the physical parameters of the array elements and draw the sound field according to the normalized far-field solution obtained in step (2) until the ideal sound field state is achieved; (4) Obtain the physical parameters of the array elements that comprehensively consider meeting various optimization indexes, and obtain the corresponding far-field solution of the array element delay scan and the sound field distribution map.

2. A sector-scanning circular ultrasonic phased array sensor, applicable to the measurement of the gas-liquid two-phase flow holdup in a pipeline with an inner diameter D = 20 mm, is characterized in that, The array parameters include the number of transmitting array elements N = 16, the natural frequency of the ultrasonic waves generated by the transmitting array elements f = 3 MHz, the arc length of the element width d = 0.2 mm, the central angle subtended 1.15°, the arc length of the element spacing g = 0.1 mm, the central angle subtended 0.573°; the total arc length of the transmitting array is 5.3 mm, and the central angle subtended by the total arc length of the transmitting array is 30.37°; the receiving array parameters include 13 receiving array elements, namely R1 to R13. The arrangement method is based on the transmitting array element passing through the center of the pipeline to the 7th element on the opposite side as the baseline, and a receiving array element is arranged every 7.5° to both sides until 45°. The centroids of the transmitting array and the receiving array are opposite to each other and are in the same measurement channel cross-section.

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