Method for predicting flow resistance characteristics of subcooled boiling in tubes

Abstract

This invention discloses a method for predicting the resistance characteristics of subcooled boiling flow in a pipe, specifically comprising: acquiring basic data from a flow heat transfer experiment; calculating the Reynolds number Re, boiling number Bo, and Jacobian number Ja based on inlet parameters; determining the input and output parameters of the prediction model and obtaining the correspondence between the input and output parameters; normalizing the input and output parameters from step 3; constructing an extreme learning machine model using the normalized input and output parameters; optimizing the initial weights and thresholds of the constructed extreme learning machine model using a genetic algorithm to obtain a new prediction model; and obtaining the regression determination coefficient R of the prediction set data. 2 The mean absolute error (MAE) and root mean square error (RMSE) of all data; select the regression coefficient of determination R. 2 The prediction model using the number of neurons in the minimum mean absolute error (MAE) and root mean square error (RMSE) is used as the final prediction model. This method can accurately predict the resistance characteristics of subcooled boiling in a tube.

Description

Technical Field

[0001] This invention belongs to the field of multiphase flow and heat transfer technology, specifically relating to a method for predicting the resistance characteristics of subcooled boiling flow in a pipe. Background Technology

[0002] Supercooled boiling is widely used in high heat flux heat transfer fields such as chip cooling and the International Thermonuclear Experimental Reactor (ITER) (Review on high heat flux flow boiling of refrigerants and water for electronics cooling, Int. J. Heat Mass Transf. 180 (2021) 121787). Among these applications, the flow resistance of supercooled boiling is a key research topic in this field, as the fluid flow resistance characteristics are crucial to the safety, stability, and economy of the heat transfer system. Therefore, accurately predicting the resistance characteristics of supercooled boiling is essential in this area.

[0003] Currently, the prediction method for the flow resistance characteristics of subcooled boiling still mainly relies on the traditional empirical correlation method (Prediction of subcooled flow boiling pressure drops in small circular tubes[J]. International Journal of Heat and Mass Transfer,2017,115:1074-1090).Currently, common empirical correlations include: Owens–Schrock correlation (Local pressure gradients for subcooled boiling of water in vertical tubes[J]. ASME Paper, 1960, 60), Tarasova correlation (Pressure drop of boiling subcooled water and steam-water mixture flowing in heated channels[C]: Begel House Inc., 1966), Hahne correlation (A new pressure drop correlation for subcooled flow boiling of refrigerants[J]. International Journal of Heat and Mass Transfer, 1993, 36(17): 4267-4274), Tong correlation (Pressure drop with highly subcooled flow boiling in small-diameter tubes[J]. Experimental Thermal and Fluid Science, 1997, 15(3): 202-212), and Yan correlation (Pressure drop for highly subcooled water flow boiling under high heat and mass fluxes[J]. Applied Thermal Engineering, 2017, 124: 1061-1074) and Sharifi correlation (On the prediction of pressure drop in subcooled flow boiling of water [J]. Applied Thermal Engineering, 2019, 155: 386-396).

[0004] Subcooled boiling is influenced by numerous factors. The evolution of subcooled boiling bubbles, including their initial formation, development, condensation, and disappearance, is significantly affected by operating parameters and other factors. This is especially true under high temperature and high pressure conditions, where the evolution of subcooled boiling bubbles becomes even more complex (Experimental study of subcooled flow boiling heat transfer of water in a circular channel under one-side heating conditions, Int. J. Heat Mass Transf. 119 (2018) 484-495). This leads to generally large prediction errors and limited applicability of traditional empirical correlation methods. Therefore, there is an urgent need to explore prediction methods with higher accuracy and wider applicability. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the flow resistance characteristics of subcooled boiling inside a pipe, which can accurately predict the resistance characteristics of subcooled boiling inside a pipe.

[0006] The technical solution adopted in this invention is a method for predicting the flow resistance characteristics of subcooled boiling inside a pipe, which is implemented according to the following steps:

[0007] Step 1: Conduct subcooled flow boiling experiments to obtain basic data for flow heat transfer experiments;

[0008] Step 2: Using the basic data from Step 1, calculate the Reynolds number Re, boiling number Bo, and Jacob number Ja based on the inlet parameters;

[0009] Step 3: Determine the input and output parameters of the prediction model, and obtain the correspondence between the input and output parameters;

[0010] Step 4: Normalize the input and output parameters from Step 3;

[0011] Step 5: Using the input and output parameters after normalization in Step 4, and the LeakyReLU function, build the Extreme Learning Machine model;

[0012] Step 6: Use a genetic algorithm (GA) to optimize the initial weights and thresholds of the Extreme Learning Machine (ELM) model built in Step 5 to obtain an updated prediction model;

[0013] Step 7: Randomly divide all supercooled boiling experimental data into two parts, a training set and a prediction set, according to a certain proportion. The training set data is used to train the prediction model, and the prediction set data is used to verify the accuracy of the prediction model. Adjust the number of hidden layer neurons in the prediction model in Step 6 and repeat the above steps.

[0014] Step 8: Compare the impact of the number of hidden layer neurons on prediction accuracy in Step 7, and select the one with the largest regression determination coefficient R. 2 A predictive model for the number of neurons in the minimum mean absolute error (MAE) and root mean square error (RMSE) is developed and used as the final predictive model.

[0015] The invention is further characterized in that,

[0016] In step 1, the basic data for obtaining the experimental pipe is: pipe diameter d. in Pipe length L, heat flux density q, flow velocity u, mass flow velocity G, pressure p, resistance Δp, and the resistance Δp of the all-liquid phase adiabatic flow under the same conditions. ad Inlet fluid temperature T b,in Average fluid temperature T b Average inner wall surface temperature T w,in supercooling ΔT sub Fluid density ρ, fluid enthalpy H b Enthalpy of saturated liquid H l,sat Latent heat of vaporization H fg Specific heat capacity at constant pressure c p Dynamic viscosity μ b and liquid-to-vapor density ratio ρ l / ρ g .

[0017] In step 2, the expressions for the Reynolds number Re, the boiling number Bo, and the Jacobian number Ja based on the inlet parameters are as follows:

[0018]

[0019]

[0020]

[0021] Step 3 is implemented as follows: Select the subcooled boiling flow resistance Δp as the output parameter of the prediction model, and select the boiling number Bo, the Jacobian number Ja based on the inlet parameters, and the liquid-vapor density ratio ρ. l / ρ g The four dimensionless parameters, including the Reynolds number Re, are used as input parameters for the prediction model. The output parameters are predicted using these input parameters, and the correspondence between the output parameters and the input parameters is shown in the following formula:

[0022]

[0023] The normalization formula used in step 4 is as follows:

[0024]

[0025] In the formula, Z and Z* represent the unprocessed parameters and the normalized parameters, respectively; Z min and Z max These represent the maximum and minimum values ​​of the unprocessed parameters, respectively.

[0026] In step 5, the Extreme Learning Machine (ELM) model structure is a fully connected single-hidden-layer neural network, consisting of an input layer, an output layer, and a hidden layer. The LeakyReLU function is chosen as the activation function from the input layer to the hidden layer.

[0027]

[0028] Where σ(x) and x represent the activation function and the input parameter after normalization in step 4, respectively; a represents the hyperparameter.

[0029] Step 6 is implemented as follows: Determine the topology of the Extreme Learning Machine (ELM) model through Step 5, and initialize the weights and thresholds; Encode the initial values ​​using the GA algorithm; Select the training error as the fitness function, and the GA algorithm will calculate the fitness value through selection, crossover, and mutation operations, iteratively obtaining the optimal initial weights and thresholds; Finally, substitute the weights and thresholds obtained by the GA algorithm into the ELM model for solving, output the prediction results, and obtain a new prediction model.

[0030] Step 7 is implemented as follows: All supercooled boiling experimental data are randomly divided into a training set and a prediction set at a ratio of 8:2. The training set data is input into the prediction model built in Step 6 for training to obtain the latest prediction model. Then, the test set data is input into the latest prediction model to obtain the regression determination coefficient R0 for the test set data. 2 And the mean absolute error (MAE) and root mean square error (RMSE) of all data. Adjust the number of hidden layer neurons in the prediction model of step 6, repeat the above steps, and obtain the regression determination coefficient R of the test set data. 2 And the mean absolute error (MAE) and root mean square error (RMSE) of all data.

[0031] The beneficial effects of this invention are:

[0032] (1) The present invention provides a method for predicting the flow resistance characteristics of subcooled boiling in a pipe. This method can predict the resistance characteristics of subcooled boiling with high accuracy and has the advantages of high prediction accuracy, wide coverage, and strong versatility. The prediction accuracy is higher than that of the Owens–Schrock correlation, Tarasova et al. correlation, Hahne et al. correlation, Tong et al. correlation, Yan et al. correlation, and Sharifi et al. correlation proposed by predecessors.

[0033] (2) The method for predicting the flow resistance characteristics of subcooled boiling in the lifting pipe of the present invention calculates the liquid-vapor density ratio (ρ) based on the resistance characteristics of subcooled boiling. l / ρ g The present invention utilizes dimensionless parameters that characterize the subcooled boiling resistance, such as Reynolds number Re, boiling number Bo, and Jacobian number Ja based on inlet parameters. An Extreme Learning Machine (ELM) model is constructed using these parameters to predict the subcooled boiling flow resistance Δp. Therefore, the prediction method provided by this invention effectively applies the Extreme Learning Machine model from modern intelligent algorithms to the prediction of subcooled boiling flow resistance characteristics in pipes, offering a new approach and method for predicting subcooled boiling flow resistance characteristics.

[0034] (3) The method for predicting the flow resistance characteristics of subcooled boiling in pipes in this invention takes into account the difficulty in obtaining subcooled boiling data under complex working conditions. Based on the resistance characteristics of subcooled boiling (multidimensional, complex, and nonlinear), the model structure of the traditional extreme learning machine model is optimized and improved. The LeakyReLU function is selected as the activation function from the input layer to the hidden layer. The initial weights and thresholds of the traditional extreme learning machine model are selected using a genetic algorithm. The extreme learning machine model in modern artificial intelligence algorithms is applied to the prediction research of the flow resistance characteristics of subcooled boiling. Combined with the unique laws of the flow resistance characteristics of subcooled boiling, the traditional extreme learning machine model is optimized in all aspects, providing a reference and method for the application of modern intelligent algorithms in the field of fluid flow heat transfer technology. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the structure of the method for predicting the flow resistance characteristics of subcooled boiling inside a pipe according to the present invention;

[0036] Figure 2 This is a flowchart of the method for predicting the flow resistance characteristics of subcooled boiling in a pipe according to the present invention.

[0037] Figure 3 This is a comparison chart of experimental and predicted values ​​of the Owens–Schrock correlation in the embodiment;

[0038] Figure 4 This is a comparison chart of the experimental and predicted values ​​of the correlation equation from Tarasova et al. in the example;

[0039] Figure 5 This is a comparison chart of the experimental and predicted values ​​of the correlation equation from Hahne et al. in the example;

[0040] Figure 6 This is a comparison chart of the experimental and predicted values ​​of the correlation equation in the example provided by Tong et al.;

[0041] Figure 7 This is a comparison chart of the experimental and predicted values ​​of the correlation equations in the example provided by Yan et al.;

[0042] Figure 8 This is a comparison chart of the experimental and predicted values ​​of the correlation equation in the embodiment by Sharifi et al.;

[0043] Figure 9 This is a comparison chart of the prediction performance of the prediction method for the number of hidden layer neurons in the embodiments;

[0044] Figure 10 This is a comparison chart of the experimental and predicted values ​​of the prediction method of the present invention in the embodiment. Detailed Implementation

[0045] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0046] This invention provides a method for predicting the flow resistance characteristics of subcooled boiling in a pipe, specifically implemented according to the following steps:

[0047] Step 1: Conduct subcooled flow boiling test to obtain the pipe diameter d. in Pipe length L, heat flux density q, flow velocity u, mass flow velocity G, pressure p, resistance Δp, and the resistance Δp of the all-liquid phase adiabatic flow under the same conditions. ad Inlet fluid temperature T b,in Average fluid temperature T b Average inner wall surface temperature T w,in supercooling ΔT sub Fluid density ρ, fluid enthalpy H b Enthalpy of saturated liquid H l,sat Latent heat of vaporization H fg Specific heat capacity at constant pressure c p Dynamic viscosity μ b Liquid-to-vapor density ratio (ρ) l / ρ g These are the basic data from the flow heat transfer experiments;

[0048] Step 2: Using the data from Step 1, calculate the Reynolds number Re, boiling number Bo, and Jacobian number Ja based on the inlet parameters.

[0049]

[0050]

[0051]

[0052] Step 3: Based on the laws and characteristics of subcooled boiling, the subcooled boiling flow resistance Δp is selected as the output parameter of the prediction model. The boiling number Bo, the Jacobian number Ja based on the inlet parameters, and the liquid-vapor density ratio ρ are also selected. l / ρ g The four dimensionless parameters, including the Reynolds number Re, are used as input parameters for the prediction model. The input parameters are used to predict the output parameters. The correspondence between the input parameters and the output parameters is shown in the following formula.

[0053]

[0054] Step 4: To improve the accuracy and computation speed of the prediction method, the input and output parameters in formula (4) of step 3 are preprocessed, i.e., normalized:

[0055]

[0056] In the formula, Z and Z* represent the unprocessed parameters and the normalized parameters, respectively; Z min and Z max These represent the maximum and minimum values ​​of the unprocessed parameters, respectively.

[0057] Step 5: Based on the correspondence between the input and output parameters in formula (4) of Step 3, and using the input and output parameters processed in Step 4, construct the Extreme Learning Machine (ELM) model; the Extreme Learning Machine (ELM) model structure is a fully connected single hidden layer neural network structure, consisting of an input layer, an output layer, and a hidden layer, as shown in the figure. Figure 1 As shown. Given the highly complex characteristics of supercooled boiling, prediction is prone to getting trapped in local optima. Therefore, the LeakyReLU function, which can escape local optima and explore the global optimum, is chosen as the activation function from the input layer to the hidden layer:

[0058]

[0059] Where σ(x) and x represent the activation function and the input parameter after processing in step 4, respectively; a represents the hyperparameter (the minimum value, generally a value less than 0.1).

[0060] Step 6: Use a genetic algorithm (GA) to optimize the initial weights and thresholds of the Extreme Learning Machine (ELM) model built in Step 5 to obtain an updated prediction model; the flowchart of the prediction model is as follows. Figure 2 As shown: Step 5 determines the topology of the ELM model. Figure 1The system first sets the initial weights and thresholds, then initializes them. The initial values ​​are encoded using the GA algorithm. The training error is selected as the fitness function. The GA algorithm calculates the fitness value through selection, crossover, and mutation operations, iteratively obtaining the optimal initial weights and thresholds. Finally, the weights and thresholds obtained by the GA algorithm are substituted into the ELM model for solution, and the prediction results are output.

[0061] Step 7: Randomly divide all supercooled boiling experimental data into a training set and a prediction set at a ratio of 8:2. Input the training set data into the prediction model built in Step 6 for learning and training to obtain the latest prediction model. Then, input the test set data into the latest prediction model to obtain the regression determination coefficient R of the test set data. 2 And the mean absolute error (MAE) and root mean square error (RMSE) of all data. Adjust the number of hidden layer neurons in the prediction model from step 6, repeat the above steps, and obtain the regression determination coefficient R for the test set data. 2 And the mean absolute error (MAE) and root mean square error (RMSE) of all data.

[0062] Step 8: Compare the impact of the number of hidden layer neurons on prediction accuracy in Step 7, and select the one with the largest regression determination coefficient R. 2 A prediction model for the number of neurons with minimum mean absolute error (MAE) and root mean square error (RMSE) was developed and used as the final prediction model in production.

[0063] Example

[0064] To demonstrate the practical application effect of the present invention, this paper selects experimental data on cold boiling resistance under high temperature and high pressure conditions in a micro-pipe as an example (this supercooled boiling flow resistance data is difficult to obtain, and the resistance characteristics under this condition are much more complex than those under normal temperature and pressure, making prediction more difficult). Based on the prediction method of the present invention, the application of the present invention is demonstrated in detail.

[0065] The main operating parameters of the embodiment are as follows:

[0066]

[0067] Based on the basic parameters from step 1, calculate the drag ratio Φ. 2 The size of the drag ratio Φ was obtained using experimental data. 2 (Experimental value) and drag ratio Φ obtained from correlation calculation 2 (Predicted values) Compare the prediction accuracy of the Owens–Schrock correlation, Tarasova et al. correlation, Hahne et al. correlation, Tong et al. correlation, Yan et al. correlation, and Sharifi et al. correlation. Figure 3-8It can be seen that the prediction accuracy of the above empirical correlation formulas is generally low. Among them, the correlation formula of Yan et al has the highest accuracy, with more than 95% of the data errors within ±25%.

[0068]

[0069] Using the prediction method for supercooled boiling flow resistance characteristics constructed in this invention, experimental data are predicted and analyzed, and according to step 7, the optimal number of hidden layer neurons is obtained, such as... Figure 9 As shown, when the number of hidden layer neurons is greater than or equal to 80, the prediction accuracy remains basically stable; when the number of hidden layer neurons is equal to 99, the prediction method has the smallest MAE and RMSE on all experimental data, and a larger R-value on the test set data. 2 Considering that the more neurons there are, the slower the model's computation speed becomes and the accuracy no longer improves, the number of neurons in the hidden layer was determined to be 99.

[0070] Using the prediction model obtained in steps 7-8, the supercooled boiling flow resistance Δp in this embodiment is predicted and analyzed, such as... Figure 10 As shown, the prediction errors for all data are within ±9%. The MAE and RMSE of six typical empirical correlations and the prediction method of this invention for the example data were calculated for quantitative comparison. As shown in the table below, the prediction accuracy of the prediction method constructed in this invention is far higher than that of these six typical empirical correlations. This method can accurately predict the resistance characteristics of subcooled boiling in the tube.

[0071]

Claims

1. A method for predicting the flow resistance characteristics of subcooled boiling in a pipe, characterized in that, The specific steps are as follows: Step 1: Conduct subcooled flow boiling experiments to obtain basic data for flow heat transfer experiments; Step 2: Using the basic data from Step 1, calculate the Reynolds number Re, boiling number Bo, and Jacob number Ja based on the inlet parameters; Step 3: Determine the input and output parameters of the prediction model, and obtain the correspondence between the input and output parameters; Step 4: Normalize the input and output parameters from Step 3; Step 5: Using the input and output parameters after normalization in Step 4, and the LeakyReLU function, build the Extreme Learning Machine model; Step 6: Use a genetic algorithm to optimize the initial weights and thresholds of the extreme learning machine model built in Step 5 to obtain an updated prediction model; Step 7: Randomly divide all supercooled boiling experimental data into two parts: a training set and a prediction set. The training set data is used to train the prediction model, and the prediction set data is used to verify the accuracy of the prediction model. Adjust the number of hidden layer neurons in the prediction model in Step 6 and repeat the above steps. Step 8: Compare the impact of the number of hidden layer neurons on prediction accuracy in Step 7, and select the one with the largest regression determination coefficient R. 2 A predictive model for the number of neurons in the minimum mean absolute error (MAE) and root mean square error (RMSE) is developed and used as the final predictive model.

2. The method for predicting the flow resistance characteristics of subcooled boiling in a pipe according to claim 1, characterized in that, In step 1, the basic data for obtaining the experimental pipe is: pipe diameter d. in The pipe length L, heat flux density q, flow velocity u, mass flow velocity G, pressure p, resistance Δp, and the resistance Δp of the all-liquid phase adiabatic flow under the same conditions are compared. ad Inlet fluid temperature T b,in Average fluid temperature T b Average inner wall surface temperature T w,in supercooling ΔT sub Fluid density ρ, fluid enthalpy H b Enthalpy of saturated liquid H l,sat Latent heat of vaporization H fg Specific heat capacity at constant pressure c p Dynamic viscosity μ b and liquid-to-vapor density ratio ρ l / ρ g .

3. The method for predicting the flow resistance characteristics of subcooled boiling in a pipe according to claim 2, characterized in that, In step 2, the expressions for the Reynolds number Re, the boiling number Bo, and the Jacobian number Ja based on the inlet parameters are as follows:

4. The method for predicting the flow resistance characteristics of subcooled boiling in a pipe according to claim 3, characterized in that, Step 3 is implemented as follows: Select the subcooled boiling flow resistance Δp as the output parameter of the prediction model, and select the boiling number Bo, the Jacobian number Ja based on the inlet parameters, and the liquid-vapor density ratio ρ. l / ρ g The four dimensionless parameters, including the Reynolds number Re, are used as input parameters for the prediction model. The output parameters are predicted using these input parameters, and the correspondence between the output parameters and the input parameters is shown in the following formula:

5. The method for predicting the flow resistance characteristics of subcooled boiling in a pipe according to claim 4, characterized in that, The normalization formula used in step 4 is as follows: In the formula, Z and Z* represent the unprocessed parameters and the normalized parameters, respectively; Z min and Z max These represent the maximum and minimum values ​​of the unprocessed parameters, respectively.

6. The method for predicting the flow resistance characteristics of subcooled boiling in a pipe according to claim 5, characterized in that, In step 5, the Extreme Learning Machine (ELM) model structure is a fully connected single-hidden-layer neural network, consisting of an input layer, an output layer, and a hidden layer. The LeakyReLU function is chosen as the activation function from the input layer to the hidden layer. Where σ(x) and x represent the activation function and the input parameter after normalization in step 4, respectively; a represents the hyperparameter.

7. The method for predicting the flow resistance characteristics of subcooled boiling in a pipe according to claim 6, characterized in that, Step 6 is implemented as follows: Determine the topology of the Extreme Learning Machine model through step 5, and initialize the weights and thresholds; use the GA algorithm to encode the initial values; By selecting the training error as the fitness function, the GA algorithm calculates the fitness value through selection, crossover, and mutation operations, and iteratively obtains the optimal initial weights and thresholds. Finally, the weights and thresholds obtained by the GA algorithm are substituted into the ELM model for solution, and the prediction results are output to obtain a new prediction model.

8. The method for predicting the flow resistance characteristics of subcooled boiling in a pipe according to claim 7, characterized in that, Step 7 is implemented as follows: All supercooled boiling experimental data are randomly divided into a training set and a prediction set at a ratio of 8:

2. The training set data is input into the prediction model built in Step 6 for training to obtain the latest prediction model. Then, the test set data is input into the latest prediction model to obtain the regression determination coefficient R0 for the test set data. 2 The mean absolute error (MAE) and root mean square error (RMSE) of all data are calculated; the number of hidden layer neurons in the prediction model of step 6 is adjusted, the above steps are repeated, and the regression determination coefficient R of the test set data is obtained. 2 And the mean absolute error (MAE) and root mean square error (RMSE) of all data.

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