Self-calibration method for time-of-flight flow measurement system with arcsine vertical velocity distribution

Abstract

A self-calibration method for a time-of-flight (TOF) flow measurement system based on an arcsine vertical velocity distribution includes the following steps: installing a pair of vertically sliding ultrasonic transducers on each bank of a river cross-section; measuring the actual flow velocity at two or more layers each time; calculating the upper and lower horizontal layer velocity coefficients and the bottom blind zone velocity coefficient using a laminar velocity-cross-section velocity conversion model based on the arcsine vertical velocity distribution; calculating the real-time flow rate of the two-layer method from the average cross-section velocity and cross-sectional area; or calculating the real-time flow rate of the multi-layer method by accumulating the layered flow velocities, thereby realizing online real-time monitoring of river flow using the ultrasonic time-of-flight method. This invention enables the ultrasonic time-of-flight method to become a flow measurement method independent of other conventional flow measurement methods, eliminating the need to deploy a separate set of conventional testing facilities such as a rotor velocity meter for comparative calibration, thus allowing the ultrasonic time-of-flight flow monitoring system to be built, put into operation, and applied immediately upon commissioning.

Description

Technical Field

[0001] This invention belongs to the field of water flow measurement technology, specifically a self-calibration method for a time-difference flow measurement system based on arcsine vertical velocity distribution. Background Technology

[0002] Ultrasound waves are directional, capable of propagating in straight lines like light waves, and can travel through gases, liquids, and solids. The ultrasonic time-of-flight method is based on the principle that the time difference between the downstream and upstream propagation of ultrasound waves is proportional to the fluid velocity. By measuring the time difference required for the ultrasound waves to travel downstream and upstream, the river's flow velocity can be determined.

[0003] The ultrasonic time-of-flight (TOF) method, which began experimental research in Hunan Province in 1970, has undergone nearly 50 years of research and development in my country and has been initially applied, playing a significant role, especially in flow monitoring of some artificial canals. However, due to the irregular cross-sections of natural rivers and the complexity of influencing factors, the representativeness of the velocity at one or more horizontal layers measured by the TOF method for the entire cross-section, or the ability to establish a relationship between the measured horizontal layer velocity and the actual cross-sectional velocity, directly determines the success or failure of the construction and deployment of the TOF flow measurement system. Therefore, in the early stages of constructing a TOF monitoring system for natural rivers, in-depth technical demonstrations and a lengthy system comparison and calibration process are required, which to some extent restricts the widespread application of the TOF method in river flow monitoring.

[0004] Depending on the number of transducers and the installation method, ultrasonic time-of-flight flow measurement methods include multi-layer flow measurement and single-layer flow measurement.

[0005] The multi-level flow measurement method involves installing multiple pairs of transducers in parallel at different water depths along both banks of a river or canal. The average velocity at each horizontal level is measured across the cross-section to obtain the velocity distribution, which is then used to calculate the flow rate at each level and ultimately estimate the overall cross-sectional flow rate. The fixed installation arrangement of the multi-channel transducers in the multi-level flow measurement method is as follows: Figure 1 As shown.

[0006] The cross-sectional flow rate calculation using the multi-layer flow measurement method is similar to that of the conventional flow meter method, employing the accumulation of flow rates from different layers. Its finite difference formula is as follows:

[0007]

[0008] In the formula: v μ Let μ be the horizontal flow velocity of the μ-th velocity-measuring layer (μ = 1, 2, 3, ..., n), and when μ = n, it is the flow velocity at the boundary of the riverbed blind zone; A μ Let k be the cross-sectional area of ​​the μ-th part of the water passage; 底 This represents the bottom velocity coefficient; the other symbols have the same meaning as above.

[0009] The single-layer flow measurement method involves selecting a suitable fixed location on each bank of a river or canal and horizontally installing a pair of transducers. The average horizontal velocity measured by the transducers at that level represents the average velocity across the entire cross-section, from which the flow rate is calculated. The transducer arrangement in the single-layer flow measurement method is as follows: Figure 2 As shown.

[0010] The formula for calculating the cross-sectional flow rate using the single-layer flow measurement method can be expressed as:

[0011]

[0012] In the formula: V is the average velocity across the cross section; A is the cross section area; v θ To fix the flow velocity of each velocity measurement layer; k θ This is the conversion coefficient between horizontal layer velocity and cross-sectional average velocity, generally referred to as the horizontal layer velocity coefficient; the meanings of the other symbols are the same as above.

[0013] As can be seen from the above two equations, when using the ultrasonic time-of-flight method to measure river and canal flow, it is difficult to obtain a complete profile velocity distribution through measurement, regardless of whether the method uses multiple layers or a single layer. Therefore, in the application of the ultrasonic time-of-flight method, system calibration must be performed after instrument installation to establish the relationship between the measured velocity and the actual average velocity of the cross-section, i.e., to calculate k in the above two equations. 底 or k θ .

[0014] It is evident that both multi-layer and single-layer flow measurement methods require calibration of the time-of-flight (TOF) flow measurement system. Therefore, when arranging an ultrasonic TOF river flow measurement system, a rotor current meter or mobile acoustic Doppler current profiler (ADCP) flow measurement facility must be installed according to the requirements of the "River Flow Measurement Standard" (GB50179) to simultaneously perform precise full-section flow measurement with the TOF method, in order to analyze the relationship between the flow velocity measured by the TOF method and the full-section flow velocity. Due to the complex hydrological conditions of natural rivers, calibration may require a lengthy process, which is not only time-consuming and labor-intensive but also hinders the timely deployment and effectiveness of the TOF method. This is highly detrimental to the application of the TOF method in newly established hydrological stations. Summary of the Invention

[0015] The purpose of this invention is to provide a self-calibration method for a time-of-flight flow measurement system based on an arcsine vertical velocity distribution. Based on a laminar velocity to cross-sectional velocity conversion model using the arcsine vertical velocity distribution, the method calculates the conversion between laminar velocity, cross-sectional average velocity, and blind zone velocity using the velocity measurement information of the ultrasonic time-of-flight method itself. This allows the ultrasonic time-of-flight method to become a flow measurement method independent of other conventional flow measurement methods, eliminating the need for a separate set of conventional testing facilities such as a rotor velocity meter for comparative calibration. This enables the ultrasonic time-of-flight flow monitoring system to be built, put into production, and applied immediately upon production.

[0016] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0017] A self-calibration method for a time-difference flow measurement system with an arcsine vertical velocity distribution, characterized by comprising the following steps:

[0018] (1) Install a set of train tracks on each bank of the river section and install a pair of ultrasonic transducers on the train.

[0019] (2) The trolley carrying the ultrasonic transducer moves synchronously from top to bottom on the track and measures the actual flow velocity of two or more layers.

[0020] (3) At the beginning and end of ultrasonic velocity measurement, the water level Z at the river section is observed according to the "Water Level Observation Standard" (GB / T50138);

[0021] (4) Take ultrasonic waves from the upper and lower layers and measure the actual flow velocities v from the upper and lower layers. θ1 v θ2 Using river cross-section measurement data and a velocity coefficient conversion model based on arcsine velocity distribution, the surface velocity coefficient K0 is derived. Then, based on the surface velocity coefficient K0 and the river cross-section measurement data, the corresponding upper layer velocity coefficient k for this flow measurement is calculated. θ1 Lower layer velocity coefficient k θ2 and the bottom velocity coefficient k 底 ;

[0022] (6) Based on the measured water level Z, obtain the river cross-sectional area A corresponding to the measured water level Z from the actual measured value of the cross section;

[0023] (6) The measured flow velocity v in the upper layer θ1 and the upper velocity coefficient k θ1 The product (or the product of the measured flow velocity v in the lower layer) θ2 and the upper velocity coefficient k θ2 The product of the two is used to calculate the average velocity of the cross section. Then, the average flow velocity of the cross section Given the cross-sectional area A, calculate the real-time flow rate Q using the velocity area method;

[0024] (7) From the bottom velocity coefficient k 底 The bottom velocity is calculated by combining the measured velocity at the lowest layer, and the real-time flow rate of the cross-section is estimated by accumulating the velocity across the layers.

[0025] (8) Repeat steps (2) to (7) multiple times, plot the correlation diagram between water level Z and surface velocity coefficient K0 for each flow measurement, and draw the relationship line between water level Z and surface velocity coefficient K0 (i.e., the Z-K0 relationship line) based on the centroid of the point group distribution. Then, obtain the corresponding K0 and cross-sectional measurement data for each water level from the Z-K0 relationship line, and calculate the upper and lower layer velocity coefficients k corresponding to each water level.θ1 k θ2 With bottom velocity coefficient k 底 And establish the relationship lines between water level and the velocity coefficients of the upper and lower layers and the bottom velocity coefficient (i.e., Z~k). θ1 Z~k θ2 and Z~k 底 Relationship line), from the Z~k θ1 Z~k θ2 Z~k 底 The relationship line is used to calculate the laminar flow velocity coefficient k based on the water level. θ1 k θ2 Then, proceed to step (6) or (7) to calculate the cross-sectional flow rate, which can further improve the accuracy of flow measurement.

[0026] In the above steps (6) and (7), step (6) is executed when the two-layer method is used for flow measurement, and step (7) is executed when the multi-layer method is used for flow measurement.

[0027] As a preferred embodiment of the above method, in step (4),

[0028] The formula for calculating the water surface velocity coefficient is as follows:

[0029]

[0030] in,

[0031]

[0032] In the formula: K0 is the surface velocity coefficient; B1 is the width of the upper horizontal layer of the river; B2 is the width of the lower horizontal layer of the river; v θ1 The measured flow velocity at the upper layer; v θ2 B1 is the measured flow velocity in the lower layer; B2 is the width of the river surface in the upper horizontal layer; π is pi, taken as 3.1416; h μ Let b be the average water depth of the μ-th part of the area (μ = 1, 2, ..., n); μ denoted as μ, representing the width of the water surface in the μ-th part of the area; j1 represents the starting vertical line number below the upper horizontal layer; j2 represents the starting vertical line number below the lower horizontal layer; m1 represents the final vertical line number below the upper horizontal layer; m2 represents the final vertical line number below the lower horizontal layer; θ is the relative water depth value calculated from the riverbed, which is between 0 and 1.

[0033] As a preferred embodiment of the above method, in step (4),

[0034] The formula for calculating the upper layer velocity coefficient is as follows:

[0035]

[0036] The formula for calculating the lower layer velocity coefficient is as follows:

[0037]

[0038] The formula for calculating the bottom velocity coefficient is as follows:

[0039]

[0040] in,

[0041]

[0042] In the formula: k θ1 k is the upper-layer velocity coefficient. θ2 k is the velocity coefficient of the lower layer. 底 B is the bottom velocity coefficient; n h is the width of the river surface in the lowest velocity measurement layer of the multi-layer method. y The water depth below the lowest velocity measuring layer in the multi-layer method, i.e., the height from the bottom of the canal to the nth horizontal layer, varies with the distance from the starting point of the cross-section and is usually represented by h. y =f(B);d μ h is the water depth along the μ-th vertical line on the cross-section. y，μ b is the water depth below the nth horizontal layer on the μth vertical line of the cross section; μ The width of the water surface in the μ-th part of the cross-section; θ n is the relative water depth of a certain vertical line in the lowest velocity measurement layer of the multi-layer method, measured from the riverbed; j and m are the serial numbers of the starting and ending vertical lines of the bottom layer, respectively; the meanings of the other symbols are the same as above.

[0043] As a preferred embodiment of the above method, in step (6), the formula for calculating the real-time flow Q using the two-layer method is:

[0044]

[0045] In the formula: Q is the flow rate; A is the cross-sectional area of ​​the river; This represents the cross-sectional average velocity; the other symbols have the same meaning as above.

[0046] As a preferred embodiment of the above method, in step (7), the formula for calculating the real-time flow rate Q using the multi-layer method is:

[0047]

[0048] In the formula: v μ Let μ be the horizontal flow velocity of the μ-th velocity-measuring layer (μ = 1, 2, 3, ..., n), and when μ = n, it is the flow velocity at the boundary of the riverbed blind zone; A μ Let k be the cross-sectional area of ​​the μ-th part of the water passage; 底 This represents the bottom velocity coefficient; the other symbols have the same meaning as above.

[0049] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0050] (1) The accuracy of the flow rate calculated by the laminar velocity and cross-sectional average velocity conversion model constructed by this invention basically meets the accuracy requirements of normal hydrological measurements. Among them, after collecting a certain number of two-layer velocity measurements to self-calibrate the relationship between water level (or other hydraulic factors) and laminar velocity coefficient, the accuracy of the flow rate calculation meets the accuracy requirements of Class I stations in the "River Flow Measurement Specification". The accuracy of the flow rate calculation is reduced by directly estimating the flow rate by instantly calculating the laminar velocity and cross-sectional velocity conversion coefficient using single two-layer velocity measurement information, but it can still basically meet the accuracy requirements of Class II stations in the "River Flow Measurement Specification".

[0051] (2) The laminar velocity and cross-sectional velocity conversion model based on vertical velocity distribution is calculated by using the velocity measurement information of the ultrasonic time difference method itself to convert laminar velocity and cross-sectional average velocity. This makes the ultrasonic time difference method an independent flow measurement method from other conventional flow measurement methods. Therefore, it is not necessary to set up a set of conventional testing facilities such as rotor velocity meters for comparison and calibration, so that the ultrasonic time difference method flow monitoring system can be put into production and applied immediately after construction.

[0052] (3) From the calculation parameters of the laminar velocity to cross-sectional velocity conversion model based on vertical velocity distribution, the laminar velocity coefficient mainly depends on the structural characteristics of the water flow (represented by K0 in the formula) and the river cross-sectional morphology. Therefore, on the one hand, the arrangement of the ultrasonic time-of-flight velocity measurement layers should reflect the information of the vertical velocity distribution of the river cross-section, so as to achieve the complementarity of velocity distribution information between the velocity measurement layers. Regarding the optimal arrangement of the measurement layer spacing, this invention proposes a corresponding algorithm. On the other hand, when the river cross-section changes significantly or the station control conditions change significantly, causing the vertical velocity distribution law to change, this invention proposes technical requirements for laminar velocity coefficient correction and verification. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the velocity measurement position of a multilayer transducer.

[0054] Figure 2 This is a schematic diagram of the velocity measurement position of a single-layer transducer.

[0055] Figure 3 This is a schematic diagram of the velocity measurement position of a two-fixed-layer transducer.

[0056] Figure 4 This is a graph showing the relationship between water level and surface velocity coefficient, and between water level and laminar velocity coefficient. Detailed Implementation

[0057] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be described in detail below with reference to embodiments. The description in this part is only exemplary and explanatory, and should not be used to limit the scope of protection of the present invention in any way.

[0058] Example 1:

[0059] The vertical velocity distribution of a river refers to the variation of velocity along the vertical line at different locations on a cross-section. It is mainly influenced by many factors such as water depth, riverbed roughness, sediment content, and upstream and downstream cross-sectional variations, resulting in a highly complex morphology. Therefore, it is necessary to conduct in-depth research on cross-sectional flow measurement methods for velocity distributions with different patterns. In our long-term ultrasonic time-of-flight flow measurement experiments, we have found that there is always a certain complementarity in the velocity information of different horizontal layers. The velocity of each horizontal layer reflects the cross-sectional velocity distribution pattern. By technically mining and model adaptation of velocity information from two or more complementary layers, the morphological distribution of velocity on the river cross-section can be obtained. Combined with cross-sectional area measurement information, cross-sectional flow information can then be obtained.

[0060] The specific implementation steps are as follows:

[0061] (1) Install a set of train tracks on each bank of the river section and install a pair of ultrasonic transducers on the train.

[0062] (2) The trolley carrying the ultrasonic transducer moves synchronously from top to bottom on the track and measures the actual flow velocity of two or more layers.

[0063] (3) At the beginning and end of ultrasonic velocity measurement, the water level Z at the river section is observed according to the "Water Level Observation Standard" (GB / T50138);

[0064] (4) Take ultrasonic waves from the upper and lower layers and measure the actual flow velocities v from the upper and lower layers. θ1 v θ2 Using river cross-section measurement data and a velocity coefficient conversion model based on arcsine velocity distribution, the surface velocity coefficient K0 is derived. Then, based on the surface velocity coefficient K0 and the river cross-section measurement data, the corresponding upper layer velocity coefficient k for this flow measurement is calculated. θ1 Lower layer velocity coefficient k θ2 and the bottom velocity coefficient k 底 ;

[0065] (5) Based on the measured water level Z, the cross-sectional area A of the river at the corresponding measured water level Z is obtained from the actual measured value of the cross section;

[0066] (6) The measured flow velocity v in the upper layer θ1 and the upper velocity coefficient k θ1 The product (or the product of the measured flow velocity v in the lower layer) θ2 and the upper velocity coefficient k θ2The product of the two is used to calculate the average velocity of the cross section. Then, the average flow velocity of the cross section Given the cross-sectional area A, calculate the real-time flow rate Q using the velocity area method;

[0067] (7) From the bottom velocity coefficient k 底 The bottom velocity is calculated by combining the measured velocity at the lowest layer, and the real-time flow rate of the cross-section is estimated by accumulating the velocity across the layers.

[0068] (8) Repeat steps (2) to (7) multiple times, plot the correlation diagram between water level Z and surface velocity coefficient K0 for each flow measurement, and draw the relationship line between water level Z and surface velocity coefficient K0 (i.e., the Z-K0 relationship line) based on the centroid of the point group distribution. Then, obtain the corresponding K0 and cross-sectional measurement data for each water level from the Z-K0 relationship line, and calculate the upper and lower layer velocity coefficients k corresponding to each water level. θ1 k θ2 With bottom velocity coefficient k 底 And establish the relationship lines between water level and the velocity coefficients of the upper and lower layers and the bottom velocity coefficient (i.e., Z~k). θ1 Z~k θ2 and Z~k 底 Relationship line), from the Z~k θ1 Z~k θ2 Z~k 底 The relationship line is used to calculate the laminar flow velocity coefficient k based on the water level. θ1 k θ2 Then, proceed to step (6) or (7) to calculate the cross-sectional flow rate, which can further improve the accuracy of flow measurement.

[0069] In the above steps (6) and (7), step (6) is executed when the two-layer method is used for flow measurement, and step (7) is executed when the multi-layer method is used for flow measurement.

[0070] Derivation of the conversion between horizontal laminar flow velocity and cross-sectional flow velocity based on arcsine velocity distribution:

[0071] The vertical velocity distribution along the arcuate curve is a universal velocity distribution model derived from the eddy current interchange theory. Its vertical velocity distribution is as follows:

[0072]

[0073] In the formula: v θ Let θ be the flow velocity at a relative water depth of θ on the vertical line of the river cross-section; θ is the relative water depth value measured from the riverbed, which is between 0 and 1. Here is the formula for the average velocity along the vertical line; C is the Chezy coefficient; h is the vertical water depth; s is the water surface slope; g is the acceleration due to gravity, generally taken as g = 9.81 m / s²; K4 is the universal coefficient for the arcsine velocity distribution, which can be derived when the arcsine velocity distribution is set to be equal to the logarithmic velocity distribution. K1 is Kármán's constant; π is pi, taken as 3.1416; the meanings of the other symbols are the same as above.

[0074] Therefore, the cross-sectional average velocity at the flow measurement section can be obtained by the following formula:

[0075]

[0076] Where: h μ Let b be the average water depth of the μ-th part of the area (μ = 1, 2, ..., n); μ The area of ​​the μ-th part is the width of the water surface; the meanings of the other symbols are the same as above.

[0077] If the flow velocities of layers 1-1 and 2-2 are measured at the cross-section, such as Figure 3 As shown.

[0078] For the 1-1 level plane, its cross-sectional average velocity can be obtained by integration after appropriate transformation, that is:

[0079]

[0080] Substituting equation (8) into the equation and writing it in finite difference form, we obtain the formula for the average velocity of the 1-1 horizontal layer:

[0081]

[0082] in,

[0083]

[0084] In the formula: B1 represents the average flow velocity of the 1-1 horizontal layer; B1 represents the width of the river surface in the 1-1 horizontal layer; the meanings of the other symbols are the same as above.

[0085] Because there is a hydraulic relationship between the KAMAN constant K1 and the surface velocity coefficient K0, and we have:

[0086]

[0087] Therefore:

[0088]

[0089] Substituting (13) into equation (11) yields:

[0090]

[0091] Since the laminar velocity coefficient is the ratio of the average cross-sectional velocity to the laminar velocity, that is: Substituting equations (9) and (14) into the equations respectively, we can obtain the upper layer velocity coefficient:

[0092]

[0093] in,

[0094] exist Figure 3 Then, for the 2-2 horizontal layer, calculate the layer-average velocity. Similarly, we can obtain:

[0095]

[0096] in,

[0097]

[0098] In the above two formulas: The average flow velocity is 2-2 horizontal layer; 2-2 represents the flow velocity coefficient of the horizontal layer; the meanings of the other symbols are the same as before.

[0099] Calculating the cross-sectional flow rates for the upper and lower floors separately, we have:

[0100]

[0101] Substituting equations (14), (15) and (16), (17) into equation (18), and rearranging, we get:

[0102]

[0103] As can be seen from the above equation, the surface velocity coefficient is only related to the cross-sectional shape and the horizontal velocities of the two horizontal layers. Therefore, during flow measurement, the velocities of the two horizontal layers are measured each time. Combined with the cross-sectional measurement data, the surface velocity coefficient K0 can be calculated by equation (19); then, the laminar velocity coefficients of the two velocity measurement layers can be easily solved by equations (15) and (17). and This enables the self-calibration of the time difference method measurement system.

[0104] Derivation of the blind zone velocity estimation model based on the multilayer flow measurement method for arcsine velocity distribution:

[0105] Multi-level flow measurement, by measuring the average velocity of multiple horizontal layers, can effectively control the vertical velocity distribution of a river or canal cross-section. However, due to the limitations of the actual shape of the river or canal cross-section, it is not possible to measure the flow velocity across the entire cross-section using measuring instruments. This area where flow velocity cannot be measured using instruments is called the blind zone. Blind zone velocity measurement is one of the most complex problems to be solved in hydrological surveying, but so far there is no effective solution. Therefore, an approximate estimation method for blind zone flow must be proposed in multi-level flow measurement. For general river or canal cross-sections, the blind zone of multi-level flow measurement using a transducer mounted on a railcar is mainly the adjacent cross-sectional area near the bottom of the river or canal. The blind zone velocity can only be estimated using the measured velocity at the top of the blind zone. A common method is to multiply the velocity at the top of the bottom layer by the bottom layer velocity coefficient to obtain the average velocity at the bottom layer, i.e.:

[0106] v 底 =k 底 v n (20)

[0107] Given that the flow velocity distribution at the bottom of the canal is influenced by the cross-sectional shape of the canal bottom, the velocity distribution is relatively complex. Considering the universal formula for vertical velocity distribution, namely the arcsine vertical velocity distribution (7), the average velocity of the vertical line in the blind zone can be calculated. The average velocity of the part below the nth horizontal layer of a certain vertical line on the canal cross-section can be calculated, that is:

[0108]

[0109] In the formula: The average flow velocity of the portion of a vertical line below the nth horizontal layer, i.e., the segment from the riverbed to the nth horizontal layer; θ n This represents the relative water depth at the nth layer of a certain vertical line, measured from the riverbed; the meanings of the other symbols are the same as above.

[0110] The above equation is transformed by integration, and let:

[0111]

[0112] Then we have:

[0113]

[0114] Therefore, the blind zone traffic, i.e., the underlying traffic, is:

[0115]

[0116] In the formula: Q 底 For underlying traffic (blind spot traffic); B n h is the width of the river surface at the nth horizontal level. y The water depth below the nth horizontal layer, i.e., the height from the bottom of the canal to the nth horizontal layer, varies with the distance from the starting point of the cross-section and is usually represented by h.y =f(B); the meanings of the other symbols are the same as above.

[0117] Substituting equation (22) into equation (23) and rewriting it in finite difference form, we have:

[0118]

[0119] in:

[0120]

[0121] In the above three equations, d μ h is the water depth along the μ-th vertical line on the cross-section. y,μ b is the water depth below the nth horizontal layer on the μth vertical line of the cross section; μ The width of the water surface in the μth part of the cross section; j and m are the serial numbers of the starting and ending vertical lines of the bottom layer, respectively, and the meanings of the other symbols are the same as above.

[0122] Therefore, the average flow velocity at the bottom of the canal can be expressed as:

[0123]

[0124] According to equation (14), the average velocity of the nth horizontal layer on the cross section can be written as:

[0125]

[0126] in:

[0127]

[0128] Will After substituting into equation (26), and then substituting equations (25) and (26) into equation (20), we can obtain the following after analysis and simplification:

[0129]

[0130] As can be seen from the above equation, the bottom velocity coefficient is only related to the bottom cross-sectional shape and the surface velocity coefficient K0. Therefore, once the bottom region is delineated, the bottom velocity coefficient k can be calculated from the surface velocity coefficient K0 and the bottom cross-sectional measurement data using equation (40). 底 Therefore, after the surface velocity coefficient is calibrated in the multi-layer method, the bottom velocity coefficient can be calculated from the cross-sectional measurement data below the lowest velocity measuring layer and the surface velocity coefficient.

[0131] The experimental data are as follows:

[0132] Using ultrasonic time-of-flight test data from the Xiangtan Hydrological Station, this paper presents a case study to verify the laminar velocity to cross-sectional velocity conversion model based on the sinusoidal vertical velocity distribution, as well as the self-calibration and flow measurement methods of the ultrasonic time-of-flight flow monitoring system.

[0133] Xiangtan Station is the main control station for the Xiangjiang River flowing into Dongting Lake, controlling a catchment area of ​​81,638 km². 2 The highest historically recorded water level was 41.95m, and the highest historically recorded flow rate was 26200m³. 3 / s. The river section measured at this station is straight, with a riverbed composed of fine sand and pebbles. The cross-section is basically stable, and the water surface width can reach 750m during high water periods. The backwater effects of floods from the Yangtze River and Dongting Lake can reach the measured cross-section. Therefore, the water level-discharge relationship at this station is relatively complex due to the combined effects of flood rise and fall rates and the backwater from the Yangtze River and Dongting Lake. Methods such as rope curves, time series analysis, and drop methods are commonly used to compile discharge data. To explore the feasibility of applying the ultrasonic time-of-flight method in wide river channels, this station has conducted ultrasonic dual-machine time-of-flight flow measurement experiments for more than 10 consecutive years, obtaining a large amount of experimental data.

[0134] (I) Verification of the conversion between laminar flow velocity and cross-sectional flow velocity

[0135] Data from 92 ultrasonic time-difference method two-layer velocity measurement tests were collected at Xiangtan Station. The time-difference method velocity measurement layer setup was as follows:

[0136] (1) When the water level is higher than 38.50m, the time difference method velocity measurement layer is the fixed elevation layer of 30.0m and 37.5m (the elevation of the frozen datum of the hydrological station, the same below);

[0137] (2) When the water level is between 34.50m and 37.50m, the time difference method velocity measurement layer is the fixed elevation layer at 30.0m and 34.2m.

[0138] Using 92 ultrasonic time-of-flight velocity measurements, the surface velocity coefficient K0 based on the arcsine vertical velocity distribution was calculated using equation (1). Then, a relationship line between water level and surface velocity coefficient was plotted. Based on the water level and surface velocity coefficient, the surface velocity coefficient K0 at different water levels was calculated. Combining this with river cross-section measurement data, the relationship between water level and layer velocity coefficient at different fixed-point elevations corresponding to the arcsine velocity distribution was solved using equations (2) and (3). The relationships between water level and surface velocity coefficient, and between water level and layer velocity coefficient at Xiangtan Station are shown in [reference needed]. Figure 4 .

[0139] The aforementioned 92 time-difference velocity measurements were conducted simultaneously using a multi-method, multi-point flow meter mounted on a survey vessel. The flow rate variation across the 92 measurements was 493 m³ / s. 3 / s~19200m 3 / s. Take the flow velocity value of any layer in the two-layer velocity test, and solve the flow rate value by time difference method according to Equation (1) and the corresponding layer flow velocity coefficient. Take the measurement result of the rotor flow meter as the standard value, and calculate the single flow error, systematic error, standard deviation and random uncertainty respectively.

[0140] (1) Single flow rate error:

[0141]

[0142] In the formula: R i Let Q be the relative error of the i-th flow rate, %; ms,i The flow rate value calculated by the i-th time difference method, m 3 / s;Q mc,i Let m be the flow rate value measured by the i-th rotor flow meter using the multi-line, multi-point method. 3 / s.

[0143] (2) Systematic error:

[0144]

[0145] Where: m Q denoted as % for flow rate systematic error; n represents the total number of flow rate measurements.

[0146] (3) Standard deviation:

[0147]

[0148] Where: σ Q The standard deviation of the flow rate is expressed as a percentage; the other symbols have the same meaning as before.

[0149] (4) Random uncertainty:

[0150] X' Q =2σ Q (31)

[0151] In the formula: X' Q This represents the random uncertainty with a confidence level of 95%; the other symbols have the same meaning as before.

[0152] The error results of the 92 flow measurements calculated above are listed in Table 1. It is evident that the measurement accuracy is high; compared with the "River Flow Measurement Standard," its error meets the accuracy requirements for Class I hydrological station flow measurements.

[0153] Table 1 shows the statistical results of flow rate error calculated from the single-layer velocity coefficient using the time-difference method.

[0154] Single flow rate error range (%) -4.0～4.3 Systematic error (%) 0 Standard deviation of tests (%) 2.2 Random uncertainty of the test (%) 4.4

[0155] (II) Verification of Instantaneous Flow Conversion in a Single Speed ​​Measurement Using the Two-Layer Method

[0156] The first verification calculation method involves collecting velocity data from multiple measurements and establishing an average relationship between water level and surface velocity coefficients to calculate flow rate. However, for newly established stations using the time-of-flight method, this method still requires a period of preliminary data collection. It involves measuring the velocities of two water layers to obtain velocity distribution parameters (such as surface velocity coefficients and laminar velocity coefficients), establishing the relationship between water level or other factors and the velocity coefficients at the test section, before the conversion between laminar velocity and cross-sectional velocity can be achieved.

[0157] As can be seen from equation (1), the surface velocity K0 corresponding to the arcsine distribution can be calculated instantly for each single two-level horizontal layer velocity measurement. Substituting K0 into equations (2) and (3), the laminar velocity coefficients corresponding to the arcsine distribution of the two horizontal layers can be obtained. Therefore, the conversion coefficient between laminar velocity and cross-sectional average velocity can be directly obtained through a single ultrasonic time-of-flight method two-level layer velocity measurement. The laminar velocity coefficient was solved independently for 92 ultrasonic time-of-flight method two-level layer velocity data, and the flow rate was calculated accordingly. Similarly, the synchronous flow measurement results of the rotor flow meter were used as the standard value, and error statistics were performed. The results are listed in Table 2.

[0158] Table 2 shows the flow error statistics based on the two-layer method single velocity measurement self-rate timing difference method.

[0159] Single flow rate error range (%) -7.2～7.0 Systematic error (%) -0.2 Standard deviation of tests (%) 3.5 Random uncertainty of the test (%) 7.0

[0160] As shown in the table above, due to the influence of velocity fluctuations and other accidental factors, directly converting laminar velocity to cross-sectional velocity using a single two-layer velocity measurement results in a larger flow error compared to the flow error calculated by establishing a laminar velocity coefficient conversion line using multiple two-layer velocity measurement data. Compared with the "River Flow Measurement Specification," the errors in Table 2 basically meet the accuracy requirements for flow measurement at Class II hydrological stations.

[0161] (III) Calibration and Verification of Velocity Coefficient in the Blind Zone of the Multilayer Method

[0162] Data from 21 ultrasonic time-difference multi-stage velocimetry tests conducted at Xiangtan Station were collected and utilized. Figure 4 Based on the surface velocity coefficient relationship calibrated by the two-layer method, and combined with data from cross-sectional measurements and vertical layout, the flow rate value of the multi-layer method using the time-difference method can be calculated using formula (4), similar to the calculation method of the layer velocity coefficient. Similarly, using the synchronous flow measurement results of the rotor current meter as the standard value, the single flow rate error, systematic error, standard deviation, and random uncertainty are calculated respectively. The error statistics of the 21 results are listed in Table 3.

[0163] Table 3 shows the flow error statistics of the time difference method for estimating the bottom velocity coefficient using the multi-layer method. It can be seen that the multi-layer method is a method with high flow measurement accuracy among time difference methods.

[0164] Single flow rate error range (%) -2.5～2.0 Systematic error (%) 0 Standard deviation of tests (%) 1.0 Random uncertainty of the test (%) 2.0

[0165] It should be noted that, in this document, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0166] This article uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only for the purpose of helping to understand the method and core ideas of the present invention.

[0167] The above description is merely a preferred embodiment of the present invention. It should be noted that, due to the limitations of written expression, there are objectively infinite specific structures. For those skilled in the art, several improvements, modifications, or variations can be made without departing from the principle of the present invention, and the above technical features can be combined in an appropriate manner. These improvements, modifications, variations, or combinations, or the direct application of the inventive concept and technical solution to other situations without modification, should all be considered within the scope of protection of the present invention.

Claims

1. A self-calibration method for a time-difference flow measurement system with an arcsine vertical velocity distribution, characterized in that, Includes the following steps: (1) Install a set of train tracks on each bank of the river section and install a pair of ultrasonic transducers on the train. (2) The trolley carrying the ultrasonic transducer moves synchronously from top to bottom on the track and measures the actual flow velocity of two or more layers. (3) At the beginning and end of ultrasonic velocity measurement, the water level Z of the river section is measured according to the water level observation standard. (4) Take ultrasonic waves from the upper and lower layers and measure the actual flow velocities v from the upper and lower layers. θ1 v θ2 Using river cross-section measurement data and a velocity coefficient conversion model based on arcsine velocity distribution, the surface velocity coefficient K0 is derived. Then, based on the surface velocity coefficient K0 and the river cross-section measurement data, the corresponding upper layer velocity coefficient k for this flow measurement is calculated. θ1 Lower layer velocity coefficient k θ2 and the bottom velocity coefficient k 底 ; (5) Based on the measured water level Z, the cross-sectional area A of the river at the corresponding measured water level Z is obtained from the actual measured value of the cross section; (6) The measured flow velocity v in the upper layer θ1 and the upper velocity coefficient k θ1 The product, or the measured flow velocity v in the lower layer. θ2 and the upper velocity coefficient k θ2 The product of the average flow velocity of the cross section Then, the average flow velocity of the cross section Given the cross-sectional area A, calculate the real-time flow rate Q using the velocity area method; (7) From the bottom velocity coefficient k 底 The bottom velocity is calculated by combining the measured velocity at the lowest layer, and the real-time flow rate of the cross-section is estimated by accumulating the flow rates at each layer. (8) Repeat steps (2) to (7) multiple times, plot the correlation diagram between water level Z and surface velocity coefficient K0 for each flow measurement, and draw the relationship line between water level Z and surface velocity coefficient K0 based on the centroid of the point group distribution, i.e., the Z-K0 relationship line. Then, find the corresponding K0 and cross-sectional measurement data for each water level from the Z-K0 relationship line, and calculate the upper and lower layer velocity coefficients k corresponding to each water level. θ1 k θ2 With bottom velocity coefficient k 底 And establish the relationship lines between water level and the velocity coefficients of the upper and lower layers and the bottom velocity coefficient, i.e., Z~k θ1 Z~k θ2 and Z~k 底 The relationship line is formed by the aforementioned Z~k θ1 Z~k θ2 Z~k 底 The relationship line is used to calculate the laminar flow velocity coefficient k based on the water level. θ1 k θ2 Then, proceed to step (6) or (7) to calculate the cross-sectional flow rate and improve the accuracy of flow measurement; In the above steps (6) and (7), step (6) is executed when the two-layer method is used for flow measurement, and step (7) is executed when the multi-layer method is used for flow measurement.

2. The self-calibration method for the time-difference flow measurement system with arcsine vertical velocity distribution according to claim 1, characterized in that, In step (4), The formula for calculating the water surface velocity coefficient is as follows: in, In the formula: K0 is the surface velocity coefficient; B1 is the width of the upper horizontal layer of the river; B2 is the width of the lower horizontal layer of the river; v θ1 The measured flow velocity at the upper layer; v θ2 B1 is the measured flow velocity in the lower layer; B2 is the width of the river surface in the upper horizontal layer; π is pi, taken as 3.1416; h μ Let b be the average water depth of the μ-th part of the area, where μ = 1, 2, ..., n; μ denoted as μ, representing the width of the water surface in the μ-th part of the area; j1 represents the starting vertical line number below the upper horizontal layer; j2 represents the starting vertical line number below the lower horizontal layer; m1 represents the final vertical line number below the upper horizontal layer; m2 represents the final vertical line number below the lower horizontal layer; θ is the relative water depth value calculated from the riverbed, which is between 0 and 1.

3. The self-calibration method for the time-difference flow measurement system with arcsine vertical velocity distribution according to claim 1, characterized in that, In step (4), The formula for calculating the upper layer velocity coefficient is as follows: The formula for calculating the lower layer velocity coefficient is as follows: The formula for calculating the bottom velocity coefficient is as follows: in, In the formula: k θ1 k is the upper-layer velocity coefficient. θ2 k is the velocity coefficient of the lower layer. 底 B is the bottom velocity coefficient; n h is the width of the river surface in the lowest velocity measurement layer of the multi-layer method. y The water depth below the lowest velocity measuring layer in the multi-layer method, i.e., the height from the bottom of the canal to the nth horizontal layer, varies with the distance from the starting point of the cross-section and is usually represented by h. y =f(B);d μ h is the water depth along the μ-th vertical line on the cross-section. y，μ b is the water depth below the nth horizontal layer on the μth vertical line of the cross section; μ The width of the water surface in the μ-th part of the cross-section; θ n is the relative water depth of a certain vertical line in the lowest velocity measurement layer of the multi-layer method, measured from the riverbed; j and m are the serial numbers of the starting and ending vertical lines of the bottom layer, respectively; the meanings of the other symbols are the same as above.

4. The self-calibration method for the time-difference flow measurement system with arcsine vertical velocity distribution according to claim 1, characterized in that, In step (6), The formula for calculating the real-time flow Q using the two-layer method is as follows: In the formula: Q is the flow rate; A is the cross-sectional area of ​​the river; This represents the cross-sectional average velocity; the other symbols have the same meaning as above.

5. The self-calibration method for a time-difference flow measurement system with an arcsine vertical velocity distribution according to claim 1, characterized in that, In step (7), The formula for calculating the real-time flow Q using the multi-layer method is as follows: In the formula: v μ Let μ be the horizontal flow velocity of the μ-th velocity-measuring layer (μ = 1, 2, 3, ..., n), and when μ = n, it is the flow velocity at the boundary of the riverbed blind zone; A μ Let k be the cross-sectional area of ​​the μ-th part of the water passage; 底 This represents the bottom velocity coefficient; the other symbols have the same meaning as above.

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