A complex mountain flow field simulation method based on an improved GEKO turbulence model

Abstract

The application discloses a complex mountain flow field simulation method based on an improved GEKO turbulent flow model, and comprises the following steps: obtaining the flow field parameters of a complex mountain terrain and a reference position, generating a calculation domain grid and boundary conditions; obtaining high-fidelity data, determining a training set and a test set, determining an optimization objective function and neural network input variables; obtaining an improved GEKO turbulent flow model based on an adjoint optimization method and machine learning, and obtaining the closed coefficient of the improved turbulent flow model; and performing complex mountain flow field numerical simulation based on the improved GEKO turbulent flow model, and obtaining the distribution of the wind speed and turbulent kinetic energy around the complex mountain. The application can accurately simulate the distribution of the wind speed and turbulent kinetic energy around the complex mountain, and the calculation precision is superior to the numerical simulation result of a standard GEKO model.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of wind power generation technology, in particular to a complex mountain flow field simulation method based on an improved GEKO turbulence model. BACKGROUND

[0002] The complex mountain terrain will change the wind direction and turbulence characteristics of the wind field, resulting in variable wind direction, high turbulence intensity, and flow separation. In this context, to improve the power generation of wind turbines and reduce their load, it is essential to conduct a detailed assessment of wind energy resources in wind farms, which helps to select a reasonable site. However, in complex mountain flow fields, the representativeness of traditional wind towers is reduced, and it is difficult to accurately assess the wind resources away from the wind tower location. The applicability of theoretical models based on various assumptions in complex mountain flow field prediction is also reduced. Currently, the CFD method based on RANS has become a common means of complex mountain wind resource assessment. This method is widely used due to its high computational efficiency, good accuracy, and ability to fully reflect the flow field around complex mountains.

[0003] Currently, the commonly used RANS turbulence model in complex mountain flow field numerical simulation is the k-ε model and the SST k-ω model. Although the SST k-ω model performs slightly better than the k-ε model in simulating separated flow, its predictive ability is still limited on the leeward slope. This is because there is an imbalance between the generation and dissipation of turbulent kinetic energy on the leeward slope, which is a major challenge for common two-equation turbulence models. In addition, these two common models have limited predictive ability for separated flow, and their fixed turbulence model closure coefficients make it difficult to accurately simulate the flow field characteristics of complex terrain.

[0004] The recently released GEKO turbulence model is an upgraded version of the k-ω model, which features six free parameters designed to allow users to calibrate the turbulence model for different flow scenarios without changing the basic calibration of the model. The GEKO model provides the possibility of adjusting the turbulence model for specific applications, but also requires an effective framework to fine-tune the six free parameters covering specific flow scenarios. Using machine learning methods to optimize the GEKO turbulence model closure coefficients is a relatively effective method. However, in complex mountain flow field simulation, it is necessary to balance the simulation of turbulence and wind speed, and there is no unified conclusion on the optimal target variable; the sensitivity of neural network input parameters has not been conclusively determined; the selection of six closure coefficients of the GEKO turbulence model is also not conclusive; and the generalization of the trained GEKO model still needs to be verified. SUMMARY

[0005] The purpose of the present application is to provide a complex mountain flow field simulation method based on an improved GEKO turbulent flow model, which obtains an optimal turbulent flow model closure coefficient based on the adjoint optimization method and machine learning by optimizing the objective function and reducing the input variables, improves the model precision and efficiency, and has strong generalization ability, can accurately simulate the distribution of wind speed and turbulent kinetic energy around complex mountains, and the calculation precision is better than the numerical simulation results of the standard GEKO model.

[0006] To achieve the above technical purpose, the technical scheme adopted by the present application is:

[0007] A complex mountain flow field simulation method based on an improved GEKO turbulent flow model, the method comprising the following steps:

[0008] Step 1, obtaining the terrain data of the complex mountain and the flow field parameters of the reference position, generating the calculation domain grid and the boundary condition;

[0009] Step 2, obtaining high-fidelity data reflecting the trend of the entire flow field, determining the training set and the test set, determining the optimization objective function and the neural network input variable; the high-fidelity data is large eddy simulation data or direct numerical simulation data;

[0010] Step 3, introducing the Lagrange multiplier, constructing the Lagrange function, obtaining the adjoint equation by deriving the Lagrange function and setting it to zero, solving the adjoint equation to obtain the adjoint variable, and then calculating the gradient of the optimization objective function to the design variable; combine neural network training with adjoint optimization, gradually adjust the design variable, so that the optimization objective function reaches the minimum value, obtain the improved GEKO turbulent flow model, and combine the calculation domain grid and the boundary condition to obtain the improved turbulent flow model closure coefficient;

[0011] Step 4, based on the improved GEKO turbulent flow model, the numerical simulation of the complex mountain flow field is carried out, and the distribution of wind speed and turbulent kinetic energy around the complex mountain is obtained;

[0012] Step 5, verifying the precision of the numerical simulation results.

[0013] Further, in step 1, the terrain data of the complex mountain includes two-dimensional terrain data including the expression of the terrain function, the distribution data of the terrain scattered points, and the stl format three-dimensional terrain data.

[0014] Further, in step 1, the flow field parameters of the reference position include wind speed, turbulent kinetic energy and specific dissipation rate; wherein for the wind speed, turbulent kinetic energy and specific dissipation rate of the inlet boundary, if there is high-fidelity data, the high-fidelity data is used, if there is part of the measured data, the measured data is combined with the wind speed profile model to obtain.

[0015] Further, in step 1, the range of the calculation domain is determined according to the height of the mountain and the thickness of the atmospheric boundary layer, so that the atmospheric boundary layer and the mountain wake are fully developed; the calculation domain grid is generated, and the encryption processing is performed near the mountain, in the mountain wake area and near the ground.

[0016] Further, in step 2, high-fidelity data reflecting the trend of the entire flow field are obtained, the training set and the test set are determined, the closed coefficients to be optimized of the GEKO turbulence model, the optimization objective function, the optimization strategy, the feedforward neural network structure, the activation function and the optimization input variables are determined.

[0017] The closed coefficients to be optimized of the GEKO turbulence model are the first parameter C SEP , the second parameter C NW influencing the internal wall boundary layer and the third parameter C MIX influencing the free shear flow.

[0018] The optimization objective function of the GEKO turbulence model is:

[0019]

[0020] In the formula, X represents a region of interest, represents a high-fidelity velocity field obtained by a large eddy simulation (LES) method, represents a current velocity field when the GEKO (Generalized k-ω) turbulence model is optimized.

[0021] The optimization strategy of the GEKO turbulence model is an online optimization strategy.

[0022] The feedforward neural network structure includes an input layer, a hidden layer and an output layer; the input layer represents a characteristic flow, the hidden layer is responsible for information propagation, and the output layer represents the GEKO turbulence model parameters; each layer of neurons receives the weighted input signal of the previous layer of neurons, combines the bias value and generates an output signal through an activation function; the activation function selects a Softsign function.

[0023] The optimization input variables are the non-equilibrium parameter φ1, the second-order stress-strain tensor φ2, the length ratio φ6, the turbulence Reynolds number φ7 and the turbulence viscosity ratio φ8.

[0024] Further, in step 3, an improved GEKO turbulence model is obtained based on the adjoint optimization method and machine learning, and the process of obtaining the improved turbulence model closed coefficient includes the following steps:

[0025] A Lagrange multiplier is introduced to construct a Lagrange function L:

[0026] ;

[0027] where q is the flow field solution vector including velocity, pressure, turbulent kinetic energy, c is the design variable including the turbulence model parameters, R(q,c) is the residual of the original fluid dynamics equation, K is the adjoint variable, K T denotes the transpose of the adjoint variable K, J is the optimization objective function;

[0028] The adjoint equation is obtained by taking the derivative of the Lagrangian function and setting it equal to zero:

[0029] ;

[0030] The adjoint equation is solved to obtain the adjoint variable K, and then the gradient of the optimization objective function with respect to the design variable is calculated:

[0031] ;

[0032] The neural network training is combined with the adjoint optimization, and the design variables are gradually adjusted so that the optimization objective function reaches a minimum value. After the training is completed, the optimal closure coefficient distribution of the improved GEKO turbulence model is obtained, and the obtained improved GEKO turbulence model is saved in the scm format for model verification and generalization research.

[0033] Further, the solving process of the adjoint equation includes the following processes:

[0034] Solving the original fluid dynamics equation to obtain the flow field solution vector q;

[0035] Based on the obtained flow field solution vector, the adjoint equation is solved to obtain the adjoint variable K;

[0036] The adjoint variable and the residual of the original equation are used to calculate the gradient of the optimization objective function with respect to the design variable;

[0037] According to the calculated gradient, the design variable is adjusted to optimize the objective function. In the optimization process, the design variable is gradually adjusted using an iterative method so that the objective function reaches a minimum value.

[0038] Further, in step 4, the process of performing complex mountain flow field numerical simulation based on the improved GEKO turbulence model to obtain the distribution of complex mountain surrounding wind speed and turbulent kinetic energy includes the following steps:

[0039] The turbulence model closure coefficient of the improved GEKO turbulence model is used to replace the standard GEKO model closure coefficient. The N-S equation is solved using the SIMPLE algorithm, and the discrete format is second order or higher. The residual is reduced to 10 -6 times when the flow field is considered to be converged. After the solution is completed, the distribution of the average velocity and turbulent kinetic energy around the complex mountain is obtained.

[0040] Further, in step 5, the results of the test set are verified by experimental data or high-fidelity simulation data.

[0041] Compared with the prior art, the beneficial effects of the present application are as follows:

[0042] First, the complex mountain flow field simulation method based on the improved GEKO turbulence model of the present application, when simulating the complex mountain flow field based on the improved GEKO turbulence model, the wind speed and turbulent kinetic energy on the leeward slope are highly consistent with the high-fidelity data, and the generalization ability is excellent.

[0043] Second, the complex mountain flow field simulation method based on the improved GEKO turbulence model of the present application, based on the improved GEKO turbulence model, reduces the input variables, improves the efficiency, optimizes the objective function, and obtains the optimal turbulence model closure coefficient distribution based on the adjoint optimization and machine learning, has good generalization, is simple to operate, easy to code, and efficient in calculation, and has high prediction accuracy of wind speed and turbulent kinetic energy on the leeward slope, which is better than the results of the standard GEKO turbulence model.

[0044] Third, the complex mountain flow field simulation method based on the improved GEKO turbulence model of the present application, when the wind speed vector is selected as the optimization target, the accuracy of the wind speed and the turbulent kinetic energy can be ensured at the same time, and the training effect is better than that when other variables (such as pressure, velocity, turbulent kinetic energy, etc.) are selected as the optimization target.

[0045] Fourth, the complex mountain flow field simulation method based on the improved GEKO turbulence model of the present application, when the neural network input parameters are selected as φ1, φ2, φ6, φ7, and φ8, the numerical simulation accuracy is equivalent to the accuracy when eight input variables φ1-φ8 are selected. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is a schematic diagram of a complex mountain terrain;

[0047] Figure 2 is a schematic diagram of a h42 case calculation domain grid;

[0048] Figure 3 is a schematic diagram of a feedforward neural network grid;

[0049] Figure 4 is an adjoint optimization and neural network grid framework flowchart for obtaining an improved GEKO turbulence model;

[0050] Figure 5a is a schematic diagram of the change trend of the objective function J(u x ) in the optimization process;

[0051] Figure 5bis the change trend of the objective function J(u y ) in the optimization process;

[0052] Figure 6a is the change trend of the wind speed with height at different positions in the h42 case (under different optimization objectives);

[0053] Figure 6b is a partial enlarged view of some positions in Figure 6a ;

[0054] Figure 6c is the change trend of the turbulent kinetic energy with height at different positions in the h42 case (under different optimization objectives);

[0055] Figure 6d is a partial enlarged view of some positions in Figure 6c ;

[0056] Figure 7a is the change trend of the wind speed with height at different positions in the h42 case (under different input variables);

[0057] Figure 7b is the change trend of the turbulent kinetic energy with height at different positions in the h42 case (under different input variables);

[0058] Figure 8a is the change trend of the wind speed with height at different positions in the h38 case (comparison before and after the improvement of the GEKO model);

[0059] Figure 8b is the change trend of the turbulent kinetic energy with height at different positions in the h38 case (comparison before and after the improvement of the GEKO model);

[0060] Figure 9 is a schematic diagram of a complex mountain flow field simulation method based on an improved GEKO turbulent flow model. DETAILED DESCRIPTION

[0061] The embodiments of the present application will be further described in detail below with reference to the accompanying drawings.

[0062] Referring to Figure 9 , the embodiments of the present application disclose a complex mountain flow field simulation method based on an improved GEKO turbulent flow model, which comprises the following steps:

[0063] Step 1, obtaining the terrain data of the complex mountain and the flow field parameters of the reference position, generating the calculation domain grid and the boundary conditions;

[0064] Step 2, obtain high-fidelity data reflecting the trend of the entire flow field, determine the training set and test set, determine the optimization objective function and neural network input variables; the high-fidelity data is large eddy simulation data or direct numerical simulation data;

[0065] Step 3, introduce the Lagrange multiplier, construct the Lagrange function, obtain the adjoint equation by taking the derivative of the Lagrange function and setting it to zero; solve the adjoint equation to obtain the adjoint variable, and then calculate the gradient of the optimization objective function with respect to the design variable; combine neural network training with adjoint optimization, gradually adjust the design variable, so that the optimization objective function reaches the minimum value, and obtain the improved GEKO turbulence model, and combine the calculation domain grid and boundary conditions to obtain the improved turbulence model closure coefficient;

[0066] Step 4, based on the improved GEKO turbulence model, numerical simulation of complex mountain flow field is carried out, and the distribution of wind speed and turbulent kinetic energy around the complex mountain is obtained;

[0067] Step 5, verify the accuracy of the numerical simulation results.

[0068] The principles of the simulation method and preferred examples thereof will be described in detail below with reference to the accompanying drawings. The simulation method specifically includes the following steps:

[0069] I. Obtain the flow field parameters such as wind speed, turbulent kinetic energy and specific dissipation rate of the complex mountain terrain and the reference position, generate the calculation domain grid and boundary conditions;

[0070] Firstly, the target area terrain is obtained. If it is a two-dimensional terrain, the expression of the terrain function or the distribution data of the terrain scatter points need to be given; if it is a three-dimensional terrain, the stl format terrain data needs to be given;

[0071] Then, the reference point of the current area is determined, and the wind speed, turbulent kinetic energy and specific dissipation rate of the reference point position are obtained. If there are high-fidelity LES (large eddy simulation) or DNS (direct numerical simulation) data, high-fidelity simulation data is used; if there are some measured data, the inflow variable can be fitted by combining the measured data with the theoretical model. Common wind speed profile models include exponential rate and logarithmic rate functions;

[0072] Secondly, the calculation domain range is determined. According to the mountain height and the atmospheric boundary layer thickness, at least the atmospheric boundary layer and the mountain wake are completely developed. If it is to verify the wind tunnel experiment, the size of the wind tunnel experiment needs to be consistent.

[0073] Finally, the numerical simulation grid is generated according to the terrain and the calculation domain. The grid can be generated by commercial software such as ICEM, or by open source code such as OpenFOAM, and needs to be encrypted near the mountain, in the mountain wake area and near the ground.

[0074] II. Obtain high-fidelity data, determine training set and test set, determine optimization objective function and neural network input variable;

[0075] First, obtain high-fidelity data. In the simulation of complex mountain flow field, in order to obtain comprehensive flow field information, high-fidelity data is LES or DNS data, which can reflect the trend of the whole flow field;

[0076] Then, determine the training set and test set. For the training set, determine the GEKO model to be optimized, the optimization objective function, the optimization strategy, the feedforward neural network structure, the activation function and the optimization input variable.

[0077] The expression of GEKO turbulence model is:

[0078] ;

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] ;

[0085] ;

[0086] wherein x i , x j are spatial variables, t is a time variable, , are velocity components, is the fluid density, k is the turbulent kinetic energy, ω is the specific dissipation rate, is the molecular dynamic viscosity, is the turbulent viscosity; , , , , , , are model constants; CD is used to adjust the strength of the turbulent viscosity correction term; F1 and F2 are mainly used to adjust the source term and the dissipation term in the turbulent frequency equation to adapt to different flow conditions; F3 is used to adjust the calculation of turbulent viscosity, to ensure the applicability and stability of the model in different flow scenarios; is the turbulent kinetic energy generation term, is the modified Reynolds stress tensor, is the Reynolds stress, is the original Reynolds stress tensor, is the Kronecker symbol; is the strain rate tensor, , , are the rotation rate tensors, is the norm of the strain rate tensor, is the norm of the rotation rate tensor; denotes the kinematic viscosity of the turbulent motion.

[0087] The free coefficients of the GEKO model are realized by functions (F1, F2, F3) and currently include six parameters:

[0088] C SEP : mainly adjusts the prediction of boundary layer separation;

[0089] C NW : mainly affects the interior of the wall boundary layer;

[0090] C MIX : only affects the free shear flow;

[0091] C JET : activated in the sub-model of C MIX (when C MIX = 0, no effect);

[0092] C CORNER : nonlinear stress-strain term to explain the secondary flow of the corner;

[0093] C CURV : for curvature correction;

[0094] Considering the characteristics of complex mountain flow fields, only three closure coefficients C SEP , C NW , C MIX need to be optimized to obtain the improved GEKO turbulence model.

[0095] The adjoint optimization method uses discrete adjoint, and the optimization objective function is defined as:

[0096] ;

[0097] In the formula: X represents the region of interest, represents the high-fidelity velocity field obtained by the large eddy simulation (LES, Large Eddy Simulation) method, represents the current velocity field when the GEKO (Generalized k-ω ) turbulence model is optimized.

[0098] In the simulation of complex mountainous flow field, the target variable is the velocity component, i.e., u x and u z , respectively, as the optimization objective; if it is a three-dimensional flow field, u y also needs to be considered.

[0099] When training the improved GEKO turbulence model, high-fidelity velocity vector distribution data is required; other data such as turbulent kinetic energy, pressure, and combined velocity can be used for model verification.

[0100] In order to obtain the improved GEKO turbulence model, an online optimization strategy is adopted.

[0101] The network structure adopts a feedforward neural network, which includes an input layer, a hidden layer, and an output layer. The input layer represents the characteristic flow, the hidden layer is responsible for information propagation, and the output layer represents the GEKO model parameters. Each layer of neurons receives the weighted input signal of the previous layer of neurons, combines the bias value, and generates an output signal through an activation function. The activation function selects the Softsign function.

[0102] The selected input flow characteristics should be independent of the geometry to facilitate the generalization of the neural network model. These characteristics include non-equilibrium parameters (φ1), second-order (φ2), third-order (φ3), fourth-order (φ4), and fifth-order invariants (φ5) of the stress-strain tensor, length ratio (φ6), turbulent Reynolds number (φ7), and turbulent viscosity ratio (φ8).

[0103] In the simulation of complex mountainous flow field, according to theoretical analysis and test results, the input variables of the improved GEKO turbulence model can be reduced from eight to five, i.e., the third-order, fourth-order, and fifth-order invariants are removed, and the remaining five are retained, i.e., the input parameters are selected as φ1, φ2, φ6, φ7, and φ8.

[0104] III. Based on the adjoint optimization method and machine learning, an improved GEKO turbulence model is obtained, and the closed coefficients of the improved turbulence model are obtained;

[0105] In order to incorporate the constraint conditions into the optimization problem, the Lagrange multiplier (adjoint variable) is introduced, and the Lagrange function L is constructed:

[0106]

[0107] where q is the flow field solution vector (including velocity, pressure, turbulent kinetic energy, etc.), c is the design variable (such as turbulence model parameters), R(q, c) is the residual of the original fluid dynamics equation, κ is the adjoint variable, κ T represents the transpose of the adjoint variable κ, and J is the optimization objective function.

[0108] By taking the derivative of the Lagrange function and setting it equal to zero, the adjoint equation is obtained:

[0109]

[0110] Solving this equation gives the adjoint variable κ, which is used to calculate the gradient of the optimization objective function with respect to the design variables:

[0111]

[0112] The adjoint optimization method uses discrete adjoint, and the adjoint optimization solving steps are as follows:

[0113] ① Solve the original equation: First, solve the original fluid dynamics equation to get the flow field solution vector q.

[0114] ② Solve the adjoint equation: Based on the obtained flow field solution vector, solve the adjoint equation to get the adjoint variable κ.

[0115] ③ Calculate the gradient: Use the adjoint variable and the residual of the original equation to calculate the gradient of the optimization objective function with respect to the design variables.

[0116] ④ Optimize parameters: According to the calculated gradient, adjust the design variables (such as turbulence model parameters) to optimize the objective function.

[0117] In the optimization process, the iterative method of FLUENT 2022R1 version is used to gradually adjust the design variables so that the objective function reaches the minimum value. The application principle of the machine learning method in the improved GEKO turbulence modeling is to combine neural network training with adjoint optimization.

[0118] First, obtain the CFD case for adjoint optimization. The computational domain mesh and boundary conditions are obtained from step 1. The inlet boundary condition is a velocity inlet, the outlet boundary is a pressure outlet, the top and side boundaries are symmetric, and the bottom boundary is a wall boundary condition.

[0119] Then, after training, the optimal closure coefficient distribution of the improved GEKO turbulence model is obtained. Save the obtained improved GEKO model in scm format for model verification and generalization research.

[0120] Four, based on the improved GEKO turbulence model, the complex mountain flow field is numerically simulated, and the distribution of wind speed and turbulent kinetic energy around the complex mountain is obtained;

[0121] First, obtain the computational domain and mesh of the numerical simulation case.

[0122] Then, the turbulence model uses the improved GEKO turbulence model obtained from step 3, and replaces the closure coefficient of the standard GEKO model with the improved GEKO turbulence model closure coefficient. The SIMPLE algorithm is used to solve the N-S equation, and the discrete format is second order or higher, with a residual of 10 -6The flow field is considered to converge.

[0123] Finally, after the solution is completed, the distribution of average velocity and turbulent kinetic energy around the complex mountain is obtained.

[0124] V. Verify the accuracy of the numerical simulation results;

[0125] First, obtain test set experimental data or high-fidelity simulation data;

[0126] Then, the results of the test set (flow fields of complex mountain shapes) are verified by experimental data or high-fidelity simulation data.

[0127] VI. New Model Validation (Acquisition, Validation, and Generalization Study of the Improved GEKO Turbulence Model).

[0128] Example

[0129] h42 (e.g.) Figure 1 (The diagram shows a complex mountainous terrain.) The geometry of the complex mountain is a two-dimensional circular arc with a length L of 254 mm and a height h ranging from 20 to 42 mm. Convex fillets were added before and after the arc, bringing the total length C of the structure to 305 mm. This design is used to simulate the flow of the turbulent boundary layer on a two-dimensional protrusion, serving as a basic geometric model to study the impact of protrusions of different heights on the turbulent boundary layer. The protrusion heights vary at h = 20, 26, 31, 38, and 42 mm. Two geometric shapes are chosen: h = 42 mm (where the largest separation region was observed) and h = 38 mm (where the separation region increases), to analyze the predictive capabilities of the standard and improved GEKO turbulence models for the separation region.

[0130] Step 1: Obtain flow field parameters such as wind speed, turbulent kinetic energy, and specific dissipation rate for complex mountainous terrain and reference locations, and generate computational domain grids and boundary conditions.

[0131] First, obtain the terrain of the target area: h42 and h38, such as Figure 1 As shown; then, determine the reference point for the current area, obtain the wind speed, turbulent kinetic energy, and specific dissipation rate at the reference point location, and use the high-guarantee LES numerical simulation results as the inflow conditions, adding them using Fluent UDM; secondly, determine the computational domain range, keeping it consistent with the LES simulation area; finally, generate the numerical simulation mesh based on the terrain and computational domain, requiring refinement near the mountains, in the wake of the mountains, and near the ground. The computational domain and mesh for the h42 case are as follows. Figure 2 As shown.

[0132] Step 2: Obtain high-fidelity data, determine the training and test sets, and determine the optimization objective function and neural network input variables.

[0133] First, acquire high-fidelity data. Obtain high-fidelity LES data for two cases, h42 and h38, including parameters such as velocity, pressure, and Reynolds stress. Then, determine the training and test sets. Use case h42 as the training set and case h38 as the test set.

[0134] For the training set, determine the closure coefficient to be optimized in the GEKO model: Considering the complex flow field characteristics in mountainous areas, when obtaining the improved GEKO turbulence model, only C needs to be optimized. SEP C NW C MIX Three closure coefficients.

[0135] Determine the objective function: Define the objective function, considering the difference between RANS and high-fidelity or experimental data. The adjoint optimization method uses discrete adjoint optimization, and the objective function is defined as follows:

[0136] ;

[0137] In the formula: X represents the region of interest (the entire computational domain), u i This represents the velocity field (in simulations of complex mountain flow fields, the objective variable is the velocity component, specifically the flow velocity u). x and vertical velocity u y These are respectively used as optimization objectives; other data such as turbulent kinetic energy, pressure, and resultant velocity can be used for model validation.

[0138] To verify the rationality of the optimization objective, u was used as the basis for the calculation. x (GEKO-OPT-01), u x and u y (GEKO-OPT-02), U mag (GEKO-OPT-03), k(GEKO-OPT-04), and p(GEKO-OPT-05) were tested as optimization targets.

[0139] Determine the feedforward neural grid (e.g.) Figure 3 (As shown): To obtain the improved GEKO turbulence model, an online optimization strategy was employed. The network structure uses a feedforward neural network, comprising an input layer, hidden layers, and an output layer. The input layer represents the feature flow, the hidden layers are responsible for information propagation, and the output layer represents the GEKO turbulence model parameters. Each neuron in each layer receives a weighted input signal from the neurons in the previous layer, combines it with bias values, and generates an output signal through an activation function. Hidden layers: There are three hidden layers with decreasing numbers of neurons: 24, 16, and 8 neurons respectively. This design helps the network progressively reduce the data dimensionality when extracting features and learning patterns, while maintaining sufficient expressive power to capture complex nonlinear relationships.

[0140] Determine the activation function: Select the Softsign function as the activation function.

[0141] Determine input variables: The selected input flow characteristics should be independent of the geometry to facilitate the generalization of the neural network model. These features include non-equilibrium parameters (φ1), second-order (φ2), third-order (φ3), fourth-order (φ4), and fifth-order invariants (φ5) of the stress-strain tensor, length ratio (φ6), turbulent Reynolds number (φ7), and turbulent viscosity ratio (φ8), etc. In the simulation case of complex mountain flow field, according to theoretical analysis and test results, the input variables of the improved GEKO turbulent model can be reduced from eight to five, by removing the third-order, fourth-order and fifth-order invariants, and retaining the remaining five.

[0142] To verify the effectiveness of the input variable reduction, φ1-φ8 (GEKO-OPT-02) eight input parameters and φ1, φ2, φ6, φ7, φ8 five input parameters (GEKO-OPT-NEW) were used as input layer for testing.

[0143] Step 3, based on the adjoint optimization method and machine learning to obtain the improved GEKO turbulent model, and get the improved turbulent model closure coefficient.

[0144] First, obtain the CFD case (h42 case) for adjoint optimization. The model is trained using FLUENT 2022R1 version, and the computational domain grid and boundary conditions are obtained from step 1. The inlet boundary condition is velocity inlet, the outlet boundary is pressure outlet, the top is no-slip boundary, and the bottom boundary is wall boundary condition. (The boundary conditions are consistent with the LES case as much as possible). The inlet boundary condition is added using Fluent UDM.

[0145] Figure 4 is the flowchart of the adjoint optimization and neural network framework for obtaining the improved GEKO turbulent model. The adjoint optimization solving steps include:

[0146] Solve the original equation: First, solve the original fluid dynamics equation to get the flow field solution vector q.

[0147] Solve the adjoint equation: Based on the obtained flow field solution vector, solve the adjoint equation to get the adjoint variable κ.

[0148] Calculate the gradient: Use the adjoint variable and the residual of the original equation to calculate the gradient of the optimization objective function with respect to the design variable.

[0149] Optimize parameters: According to the calculated gradient, adjust the design variable (such as the turbulent model parameter) to optimize the objective function.

[0150] During the optimization process, Fluent uses an iterative method to gradually adjust the design variable, so that the optimization objective function reaches a minimum value (such as Figure 5a andFigure 5b The obtained improved GEKO turbulence model is saved in scm format after training for model validation and generalization study.

[0151] Step 4, numerical simulation of complex mountain flow field based on improved GEKO turbulence model, to obtain the distribution of wind speed and turbulent kinetic energy around complex mountains.

[0152] First, the computational domain grid of the numerical simulation case is obtained, as shown in Figure 2 Then, the turbulence model adopts the improved GEKO turbulence model obtained in step 3, and the improved GEKO turbulence model closure coefficient is used to replace the standard GEKO model closure coefficient (step 3, the scm format turbulence model is re-imported). The N-S equation is solved by using the SIMPLE algorithm, and the discrete format is second order or higher, and the residual error is reduced to 10 -6 When the flow field is considered to be converged. Finally, after solving, the distribution of average velocity and turbulent kinetic energy around complex mountains is obtained, as shown in Figure 6a 、 Figure 6b 、 Figure 6c 、 Figure 6d 、 Figure 7a and Figure 7b , including LES and numerical results of standard GEKO turbulence model.

[0153] Step 5, verify the accuracy of the numerical simulation results.

[0154] First, obtain the experimental data or high-fidelity simulation data of the test set, obtain the LES numerical simulation results of h38 case, and determine the computational domain grid, boundary conditions and numerical solution method, etc. as in h42 case; then, the results of the test set (flow field of complex mountains of other shapes) are verified by experimental data or high-fidelity simulation data, as shown in Figure 8a and Figure 8b .

[0155] After analysis, compared with the standard GEKO turbulence model (GEKO), the improved GEKO turbulence model based on adjoint optimization and machine learning (GEKO-OPT-*) can better simulate the wind speed and turbulent kinetic energy on the leeward slope by optimizing the objective function and reducing the input variables, and has good consistency with the high-fidelity LES data (LES); and when the optimization target is the velocity vector, i.e. x andu yWhen the optimization target is optimized respectively (GEKO-OPT-01), the accuracy is better than that of other variables as the optimization target (GEKO-OPT-02, GEKO-OPT-03, GEKO-OPT-04, GEKO-OPT-05); when the neural network input variables are reduced from eight input parameters of φ1-φ8 (GEKO-OPT-02) to five input parameters of φ1, φ2, φ6, φ7 and φ8 (GEKO-OPT-NEW), the simulation accuracy of wind speed and turbulent kinetic energy is not reduced, and still has good prediction ability. Compared with the standard GEKO turbulent model (GEKO), the simulation accuracy of wind speed of the improved GEKO turbulent model (GEKO-OPT-NEW) is improved by 38.4%, and the simulation accuracy of turbulent kinetic energy is improved by 17.6%.

[0156] Through analysis Figure 8a and Figure 8b It can be known that for the h38 case, the improved GEKO turbulent model also has higher accuracy than the standard GEKO turbulent model, the prediction accuracy of wind speed is improved by 29.8%, and the prediction accuracy of turbulent kinetic energy is improved by 13.7%, which shows that the improved GEKO turbulent model has good generalization ability.

[0157] Through comparison with multiple complex mountain high-fidelity data, it is found that the newly proposed improved GEKO turbulent model has good prediction ability for wind speed and turbulent kinetic energy on the leeward slope, and the numerical simulation accuracy is greatly improved compared with the standard GEKO turbulent model, and is very close to the numerical results of LES. The improved GEKO turbulent model reduces the input parameters of the neural network, optimizes the target and selects the closure coefficient, obtains the optimal turbulent model closure coefficient based on the adjoint optimization method and machine learning, improves the efficiency and accuracy, and has good generalization ability, and has the advantages of simple operation, easy coding and the like.

[0158] Although the preferred embodiments of the present application have been described, those skilled in the art can make further changes and modifications to the embodiments once they know the basic inventive concept. Therefore, the appended claims are intended to be interpreted as including all changes and modifications falling within the scope of the present application.

[0159] Obviously, those skilled in the art can make various modifications and variations to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application also intends to include these modifications and variations.

Claims

1. A complex mountainous flow field simulation method based on an improved GEKO turbulence model, characterized in that, The method comprises the following steps: Step 1, obtaining terrain data of complex mountainous area and flow field parameters of reference position, generating calculation domain grid and boundary conditions; Step 2, obtaining high-fidelity data reflecting the trend of the entire flow field, determining the training set and the test set, determining the optimization objective function and the neural network input variable; the high-fidelity data is large eddy simulation data or direct numerical simulation data; Step 3, introducing a Lagrange multiplier, constructing a Lagrange function, and obtaining an adjoint equation by deriving the Lagrange function and setting it equal to zero; the adjoint variable is obtained by solving the adjoint equation, and then the gradient of the optimization objective function with respect to the design variable is calculated; the neural network training is combined with the adjoint optimization, and the design variable is gradually adjusted so that the optimization objective function reaches a minimum value, and an improved GEKO turbulent flow model is obtained, and the improved turbulent flow model closure coefficient is obtained in combination with the calculation domain grid and the boundary conditions; Step 4, numerical simulation of complex mountainous area flow field based on the improved GEKO turbulent flow model, obtaining the distribution of wind speed and turbulent kinetic energy around the complex mountainous area; Step 5, verifying the accuracy of the numerical simulation result; In step 2, high-fidelity data reflecting the trend of the entire flow field is obtained, the training set and the test set are determined, the GEKO turbulent flow model to be optimized closure coefficient, the optimization objective function, the optimization strategy, the feedforward neural network structure, the activation function and the optimization input variable are determined; In this context, the closure coefficient to be optimized in the GEKO turbulence model is the first parameter C used to adjust the boundary layer separation prediction. SEP The second parameter C that affects the interior of the wall boundary layer NW and the third parameter C that affects free shear flow MIX ; The optimization objective function of the GEKO turbulent flow model is: wherein: X denotes the region of interest, denotes the high-fidelity velocity field obtained by the large eddy simulation method, denotes the current velocity field optimized with the GEKO turbulence model. The optimization strategy of the GEKO turbulent flow model is an online optimization strategy; The feedforward neural network structure comprises an input layer, a hidden layer and an output layer; the input layer represents a characteristic flow, the hidden layer is responsible for information propagation, and the output layer represents a GEKO turbulent flow model parameter; each layer of neurons receives a weighted input signal from the previous layer of neurons, combines a bias value and generates an output signal through an activation function; the activation function selects a Softsign function; The optimization input variable is a non-equilibrium parameter φ1, a second-order stress-strain tensor φ2, a length ratio φ6, a turbulent Reynolds number φ7 and a turbulent viscosity ratio φ8.

2. The complex mountainous flow field simulation method based on the improved GEKO turbulence model according to claim 1, characterized in that, In step 1, the terrain data of the complex mountainous area is two-dimensional terrain data including an expression of a terrain function and distribution data of terrain scattered points, and stl format three-dimensional terrain data.

3. The complex mountain flow field simulation method based on the improved GEKO turbulence model according to claim 1, characterized in that, In step 1, the flow field parameters of the reference position include wind speed, turbulent kinetic energy and specific dissipation rate; wherein for the wind speed, the turbulent kinetic energy and the specific dissipation rate of the inlet boundary, if there is high-fidelity data, the high-fidelity data is adopted, and if there is part of the measured data, the measured data is combined with a wind speed profile model to obtain.

4. The complex mountain flow field simulation method based on the improved GEKO turbulence model according to claim 1, characterized in that, In step 1, the calculation domain range is determined according to the mountain height and the atmospheric boundary layer thickness, so that the atmospheric boundary layer and the mountain wake are fully developed; the calculation domain grid is generated, and the encryption processing is performed near the mountain, in the mountain wake area and near the ground.

5. The complex mountain flow field simulation method based on the improved GEKO turbulence model according to claim 1, characterized in that, In step 3, the improved GEKO turbulent flow model is obtained based on the adjoint optimization method and machine learning, and the process of obtaining the improved turbulent flow model closure coefficient comprises the following steps: A Lagrange multiplier is introduced to construct a Lagrange function L: L(q, c, k) = J(q, c) - K T R(q, c); where q is a flow field solution vector including velocity, pressure, turbulent kinetic energy, etc., c is a design variable including turbulent model parameters, R(q, c) is the residual of the original fluid dynamics equations, K is an adjoint variable, K T denotes the transpose of the adjoint variable K, and J is the optimization objective function. An adjoint equation is obtained by deriving the Lagrange function and setting it equal to zero: Solving the adjoint equation to obtain the adjoint variable κ, and then calculating the gradient of the optimization objective function with respect to the design variables: The neural network is trained in combination with the adjoint optimization, and the design variables are gradually adjusted so that the optimization objective function reaches a minimum value; after the training is completed, the optimal closed coefficient distribution of the improved GEKO turbulent flow model is obtained, the obtained improved GEKO turbulent flow model is saved in an scm format, and is used for model verification and generalization research.

6. The complex mountain flow field simulation method based on the improved GEKO turbulence model according to claim 5, characterized in that, The solving process of the adjoint equation includes the following processes: Solving the original fluid dynamics equation to obtain a flow field solution vector q; Based on the obtained flow field solution vector, the adjoint equation is solved to obtain an adjoint variable κ; Using the adjoint variable and the residual of the original equation, the gradient of the optimization objective function to the design variable is calculated; According to the calculated gradient, the design variable is adjusted to optimize the objective function; In the optimization process, the design variable is gradually adjusted by using an iterative method, so that the objective function reaches a minimum value.

7. The complex mountain flow field simulation method based on the improved GEKO turbulence model according to claim 1, characterized in that, In step 4, the process of performing numerical simulation of a complex mountain flow field based on the improved GEKO turbulent flow model to obtain the distribution of the wind speed and the turbulent kinetic energy around the complex mountain includes the following steps: The improved GEKO turbulence model is used to replace the standard GEKO model closure coefficient; the SIMPLE algorithm is used to solve the N-S equation, and the second-order and above discrete format is used, and the residual error is reduced to 10 -6 When the flow field converges, the average velocity and turbulent kinetic energy distribution around the complex mountain are obtained.

8. The complex mountain flow field simulation method based on the improved GEKO turbulence model according to claim 1, characterized in that, In step 5, the results of the test set are verified through experimental data or high-fidelity simulation data.

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