CN114068051A - Method for calculating temperature and flow of coolant of main pipeline of nuclear reactor based on ultrasonic array - Google Patents
Method for calculating temperature and flow of coolant of main pipeline of nuclear reactor based on ultrasonic array Download PDFInfo
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- G—PHYSICS
- G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
- G21C—NUCLEAR REACTORS
- G21C17/00—Monitoring; Testing ; Maintaining
- G21C17/017—Inspection or maintenance of pipe-lines or tubes in nuclear installations
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- G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
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- G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
- G21C—NUCLEAR REACTORS
- G21C17/00—Monitoring; Testing ; Maintaining
- G21C17/02—Devices or arrangements for monitoring coolant or moderator
- G21C17/032—Reactor-coolant flow measuring or monitoring
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- Y02E30/00—Energy generation of nuclear origin
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Abstract
The invention relates to the field of ultrasonic measurement, in particular to a method for calculating the temperature and the flow of a coolant of a nuclear reactor main pipeline based on an ultrasonic array, which solves the problem of low measurement precision in the process of measuring the flow by ultrasonic in the prior art. The invention sets ultrasonic transducer group on the outer side of the pipeline, and connects with the remote server through the network module, one through CFD to build model to calculate the model field of temperature and flow speed under the input parameter; secondly, establishing a relation description model; measuring and calculating a three-reconstruction field; and fourthly, performing feedback setting on the topological structure of the ultrasonic transducer group through errors of the reconstruction field and the model field. According to the invention, the measurement precision of the transducer group is improved by eliminating the influence factors of ultrasonic waves in a non-aqueous medium; the temperature and the flow velocity under the input parameters are calculated through the CFD and the neural network model, variance calculation is carried out on the temperature and the flow velocity measured by the transducer group, and the measurement precision is further improved by adjusting the topological structure of the transducer group. The remote server is connected with the transducer group to realize real-time monitoring of measurement.
Description
Technical Field
The invention relates to the field of ultrasonic wave application, in particular to a method for calculating the temperature and the flow of a coolant of a main pipeline of a nuclear reactor based on an ultrasonic array.
Background
The nuclear reactor is a complex and efficient nuclear heat conversion device, coolant in a hot section of a main pipeline has the characteristics of high temperature, high pressure, high radiation and high flow rate, and meanwhile, because the enrichment degrees of all fuel assemblies of a reactor core are different, the temperature of the coolant flowing into the hot section of the main pipeline from different fuel channels is different, and the obvious temperature stratification phenomenon exists in the hot section of the main pipeline. The temperature and the flow of the coolant of the main pipeline of the nuclear reactor directly reflect the nuclear power and the heat conducting capacity of the reactor core, and are one of the very important thermal parameters in the safety protection and the operation control of the reactor. The accurate measurement and calculation of the temperature and the flow of the coolant of the main pipeline have important significance for the safety and the economical efficiency of the reactor.
The problems of insufficient reactor output, frequent control rod action and even unplanned shutdown caused by inaccurate and untimely measurement of the temperature of the coolant of the main reactor pipeline become important bottlenecks which seriously restrict further improving the safety and the economical efficiency of the reactor. Research data at home and abroad show that the thermal stratification temperature difference of the outlet of the pressurized water reactor core can reach 15 ℃, the thermal stratification temperature difference of the hot section of the main pipeline 1.5 meters away from the outlet of the core still reaches 10 ℃, and the stratification state continuously changes along with the operation of the reactor, so that the accurate and timely measurement of a representative coolant thermal physical field is very difficult.
The method for measuring the temperature of the coolant of the reactor main pipeline in the prior art is generally a thermal resistance method and an ultrasonic temperature measuring method: the thermal resistance point type temperature measurement technology has the following problems: 1. because the coolant in the hot section has a dynamic change layering phenomenon and is limited by the installation space of a main pipeline of the reactor, the problems of insufficient representativeness and large measurement error exist, the typical measurement error reaches 1.95 ℃ (equivalent to 5.5% of full power), and the operation capacity of the reactor is severely limited; 2. because the thermometer has the problem of larger thermal inertia, the response time of a temperature measurement channel exceeds 10s, and the timeliness of safety protection and control is seriously restricted; 3. the intrinsic safety of the reactor is reduced due to the need to open holes in the pressure boundary for installing the thermometer. Ultrasonic temperature measurement is used as a non-contact temperature measurement method, has the characteristics of timely response and high safety, can form surface temperature and even body temperature by measured linear temperature through a reconstruction algorithm, can greatly reduce calculation errors caused by temperature stratification compared with traditional point temperature measurement, and improves the measurement precision of average temperature. However, because the temperature, the pressure and the concentration of the reactor coolant have dynamic change characteristics, a composite relation between the ultrasonic propagation speed and multiple elements of the coolant is not established at present; the problem of large error caused by unreasonable division of sub-temperature zones also exists.
The traditional pipeline flow measurement method is widely applied to calculating the pipeline flow by measuring the pipeline flow speed based on ultrasonic waves, however, the propagation speed of the ultrasonic waves in a medium is influenced by various factors such as temperature, pressure, medium density and the like. When the influence factors change greatly, the calculation accuracy of the conventional flowmeter is greatly reduced, and the problems of low robustness, complex structure and the like of the ultrasonic flowmeter exist;
in the ultrasonic pipeline flow meter designed by the time difference principle, the measurement accuracy of the average flow velocity is determined by the measurement accuracy of the propagation time of the ultrasonic waves in the pipeline, and the measurement of the pipeline flow is influenced finally. However, in the actual measurement of the propagation time, the propagation time in the solid medium such as the pipe wall and the transducer is also included in the measurement of the propagation time, and the measurement accuracy is difficult to guarantee because the propagation speed of the ultrasonic wave in the pipe is interfered by factors such as temperature, pressure, liquid density and the like.
A new method for calculating temperature and flow rate that can solve the above problems is desired.
Disclosure of Invention
The invention provides a method for calculating the temperature and the flow of a coolant of a main pipeline of a nuclear reactor based on an ultrasonic array, which solves the problem of low energy calculation precision of the nuclear reactor in the prior art, and can realize the simultaneous online high-precision measurement of average temperature and flow.
The technical scheme of the invention is realized as follows: the method for calculating the temperature and the flow of the coolant of the main pipeline of the nuclear reactor based on the ultrasonic array comprises the following steps that an ultrasonic transducer group is arranged on the outer side of the pipeline and is connected with a remote server through a network module, and a model field is established: establishing a complete and continuous main pipeline coolant air-time domain temperature layered diffusion model and a flow velocity distribution model under input parameters through a CFD (computational fluid dynamics) construction model; secondly, establishing a relation description model of three elements of the ultrasonic propagation speed and the coolant; three-reconstruction field measurement and calculation: measuring the flight time of each effective sound wave propagation path; the network module transmits the signals of the transducer group to a remote server through the network module; reconstructing the real-time temperature distribution and the flow velocity distribution of the coolant in the pipeline; calculating the average temperature and flow; and fourthly, performing feedback setting on the topological structure of the ultrasonic transducer group through errors of the reconstruction field and the model field.
The third step comprises ultrasonic transmission time calibration, which comprises simulating an experiment platform and acquiring experiment data; the simulation experiment platform comprises a pipeline with controllable temperature and an ultrasonic transducer arranged on the outer side of the pipeline.
The ultrasonic transmission time calibration specifically comprises the following steps:
1 in the empty tube state and at a temperature T0Then, τ at this temperature is obtained by changing the propagation path of the ultrasonic wave0The result of (1);
2 changing the temperature, and repeatedly calculating the temperature tau at different temperatures by experiments0The result of (1);
3, fitting the experimental calculation results to obtain a description model tau between the time delay and the temperature of the ultrasonic wave in the non-aqueous medium0＝F(T)。
The second step is specifically as follows: (1) establishing a relational expression of three elements of ultrasonic sound velocity and coolant; (2) simulating an experiment platform and acquiring experiment data; (3) establishing a relation description model between the ultrasonic sound velocity and the temperature, pressure and concentration of the coolant by adopting a machine learning method; the simulation experiment platform also comprises a thermostatic bath with a water inlet, a water outlet and a concentration control device, and a metal pipeline for controlling pressure; the ultrasonic transducer is connected with the micro-control device.
The fourth step is specifically sub-area division: adjusting the ultrasonic transducer topology: adjusting the topological structure of the ultrasonic transducer array based on the error distribution of the reconstruction field and the model field; dynamic adjustment based on feedback mechanism: the radius R of the inner ring of the subarea by taking the reconstruction error as a target variableirAnd the radial angle theta is used as a control variable to determine the optimal inner ring radius RirAnd a radial angle theta.
The ultrasonic transducer array topological structure is in a broadcast type, and specifically, the ultrasonic transducers are uniformly arranged on the cross section of the pipeline to be measured.
The first step is specifically as follows: a, calculating the temperature and flow rate data of the coolant of the typical section of the pipeline under set parameters by calculating the fluid mechanics (CFD); b, training a CFD simulation result by using a neural network model: training the simulation result in the step a through a neural network model; c, prediction result: and c, predicting to obtain continuous and complete temperature and flow velocity distribution of the coolant in the pipeline by using the neural network model in the step b.
The fitting of the step 3 is a machine learning method combining more than two ultrasonic transmission characteristic individual learner learning and individual learner strategies.
The invention discloses a method for calculating the temperature and the flow of a coolant of a main pipeline of a nuclear reactor based on an ultrasonic array, which improves the measurement precision of a transducer group by eliminating the influence factors of ultrasonic waves in a non-aqueous medium; the temperature and the flow velocity under the input parameters are calculated through a CFD and a neural network model, variance calculation is carried out on the temperature and the flow velocity measured by the transducer group, a main pipeline hot section coolant space-time domain temperature layered diffusion model is reconstructed through ultrasonic measurement, a relation description model of three elements of an ultrasonic sound velocity coolant is obtained through a simulation experiment platform, and the measurement precision is further improved through adjusting the topological structure of the transducer group. The remote server is connected with the transducer group to realize real-time monitoring of measurement.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1: simulating an experiment platform;
FIG. 2: a pipeline subregion division schematic diagram;
FIG. 3: establishing a flow chart of a space-time domain temperature hierarchical diffusion description model of the coolant in the hot section of the main pipeline;
FIG. 4: an ultrasonic transducer array diagram;
wherein: 1. an ultrasonic transducer; 2. a metal pipe; 3. a micro-control device; 4. a thermostatic bath; 5. a pump; 6. A boric acid concentration control device; 7. a water inlet; 8. a water outlet; 9. a pressure controller.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention discloses a method for calculating the temperature and the flow of a coolant of a main pipeline of a nuclear reactor based on an ultrasonic array, wherein an ultrasonic transducer 1 group is arranged outside the pipeline, the transducer group is connected with a remote server through a network module, and a model field is established: establishing a complete and continuous main pipeline coolant air-time domain temperature layered diffusion model and a flow velocity distribution model under input parameters through a CFD (computational fluid dynamics) construction model; secondly, establishing a relation description model of three elements of the ultrasonic propagation speed and the coolant; three-reconstruction field measurement and calculation: measuring the flight time of each effective sound wave propagation path; the network module transmits the signals of the transducer group to a remote server through the network module; reconstructing the real-time temperature distribution and the flow velocity distribution of the coolant in the pipeline; calculating the average temperature and flow; specifically, three-dimensional flow velocity field reconstruction and three-dimensional temperature field reconstruction; fourthly, feedback setting of the topological structure of the ultrasonic transducer 1 group is carried out through errors of the reconstruction field and the model field.
The third step comprises ultrasonic transmission time calibration, which comprises simulating an experiment platform and acquiring experiment data; the simulation experiment platform comprises a pipeline with controllable temperature and an ultrasonic transducer 1 arranged on the outer side of the pipeline.
The ultrasonic transmission time calibration specifically comprises the following steps:
1 in the empty tube state and at a temperature T0Then, τ at this temperature is obtained by changing the propagation path of the ultrasonic wave0The result of (1);
2 changing the temperature, and repeatedly calculating the temperature tau at different temperatures by experiments0The result of (1);
3, fitting the experimental calculation results to obtain a description model tau between the time delay and the temperature of the ultrasonic wave in the non-aqueous medium0＝F(T)。
The second step is specifically as follows: (1) establishing a relational expression of three elements of ultrasonic sound velocity and coolant; (2) simulating an experiment platform and acquiring experiment data; (3) establishing a relation description model between the ultrasonic sound velocity and the temperature, pressure and concentration of the coolant by adopting a machine learning method; the simulation experiment platform also comprises a thermostatic bath 4 with a water inlet 7, a water outlet 8 and a concentration control device, and a metal pipeline 2 for controlling pressure; the ultrasonic transducer 1 is connected with a micro-control device 3.
The first step is specifically as follows: a, calculating the temperature and flow rate data of the coolant of the typical section of the pipeline under set parameters by calculating the fluid mechanics (CFD); b, training a CFD simulation result by using a neural network model: training the simulation result in the step a through a neural network model; c, prediction result: and c, predicting to obtain continuous and complete temperature and flow velocity distribution of the coolant in the pipeline by using the neural network model in the step b.
The fitting of the step 3 is a machine learning method combining more than two ultrasonic transmission characteristic individual learner learning and individual learner strategies.
The temperature data prediction using ELM was performed in the following manner: the cross-section data obtained by CFD analysis is used as a training sample with the format of { locmn,TmnWhere M is 1, …, M is the total number of temperature measurement cross sections calculated by the CFD software, N is 1, …, N is the total number of grids divided on the temperature measurement cross sections, and a grid diagram of the main pipe and the temperature measurement cross sections is shown in fig. 3. locmn＝{[(xmn,ymn),dm,tm]In which d ismDistance from m cross section to core outlet, tmFor the m-th cross-sectional coolant relative movement time, (x)mn,ymn) Is the coordinate of the center point of the nth region on the mth section, TmnCorresponding to the nth region of the m-th cross-sectionA temperature value. The ELM regression model for an activation function g (x) containing R hidden layer nodes is represented as:
in the formula, ωr＝[ωr1,ωr2,L,ωrm]TRepresenting a weight between the input node and the r-th hidden layer node; beta is ar＝[βr1,βr2,L,βrm]TRepresenting a weight between the output node and the r-th hidden layer node; brIs the ith hidden layer threshold; r is the number of hidden layer nodes.
To improve the model prediction capability, g (x) can be selected to train the samples in a zero-error approximation manner, i.e.
Then there is
The rewriting of the above formula into a matrix form can be expressed as
Gβ＝T
Where G is the hidden layer output matrix, the input weight ωrAnd hidden layer threshold brAll the values are randomly assigned, so that the output matrix G of the hidden layer is known, and the training is completed after the output weight matrix beta is obtained. Setting the number of the predicted sections as H, and predicting the coordinate information loc of the H predicted sectionshnInputting into the trained ELM model, and outputting the predicted temperature value ThnAnd the establishment of a space-time domain temperature hierarchical diffusion description model of the coolant in the hot section of the main pipeline is realized. The whole process flow of the method is shown in FIG. 3;
establishing a relation description model of three elements of ultrasonic propagation speed and coolant;
(1) and establishing a relation between the ultrasonic sound velocity and the coolant. According to the wave equation, the propagation velocity of ultrasonic waves in a liquid medium is related to the adiabatic coefficient of compression K and the density ρ of the liquid, which are expressed as follows:
the adiabatic compression coefficient K and the density ρ are related to temperature and pressure. The coolant of the hot section of the reactor main pipeline is boric acid solution, and the temperature, the pressure and the boron concentration of the boric acid solution can influence the propagation speed of the ultrasonic wave. Therefore, the relationship between the propagation speed of the ultrasonic wave and the coolant is expressed as follows:
w＝f(T,P,S) (X)
where w is the ultrasonic sound velocity, T is the coolant temperature, P is the coolant pressure, and S is the coolant boron concentration. And (3) giving an ultrasonic sound velocity expression under the multi-element composite influence in the coolant by referring to the ultrasonic transmission characteristics in seawater:
w＝w0+wT+wP+wS+wTPS (XI)
in the formula w0Is a constant value, wTThe relationship between the speed of sound of the ultrasonic wave and the temperature of the coolant, wPThe relationship between the speed of sound of the ultrasonic wave and the pressure of the coolant, wSThe relationship between the ultrasonic sound velocity and the boron concentration of the coolant, wTPSIs the relationship between the ultrasonic sound velocity and the coolant temperature, pressure and boron concentration.
(2) Simulating an experiment platform and acquiring experiment data; and establishing a relation description model between the ultrasonic sound velocity and the temperature, pressure and concentration of the coolant by adopting a machine learning method. A real environment is simulated, a multi-element ultrasonic transmission characteristic experiment platform is built, the incidence relation between the ultrasonic sound velocity and the coolant is researched, and the schematic diagram of the experiment platform is shown in figure 1. The experimental platform takes boric acid solution (coolant) as an ultrasonic wave propagation medium, and the device can control and adjust the temperature, the pressure and the concentration of the coolant. In the experiment, the influence of each element of the coolant on the propagation speed of the ultrasonic wave is respectively researched by adopting a controlled variable method, and a large amount of experimental data is obtained.
Further, the simulation experiment platform comprises a thermostatic bath 4 with a water inlet 7, a water outlet 8 and a concentration control device, and a metal pipeline 2 for controlling pressure, wherein the metal pipeline 2 is also provided with an ultrasonic transducer 1; the ultrasonic transducer 1 is connected with a micro-control device 3.
Preferably, the method of machine learning employs more than two ultrasound transmission characteristics individual learner learning and individual learner combination strategies.
(1) Determining the topological structure and the effective sound wave path of the ultrasonic transducer 1; a radial axial array of several ultrasonic transducers is shown in fig. 4(a), taking 20 ultrasonic transducers 1 as an example, the transducers are uniformly mounted around the pipe, as indicated by the black dots in fig. 4 (a). These transducers are considered transceivers, which are controlled to transmit and detect ultrasonic signals at different times. The ultrasonic signal propagates from one transducer to another, resulting in an effective acoustic path as shown in fig. 4 (a). In theory, an ultrasonic path exists between every two transducers. However, since the ultrasonic path on the edge or surface does not contribute much to the reconstruction of the internal temperature, they are not necessary.
(2) Reconstructing a three-dimensional temperature field;
and after the flight time on each effective sound wave path is obtained, the three-dimensional cylindrical temperature field is inverted by using a radial basis temperature field reconstruction algorithm according to the mapping relation between the ultrasonic wave propagation speed and the three elements of the coolant. The several ultrasonic transducers 1 generate between each other I effective ultrasonic paths, which are divided into J sub-temperature zones, as shown in fig. 2. The obtained sonic wave flight time on each ultrasonic wave propagation path can be expressed as:
where a (x, y, z) represents the reciprocal of the sound velocity of the ultrasonic wave, and when radial basis functions are used, a (x, y, z) is expressed as a linear combination of J radial basis functions:
in the formula: epsilonjIs the undetermined coefficient; (x)j,yj,zj) The coordinates of the central point of the jth sub-temperature zone; alpha is a radial basis function phijThe shape parameters of (x, y, z) are determined as appropriate during the course of a particular experiment.
Order to
Then can obtain
Rewriting formula (XVI) to matrix form
t＝F·E (XVII)
In the formula: t ═ t1,t2,...,tI]T，F＝(fkj)k＝1,2,...I；j＝1,2,...J，E＝[ε1,ε2,...,εJ]T；
Using singular value decomposition of the matrix F and Tikhonov regularization technique, the regularization solution of equation (XVII) is:
in the formula: sigma is a nonzero singular value of the coefficient matrix F, and J is the total number of the nonzero singular values; u. ofj、vjThe left and right singular vectors of F are respectively; μ is a regularization parameter. When the ultrasonic wave is receivedAfter the array position is determined, the shape parameter alpha of the radial basis function is given, and the coefficient matrix F and the singular value thereof can be obtained. After the time-of-flight matrix t on each acoustic path is obtained, the parameter vector epsilon can be determined according to formula (XVIII). After obtaining the reciprocal of the sound velocity a (x, y, z) of the ultrasonic wave, the reciprocal is substituted into the acquired experimental data to establish the mapping relation between the propagation velocity of the ultrasonic wave and the three elements of the coolant:
T＝f-1(w,P,S) (XIX)
the three-dimensional temperature distribution of the coolant can be reconstructed from the formula (XIX).
And calculating the error between the radial direction and the axial direction of the reconstructed field and the model field according to the established pipeline space-time domain temperature distribution model. And substituting the central coordinates of the divided sub-temperature areas to obtain the temperature value of the central coordinate of each sub-temperature area, solving the temperature value of the central coordinate point of each sub-temperature area of the reconstructed temperature field and calculating the maximum absolute error, the minimum absolute error, the average relative error and the root mean square error of the temperature value by using a model. The expression is as follows:
Emax＝max|T(xi,yi,zi)-Tm(xi,yi,zi)| (XX)
Emin＝min|T(xi,yi,zi)-Tm(xi,yi,zi)| (XXI)
in the formulas (XX) - (XXIII), n is the number of all central coordinate temperature values in the region to be measured; t isaIs the average temperature of the simulated field; t (x)i,yi,zi) For model field in coordinates (x)i,yi,zi) The temperature value of (a); t ism(xi,yi,zi) For reconstructing the field in coordinates (x)i,yi,zi) The temperature value of (2).
(3) Reconstructing a three-dimensional flow velocity field;
aiming at the complex flow state of different positions of a reactor pipeline, the existence of turbulent vortex in a pipeline flow field is considered, and compared with a two-dimensional pipeline section average flow velocity calculation scheme, the flow calculation method based on three-dimensional cylindrical flow field distribution is more accurate.
And (3) installing an ultrasonic detection array on a reactor pipeline, selecting a proper ultrasonic signal emission period, measuring the flight time of a sound wave path, calculating the flow velocity according to the difference of the countercurrent flight time and the downstream flight time after obtaining the flight time, and inverting the three-dimensional flow velocity field.
Time t of propagation of ultrasonic wave from downstream to upstreamuAnd upstream to downstream propagation time tdCan be respectively expressed as:
the relationship between the ultrasonic flight time and the flow velocity can be obtained by the formula (1):
therefore, after the flight time on each effective sound wave path is obtained, the three-dimensional flow velocity field is inverted by using a reconstruction algorithm based on a radial basis according to the relation between the ultrasonic flight time and the flow velocity.
Several ultrasound transducers 1 generate between each other I active ultrasound paths, dividing them into J sub-regions, as shown in fig. 2. The sub-regions being divided by an inner radius RirAnd the divided sub-regions are changed along with two key parameters of the radial angle theta, the radius of the inner ring is different, and the radial angle is different. The relationship between the flight time of the ultrasonic wave along a specific propagation path in the region to be measured and the flow velocity can be expressed as a line integral as follows:
wherein a (x, y, z) represents the inverse of the flow rate, lkIs an ultrasonic wave propagation path. When radial basis functions are used, a (x, y, z) is expressed as a linear combination of J radial basis functions:
in the formula: epsilonjIs the undetermined coefficient; (x)j,yj,zj) The coordinates of the center point of the jth sub-region; alpha is a radial basis function phijThe shape parameters of (x, y, z) are determined as appropriate during the course of a particular experiment.
Order to
Then can obtain
Rewriting the formula (6) to a matrix form
Δt＝F·E (8)
In the formula: Δ t ═ Δ t1,Δt2,...,ΔtI]T，F＝(fkj)k＝1,2,...I；j＝1,2,...J，E＝[ε1,ε2,...,εJ]T；
Using the singular value decomposition of the matrix F and the Tikhonov regularization technique, the regularization solution of equation (27) is:
in the formula: sigma is a non-zero singular value of the matrix F, and J is the total number of the non-zero singular values; u. ofj、vjThe left and right singular vectors of F are respectively; μ is a regularization parameter. After the position of the ultrasonic receiving and transmitting array is determined, the shape parameter alpha of the radial basis function is given, and then the matrix F and the singular value thereof can be obtained. The delta t can also be determined by actually measuring the sound wave flight time and the sound channel angle theta, the parameter vector epsilon can be determined according to the formula (28), and the parameter vector epsilon is substituted into the formula (23) to obtain the distribution function of the flow velocity reciprocal, so that the distribution function of the flow velocity can be obtained through the following formula, and the reconstruction of the flow velocity field is realized.
Calculating the error between a reconstructed field and a model field according to the established pipeline space-time domain flow velocity distribution model, introducing the central coordinates in the divided sub-regions to obtain the flow velocity value of the central coordinate of each sub-region, and solving the flow velocity value of the central coordinate point of each sub-region of the reconstructed flow velocity field and the model to calculate the maximum absolute error, the minimum absolute error, the average relative error and the root mean square error of the flow velocity value. The expression is as follows:
Emax＝max|v(xi,yi,zi)-vm(xi,yi,zi)| (11)
Emin＝min|v(xi,yi,zi)-vm(xi,yi,zi)| (12)
in formulae (11) to (14):
n: the number of all central coordinate flow velocity values in the region to be measured
va: mean flow velocity of the simulated field
v(xi,yi,zi): model field in coordinates (x)i,yi,zi) Flow rate value of
vm(xi,yi,zi): flow velocity field in coordinate (x)i,yi,zi) Flow rate value of
Further, the third step further includes: a, calculating the average temperature in the measurement area according to the reconstructed temperature field; and b, calculating the average flow in the measurement area according to the reconstructed flow velocity field.
As shown in the modeling flowchart of the three-dimensional cylindrical pipe of the reactor in fig. 3, specifically: the reactor cylindrical pipeline is modeled by a space-time domain temperature and flow velocity distribution model, and the fluid can be modeled by single-phase turbulence because the fluid does not generate phase change in the pipeline. The following time-averaged monophasic continuity equations, momentum equations and energy equations may thus be established for describing the fluid flow process in the pipe.
Continuity equation:
the momentum equation:
wherein mueff＝μ+μturb。
Energy equation:
wherein k iseff＝k+Prt(μt/ρα)。
Since turbulence affects both mass and energy transfer, it is necessary to build a suitable turbulence model to quantify the turbulence viscosity. The method can be used for assisting analysis based on a standard k-epsilon turbulence model, the k-epsilon model solves the equation of turbulence momentum k and dissipation rate epsilon thereof, and the expression is as follows:
wherein the turbulent viscosity is defined as mut＝ρCμ(k2/. epsilon.). The turbulence prandtl number is also introduced in the above equations (4) and (5) to quantify the turbulence energy dissipation coefficient of the turbulence viscosity.
As shown in a grid division diagram of the reactor cylindrical pipeline modeling in fig. 4, because the calculation for the above equation is converted into discrete equation calculation, the modeling area is subjected to grid division by using CFD software to realize discretization, and the temperature and flow velocity distribution of the pipeline flow measurement section is obtained.
In order to establish an overall space-time domain temperature distribution model and a flow velocity distribution model of a flow measuring section of a three-dimensional cylindrical pipeline of a reactor, data prediction needs to be carried out on the basis of existing data. And predicting the flow speed data by adopting a radial basis function RBF neural network, and predicting the temperature data by adopting an extreme learning machine ELM.
The flow rate data prediction by using the RBF neural network can adopt the following modes: and using the flow velocity data obtained by the CFD analysis as a training sample, wherein the format of the training sample is { X, V }, and X is [ X ═ X [ ]1,x2,x3,x4]T，x1Is the abscissa, x, of the position of the model mesh2Is the ordinate, x, of the position of the model mesh3Being the vertical coordinate, x, of the position of the model mesh4The relative movement time t of water in a reactor pipeline is taken as the time t; v is a one-dimensional output speed obtained by CFD simulation; RBF networkThe output is Y ═ Y](ii) a p is the number of hidden layer nodes (p)>4) N is the total number of input samples; the iteration is terminated with precision. The output of the RBF neural network can be expressed as:
the structure of the radial basis neuron is shown in fig. 4, and the formula is as follows:
the purpose of model training is to obtain three parameters W in the formulaj、CjAnd DjAnd obtaining a space-time domain flow velocity distribution model. The training of the RBF neural network is mainly divided into two steps, firstly, the parameter C between an input layer and a hidden layer needs to be determined through unsupervised learningjAnd DjThen, supervised learning is carried out to determine the weight W between the hidden layer and the output layerj。
First, the connection weight W from the hidden layer to the output layer is [ W ]1,w2,…,wp]TAnd center parameter C of each node of the hidden layerj＝[cj1,cj2,cj3,cj4]TWidth vector D of each node of hidden layerj＝[dj1,dj2,dj3,dj4]T(j ═ 1,2, …, p) is initialized, with the initialization equations:
in the formula (22), p is the number of hidden layer nodes (p > 4), min (V)k) Is the minimum value of all expected outputs in the output neurons in the training set, max (V)k) Is the maximum of all expected outputs in the output neurons in the training set.
In formula (23), min (x)i) Is the minimum value, max (x), of all input information in the ith input feature of the training seti) Is the maximum value of all input information in the ith input feature of the training set.
In the formula (24), dfThe width adjustment coefficient is generally less than 1, so that each hidden layer neuron can easily sense local information, and the RBF neural network is helped to improve the local response capability.
Then, a gradient descent method is used for carrying out self-adaptive adjustment on the central parameters, the width vectors and the adjustment weights, and the iterative calculation formulas are respectively as follows:
wherein, the E is a learning factor, and the E is an RBF network evaluation function:
and finally, judging whether the condition of quitting the iterative operation is met, namely the root mean square error RMS is less than or equal to epsilon, if so, finishing the training, and if not, continuing to perform the weight iterative calculation.
After training is finished, values of relevant parameters can be obtained, namely, the establishment of the space-time domain flow velocity distribution model of the reactor three-dimensional cylindrical pipeline is realized.
The fourth step is specifically sub-area division: adjusting the ultrasound transducer 1 topology: adjusting the topological structure of the ultrasonic transducer 1 array based on the error distribution of the reconstructed field and the model field; dynamic adjustment based on feedback mechanism: the radius R of the inner ring of the subarea by taking the reconstruction error as a target variableirAnd the radial angle theta is used as a control variable to determine the optimal inner ring radius RirAnd a radial angle theta.
The ultrasonic transducer 1 array topological structure is in a broadcast type, and specifically, the ultrasonic transducers 1 are uniformly arranged on the section of the pipeline to be measured.
Further, the fitting of step 3 is a machine learning method using more than two ultrasound transmission characteristics individual learner learning and individual learner strategy combination. The method divides experimental data for ultrasonic transmission time calibration into a training set, a verification set and a test set, wherein the training set is used for model training and optimizing parameters such as weight, bias and the like; the verification set is used for optimizing hyper-parameters, learning rate, regularization coefficients and the like; the test set is used to evaluate the generalization ability of the model. And determining the optimal data classification method, the individual learner model and the integration strategy through experiments to finally obtain the mapping relation description model.
The method adopts an average method for integration, and comprises a simple average method, a weighted average method and the like; when the data volume is very large, the data can be integrated by adopting a learning method, namely, a plurality of individual learners are combined by a new learner so as to improve the learning accuracy. And finally, the model with the minimum root mean square error obtained by using the test set is the optimal model.
The invention discloses a method for calculating the temperature and the flow of a coolant of a main pipeline of a nuclear reactor based on an ultrasonic array, which improves the measurement precision of a transducer group by eliminating the influence factors of ultrasonic waves in a non-aqueous medium; the temperature and the flow velocity under the input parameters are calculated through the CFD and the neural network model, variance calculation is carried out on the temperature and the flow velocity measured by the transducer group, and the measurement precision is further improved by adjusting the topological structure of the transducer group. The remote server is connected with the transducer group to realize real-time monitoring of measurement.
It is understood that various changes and modifications may be made by those skilled in the art without departing from the spirit and scope of the invention, and it is intended to cover in the appended claims all such changes and modifications.
Claims (8)
1. A method for calculating the temperature and the flow of a coolant of a main pipeline of a nuclear reactor based on an ultrasonic array is characterized in that an ultrasonic transducer group is arranged on the outer side of the pipeline and is connected with a remote server through a network module, and the method comprises the following steps:
a model field is established: establishing a complete and continuous main pipeline coolant air-time domain temperature layered diffusion model and a flow velocity distribution model under input parameters through a CFD (computational fluid dynamics) construction model;
secondly, establishing a relation description model of three elements of the ultrasonic propagation speed and the coolant;
three-reconstruction field measurement and calculation: measuring the flight time of each effective sound wave propagation path; the network module transmits the signals of the transducer group to a remote server through the network module; reconstructing the real-time temperature distribution and the flow velocity distribution of the coolant in the pipeline; calculating the average temperature and flow;
and fourthly, performing feedback setting on the topological structure of the ultrasonic transducer group through errors of the reconstruction field and the model field.
2. The method for calculating the temperature and the flow of the coolant of the main pipeline of the nuclear reactor based on the ultrasonic array as claimed in claim 1, wherein the method comprises the following steps: the third step comprises ultrasonic transmission time calibration, which comprises simulating an experiment platform and acquiring experiment data; the simulation experiment platform comprises a pipeline with controllable temperature and an ultrasonic transducer arranged on the outer side of the pipeline.
3. The method for calculating the temperature and the flow of the coolant of the main pipeline of the nuclear reactor based on the ultrasonic array as claimed in claim 2, wherein the method comprises the following steps: the ultrasonic transmission time calibration specifically comprises the following steps:
1 in the empty tube state and at a temperature T0Then, τ at this temperature is obtained by changing the propagation path of the ultrasonic wave0The result of (1);
2 changing the temperature, and repeatedly calculating the temperature tau at different temperatures by experiments0The result of (1);
3, fitting the experimental calculation results to obtain a description model tau between the time delay and the temperature of the ultrasonic wave in the non-aqueous medium0＝F(T)。
4. The method for calculating the temperature and the flow of the coolant of the main pipeline of the nuclear reactor based on the ultrasonic array as claimed in claim 3, wherein the method comprises the following steps: the second step is specifically as follows: (1) establishing a relational expression of three elements of ultrasonic sound velocity and coolant; (2) simulating an experiment platform and acquiring experiment data; (3) establishing a relation description model between the ultrasonic sound velocity and the temperature, pressure and concentration of the coolant by adopting a machine learning method; the simulation experiment platform also comprises a thermostatic bath with a water inlet, a water outlet and a concentration control device, and a metal pipeline for controlling pressure; the ultrasonic transducer is connected with the micro-control device.
5. The method for calculating the temperature and the flow of the coolant of the main pipeline of the nuclear reactor based on the ultrasonic array as claimed in claim 3, wherein the method comprises the following steps: the fourth step is specifically sub-area division:
adjusting the ultrasonic transducer topology: adjusting the topological structure of the ultrasonic transducer array based on the error distribution of the reconstruction field and the model field;
dynamic adjustment based on feedback mechanism: the radius R of the inner ring of the subarea by taking the reconstruction error as a target variableirAnd the radial angle theta is used as a control variable to determine the optimal inner ring radius RirAnd a radial angle theta.
6. The method for calculating the temperature and the flow of the coolant of the main pipeline of the nuclear reactor based on the ultrasonic array as claimed in claim 5, wherein the method comprises the following steps: the ultrasonic transducer array topological structure is in a broadcast type, and specifically, the ultrasonic transducers are uniformly arranged on the cross section of the pipeline to be measured.
7. The method for calculating the temperature and the flow of the coolant of the main pipeline of the nuclear reactor based on the ultrasonic array as claimed in claim 6, wherein the method comprises the following steps: the first step is specifically as follows:
a, calculating the temperature and flow rate data of the coolant of the typical section of the pipeline under set parameters by calculating the fluid mechanics (CFD);
b, training a CFD simulation result by using a neural network model: training the simulation result in the step a through a neural network model;
c, prediction result: and c, predicting to obtain continuous and complete temperature and flow velocity distribution of the coolant in the pipeline by using the neural network model in the step b.
8. The method for calculating the temperature and the flow of the coolant of the main pipeline of the nuclear reactor based on the ultrasonic array as claimed in claim 3, wherein the method comprises the following steps: the fitting of the step 3 is a machine learning method combining more than two ultrasonic transmission characteristic individual learner learning and individual learner strategies.
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