Physical knowledge and graph network fused modeling method for multiphase flow characteristics of check valve

Abstract

The invention discloses a modeling method for multiphase flow characteristics of a check valve fusing physical knowledge and a graph network. The modeling method comprises the following steps: 1) establishing a theoretical model of the check valve for a multiphase flow pump in an opening stage; 2) establishing a theoretical model of the conveying stage of the check valve for the multiphase flow pump; 3) collecting input and output training samples under different gas-liquid mixed transportation working conditions, and establishing a graph convolution (GCN for short) model of the flow characteristics of the check valve; 4) integrating physical knowledge in the opening stage of the check valve into a training process of a GCN model, and constructing a loss function integrating the physical knowledge and a PGCN model; 5) utilizing the PGCN model trained in the step 4) to carry out online prediction on the flow characteristics of L input sample sets # imgabs0 # under a new working condition; and 6) correcting the prediction result of the conveying stage of the check valve obtained in the step 5). According to the method, modeling and prediction of the flow characteristics of the check valve for the multiphase flow pump under the complex and changeable gas-liquid mixed transportation working condition can be achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of multiphase flow pump valve design, and in particular to a modeling method for flow characteristics of a check valve for a multiphase flow pump that integrates physical knowledge and a graph network. Background Art

[0002] A multiphase flow pump is a device that can transport gas and liquid together. It is widely used in the fields of chemical industry, petroleum, environmental protection, etc. The check valve is an important and vulnerable hydraulic component of a multiphase flow pump. During the design process, it is necessary to ensure that the valve can operate reliably under frequency-varying conditions. However, in some complex frequency-varying conveying conditions, the non-uniform flow of gas and liquid in the pump will produce alternating loads, causing the check valve core to shift and collide at the moment of opening, resulting in fatigue damage and failure of the check valve spring, making it unable to work normally, causing noise and vibration in the pump, resulting in a reduction in conveying flow and reduced pump efficiency. Therefore, constructing the relationship between the instantaneous flow characteristics of the check valve in the two stages of opening and conveying and the complex frequency-varying gas-liquid mixed conveying conditions is of great significance for guiding the engineering design of the check valve and ensuring the stable operation of the multiphase flow pump.

[0003] In recent years, domestic and foreign scholars have established many theoretical models and computational fluid dynamics (CFD) models of check valves. Most of the theoretical models are based on continuity and kinematic theorems to describe the opening and closing characteristics of check valves in pure liquid and hot liquid systems, and rarely involve complex multiphase flows. Furthermore, given the limited multiphase flow theory, testing technology, and complex valve gap flow field characteristics, it is difficult to obtain the time-varying non-uniform pressure and velocity distribution characteristics in the valve gap, resulting in the existing theoretical models often making some assumptions when used in engineering practice. For example, it is assumed that the pressure, velocity, density and other parameters in the valve gap are uniformly distributed, and the valve gap parameters are replaced by the valve inlet and outlet parameters; it is assumed that the valve core does not deflect or bump, and only the vertical force balance is considered. Therefore, the existing theoretical models are not sufficient to describe the instantaneous flow characteristics of the check valve under gas-liquid mixed transmission conditions. CFD models are widely used to solve engineering problems in fluid dynamics due to their advantages in handling complex flow calculations. However, the performance of CFD models is closely related to the experience of researchers. For example, the grid division scheme, the selection of turbulence models, the setting of boundary conditions, etc. At present, only the CFD modeling of check valves for nuclear industry hydrothermal systems has been carried out. Based on their own experience, scholars have selected standard k-ε, RNGk-ε, and turbulence models such as k-ε and SST k-ω models. Therefore, the rationality of CFD modeling usually requires experimental verification. At the same time, in order to obtain more accurate calculation results, it is usually necessary to construct a more complex CFD model, which consumes a long calculation time. Therefore, CFD tools are difficult to use in complex modeling processes that lack engineering experience and require repeated exploration and continuous correction of models. In summary, it is necessary to establish a check valve flow characteristic model with strong versatility, fast calculation speed, and high accuracy to adapt to complex frequency-varying multiphase flow conditions.

[0004] In recent years, some data-driven empirical models have been gradually used to solve some problems of multiphase flow because they do not require substantial understanding of the complex internal mechanisms of multiphase flow. However, the quality of a simple data-driven empirical model depends on whether there is a large amount of reliable modeling data. Furthermore, the black box model generated by it is difficult to explain the internal mechanism of the research object and cannot provide effective theoretical support for engineering design. Considering the limited multiphase flow test technology and the complex multiphase flow characteristics in the valve gap during the opening stage, it is difficult to obtain a large amount of effective experimental data; at the same time, the check valve for multiphase flow pumps, which is still in the development stage, also urgently needs to explore the internal mechanism of the operating conditions and valve working characteristics. Therefore, a modeling method for the flow characteristics of the check valve for multiphase flow pumps that integrates physical knowledge and graph convolutional networks (PGCNs) is proposed. Graph convolutional networks (GCNs) can describe the topological relationship between input variables and between input and output variables. At the same time, physical equations can be embedded in the training process of GCN to ensure that the output of GCN meets the physical laws, reduce the dependence of the traditional GCN modeling method on a large amount of effective modeling data, and improve the generalization ability of the model. A literature search found that there is no report on modeling the flow characteristics of a check valve for a multiphase flow pump that integrates physical knowledge and graph convolutional networks. Summary of the invention

[0005] The present invention aims to overcome the above-mentioned shortcomings of the prior art and provide a modeling method for the multiphase flow characteristics of a check valve that integrates physical knowledge and graph networks. The method can learn the relationship between the flow characteristics of a check valve for a multiphase flow pump and the complex gas-liquid mixed transmission conditions based on limited samples, and assist engineers to better understand the internal mechanism of the multiphase flow in the check valve, so as to optimize the engineering design of the check valve.

[0006] The technical solution of the present invention is as follows:

[0007] The modeling method of multiphase flow characteristics of a check valve integrating physical knowledge and graph network includes the following steps:

[0008] 1) Establish a theoretical model for the opening stage of a check valve for a multiphase flow pump;

[0009] First, taking the cone check valve for a reciprocating gas-liquid multiphase flow pump as an example, based on the continuity theorem, assuming that the gas-liquid two-phase flow in the valve gap is uniformly distributed, it can be known that the mass flow rate Q discharged by the valve at time t is t for:

[0010]

[0011] Where C is the flow coefficient of the valve, ρ t and P tare the flow area of ​​the valve gap, the density and pressure of the gas-liquid mixture in the valve gap at time t, d is the equivalent diameter of the valve plate, h is the t is the valve lift height at time t, P d is the pressure at the valve outlet. In the project, due to the narrow valve gap, it is difficult to install the sensor and it is impossible to obtain ρ in real time. t and P t Therefore, other theoretical formulas need to be added to obtain Q from formula (1). t The calculated value of .

[0012] Therefore, we consider the check valve plate as the research object, assuming that the valve core does not deviate or bump, and establish the kinematic equation described by formula (2) based on Newton's law:

[0013] Where m is the mass of the valve plate, h t The second-order derivative of is the valve plate area, g is the acceleration of gravity, k and F are the stiffness coefficient and preload of the spring respectively.

[0014] Secondly, according to the multiphase flow theory, it can be known that the average density ρ of the gas-liquid mixture in the valve gap at time t is t It can be expressed as

[0015] ρ t =ρ l (1-β t )+ρ g β t (3)

[0016] In the formula, ρ l and ρ g are the densities of liquid and gas, respectively, β t It is the percentage of the gas volume in the valve gap at time t to the total volume of the gas-liquid mixture.

[0017] To simplify the solution process, it is assumed that the discharge process of the multiphase flow pump at the start-up stage is an isothermal process, then equation (4) can be established:

[0018] P t V gt =P s V gs =constant(4)

[0019] Where V gt =(As t +V c +V t )-(1-β s )V s is the volume of gas in the valve gap at time t, P s , Vgs =β s V s , V s and β s They are respectively the pump inlet pressure, the volume of the gas sucked in, the total volume of the gas-liquid mixture and the gas volume as a percentage of V s The percentage of is the pump chamber piston area, D is the piston diameter, is the displacement of the piston at time t, r is the crank radius, ω is the pump speed, λ is the ratio of the crank radius to the connecting rod length, V c and are the clearance volume and the volume change caused by the movement of the valve plate. Formula (5) can be derived from formulas (3) and (4):

[0020]

[0021] In summary, according to formulas (1)-(5), it can be deduced that the discharge flow Q of the check valve at the opening stage at time t is t Theoretical formulas (6) and (7)

[0022]

[0023] 2) Establish a theoretical model for the delivery phase of a multiphase flow pump using a check valve;

[0024] From the working principle of the pump, it can be seen that after the check valve opening stage ends and enters the normal delivery stage, if the hydraulic loss and friction resistance loss are ignored, the mass and volume changes of the mixture in the pump chamber are theoretically equal to the mass and volume flow rate output by the check valve. That is, the check valve delivery stage can be regarded as a non-isothermal compression process in which the density of the mixture remains unchanged. Therefore, the flow characteristics of the check valve delivery stage can be obtained by the following formula (8):

[0025] In the formula, ρ=(ρ l P d (1-β s )+ρ g P s β s ) / (P d (1-β s )+P s β s ) is the density of the mixture in the pump chamber after the start phase.

[0026] 3) Collect input and output training samples under different gas-liquid mixed transmission conditions and establish a graph convolution (GCN) model of check valve flow characteristics;

[0027] Firstly, based on the physical knowledge provided by the theoretical formula and the valve engineering design experience, the variables affecting the flow characteristics of the check valve are analyzed to determine the input matrix X and output matrix Y of the GCN model;

[0028] Secondly, we collected the input and output training samples of the pump discharge process (crank angle θ = ωt = 180° to 360°) under different gas-liquid mixed transport conditions. where x m is the mth input sample, y m is the mth output sample, and M is the total number of samples. Taking the GCN model with 2 hidden layers as an example, the predicted output f(X,A) of GCN is

[0029]

[0030] Where σ(·) is the activation function and ReLU is the linear rectification function. middle, is the degree matrix of A, A and I are the N×M adjacency matrix and the identity matrix respectively, N is the number of nodes in the GCN model, A n,m , I n,m W represents the nth row and mth column elements of A and I respectively. 0 and W 1 Represent the weight matrices between the input layer and the hidden layer, and between the hidden layer and the output layer respectively.

[0031] 4) Incorporate the physical knowledge of the check valve opening stage into the training process of the GCN model and construct a loss function that integrates the physical knowledge and graph network (PGCN for short) model;

[0032] Based on formulas (6) and (7), the traffic value calculated by the theoretical formula is compared with the predicted value of GCN, and is integrated into the comparison result of the predicted value and the actual value output by GCN to form the loss function of training the GCN model. Then, A and W are calculated based on the back propagation algorithm. 0 and W 1 The valve discharge flow and lift height are used as the output of the GCN model. For example, the loss function can be described as:

[0033]

[0034] in, and Q m The predicted and calculated values ​​of Yes m When Loss reaches the minimum value, A, W 0 and W 1The optimal value of is confirmed, and the GCN model shown in formula (9) completes the training process to obtain the PGCN model.

[0035] 5) Using the PGCN model trained in step 4), the L input sample sets of the new working condition Online prediction of traffic characteristics;

[0036] 6) Correct the prediction result of the check valve delivery phase obtained in step 5).

[0037] The check valve delivery stage can be regarded as a non-isothermal compression process in which the density of the mixture remains unchanged. Its flow characteristics can be described by formula (8), which does not satisfy the isothermal compression process described by formula (4). Therefore, in step 5), the prediction results of the flow characteristics of the delivery stage by the PGCN model that incorporates the theoretical knowledge of the opening stage need to be replaced by the calculation results of formula (8).

[0038] The beneficial effects of the present invention are as follows:

[0039] The modeling method of the multiphase flow characteristics of a check valve that integrates physical knowledge and graph networks proposed in the present invention can realize the modeling and prediction of the flow characteristics of a check valve for a multiphase flow pump under time-varying gas-liquid mixed transmission conditions. Compared with theoretical models and CFD simulation models, this method integrates physical knowledge with graph convolutional neural networks, providing a method that is easy and fast to implement in engineering. Compared with conventional data-driven empirical modeling, this method adds the information of physical equations to the constraints to train the parameters of the data-driven empirical model, ensuring that the output of the data-driven empirical model meets the physical laws, improving the generalization ability of the model, reducing the demand for large amounts of labeled data, and reducing the complexity of model training. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flow chart of the method of the present invention;

[0041] Figure 2 Comparison of the prediction results of the flow characteristics of the check valve for multiphase flow pumps by PGCN, GCN and theoretical model Figure 1 ;

[0042] Figure 3 Comparison of prediction results of flow characteristics of check valve for multiphase flow pump using PGCN, GCN and theoretical model Figure 2 ;

[0043] Figure 4 Comparison of the prediction results of the flow characteristics of the check valve for multiphase flow pumps by PGCN, GCN and theoretical model Figure 3 . DETAILED DESCRIPTION

[0044] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0045] like Figure 1 As shown, the modeling method of multiphase flow characteristics of a check valve integrating physical knowledge and graph network includes the following steps:

[0046] 1) Establish a theoretical model for the opening stage of a check valve for a multiphase flow pump;

[0047] Taking a conical check valve for a reciprocating gas-liquid multiphase flow pump as an example, its parameters are: C = 0.34, m = 0.0103kg, g = 9.80665m / s 2 , k=3500N / m, F=12N, d=0.032m, D=0.115m, V c =1.9×10 -4 m 3 , ρ l =856kg / m 3 , ρ g =0.667kg / m 3 , ω=1440rpm, λ=0.125, r=0.036m. P s , β s , V s , P d and crank angle θ = ωt can be obtained by measurement. Assuming that the flow field in the valve gap is uniform, the valve core does not deviate or bump during the opening phase, the discharge process of the multiphase flow pump during the opening phase is an isothermal process, the pump suction, discharge and gas-liquid ratio are all constants, and the hydraulic loss and friction resistance loss are ignored, the mass flow characteristics of the check valve at time t during the opening phase can be described using formulas (1) to (7).

[0048] 2) Establish a theoretical model for the delivery phase of a multiphase flow pump using a check valve;

[0049] Assuming that the flow field in the valve gap is uniform during the delivery phase, the valve core does not deviate or bump, the discharge process during the delivery phase is a non-isothermal process with a constant density of the mixed medium, the pump suction, discharge and gas-liquid ratio are all constants, and the hydraulic loss and friction resistance loss are ignored, the theoretical model of the check valve during the delivery phase can be described by formula (8).

[0050] 3) Collect input and output training samples under different gas-liquid mixed transmission conditions and establish a graph convolution (GCN) model of check valve flow characteristics;

[0051] First, based on step 1) and valve engineering design experience, it can be known that the measurable variables that affect the flow characteristics of the check valve are P s , β s , V s , P d , crank angle θ = ωt and h tIn actual engineering, the valve is installed in the pump body, so it is difficult to install a sensor to measure the lift height h online in real time. t ; Furthermore, the lift height is also a key parameter in the valve structure design, so the input matrix X of the GCN model is determined as follows: s ,β s ,V s ,P d ,θ} and output matrix Y = {h,Q};

[0052] Secondly, we collected the input and output training samples of the pump discharge process (crank angle θ = 180° to 360°) under different gas-liquid mixed transport conditions. where x m is the mth input sample, y m is the mth output sample, and M is the total number of samples. The experiment collected 12 groups of 706 samples from 12 different mixed flow conditions, including 9 groups (S 1 ,L,S 9 ) for training, 3 groups (S 10 ,S 11 ,S 12 ) is used for testing. Any given set of A, W 0 and W 1 The initial value of can be used to start the initial training of the GCN model using formula (9).

[0053] 4) Incorporate the physical knowledge of the check valve opening stage into the training process of the GCN model and construct a loss function that integrates the physical knowledge and graph network (PGCN for short) model;

[0054] From steps 1) and 3), we can see that for the training input sample x m , the initial GCN training model can get the predicted value and Further, Substituting into formulas (6) and (7) we can get the calculated value of flow rate: because Contains physical knowledge, so it can be used in GCN conventional loss function Add loss function Based on the back propagation algorithm, A and W 0 and W 1 That is, when the Loss shown in formula (10) reaches the minimum value, A, W 0 and W 1 The optimal value of is confirmed, and the GCN model shown in formula (9) completes the training process to obtain the PGCN model.

[0055] 5) Using the PGCN model trained in step 4), the L input sample sets of the new working condition Online prediction of traffic characteristics;

[0056] 6) Correct the prediction result of the check valve delivery phase obtained in step 5).

[0057] The predicted values ​​of the flow characteristics of the three test samples by the PGCN model proposed in this method are compared with the predicted values ​​of the traditional GCN model, the calculated values ​​of the theoretical model and the experimental values. Figure 2 , Figure 3 and Figure 4 shown.

[0058] The two commonly used indicators, the absolute value of the maximum error (abbreviated as ME) and the mean square error (abbreviated as RMSE), are selected as evaluation criteria. The definitions of the two evaluation criteria are as follows:

[0059]

[0060] The smaller the value of ME and RMSE, the better. The comparison results are shown in Table 1.

[0061] Table 1 Prediction performance of the method of the present invention for the flow characteristics of the test sample set (minimum value marked in black)

[0062]

[0063] As can be seen from Table 1, by using the physical knowledge of the reciprocating multiphase flow pump, the flow characteristics of the check valve opening stage are predicted based on the graph convolutional network. After the predicted flow in the delivery stage is replaced by the calculation results of the theoretical formula, the prediction performance of the three test samples is further improved.

[0064] Therefore, the modeling method of integrating physical knowledge and graph network proposed in the present invention is universal and general, and can accurately predict the flow characteristics of the check valve for multiphase flow pumps based on limited modeling samples. In addition, compared with conventional data-driven empirical modeling, this method adds the information of physical equations to the constraint conditions to train the parameters of the data-driven empirical model, ensuring that the output of the data-driven empirical model meets the physical laws, improving the generalization ability of the model, reducing the need for a large amount of labeled data, and reducing the complexity of model training.

[0065] Its simple and reliable segmented implementation method can reduce design complexity, lower design costs, save modeling time, and provide an effective auxiliary means for the design of current check valves for multiphase flow pumps.

[0066] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms described in the embodiments. The protection scope of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A modeling method for multiphase flow characteristics of a check valve integrating physical knowledge and graph networks, characterized in that: The following steps are involved: Step 1) establishing a theoretical model of the opening stage of the check valve for a multiphase flow pump; Step 2) establishing a theoretical model of the multiphase flow pump using a check valve during the delivery phase; Step 3) collecting input and output training samples under different gas-liquid mixed transmission conditions, and establishing a graph convolution GCN model of the check valve flow characteristics; Step 4) Integrate the physical knowledge of the check valve opening stage into the training process of the GCN model, and construct a loss function that integrates the physical knowledge and the graph network PGCN model; Step 5) Using the PGCN model trained in step 4), the L input sample sets of the new working condition Online prediction of traffic characteristics; Step 6) corrects the prediction result of the check valve delivery phase obtained in step 5).

2. The modeling method of multiphase flow characteristics of a check valve integrating physical knowledge and graph network according to claim 1 is characterized in that: The specific process of step 1) is as follows: Based on the continuity theorem, assuming that the gas-liquid two-phase flow in the valve gap is uniformly distributed, the mass flow rate Q discharged by the valve at time t is obtained t for: Where C is the flow coefficient of the valve, ρ t and P t are the flow area of ​​the valve gap, the density and pressure of the gas-liquid mixture in the valve gap at time t, d is the equivalent diameter of the valve plate, h is the t is the valve lift height at time t, P d is the pressure at the valve outlet; To obtain Q t The calculated value is taken as the research object, and the valve plate of the check valve is assumed to have no displacement or bumping. The kinematic equation described by formula (2) is established based on Newton's law. Where m is the mass of the valve plate, h t The second-order derivative of is the valve plate area, g is the acceleration of gravity, k and F are the stiffness coefficient and preload of the spring respectively; According to the multiphase flow theory, the average density ρ of the gas-liquid mixture in the valve gap at time t is obtained: t Expressed as r t =ρ l (1-b) t )+r g b t (3) In the formula, ρ l and ρ g are the densities of liquid and gas, β t is the percentage of the gas volume in the valve gap at time t to the total volume of the gas-liquid mixture; To simplify the solution process, it is assumed that the discharge process of the multiphase flow pump at the start-up stage is an isothermal process, and equation (4) is established: P t V gt =P s V gs =constant (4) Where V gt =(As t +V c +V t )-(1-β s )V s is the volume of gas in the valve gap at time t, P s , V gs =β s V s , V s and β s They are respectively the pump inlet pressure, the volume of the gas sucked in, the total volume of the gas-liquid mixture and the gas volume as a percentage of V s The percentage of is the pump chamber piston area, D is the piston diameter, is the displacement of the piston at time t, r is the crank radius, ω is the pump speed, λ is the ratio of the crank radius to the connecting rod length, V c and They are the clearance volume and the volume change caused by the movement of the valve plate; Formula (5) can be derived from formula (3) and (4) In summary, according to formulas (1)-(5), the discharge flow rate Q of the check valve at the opening stage at time t is: t Theoretical formulas (6) and (7) 3. The modeling method of multiphase flow characteristics of a check valve integrating physical knowledge and graph network according to claim 2 is characterized in that: The specific process of step 2) is as follows: From the working principle of the pump, it can be seen that after the check valve opening stage ends and enters the normal delivery stage, if the hydraulic loss and friction resistance loss are ignored, the mass and volume changes of the mixture in the pump chamber are theoretically equal to the mass and volume flow rate output by the check valve. That is, the check valve delivery stage is regarded as a non-isothermal compression process in which the density of the mixture remains unchanged. Therefore, the flow characteristics of the check valve delivery stage can be obtained by the following formula (8): In the formula, ρ=(ρ l P d (1-β s )+ρ g P s β s ) / (P d (1-β s )+P s β s ) is the density of the mixture in the pump chamber after the start phase.

4. The modeling method for multiphase flow characteristics of a check valve integrating physical knowledge and graph network according to claim 3 is characterized in that: The specific process of step 3) is as follows: Analyze the variables that affect the flow characteristics of the check valve and determine the input matrix X and output matrix Y of the GCN model; Collect input and output training samples of the pump discharge process under different gas-liquid mixed transmission conditions where x m is the mth input sample, y m is the mth output sample, M is the total number of samples; a GCN model with 2 hidden layers is established, and the predicted output f(X,A) of GCN is In the formula, σ(·) is the activation function, ReLU is the linear rectification function, middle, is the degree matrix of A, A and I are the N×M adjacency matrix and the identity matrix respectively, N is the number of nodes in the GCN model, A n,m , I n,m They represent the nth row and mth column elements of A and I respectively, and W0 and W1 represent the weight matrices between the input layer and the hidden layer, and between the hidden layer and the output layer respectively.

5. The modeling method for multiphase flow characteristics of a check valve integrating physical knowledge and graph network according to claim 4 is characterized in that: The specific process of step 4) is as follows: Based on formulas (6) and (7), the traffic value calculated by the theoretical formula is compared with the predicted value of GCN, and is integrated into the comparison result of the predicted value and the actual value output by GCN to form the loss function of training the GCN model, and then A, W0 and W1 are optimized based on the back propagation algorithm; If the valve discharge flow and lift height are used as the output of the GCN model The loss function is described as: in, and Q m The predicted and calculated values ​​of Yes m When Loss reaches the minimum value, the optimal values ​​of A, W0 and W1 are confirmed, and the GCN model shown in formula (9) completes the training process and obtains the PGCN model.

6. The modeling method of multiphase flow characteristics of a check valve integrating physical knowledge and graph network according to claim 3 is characterized in that: The specific process of step 6) is as follows: The check valve delivery stage is regarded as a non-isothermal compression process in which the density of the mixture remains unchanged. Its flow characteristics are described by formula (8), which does not satisfy the isothermal compression process described by formula (4). Therefore, in step 5), the prediction results of the flow characteristics of the delivery stage by the PGCN model that incorporates the theoretical knowledge of the opening stage need to be replaced by the calculation results of formula (8).

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