Three-dimensional porous negative buoyancy jet transient flow direct numerical simulation prediction method

Abstract

The invention discloses a three-dimensional porous negative buoyancy jet transient flow direct numerical simulation prediction method. The prediction method comprises the following steps: determining a three-dimensional porous negative buoyancy jet transient control equation; constructing a physical information neural network; acquiring multiple groups of multi-working-condition experimental data as a sample data set; inputting the sample data set into a physical information neural network model for training to obtain the total loss of the sample data in the neural network model, and adjusting and optimizing hyper-parameters of the neural network by taking the minimum loss calculated by a loss function as a target to obtain a trained physical information neural network; to-be-simulated space coordinates and prediction time are input into the trained physical information neural network, key parameters representing negative buoyancy jet flow characteristics are obtained, and therefore the transportation mechanism and entrainment mixing characteristics of the negative buoyancy jet flow characteristics are studied. According to the method, meshless solution can be realized, the grid dependence of a traditional method is avoided, the calculation efficiency is improved, and the method is suitable for the buoyancy-driven flow problem of multi-physics field coupling.

Description

Technical Field

[0001] This invention relates to the fields of environmental engineering, artificial intelligence and fluid mechanics, and specifically to a direct numerical simulation and prediction method for transient flow of a three-dimensional porous negative buoyancy jet. Background Technology

[0002] Porous jet flow is a common flow phenomenon in engineering, widely used in environmental engineering, marine engineering, chemical processes, and other fields. Porous negative buoyancy jets can effectively reduce and control environmental pollution caused by waste heat, wastewater, or exhaust gas emissions, effectively promoting sustainable ecological development. Large amounts of wastewater generated in production and daily life are simply treated and then directly discharged into rivers, lakes, or oceans through underwater pipelines, causing serious pollution to the nearshore waters of major rivers and damaging their usability. How to economically and effectively improve the initial dilution of the wastewater discharge field from the diffuser and the dilution of the surrounding environmental water has always been a major concern for environmental workers. Adopting economically feasible technical measures to effectively control water pollution has become increasingly urgent. Compared with single-hole jets, porous jets have a larger contact surface; when wastewater is discharged, there is a mutual adsorption effect between adjacent porous jets, causing them to entrain each other and eventually merge into a single jet. The tailwater discharged through the porous diffuser can mix with a larger area of ​​environmental water, thereby reducing pollution and achieving a better dilution effect. Therefore, the study of porous jets can provide a more comprehensive theoretical basis and guidance for the correct analysis and accurate prediction of the diffusion and transport patterns of pollutants in environmental water bodies and their impact on the environment, as well as for the formulation of reasonable and effective control and protection measures, and for the design of industrial and municipal emission engineering projects and environmental risk assessment.

[0003] Porous jets, as a typical engineering flow, face inherent limitations with traditional numerical methods (finite volume / finite element method), including high computational cost, strong mesh dependence, and difficulties in multiphysics coupling. While emerging physical information neural networks have achieved meshless solutions, they still encounter challenges in handling such three-dimensional transient multiphysics problems, including difficulties in balancing multi-equation losses, insufficient accuracy in the high gradient region of the jet, improper time discretization, and inaccurate buoyancy effect modeling. Therefore, developing a new method capable of accurately and efficiently solving three-dimensional porous jet transient flow problems has become an urgent need.

[0004] Although PINN has shown great potential and advantages in solving complex fluid dynamics problems, its current research mainly focuses on one-dimensional steady-state two-phase flow. How to extend it to porous negative buoyancy jets under three-dimensional transient conditions at various scales has become the core problem that urgently needs to be solved in the current technology.

[0005] Therefore, in order to solve the above problems, this paper proposes a direct numerical simulation prediction method for transient flow of three-dimensional porous negative buoyancy jet. Summary of the Invention

[0006] The purpose of this invention is to provide a direct numerical simulation prediction method for transient flow of three-dimensional porous negative buoyancy jets, so as to achieve efficient and accurate simulation of the flow behavior of porous negative buoyancy jets.

[0007] To achieve the above-mentioned technical effects, the present invention is implemented through the following technical solution: a direct numerical simulation prediction method for transient flow of three-dimensional porous negative buoyancy jet, characterized by comprising the following steps:

[0008] S1. Determine the transient control equations for the three-dimensional porous negative buoyancy jet;

[0009] S2. Construct a physical information neural network model, which includes the following steps:

[0010] S2.1 The parameters characterizing the flow behavior of a porous negative buoyancy jet are expressed as follows:

[0011] P=f(V0,ρ a ,ρ0,μ,X0,S,n,T a ,T0)

[0012] In the formula, P is the characteristic parameter of the negative buoyancy jet, V0 is the incident velocity, and ρ a ρ0 represents the density of the ambient fluid and the incident fluid, respectively, and T represents the density of the incident fluid. a T0 represents the ambient fluid temperature and the incident fluid temperature, respectively; X0 represents the incident radius; S represents the distance between two adjacent negative buoyancy injection ports; n represents the number of injection ports; and μ represents the viscosity coefficient.

[0013] S2.2. Through dimensional analysis, the dimensionless parameters characterizing the porous negative buoyancy jet are obtained, and the expressions are as follows:

[0014] P = f(Fr, Re, N, S, n)

[0015] In the formula, Fr is the Froude number, Re is the Reynolds number, S is the distance between two adjacent negative buoyancy inlets, n is the number of jet inlets, and N is the buoyancy ratio;

[0016] By extracting parameters characterizing the flow behavior of porous negative buoyancy jets in S2.1, and then dimensionlessly rendering these parameters in S2.2, physical constants and unit differences in the flow process are eliminated, thus achieving standardized modeling of the porous negative buoyancy jet flow. This simplifies the computational complexity of the physical model, enabling the constructed physical information neural network (PINN) to process input data more efficiently. Using the dimensionless physical parameters as input features of PINN, the PINN learns the relationship between these input parameters and the output results to predict the flow mechanism of porous negative buoyancy jets.

[0017] S2.3. Based on the dimensionless construction of the porous negative buoyancy jet characteristic parameters obtained above, a deep physical information neural network model was constructed, containing 12 hidden layers, each with 150 neurons. This network adopts a fully connected structure, ensuring that the dimensionless physical parameters input can be effectively transmitted to each layer, learning the complex relationships between different features layer by layer. This method helps the model extract deep information from the original physical features and make accurate predictions based on the physical constraints of the flow behavior. Through the optimized network structure, the modeling accuracy and efficiency of porous negative buoyancy jet flow behavior are improved.

[0018] S2.4 The activation function of the hidden layer is the hyperbolic tangent function (tanh), and its expression is as follows:

[0019]

[0020] This activation function has an output range of [-1, 1], which can effectively introduce nonlinear characteristics and enhance the learning ability of physical information neural networks to complex porous jet flow behavior. This allows for better handling of nonlinear characteristics in porous negative buoyancy jet flow, optimizes the model training process, and improves the prediction accuracy and stability of flow behavior.

[0021] S3. Obtain sample datasets, which include multiple sets of experimental data from direct numerical simulation (DNS), large eddy simulation (LES), particle image velocimetry (PIV), and planar laser-induced fluorescence (PLIF) under various operating conditions.

[0022] The sample dataset was divided into three classes: weak, transitional, and strong negative buoyancy jet sample data. All data were randomly assigned to the training set, validation set, and test set in proportions of 60%, 20%, and 20%, respectively.

[0023] S4. Input the sample dataset into the physical information neural network model for training; this includes the following steps:

[0024] S4.1 Integrate the physical information of the sample data into the loss function, and embed the control equation into the loss function of the physical information neural network in the form of residuals;

[0025] S4.2. Use a hierarchical sampling strategy to generate training data points;

[0026] S4.3. Train the neural network model by jointly driving the training of physical information and data loss;

[0027] S4.4. By inputting the physical parameters of the jet into the three-dimensional porous negative buoyancy jet transient flow direct numerical simulation prediction model of the physical information neural network, the physical quantities of the flow field can be output, and the temperature cloud map, concentration cloud map, etc. can be reconstructed, thereby obtaining the key parameters characterizing the jet characteristics.

[0028] S5. Based on the total training loss and experimental parameters, adjust and optimize the hyperparameters of the neural network to obtain a well-trained physical information neural network; this includes the following steps:

[0029] S5.1 Compare the prediction results based on the physical information neural network model with the experimental data of DNS, LES and PIV / PLIF;

[0030] S5.2 Apply the Adam algorithm for iterative optimization, and update the adaptive network weights synchronously;

[0031] S5.3. With the goal of minimizing the total loss calculated by the loss function, adjust and optimize the hyperparameters of the neural network to obtain a complete and mature jet prediction model of the physical information neural network and save it.

[0032] S6. Input the spatial coordinates and prediction time of the three-dimensional porous negative buoyancy jet to be simulated into the trained physical information neural network to obtain key parameters characterizing the negative buoyancy jet, thereby studying its transport mechanism and entrainment mixing characteristics.

[0033] Furthermore, in S1, the transient governing equations for the three-dimensional porous negative buoyancy jet are determined to include six partial differential equations: the continuity equation, the transient momentum equation in the X direction, the transient momentum equation in the Y direction, the transient momentum equation in the Z direction, the energy equation, and the concentration equation; as detailed below:

[0034] The continuity equation is:

[0035]

[0036] In the formula, u, v, w are the components of the fluid velocity in the x, y, z directions;

[0037] The transient momentum equation in the X direction is:

[0038]

[0039] In the formula, ρ is the fluid density, u, v, w are the components of the fluid velocity in the x, y, z directions, t is time, p is pressure, and ν is the dynamic viscosity coefficient.

[0040] The transient momentum equation in the Y direction is:

[0041]

[0042] In the formula, ρ is the fluid density, u, v, w are the components of the fluid velocity in the x, y, z directions, t is time, p is pressure, and ν is the dynamic viscosity coefficient.

[0043] The transient momentum equation in the Z direction is:

[0044]

[0045] In the formula, ρ is the fluid density, u, v, w are the components of the fluid velocity in the x, y, z directions, t is time, p is pressure, ν is the dynamic viscosity coefficient, and β is the fluid density. T β is the coefficient of thermal expansion. C T is the concentration expansion coefficient. ref For reference temperature, C ref The concentration is used as a reference, and g is the acceleration due to gravity.

[0046] The energy equation is:

[0047]

[0048] In the formula, u, v, w are the components of fluid velocity in the x, y, z directions, t is time, α = υ / pr is thermal diffusivity, ν is dynamic viscosity coefficient, pr is Prandtl number, and T is fluid temperature;

[0049] The concentration equation is:

[0050]

[0051] In the formula, u, v, w are the components of fluid velocity in the x, y, z directions, t is time, C is fluid concentration, D = v / Sc is the pollutant concentration coefficient and mass diffusion coefficient, ν is the dynamic viscosity coefficient, and Sc is the Schmidt number.

[0052] Furthermore, in S3, the acquisition of the sample dataset is specifically as follows:

[0053] S3.1 Obtain sample data of weak, transitional, and strong negative buoyancy jets, and take 15 sets of data for each.

[0054] S3.2 Obtain five parameters from the sample data: Froude number Fr, Reynolds number Re, distance S between two adjacent negative buoyancy inlets, number of jet holes n, and buoyancy ratio N.

[0055] Five parameters from the jet sample data—Froude number Fr, Reynolds number Re, distance S between two adjacent negative buoyancy inlets, number of jet holes n, and buoyancy ratio N—are used as input data, along with the corresponding transport mechanism and convolutional mixing characteristics of the porous negative buoyancy jet as target vectors to train a prediction model based on a physical information neural network.

[0056] S3.3. Obtain the time-averaged maximum jet height, time to reach the initial maximum jet height, and entrainment rate as key parameters for the characteristics of the negative buoyancy jet;

[0057] S3.4. The Min-Max algorithm is used to normalize the data in the sample dataset. The formula is as follows:

[0058]

[0059] In the formula, I N This is the data after jet normalization, where I is the parameter of the initial jet sample data. max and I min These represent the maximum and minimum values ​​of the parameters in the initial sample data of the jet, respectively.

[0060] Furthermore, in S5.3, the total loss includes: data loss, physical equation loss, boundary loss, and initial condition loss.

[0061] Furthermore, in S6, the spatial coordinates and prediction time of the three-dimensional porous negative buoyancy jet to be simulated are input into a trained physical information neural network to obtain key parameters characterizing the negative buoyancy jet, thereby studying its transport mechanism and entrainment mixing characteristics, including:

[0062] S6.1 Input the spatial coordinates and prediction time of the three-dimensional porous negative buoyancy jet to be simulated into the trained physical information neural network;

[0063] S6.2 Input the initial and boundary conditions of the three-dimensional porous negative buoyancy jet to be simulated into the trained physical information neural network;

[0064] S6.3 Output the prediction results of the three-dimensional porous negative buoyancy jet through the prediction model.

[0065] The beneficial effects of this invention are:

[0066] This invention integrates the physical information of the jet into a deep learning network, eliminating the need for mesh generation and avoiding the complexity and dependency of mesh generation in traditional methods, thus reducing computational costs. The physical information neural network simultaneously predicts the velocity, pressure, temperature, and concentration fields, achieving unified solutions for multiple physics fields and avoiding the complexity of multi-field coupling iterations in traditional methods. By employing a hierarchical sampling strategy to densify sampling points near the jet inlet, the solution accuracy in critical regions is improved while maintaining overall computational efficiency. Furthermore, by accurately introducing the buoyancy term of the Boussinesq assumption into the momentum equation in the gravity direction, and considering the buoyancy effects caused by temperature and concentration differences, this invention is suitable for accurate simulation of buoyancy-driven flows. Attached Figure Description

[0067] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0068] Figure 1 This is a schematic diagram of the direct numerical simulation prediction method for transient flow of three-dimensional porous negative buoyancy jet as described in Embodiment 1 of the present invention;

[0069] Figure 2 This is a schematic diagram of the structure of the three-dimensional porous negative buoyancy jet transient flow direct numerical simulation prediction system described in Embodiment 2 of the present invention. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] Example 1

[0072] A direct numerical simulation prediction method for transient flow of a three-dimensional porous negative buoyancy jet, characterized by comprising the following steps:

[0073] S1. Determine the transient control equations for the three-dimensional porous negative buoyancy jet; the transient control equations for the three-dimensional porous negative buoyancy jet include 6 partial differential equations, namely: continuity equation, transient momentum equation in the X direction, transient momentum equation in the Y direction, transient momentum equation in the Z direction, energy equation, and concentration equation; as detailed below:

[0074] The continuity equation is:

[0075]

[0076] In the formula, u, v, w are the components of the fluid velocity in the x, y, z directions;

[0077] The transient momentum equation in the X direction is:

[0078]

[0079] In the formula, ρ is the fluid density, u, v, w are the components of the fluid velocity in the x, y, z directions, t is time, p is pressure, and ν is the dynamic viscosity coefficient.

[0080] The transient momentum equation in the Y direction is:

[0081]

[0082] In the formula, ρ is the fluid density, u, v, w are the components of the fluid velocity in the x, y, z directions, t is time, p is pressure, and ν is the dynamic viscosity coefficient.

[0083] The transient momentum equation in the Z direction is:

[0084]

[0085] In the formula, ρ is the fluid density, u, v, w are the components of the fluid velocity in the x, y, z directions, t is time, p is pressure, ν is the dynamic viscosity coefficient, and β is the fluid density. T β is the coefficient of thermal expansion. C T is the concentration expansion coefficient. ref For reference temperature, C ref The concentration is used as a reference, and g is the acceleration due to gravity.

[0086] The energy equation is:

[0087]

[0088] In the formula, u, v, w are the components of fluid velocity in the x, y, z directions, t is time, α = υ / pr is thermal diffusivity, ν is dynamic viscosity coefficient, pr is Prandtl number, and T is fluid temperature;

[0089] The concentration equation is:

[0090]

[0091] In the formula, u, v, w are the components of fluid velocity in the x, y, z directions, t is time, C is fluid concentration, D = v / Sc is the pollutant concentration coefficient and mass diffusion coefficient, ν is the dynamic viscosity coefficient, and Sc is the Schmidt number.

[0092] S2. Construct a physical information neural network model, which includes the following steps:

[0093] S2.1 The parameters characterizing the flow behavior of a porous negative buoyancy jet are expressed as follows:

[0094] P=f(V0,ρ a ,ρ0,μ,X0,S,n,T a ,T0)

[0095] In the formula, P is the characteristic parameter of the negative buoyancy jet, V0 is the incident velocity, and ρ a ρ0 represents the density of the ambient fluid and the incident fluid, respectively, and T represents the density of the incident fluid. aT0 represents the ambient fluid temperature and the incident fluid temperature, respectively; X0 represents the incident radius; S represents the distance between two adjacent negative buoyancy injection ports; n represents the number of injection ports; and μ represents the viscosity coefficient.

[0096] S2.2. Through dimensional analysis, the dimensionless parameters characterizing the porous negative buoyancy jet are obtained, and the expressions are as follows:

[0097] P = f(Fr, Re, N, S, n)

[0098] In the formula, Fr is the Froude number, Re is the Reynolds number, S is the distance between two adjacent negative buoyancy inlets, n is the number of jet inlets, and N is the buoyancy ratio;

[0099] By extracting parameters characterizing the flow behavior of porous negative buoyancy jets in S2.1, and then dimensionlessly rendering these parameters in S2.2, physical constants and unit differences in the flow process are eliminated, thus achieving standardized modeling of the porous negative buoyancy jet flow. This simplifies the computational complexity of the physical model, enabling the constructed physical information neural network (PINN) to process input data more efficiently. Using the dimensionless physical parameters as input features of PINN, the PINN learns the relationship between these input parameters and the output results to predict the flow mechanism of porous negative buoyancy jets.

[0100] S2.3. Based on the dimensionless construction of the porous negative buoyancy jet characteristic parameters obtained above, a deep physical information neural network model was constructed, containing 12 hidden layers, each with 150 neurons. This network adopts a fully connected structure, ensuring that the dimensionless physical parameters input can be effectively transmitted to each layer, learning the complex relationships between different features layer by layer. This method helps the model extract deep information from the original physical features and make accurate predictions based on the physical constraints of the flow behavior. Through the optimized network structure, the modeling accuracy and efficiency of porous negative buoyancy jet flow behavior are improved.

[0101] S2.4 The activation function of the hidden layer is the hyperbolic tangent function (tanh), and its expression is as follows:

[0102]

[0103] This activation function has an output range of [-1,1], which can effectively introduce nonlinear characteristics, enhance the learning ability of physical information neural networks to complex porous jet flow behavior, and thus better handle the nonlinear characteristics in porous negative buoyancy jet flow, optimize the training process of the model, and improve the prediction accuracy and stability of flow behavior.

[0104] S3. Obtain the sample dataset, which includes multiple sets of experimental data from direct numerical simulation (DNS), large eddy simulation (LES), particle image velocimetry (PIV), and planar laser-induced fluorescence (PLIF) under various operating conditions. Divide the sample dataset into three categories: weak, transition zone, and strong negative buoyancy jet sample data. All data are randomly assigned to the training set, validation set, and test set in proportions of 60%, 20%, and 20%, respectively.

[0105] The specific steps for obtaining the sample dataset are as follows:

[0106] S3.1 Obtain sample data of weak, transitional, and strong negative buoyancy jets, and take 15 sets of data for each.

[0107] S3.2 Obtain five parameters from the sample data: Froude number Fr, Reynolds number Re, distance S between two adjacent negative buoyancy inlets, number of jet holes n, and buoyancy ratio N.

[0108] Five parameters from the jet sample data—Froude number Fr, Reynolds number Re, distance S between two adjacent negative buoyancy inlets, number of jet holes n, and buoyancy ratio N—are used as input data, along with the corresponding transport mechanism and convolutional mixing characteristics of the porous negative buoyancy jet as target vectors to train a prediction model based on a physical information neural network.

[0109] S3.3. Obtain the time-averaged maximum jet height, time to reach the initial maximum jet height, and entrainment rate as key parameters for the characteristics of the negative buoyancy jet;

[0110] S3.4. The Min-Max algorithm is used to normalize the data in the sample dataset. The formula is as follows:

[0111]

[0112] In the formula, I N This is the data after jet normalization, where I is the parameter of the initial jet sample data. max and I min These represent the maximum and minimum values ​​of the parameters in the initial sample data of the jet, respectively.

[0113] S4. Input the sample dataset into the physical information neural network model for training; this includes the following steps:

[0114] S4.1 Integrate the physical information of the sample data into the loss function, and embed the control equation into the loss function of the physical information neural network in the form of residuals;

[0115] S4.2. Use a hierarchical sampling strategy to generate training data points;

[0116] S4.3. Train the neural network model by jointly driving the training of physical information and data loss;

[0117] S4.4. By inputting the physical parameters of the jet into the three-dimensional porous negative buoyancy jet transient flow direct numerical simulation prediction model of the physical information neural network, the physical quantities of the flow field can be output, and the temperature cloud map, concentration cloud map, etc. can be reconstructed, thereby obtaining the key parameters characterizing the jet characteristics.

[0118] S5. Based on the total training loss and experimental parameters, adjust and optimize the hyperparameters of the neural network to obtain a well-trained physical information neural network; this includes the following steps:

[0119] S5.1 Compare the prediction results based on the physical information neural network model with the experimental data of DNS, LES and PIV / PLIF;

[0120] S5.2 Apply the Adam algorithm for iterative optimization, and update the adaptive network weights synchronously;

[0121] S5.3. With the goal of minimizing the total loss calculated by the loss function, adjust and optimize the hyperparameters of the neural network to obtain a complete and mature jet prediction model of the physical information neural network and save it; the total loss includes: data loss, physical equation loss, boundary loss and initial condition loss.

[0122] S6. Input the spatial coordinates and prediction time of the three-dimensional porous negative buoyancy jet to be simulated into the trained physical information neural network to obtain key parameters characterizing the negative buoyancy jet, thereby studying its transport mechanism and entrainment mixing characteristics; specifically as follows:

[0123] S6.1 Input the spatial coordinates and prediction time of the three-dimensional porous negative buoyancy jet to be simulated into the trained physical information neural network;

[0124] S6.2 Input the initial and boundary conditions of the three-dimensional porous negative buoyancy jet to be simulated into the trained physical information neural network;

[0125] S6.3 Output the prediction results of the three-dimensional porous negative buoyancy jet through the prediction model.

[0126] Example 2

[0127] The specific steps for training the physical information neural network model using the sample dataset described in S4 of Example 1 are as follows:

[0128] To achieve accurate prediction of transient flow in complex three-dimensional porous negative buoyancy jets through direct numerical simulation, a hierarchical sampling strategy is adopted for generating training data points. Through the systematic design of configuration points, boundary points, and initial condition points, comprehensive coverage of physical information and high-precision characterization of key regions are achieved. This strategy focuses on the flow characteristics and physical boundary conditions within the computational domain, and generates data points in three levels. The specific implementation method is as follows:

[0129] I. Methods for Generating Deployment Points

[0130] The role of the placement points is to provide the model with a learning basis for the global physical field by calculating the residual terms of the governing equations. The number of placement points generated is equal to the number of placement points. In terms of spatial distribution, the placement points adopt a hybrid sampling scheme of "uniform coverage of the entire domain + local key densification": 70% of the points are distributed throughout the computational domain by random sampling to ensure uniform characterization of the velocity, temperature and concentration distribution of the mainstream field region and avoid the loss of physical information due to sampling bias; the remaining 30% of the points are densified in the area near the jet orifice with the highest flow gradient. The spatial range of the densified area is strictly defined as a cylindrical region with the center of the jet orifice as the center and a radius equal to three times the radius of the jet orifice, and is restricted along the Y-axis to 30% of the computational domain height near the inlet boundary (i.e., the Y-axis coordinate is zero). This design aims to capture key physical phenomena such as the strong shear flow, temperature diffusion front and concentration mixing interface in the initial stage of the jet. In the time dimension, the sampling time of all configuration points is uniformly selected within the range of zero to the maximum simulation time. The equal-interval distribution on the time axis ensures that the evolution characteristics of the transient process (such as the development and diffusion of the jet) are fully recorded.

[0131] II. Methods for Generating Boundary Points

[0132] The inlet boundary (where the Y-axis coordinate is zero) employs a porous jet structure. Its boundary conditions are divided into two categories based on spatial location: sampling points inside the jet orifice must satisfy forced boundary conditions where velocity, temperature, and concentration equal to the inlet velocity, temperature, and concentration, to simulate the initial state of the high-speed jet; points outside the jet orifice are subject to no-slip constraints (zero velocity), while temperature and concentration are equal to ambient values, reflecting the thermodynamic state of the surrounding static fluid. To improve the boundary resolution of the jet impact region, 40% of the samples at the inlet boundary points are adaptively concentrated at the jet orifice edge and near-field region. The density of these points is 2 to 3 times that of other regions, accurately capturing the interfacial transition characteristics between the jet and the surrounding fluid, as well as the development law of the shear layer.

[0133] The outlet boundary (located at the height of the computational domain on the Y-axis) adopts a free outflow condition, where all physical quantities tend to zero along the normal gradient. Specifically, the velocity components (including those in the X, Y, and Z directions) are all zero, and the temperature and concentration return to ambient values. The outlet boundary points are uniformly distributed along the XZ plane, and their number is dynamically adjusted based on the outlet area and the velocity gradient of the main flow field to ensure that the mass conservation and energy balance constraints at the flow outlet are fully satisfied.

[0134] A no-slip condition is applied to the wall boundary (X-axis coordinate at half the width of the positive and negative computational domain, Z-axis coordinate at half the depth of the positive and negative computational domain), meaning that the velocity in all three directions is zero, and the wall temperature and concentration are fixed at ambient values. The sampling density of the wall points is distributed in a gradient along the wall normal, with the point density in the near-wall region being higher than that in the far-wall region, in order to accurately characterize the velocity decay law and heat and mass transfer process within the boundary layer.

[0135] III. Methods for generating initial condition points

[0136] Initial condition points define the flow field state at the start time (i.e., time zero). The number of points generated is the same as the number of initial condition points, and their spatial distribution strategy is similar to that of configuration points: 70% of the points are uniformly distributed across the entire domain to ensure a basic characterization of the physical properties of the entire computational domain in the initial state; 70% of the points are densely distributed near the jet inlet to capture the local flow characteristics at the instant the jet starts. The physical state of all initial condition points is uniformly set as a static flow field: the velocity in all three directions is zero, and the temperature and concentration are equal to the ambient values. This setting conforms to the physical reality of thermodynamic equilibrium and avoids interference from non-physical disturbances on subsequent transient prediction results. The density region of the initial points is completely consistent with the density region of the jet inlet of the configuration points, ensuring high-precision monitoring of the flow and transport process of the initial segment of the jet during the simulation startup phase.

[0137] In Example 1, S5 describes adjusting and optimizing the neural network hyperparameters based on the total training loss and experimental parameters to obtain a well-trained physical information neural network; specifically as follows:

[0138] The total training loss function, including PDE loss, boundary loss, and initial condition loss, is expressed as follows:

[0139] L total =L PDE +λ BC L BC +λ BC L IC

[0140] In the formula, L PDE For PDE loss; L BC For boundary loss, calculate the mean square error between the predicted value and the target value at the boundary points; L ICFor the initial conditional loss, calculate the mean square error between the predicted value and the target value at the initial conditional point; λ BC These are the weighting coefficients for the boundary conditions and initial conditions.

[0141] The PDE loss is a weighted sum of the residuals from the six equations:

[0142] L PDE =λ cont L cont +λ mom,x L mom,x +λ mom,y L mom,y +λ mom,z L mom,z

[0143] +λ energy L energy +λ species L species

[0144] In the formula, L cont For the continuity equation loss, L mom,x L mom,y L mom,z The momentum equation losses in the X, Y, and Z directions are respectively, L energy For the energy equation loss, L species The loss is represented by the concentration equation, and λ is the corresponding weighting coefficient.

[0145] Then, a dynamic weight balancing method based on gradient norm is used, updating the weights every K steps:

[0146] For the residual R_i of each PDE equation, calculate its gradient norm with respect to the network parameters, as expressed below:

[0147]

[0148] Based on the continuity equation, the weights of other equations are calculated as follows:

[0149]

[0150] In the formula, ∈ is a small constant to avoid division by zero.

[0151] Using a smooth update strategy, the expression is as follows:

[0152]

[0153] In the formula, α is the smoothing coefficient, which is taken as 0.1.

[0154] The Xavier initialization scheme is used to randomly initialize the model parameters to ensure that the variance of the activation values ​​of each layer in the physical information neural network model is consistent, thus preventing gradient vanishing or exploding.

[0155] During training, the loss function guides backpropagation. The smaller the loss function value, the more accurate the prediction. The model parameters are then evaluated and adjusted accordingly.

[0156] The Adam optimization algorithm is chosen to learn the network parameters, combining the advantages of momentum and RMSprop, and the learning rate is adjusted based on gradient moment estimation. Iterative optimization using the Adam algorithm is then performed, simultaneously updating the adaptive and network weights to improve training efficiency and effectiveness. After optimization, a two-layer optimization strategy is employed, combining global and local optimum methods. The Limited-Memory Broyden Fletcher Goldfarb Shanno (L-BFGS) algorithm from the quasi-Newton optimization algorithm family is used for a new round of iterative optimization. The adaptive weights are kept constant, and the network weights are finely adjusted to achieve a local optimum. By combining global search breadth and local search depth, a better solution is found, resulting in a well-trained physical information neural network model suitable for porous negative buoyancy jets.

[0157] In Example 1, S6 describes inputting the spatial coordinates and prediction time of the three-dimensional porous negative buoyancy jet to be simulated into a trained physical information neural network to obtain key parameters characterizing the negative buoyancy jet, thereby studying its transport mechanism and entrainment mixing characteristics; specifically as follows:

[0158] Since the transport characteristics of porous negative buoyancy jets are affected by multiple parameters, such as the spatial coordinate independent variables x, y, z and the time parameter t, which are involved in the positioning within the entire physical field in spacetime, while the number of inlets n and the distance S between two adjacent negative buoyancy inlets do not directly participate in the constraints of the physical control equations on the prediction results of the neural network, this invention uses a method of labeling these parameters during neural network training to label the physical field information corresponding to different parameters (i.e., different operating conditions), thereby achieving the training purpose.

[0159] Therefore, the input layer of the physical information neural network model consists of spatial coordinates (x, y, z), the number of inlets n, the distance S between two adjacent negative buoyancy inlets, and time t, and the output consists of flow field variables (u, v, w, T, C).

[0160] Example 3

[0161] This embodiment is a system established based on the direct numerical simulation prediction method for transient flow of three-dimensional porous negative buoyancy jets described in this invention; the system specifically includes:

[0162] Governing equation determination module: used to determine the transport and entrainment governing equations for a three-dimensional porous negative buoyancy jet;

[0163] Neural network building module: used to build a physical information neural network, which includes an input layer, a hidden layer and an output layer;

[0164] Data acquisition module: configured to acquire sample datasets, wherein the sample datasets include multiple sets of DNS, LES and PIV / PLIF sample data for multiple operating conditions;

[0165] Control equation embedding module: used to embed control equations into the loss function of the physical information neural network in residual form;

[0166] Training module: configured to input the sample dataset into the physical information domain adversarial neural network model for training, and obtain the total loss of the sample data propagating forward in the domain adversarial neural network model; wherein, the total loss includes: data loss, physical equation loss, boundary loss and initial condition loss;

[0167] The optimization module is configured to apply the Adam algorithm to iteratively optimize the total loss during a new round of training of the wake field prediction model, simultaneously update the adaptive and network weights, and optimize the neural network parameters.

[0168] Simulation module: Used to input the spatial coordinates and prediction time of the three-dimensional porous negative buoyancy jet to be simulated into a trained physical information neural network, so as to obtain the transport and entrainment mechanism of the three-dimensional porous negative buoyancy jet to be simulated at different spatial coordinates and different prediction times.

[0169] The working principle and beneficial effects of the system established by the direct numerical simulation prediction method for transient flow of three-dimensional porous negative buoyancy jet described in this embodiment correspond one-to-one with the working principle and beneficial effects of the direct numerical simulation prediction method for transient flow of three-dimensional porous negative buoyancy jet.

[0170] Example 4

[0171] If the system established by the three-dimensional porous negative buoyancy jet transient flow direct numerical simulation prediction method of the present invention described in Example 3 is transformed into a specific electronic device, the electronic device includes: a processor, a memory, and a computer program stored in the memory and capable of running on the processor.

[0172] The computer program is a direct numerical simulation and prediction program for transient flow of three-dimensional porous negative buoyancy jet based on physical information neural network.

[0173] When the processor executes the computer program, it implements the steps in the above embodiments of the direct numerical simulation prediction method for transient flow of three-dimensional porous negative buoyancy jet based on physical information neural network, or, when the processor executes the computer program, it implements the functions of each module / unit in the above embodiments of the device, such as the optimization module.

[0174] The computer program can be divided into one or more modules / units as described in Embodiment 3. The one or more modules / units are stored in the memory and executed by the processor to complete the present invention.

[0175] The one or more modules / units may be a series of computer program instruction segments capable of performing a specific function, which are used to describe the execution process of the computer program in the electronic device.

[0176] The electronic device may be a desktop computer, laptop, handheld computer, or smart tablet, etc. The electronic device may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the above components are merely examples of electronic devices and do not constitute a limitation on the electronic device. It may include more or fewer components than described above, or combine certain components, or different components. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0177] The memory can be used to store the computer program and / or module. The processor implements various functions of the electronic device by running or executing the computer program and / or module stored in the memory and by calling the data stored in the memory.

[0178] The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, applications required for at least one function (such as sound playback function, image playback function, etc.), etc.; the data storage area may store data created based on the use of the mobile phone (such as audio data, phonebook, etc.).

[0179] Therefore, the memory can be high-speed random access memory, or it can include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0180] If the modules / units integrated in the electronic device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0181] Based on this understanding, the present invention can implement all or part of the processes in the methods of the above embodiments, or it can be accomplished by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0182] It should be noted that the device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. In addition, in the accompanying drawings of the device embodiments provided by the present invention, the connection relationship between modules indicates that they have a communication connection, which can be implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without creative effort.

[0183] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A direct numerical simulation and prediction method for transient flow of a three-dimensional porous negative buoyancy jet, characterized in that, Includes the following steps: S1. Determine the transient control equations for the three-dimensional porous negative buoyancy jet; S2. Construct a physical information neural network model, which includes the following steps: S2.1 The parameters characterizing the flow behavior of a porous negative buoyancy jet are expressed as follows: P=f(V0,ρ a ,ρ0,μ,X0,S,n,T a ,T0) In the formula, P is the characteristic parameter of the negative buoyancy jet, V0 is the incident velocity, and ρ a ρ0 represents the density of the ambient fluid and the incident fluid, respectively, and T represents the density of the incident fluid. a T0 represents the ambient fluid temperature and the incident fluid temperature, respectively; X0 represents the incident radius; S represents the distance between two adjacent negative buoyancy injection ports; n represents the number of injection ports; and μ represents the viscosity coefficient. S2.

2. Through dimensional analysis, the dimensionless parameters characterizing the porous negative buoyancy jet are obtained, and the expressions are as follows: P = f(Fr, Re, N, S, n) In the formula, Fr is the Froude number, Re is the Reynolds number, S is the distance between two adjacent negative buoyancy inlets, n is the number of jet inlets, and N is the buoyancy ratio; By extracting parameters characterizing the flow behavior of porous negative buoyancy jets in S2.1, and then dimensionlessly rendering these parameters in S2.2, the physical constants and unit differences in the flow process are eliminated, thereby achieving standardized modeling of the porous negative buoyancy jet flow. This simplifies the computational complexity of the physical model, enabling the constructed physical information neural network to process input data more efficiently. Furthermore, by using the dimensionless physical parameters as input features of PINN, the physical information neural network learns the relationship between these input parameters and the output results, thereby predicting the flow mechanism of porous negative buoyancy jets. S2.3 Based on the dimensionless construction of the porous negative buoyancy jet characteristic parameters obtained above, a deep physical information neural network model was constructed, which contains 12 hidden layers, each with 150 neurons. The network adopts a fully connected structure to ensure that the input dimensionless physical parameters can be effectively transmitted to each layer, and learns the complex relationship between different features layer by layer. S2.4 The activation function of the hidden layer is the hyperbolic tangent function (tanh), and its expression is as follows: This activation function has an output range of [-1,1], which can effectively introduce nonlinear characteristics, enhance the learning ability of physical information neural networks to complex porous jet flow behavior, and thus better handle the nonlinear characteristics in porous negative buoyancy jet flow, optimize the training process of the model, and improve the prediction accuracy and stability of flow behavior. S3. Obtain sample datasets, which include multiple sets of experimental data from direct numerical simulation, large eddy simulation, particle image velocimetry, and planar laser-induced fluorescence technology under various operating conditions. S4. Input the sample dataset into the physical information neural network model for training; this includes the following steps: S4.1 Integrate the physical information of the sample dataset into the loss function, and embed the control equation into the loss function of the physical information neural network in the form of residuals; S4.

2. Use a hierarchical sampling strategy to generate training data points; S4.

3. Train the neural network model by jointly driving the training of physical information and data loss; S4.

4. By inputting the physical parameters of the jet into the three-dimensional porous negative buoyancy jet transient flow direct numerical simulation prediction model of the physical information neural network, the physical quantities of the flow field can be output, and the temperature cloud map and concentration cloud map can be reconstructed, thereby obtaining the key parameters characterizing the jet characteristics. S5. Based on the total training loss and experimental parameters, adjust and optimize the hyperparameters of the neural network to obtain a well-trained physical information neural network; this includes the following steps: S5.1 Compare the prediction results based on the physical information neural network model with the experimental data of DNS, LES and PIV / PLIF; S5.2 Apply the Adam algorithm for iterative optimization, and update the adaptive network weights synchronously; S5.

3. With the goal of minimizing the total loss calculated by the loss function, adjust and optimize the hyperparameters of the neural network to obtain a complete and mature jet prediction model of the physical information neural network and save it. S6. Input the spatial coordinates and prediction time of the three-dimensional porous negative buoyancy jet to be simulated into the trained physical information neural network to obtain key parameters characterizing the negative buoyancy jet, thereby studying its transport mechanism and entrainment mixing characteristics.

2. The direct numerical simulation and prediction method for transient flow of a three-dimensional porous negative buoyancy jet according to claim 1, characterized in that, In S1, the transient governing equations for the three-dimensional porous negative buoyancy jet include six partial differential equations: the continuity equation, the transient momentum equation in the X direction, the transient momentum equation in the Y direction, the transient momentum equation in the Z direction, the energy equation, and the concentration equation; as detailed below: The continuity equation is: In the formula, u, v, w are the components of the fluid velocity in the x, y, z directions; The transient momentum equation in the X direction is: In the formula, ρ is the fluid density, u, v, w are the components of the fluid velocity in the x, y, z directions, t is time, p is pressure, and ν is the dynamic viscosity coefficient. The transient momentum equation in the Y direction is: In the formula, ρ is the fluid density, u, v, w are the components of the fluid velocity in the x, y, z directions, t is time, p is pressure, and ν is the dynamic viscosity coefficient. The transient momentum equation in the Z direction is: In the formula, ρ is the fluid density, u, v, w are the components of the fluid velocity in the x, y, z directions, t is time, p is pressure, ν is the dynamic viscosity coefficient, and β is the fluid density. T β is the coefficient of thermal expansion. C T is the concentration expansion coefficient. ref For reference temperature, C ref The concentration is used as a reference, and g is the acceleration due to gravity. The energy equation is: In the formula, u, v, w are the components of fluid velocity in the x, y, z directions, t is time, α = υ / pr is thermal diffusivity, ν is dynamic viscosity coefficient, pr is Prandtl number, and T is fluid temperature; The concentration equation is: In the formula, u, v, w are the components of fluid velocity in the x, y, z directions, t is time, C is fluid concentration, D = v / Sc is the pollutant concentration coefficient and mass diffusion coefficient, ν is the dynamic viscosity coefficient, and Sc is the Schmidt number.

3. The direct numerical simulation and prediction method for transient flow of a three-dimensional porous negative buoyancy jet according to claim 1, characterized in that, In S3, the acquisition of the sample dataset is specifically as follows: S3.1 Obtain 15 sets of sample data for each of the weak, transitional, and strong negative buoyancy jets; S3.2 Obtain five parameters from the sample data: Froude number Fr, Reynolds number Re, distance S between two adjacent negative buoyancy inlets, number of jet holes n, and buoyancy ratio N. S3.3 Obtain key parameters for the characteristics of negative buoyancy jets, including time-averaged maximum jet height, time to reach initial maximum jet height, and entrainment rate; S3.

4. The Min-Max algorithm is used to normalize the data in the sample dataset. The formula is as follows: In the formula, I N This is the data after jet normalization, where I is the parameter of the initial jet sample data. max and I min These represent the maximum and minimum values ​​of the parameters in the initial sample data of the jet, respectively.

4. The direct numerical simulation and prediction method for transient flow of a three-dimensional porous negative buoyancy jet according to claim 1, characterized in that, In S5.3, the total loss includes: data loss, physical equation loss, boundary loss, and initial condition loss.

5. The direct numerical simulation and prediction method for transient flow of a three-dimensional porous negative buoyancy jet according to claim 1, characterized in that, In S6, the spatial coordinates and prediction time of the three-dimensional porous negative buoyancy jet to be simulated are input into a trained physical information neural network to obtain key parameters characterizing the negative buoyancy jet, thereby studying its transport mechanism and entrainment mixing characteristics, including: S6.1 Input the spatial coordinates and prediction time of the three-dimensional porous negative buoyancy jet to be simulated into the trained physical information neural network; S6.2 Input the initial and boundary conditions of the three-dimensional porous negative buoyancy jet to be simulated into the trained physical information neural network; S6.3 Output the prediction results of the three-dimensional porous negative buoyancy jet through the prediction model.

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