Disturbance wave velocity prediction method based on physical guidance neural network

Abstract

The invention discloses a disturbance wave velocity prediction method based on a physical guidance neural network, and the method comprises the following steps: 1, carrying out the physical layer parameter correction based on a three-fluid model through employing an entrainment rate modeling result, and obtaining a corrected density ratio, a corrected gas nucleus Reynolds number, and a corrected liquid membrane Reynolds number; 2, establishing a physical guidance neural network model, and carrying out training and hyper-parameter optimization; and step 3, combining a physical layer and the trained neural network to predict the disturbance wave velocity.

Description

Technical Field

[0001] The present invention belongs to the technical field of multiphase flow measurement, and relates to a method for predicting perturbation wave speed based on a physical-guided neural network of a three-fluid model. Background Technique

[0002] Annular mist flow widely exists in industry, especially in fields such as petrochemical industry, natural gas processing, heat exchangers, and evaporators [1] . The perturbation wave speed in annular mist flow is an important parameter to describe the flow characteristics of gas-liquid two-phase flow, and is also an important parameter for studying the momentum transfer at the gas-liquid interface, predicting heat transfer and frictional pressure drop. By measuring the perturbation wave speed, the momentum transfer between the liquid film and the gas core can be understood, which has a direct impact on the estimation of the heat transfer characteristics and frictional pressure drop of the liquid film. Therefore, accurate prediction of the perturbation wave speed is of great significance in industry.

[0003] The perturbation wave speed of annular mist flow has been widely used. Due to the complexity of two-phase experimental conditions, most researchers use the superficial velocity to nondimensionalize the perturbation wave speed, and then establish a correlation with the inlet superficial parameters. For example, D. Schubring et al. [2] used the superficial gas velocity for nondimensionalization and established a correlation with the gas Reynolds number and dryness. Peng Ju [3] used the superficial liquid velocity for nondimensionalization and established a power-law form correlation with the Weber numbers of gas and liquid phases. In terms of theoretical modeling, various methods have been proposed to establish empirical correlations of the perturbation wave speed. The most famous one is the interfacial shear force model proposed by Kumar [4] . To improve the applicability of the model under different working conditions, the Kumar [4] model was modified. For example, Setyawan et al. [5] added the surface tension ratio parameter, and M Wang et al. [6] added the pressure ratio parameter. The above models are all empirical or semi-empirical formulas based on superficial parameters, and their empirical coefficients are greatly affected by experimental conditions, resulting in poor expansibility of the models. Due to the differences in internal flow conditions under different working conditions not being considered, the prediction accuracy is low in a wide range of flow conditions (flow direction, medium, diameter, pressure, etc.), and the prediction error exceeds ±50%.

[0004] To further improve the applicability of the model, researchers considered the droplet-liquid film mass transfer in annular mist to correct the entrainment rate. For example, Sun Hongjun [7] , Chao Wang et al. [8]The influence of droplets in the gas core is considered to correct the mixture density and mixture velocity. Considering the differences in entrainment rates under different working conditions and using the average velocity of the liquid film to replace the apparent velocity of the liquid phase, the prediction accuracy of the model is further improved (the prediction accuracy is about 20% - 35%). Different from this, Chao Wang et al. [8] used a complex empirical formula for the cross-sectional gas holdup to predict the entrainment rate, while Sun Hongjun et al. [7] directly established a correlation between the entrainment rate and the inlet parameters. The above semi-empirical formulas have good applicability under different entrainment conditions. However, due to the introduction of many ideal assumptions and empirical formulas in the derivation process, it is difficult to further improve the prediction accuracy (the best accuracy is about 20%), especially the prediction accuracy is poor under the condition of low disturbance wave velocity. To further improve the prediction accuracy, Sun Hongjun et al. [9] used the machine learning method to predict the disturbance wave velocity based on the BP neural network, and the prediction accuracy reached ±3.5% under their experimental conditions. However, they did not consider the influence of entrained droplets under different carrier gas conditions in the actual annular mist flow, and the interpretability and expandability of the model need to be further improved.

[0005] To improve the prediction accuracy, applicable range, and model interpretability of the disturbance wave velocity, entrainment rate correction and deep learning are carried out on the basis of the annular mist shear model. The present invention proposes a new disturbance wave velocity model based on Physics-Informed Neural Networks (PGNN), and the model is verified by 288 sets of open data under different flow conditions.

[0006] Patent 201810644726.7 designed a multi-parameter adjustable mist flow experimental system, Patent 201810226454.9 presented an annular flow liquid film collection and metering device, and Patent 201810232606.6 provided an annular flow liquid film separation and mass metering method.

[0007] Related literature

[0008] [1]. Sun Hongjun, Li Teng, Li Jinxia, et al. Prediction model of disturbance wave height based on Kelvin-Helmholtz instability and interfacial shear force [J]. Chemical Industry and Engineering Progress, 2024, 43(2): 609.

[0009] Sun HJ, Li T, Li JX, et al. Disturbance wave height prediction model based on Kelvin-Helmholtz instability and interfacial shear[J]. Chemical Industry and Engineering Progress, 2024, 43(2): 609.

[0010] [2]. Schubring D, Shedd T A. Wave behavior in horizontal annular air–water flow[J]. International Journal of Multiphase Flow, 2008.34(7): 636-646.

[0011] [3]. P. Ju, Y. Liu, X. Yang, et al., Wave characteristics of vertical upward adiabatic annular flow in pipes, Int.J.Heat Mass Transf. 145(2019), 118701.

[0012] [4]. R. Kumar, M. Gottmann, K. R. Sridhar, Film Thickness and Wave Velocity Measurements in a Vertical Duct, J.Fluids Eng. 124(3)(2002)634–642.

[0013] [5]. Setyawan A, Indarto, Deendarlianto. The effect of the fluid properties on the wave velocity and wave frequency of gas–liquid annular two-phase flow in a horizontal pipe[J]. Experimental Thermal and Fluid Science, 2016.71: 25-41.

[0014] [6]. M. Wang, D. Zheng, Y. Wu, Experimental and modeling study on interfacial disturbance wave velocity in horizontal gas-liquid flow by ultrasonic method, Exp. Therm Fluid Sci. 109 (2019), 109908.

[0015] [7]. Sun H, Li T, Li J, et al. Generalization of disturbance wave velocity of vertical annular flow considering entrained droplets effect[J]. Experimental Thermal and Fluid Science, 2024, 151: 111102.

[0016] [8]. C. Wang, N. Zhao, Y. Feng, H. Sun, L. Fang, Interfacial wave velocity of vertical gas liquid annular flow at different system pressures, Experimental Thermal and Fluid Science (2017), doi: http: / / dx.doi.org / 10.1016 / j.expthermflusci.2017.09.07

[0017] [9]. Sun H, Huang Y, Li J, et al. Disturbance Wave Velocity Model based on Physics-Guided Backpropagation Neural Network[C] / / 2024 IEEE International Instrumentation and Measurement Technology Conference (I2MTC). IEEE, 2024: 1 - 6.

[0018]

[10] . A. Al-Sarkhi, C. Sarica, K. Magrini, Inclination effects on wave characteristics in annular gas-liquid flows, American Institute of Chemical Engineers 58(4)(2012)1018–1029.

[0019]

[11] . A. Wolf, S. Jayanti, G. F. Hewitt, Flow development in vertical annular flow, Chem. Eng. Sci. 56(10)(2001)3221–3235.

[0020]

[12] . P. De Jong, K. S. Gabriel, A preliminary study of two-phase annular flow at microgravity: experimental data of film thickness, Int. J. Multiph. Flow 29(8)(2003)1203–1220.

[0021]

[13] . P. Sawant, M. Ishii, T. Hazuku, et al., Properties of disturbance waves in vertical annular two-phase flow, Nucl. Eng. Des. 238(12)(2008)3528–3541.

[0022]

[14] . M. B. Alamu, Investigation of periodic structures in gas-liquid flow, University of Nottingham, 2010.

[0023]

[15] . A. Dasgupta, D. K. Chandraker, S. Kshirasagar, et al., Experimental investigation on dominant waves in upward air - water two - phase flow in churn and annular regime, Exp. Therm Fluid Sci. 81(2017)147–163.

[0024]

[16] . T. A. Moreira, R. W. Morse, K. M. Dressler, et al., Liquid - film thickness and disturbance - wave characterization in a vertical, upward, two - phase annular flow of saturated R245fa inside a rectangular channel, Int. J. Multiph. Flow 132(2020), 103412. Summary of the Invention

[0025] The present invention aims to provide a method and device for predicting disturbance wave velocity based on a physics - informed neural network to solve problems such as low prediction accuracy, limited applicable range, and poor model interpretability in the prior art. The technical solutions are as follows:

[0026] A method for predicting disturbance wave velocity based on a physics - informed neural network includes the following steps:

[0027] Step 1, based on the three - fluid model, use the modeling result of the entrainment rate to correct the physical layer parameters to obtain the corrected density ratio, corrected gas - core Reynolds number, and corrected liquid - film Reynolds number;

[0028] Step 2, establish a physics - informed neural network model and perform training and hyperparameter optimization, as follows:

[0029] 1) The input parameters are: the corrected density ratio ρ gc / ρ l 、the corrected gas - core Reynolds number Re' g 、the corrected liquid - film Reynolds number Re lf ;

[0030] The output parameter is: the interfacial slip velocity ratio ψ';

[0031] Use the disturbance wave velocity V w data and operating condition parameters to train the physics - informed neural network model;

[0032] 2) Use the Levenberg - Marquardt algorithm for training and optimization; optimize the hyperparameters of the physics - informed neural network model;

[0033] Step 3: Combine the physical layer and the trained neural network to predict the perturbation wave speed.

[0034] Furthermore, the method of Step 1 is as follows:

[0035] 1) Input the operating conditions and test conditions, including: superficial gas velocity V sg , superficial liquid velocity V sl , gas density ρ g , liquid density ρ l , and nominal pipe diameter D;

[0036] 2) Predict the entrainment rate parameter E according to formula (1)

[0037]

[0038] where,

[0039] The entrainment rate E = W E / W l , where W E is the mass flow rate of the droplets, and W l is the mass flow rate of the liquid phase;

[0040] Gas Weber number where σ is the liquid - phase surface tension coefficient;

[0041] Liquid Reynolds number where μ l is the dynamic viscosity of the liquid;

[0042] 3) Calculate the characteristic velocity V of the gas core according to equation (2) gc

[0043]

[0044] where W g is the mass flow rate of the gas phase, A represents the cross - sectional area of the pipeline,

[0045] 4) Calculate the corrected gas - core mixture density ρ according to equation (3) gc

[0046]

[0047] 5) Calculate the average velocity on the liquid - film surface according to equation (4)

[0048]

[0049] 6) Calculate the corrected gas core Reynolds number Re' according to Equation (5). g

[0050]

[0051] where μ g is the dynamic viscosity of the gas;

[0052] Calculate the corrected liquid film Reynolds number Re according to Equation (6). lf

[0053]

[0054] Furthermore, in step two, calculate according to Kumar formula (7) to obtain

[0055]

[0056] where the average velocity on the liquid film surface is calculated by Equation (4), and the gas core characteristic velocity V gc is calculated by Equation (2), and the perturbation wave velocity V w is obtained by experimental measurement.

[0057] Furthermore, use the loss function Equation (8) to guide the learning process of the model:

[0058]

[0059] where N is the total number of data, ψ i is the true value of the i-th data point, is the predicted value of the i-th data point.

[0060] Furthermore, in step two, the size of the hidden layer of the optimized physics-guided neural network model is 4, the number of neurons in each layer is 20, the number of iterations is 10,000, the learning rate is 0.001, the momentum factor is 0.9, and the minimum performance gradient is e -10 .

[0061] Furthermore, the method of step three is as follows:

[0062] 1) Input the operating conditions and test conditions, including: gas superficial velocity V sg , liquid superficial velocity V sl , gas density ρ g , liquid density ρ l , and nominal pipe diameter D;

[0063] 2) Predict the entrainment rate parameter E according to formula (1);

[0064] 3) Calculate the correction parameters: Calculate the characteristic velocity V of the gas core according to formula (2) gc , calculate the mixed density ρ of the gas core according to formula (3) gc , calculate the average velocity on the surface of the liquid film according to formula (4)

[0065] 4) Calculate the corrected characteristic Reynolds number Re' of the gas core according to formula (5) g , calculate the corrected characteristic Reynolds number Re of the liquid film according to formula (6) lf ;

[0066] 5) Using the corrected density ratio ρ gc / ρ l , the corrected gas core Reynolds number Re', g , and the liquid film Reynolds number Re lf as input parameters, use the physically-guided neural network model trained in step two for prediction to obtain the interfacial slip velocity ratio ψ';

[0067] 6) Calculate the perturbation wave velocity V according to formula (9) w

[0068]

[0069] The above perturbation wave velocity prediction method based on a physically-guided neural network has the following advantages:

[0070] (1) Improve prediction accuracy

[0071] Combining the physical model and the data-driven method, the present invention can effectively improve the accuracy of perturbation wave velocity prediction. Especially in the complex flow state of multiphase fluids, the prediction error of the model is significantly lower than that of traditional methods.

[0072] (2) Enhance physical interpretability

[0073] Through the physically-guided loss function, the prediction results of the neural network not only conform to the experimental data but also reflect the physical laws, thus enhancing the interpretability of the model. This is of great significance for engineering applications in the field of fluid mechanics.

[0074] (3) Strong generalization ability

[0075] The method of the present invention has strong generalization ability and can adapt to the prediction of perturbation wave velocity in different fluid environments, and can be widely applied to fields such as chemical engineering, oil and gas, and nuclear energy. Description of the Drawings

[0076] Figure 1 : Droplet-liquid film-gas core three-fluid model

[0077] Figure 2:Physics-guided BP neural network structure

[0078] Figure 3 :Comparison of entrainment rate modeling and measurement results

[0079] Figure 4 : Learning rate hyperparameter optimization comparison chart

[0080] Figure 5 :Comparison of prediction results of different disturbance wave velocities DETAILED DESCRIPTION

[0081] The present invention will now be further described with reference to the accompanying drawings and embodiments.

[0082] In view of the problems existing in the prior art, the present invention proposes a disturbance wave velocity prediction method based on a physical guided neural network. The method is based on the gas phase-liquid droplet-liquid film three-fluid model, considers the influence of entrained droplets on the gas core parameters and liquid film parameters, and combines the physical guided neural network (PGNN) for prediction, thereby improving the prediction accuracy and model interpretability.

[0083] 1. Based on the three-fluid model, the entrainment rate modeling results are used to correct the physical layer parameters, specifically:

[0084] About the basis of the physical model: The liquid film is a flow region separated by the interface and the gas core. The gas core-liquid film two-phase interface is mainly affected by the gas shear stress τ i|g and the liquid shear stress τ i|l Taking into account the effect of the disturbance wave velocity on the interface shear force, a theoretical formula for the interface shear force is established, as shown in formula (2).

[0085]

[0086] in, and represent the gas interface friction factor and the liquid interface friction factor, ρ g and ρ l are the gas density and liquid density respectively, V sg and V sl Represent the gas phase superficial velocity and liquid phase superficial velocity, V w represents the disturbance wave speed.

[0087] According to Newton's third law, τ i|g =τ i|l , combining formula (1) and (2), we can derive the disturbance wave velocity V w The expression

[0088]

[0089] Among them, the dimensionless parameter Ψ represents the ratio of the two-phase slip velocity. Kumar [4] Estimate the parameter Ψ through Equation (4).

[0090]

[0091] Among them, the gas-phase Reynolds number The liquid-phase Reynolds number Among them, μ g is the dynamic viscosity of the gas, μ l is the dynamic viscosity of the liquid, and D is the nominal diameter of the pipeline. The parameter Ψ is obtained using Equation (4) and substituted into Equation (3) to predict the perturbation wave speed V w for prediction.

[0092] The above Kumar model does not consider the mass transfer between the liquid droplets and the liquid film. In actual annular mist flow, a part of the liquid phase is entrained by the high-speed gas phase in the form of tiny liquid droplets, and the other part flows slowly along the pipe wall in the form of a liquid film. There is a dynamic mass transfer process between the liquid droplets and the liquid film. Under the action of the gas-liquid interface shear stress, the wave peaks on the liquid film surface are stretched and sheared to form entrained liquid droplets. This annular mist flow containing liquid droplets can be described by a gas-liquid-droplet-liquid film three-fluid model, as shown in the appendix Figure 1 as shown.

[0093] Regarding the values of the two-phase characteristic velocity and characteristic density, Sun Hongjun [7] considered the influence of the entrainment rate E = W E / W l and obtained more accurate prediction results. Regarding the entrainment rate, there are few measured data of the entrainment rate parameter in the publicly available perturbation wave speed database, and it is also difficult to measure the entrainment rate E online. To improve the convenience of the above model in the absence of entrainment data, it is necessary to measure the entrainment rate data and establish a prediction formula. Based on the annular flow liquid film collection and measurement device proposed in Patent 201810226454.9 and the annular flow liquid film separation and mass measurement method provided by Patent 201810232606.6, a full-flow test was carried out to obtain the measured entrainment rate data under different gas-phase flow rates, gas-phase pressures, and liquid-phase flow rates, and then the entrainment rate was predicted.

[0094] Regarding the entrainment rate modeling, since it is for the purpose of correcting the inlet parameters, it is hoped that the prediction can be made only from the inlet parameters, and at the same time, it is hoped that the model has a wider application range and a simple formula form. Therefore, the entrainment rate model proposed by Al-Sarkhi

[10] is adopted and modeled with reference to the formula of Sun Hongjun [7], as shown in Equation (5)

[0095]

[0096] Among them, a and b are constant coefficients, c and e are constant coefficients, and d is the power exponent. We g is the gas-phase Weber number, as shown in Equation (6)

[0097]

[0098] Among them, σ is the liquid-phase surface tension coefficient.

[0099] The liquid-phase Reynolds number is as shown in Equation (7)

[0100] Re l = V sl ρ l D / μ l #(7)

[0101] Among them, μ l is the dynamic viscosity of the liquid.

[0102] Using the experimental data in Reference [7] and referring to its least-squares fitting results, the specific form of Equation (5) is obtained, as shown in Equation (8):

[0103]

[0104] The comparison diagram of the prediction results and the measured results of Equation (8) is as Figure 3 shown, which qualitatively conforms to the variable law of the entrainment rate. Quantitatively, the determination coefficient R 2 = 0.976, the relative root-mean-square error rRMSE = 4.51%, the error band is within ±10.0%, and the confidence level is 95.3%, indicating good prediction performance.

[0105] Modify the gas-phase characteristic velocity, liquid-phase characteristic velocity, and characteristic density: Assume that the gas and liquid droplets in the assumed gas core move at the same velocity, and use the mixed velocity V gc of the gas core, as shown in Equation (9), to estimate the gas-core characteristic velocity.

[0106]

[0107] Among them, W g and W l are the gas-phase mass flow rate and liquid-phase mass flow rate respectively, and A is the cross-sectional area of the pipeline.

[0108] For the gas-core mixture, since the density of the liquid droplets is much greater than that of the gas phase, therefore, use the volume density ρ gc of the gas-core mixture, as shown in Equation (10), to estimate the characteristic density of the gas core.

[0109]

[0110] Considering the differences in various entrainment conditions, the percentage of droplets removed from the liquid phase and the apparent velocity V of the liquid phase are sl corrected to the flow velocity at the liquid film surface as shown in Equation (11).

[0111]

[0112] To improve the scalability of the model, dimensionlessization is carried out. In the above model, the dimensionless parameter representing the interfacial slip velocity ratio is an important parameter. Among them, the modified gas core characteristic Reynolds number Re' g is shown in Equation (12)

[0113]

[0114] where μ g is the dynamic viscosity of the gas.

[0115] The modified liquid film characteristic Reynolds number Re lf is shown in Equation (13).

[0116]

[0117] where μ l is the dynamic viscosity of the liquid.

[0118] Using the above dimensionless modified parameters, Sun Hongjun [7] performed a regression fit on the interfacial slip velocity ratio parameter ψ' in the form of a power exponent, as shown in Equation (14):

[0119]

[0120] Equation (14) is obtained from the physical model inference and has strong empiricism. The coefficient 10.6, the power exponents 0.5 and 0.25 are all obtained by regressing the experimental data of the vertical downward pipeline, and it is difficult to meet the requirements of high-precision prediction under different working conditions (medium, pressure, physical property parameters, etc.). The machine learning method can perform adaptive training and can, to a certain extent, make up for the adaptability problem of the above model. Therefore, a neural network model guided by physical information is proposed for predicting the perturbation wave speed, as Figure 2 shown. Considering the influence of the entrainment rate, physical corrections are made to the inlet parameters to correct the density ratio ρ gc / ρ l , the modified gas core Reynolds number Re', g , the liquid film Reynolds number Re lf as parameters, and the dimensionless parameter ψ' is trained, expecting to improve the prediction accuracy while enhancing the adaptability and model interpretability under different working conditions.

[0121] II. Training and prediction are performed using a BPNN neural network, specifically as follows:

[0122] Training and prediction are performed using a Back Propagation Neural Network (BPNN), where the input parameters are: the corrected density ratio ρ gc / ρ l , the corrected gas core Reynolds number Re' g , and the liquid film Reynolds number Re lf ; the output parameter is: the interfacial slip velocity ratio ψ', and the interfacial slip velocity ratio ψ can be obtained according to the Kumar model (15)

[0123]

[0124] The physical-guided neural network model is trained using the collected disturbance wave speed V w data, and the learning process of the model is guided by the loss function formula (16).

[0125]

[0126] where N is the total number of data, ψ i is the true value of the i-th data point, is the predicted value of the i-th data point.

[0127] To ensure the training speed and training accuracy, the parameters of the BPNN are optimized, including the size of the hidden layer, the number of neurons in each layer, the number of iterations, the learning rate, the momentum factor of trainlm (i.e., Levenberg-Marquardt), and the minimum performance gradient. The hyperparameters of the BPNN are optimized to obtain an optimized hidden layer size of 4, the number of neurons in each layer of 20, the number of iterations of 10000, the learning rate of 0.001, the momentum factor of trainlm (i.e., Levenberg-Marquardt) of 0.9, and the minimum performance gradient of e -10 .

[0128] Taking the learning rate as an example, using a network with 4 hidden layers, 20 nodes in each hidden layer, a momentum factor of 0.9, iterating 10,000 times, and adjusting the learning rate a accordingly, the changes in the training set loss rate and the test set MAE are as Figure 4 shown. Observation shows that an increase in the learning rate is associated with a rapid decrease in the loss, resulting in faster convergence. However, this also leads to a less smooth descent curve. Although a learning rate of 0.01 would produce higher accuracy, it introduces significant instability, which is demonstrated in the graphical representation. Therefore, a learning rate of 0.001 is chosen because of its balanced combination of high accuracy and stability.

[0129] III. Combine the physical layer and the trained neural network to predict the perturbation wave velocity, specifically as follows:

[0130] 1) Input the operating conditions and test conditions, including: gas superficial velocity V sg , liquid superficial velocity V sl , gas density ρ g , liquid density ρ l , and nominal pipe diameter D;

[0131] 2) Calculate the entrainment rate parameter E according to formula (8);

[0132] 3) Calculate the correction parameters: Calculate the characteristic velocity V gc of the gas core according to formula (9), calculate the mixed density ρ gc of the gas core according to formula (10), and calculate the average velocity on the liquid film surface according to formula (11)

[0133] 4) Calculate the corrected gas core characteristic Reynolds number Re' according to formula (12) g , and calculate the corrected liquid film characteristic Reynolds number Re according to formula (13) lf ;

[0134] 5) Use the corrected density ratio ρ gc / ρ l , corrected gas core Reynolds number Re' g , and liquid film Reynolds number Re lf as input parameters, and use the trained BPNN model in step II to predict and obtain the interfacial slip velocity ratio ψ';

[0135] 6) Calculate the perturbation wave velocity V according to formula (17) w

[0136]

[0137] According to the above method, the prediction of the perturbation wave velocity based on the physics-informed neural network is finally realized.

[0138] To verify the prediction accuracy and reliability of the above perturbation wave velocity model based on the physics-informed neural network, the publicly available perturbation wave velocity database was used for training. A total of 288 groups of publicly available data with different diameters, pressures, media, and flow directions were selected, as shown in Table 1, and the prediction effect was evaluated. The evaluation index is shown in formula (18).

[0139] Table 1 Perturbation Wave Velocity Database

[0140]

[0141]

[0142] Among them, respectively represent the predicted value and the actual value of the i-th sample. PE(i) represents the prediction error of the i-th data, MPE represents the mean percentage error, MAPE represents the mean absolute percentage error, Unc,pre represents the uncertainty, and ξ m％ represents the proportion of the prediction result error within ±m%.

[0143] According to the prediction model and the parameter calculation method of formula (18), the prediction results are processed and graphs are drawn, as shown in the appendix Figure 5 shown. 76.74% is concentrated within the error of ±5%, and R 2 is 0.99, MPE is 0.41%, MAPE is 4.29%, the uncertainty Unc,pre is 10.02%, and ξ 5％ is 76.74%, and ξ 15％ is 94.10%, and ξ 30％ is 98.26%. The perturbation wave speed predicted by the theoretical model has a prediction accuracy within ±30% under a wide range of working conditions [7] , and the prediction accuracy of this model has been significantly improved.

[0144] The present invention proposes a method for predicting the perturbation wave speed based on a physically guided neural network of a three-fluid model. This method corrects the gas core parameters and liquid film parameters by considering the influence of entrained droplets, and combines the physically guided neural network for prediction, improving the prediction accuracy and the interpretability of the model, and is applicable to the prediction of the perturbation wave speed in various industrial fields.

Claims

1. A disturbance wave velocity prediction method based on a physical guided neural network, comprising the following steps: Step 1: Based on the three-fluid model, the entrainment rate modeling results are used to correct the physical layer parameters to obtain the corrected density ratio, corrected gas core Reynolds number, and corrected liquid film Reynolds number; Step 2: Establish a physical guided neural network model and perform training and hyperparameter optimization as follows: 1) Input parameters: Corrected density ratio ρ gc / ρ l , Corrected gas core Reynolds number Re' g , Corrected liquid film Reynolds number Re lf ; The output parameters are: interface slip velocity ratio ψ'; Using the disturbance wave velocity V w Data and operating parameters are used to train the physics-guided neural network model; 2) Use the Levenberg-Marquardt algorithm for training and optimization; optimize the hyperparameters of the physics-guided neural network model; Step three, combine the physical layer and the trained neural network to predict the disturbance wave speed.

2. The disturbance wave velocity prediction method based on physical guided neural network according to claim 1 is characterized in that: The method for step one is as follows: 1) Input operating parameters and test conditions, including: gas phase apparent velocity V sg , Liquid superficial velocity V sl , gas phase density ρ g , liquid density ρ l , nominal diameter of the pipe D; 2) According to formula (1), predict the entrainment rate parameter E in, Entrainment rate E = W E / W l , where W E is the mass flow rate of the droplets, W l is the mass flow rate of the liquid phase; Gas phase Weber number Where, σ is the surface tension coefficient of the liquid phase; Liquid Reynolds number Among them, μ l is the dynamic viscosity of the liquid; 3) Calculate the gas core characteristic velocity V according to formula (2): gc Among them, W g is the mass flow rate of the gas phase, A represents the cross-sectional area of ​​the pipeline, 4) Calculate the corrected gas core mixing density ρ according to formula (3): gc 5) Calculate the average velocity of the liquid film surface according to formula (4): 6) Calculate the corrected gas core Reynolds number Re' according to formula (5): g Among them, μ g is the dynamic viscosity of the gas; According to formula (6), the corrected liquid film Reynolds number Re is calculated lf 3. The disturbance wave velocity prediction method based on physical guided neural network according to claim 2 is characterized in that: In step 2, according to Kumar formula (7), we can get The average velocity of the liquid film surface is The characteristic velocity V of the gas core is calculated by formula (4): gc The disturbance wave velocity V is calculated by formula (2): w Measured for the experiment.

4. The disturbance wave velocity prediction method based on physical guided neural network according to claim 2 is characterized in that: The loss function (8) is used to guide the learning process of the model: Where N is the total number of data, ψ i is the true value of the ith data point, is the predicted value of the ith data point.

5. The disturbance wave velocity prediction method based on physical guided neural network according to claim 2 is characterized in that: In step 2, the size of the hidden layer of the optimized physical guided neural network model is 4, the number of neurons in each layer is 20, the number of iterations is 10000, the learning rate is 0.001, the momentum factor is 0.9, and the minimum performance gradient is e -10 .

6. The disturbance wave velocity prediction method based on physical guided neural network according to claim 2 is characterized in that: The method for step three is as follows: 1) Input operating parameters and test conditions, including: gas phase apparent velocity V sg , Liquid superficial velocity V sl , gas phase density ρ g , liquid density ρ l , nominal diameter of the pipe D; 2) predicting the entrainment rate parameter E according to formula (1); 3) Calculate the correction parameters: Calculate the characteristic velocity V of the gas core according to formula (2): gc , calculate the gas core mixing density ρ according to formula (3) gc , calculate the average velocity of the liquid film surface according to formula (4) 4) Calculate the corrected gas core characteristic Reynolds number Re' according to formula (5): g , according to formula (6) calculate the modified liquid film characteristic Reynolds number Re lf ; 5) To correct the density ratio ρ gc / ρ l , Corrected gas core Reynolds number Re' g , Liquid film Reynolds number Re lf As the input parameter, the physical guidance network model trained in step 2 is used for prediction to obtain the interface slip velocity ratio ψ'; 6) Calculate the disturbance wave velocity V according to formula (9): w

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