Wide-load pumped storage unit multi-scale turbulence modeling method based on high-order tensor coupling and dynamic memory effect

Abstract

The invention discloses a wide-load pumped storage unit multi-scale turbulence modeling method based on high-order tensor coupling and a dynamic memory effect. The wide-load pumped storage unit multi-scale turbulence modeling method comprises the steps of working condition parameter collection and geometric model grid division, initialization of a multi-scale turbulence field, correction of high-order curvature-rotation tensor coupling, cavitation vortex strip instability prediction and cross-scale data assimilation. Through fusion of a high-order curvature-rotation tensor coupling mechanism, a multi-scale time memory effect and a physical-data hybrid correction technology, the prediction precision of pressure pulsation, cavitation vortex strip instability and runner dynamic stress of a unit under complex working conditions of water pumping, power generation, phase modulation, rapid load change and the like is remarkably improved; and technical support is provided for safe operation and optimal design of the unit.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology of hydraulic machinery fluid dynamics, specifically involving a multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect. Background Technology

[0002] In wide-load operation scenarios of pumped storage units, traditional turbulence models face the following problems: 1) Significant bias in pressure pulsation prediction. Existing Reynolds-averaged Navier-Stokes (RANS) models, such as SST (shear stress transfer) and RSM (Reynolds stress model), have large prediction errors in the amplitude of high-frequency pressure pulsations (frequency range 200-800Hz) generated in the runner-guide vane interference zone, which cannot meet the accuracy requirements of unit vibration fatigue analysis, making it difficult to accurately assess the structural safety of the unit under high-frequency vibration. 2) Lack of description of cavitation vortex instability mechanism. Under partial load conditions, the phase difference between numerical prediction and measured results of low-frequency oscillations (frequency range 0.2-2Hz) of cavitation vortices in the tailrace exceeds 90°, and traditional cavitation models have large errors in capturing vortex morphology. This inaccurate description of the cavitation vortex instability mechanism makes it impossible to effectively predict the impact of cavitation on unit performance and lifespan. 3) Insufficient adaptability to dynamic curvature. During operation, the radius of curvature of the turbine blades in a pumped storage unit changes dynamically (ranging from 0.5 to 3 meters). Existing curvature correction models are based only on second-order tensors, which leads to an amplification of the error in the flow-head characteristic curve to over 60% under transitional operating conditions (such as switching from pumping to power generation), severely affecting the accurate prediction of the unit's operating characteristics.

[0003] 4) Multi-scale coupling failure. Traditional modeling methods lack effective means to address the cross-scale interaction between boundary layer separation eddies (microsecond scale) and system hydraulic resonance (second scale). This failure of multi-scale coupling leads to severe distortion in transient process prediction, failing to accurately reflect the unit's operating status during dynamic processes such as load changes.

[0004] To address the aforementioned issues, although existing improved methods, such as the Large Eddy Simulation-Delayed Separated Eddy Simulation (LES-DDES) hybrid method, have improved prediction accuracy to some extent, they have also led to a more than 10-fold increase in computational costs. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect to solve the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect includes the following steps:

[0008] Step S1: Based on the geometric parameters of the pumped storage unit, construct a three-dimensional geometric model of the pumped storage unit and obtain the real-time operating parameters of the unit; perform mesh generation on the entire flow channel region of the three-dimensional geometric model of the pumped storage unit to generate an unstructured dynamic mesh; and calculate the mesh curvature characteristic quantity C of the runner blades. ijkl .

[0009] Step S2: Solve the transient flow field in the runner region using the hybrid RANS-LES method, setting the time step; calculate the frequency domain characteristics of the velocity gradient tensor, vorticity, and pressure fluctuations, providing the basic flow field data for the higher-order curvature-rotation tensor coupling correction in Step S3. The pressure distribution and vortex structure of the flow field provide an initial basis for identifying cavitation phenomena in Step S4.

[0010] Step S3: Based on the basic flow field data calculated in Step S2, calculate the fourth-order curvature tensor invariant Γ in real time. c Update the eddy viscosity coefficient ν t and stress term τ ij Dynamically adjust the mesh topology of the rotating region to ensure C ijkl The spatial resolution error is ≤1%, providing more accurate flow field pressure and vortex structure data for S4. For example, the corrected pressure distribution directly affects the cavitation number calculation.

[0011] In addition, the optimized flow field data (such as stress terms) provides more reliable simulation results input for the training of the S5 neural network.

[0012] Step S4: When the local pressure at a certain point in the flow field decreases to the saturated vapor pressure p at the corresponding temperature v When the fluid undergoes a phase change, cavitation bubbles are generated, i.e., cavitation occurs. Based on the velocity gradient tensor, vorticity, and pressure fluctuation frequency domain characteristics calculated in step S2, the corrected eddy viscosity coefficient ν in step S3 is... t Stress term τ ij The optimized flow field mesh topology is used to identify cavitation phenomena in the flow field and calculate the cavitation number. When the cavitation number σ < 2, the cavitation phase transition model is activated, based on the cavitation-rotation coupling criterion Q. cav The vortex core region is identified, and the cavitation source term and turbulent kinetic energy dissipation rate ε are corrected. The cavitation volume fraction and the corrected ε obtained in this step are used as key features and input into the HPINN neural network in step S5 to support the fusion and optimization of simulation results and measured data.

[0013] Step S5: Using the basic flow field simulation data generated in steps S2-S4, namely the coupling results of the fourth-order tensor and cavitation model, and fusing the measured data pexp′ and simulation results psim′ of the pressure sensor in the impeller-guide vane interference region, as training data, construct the HPINN neural network.

[0014] By minimizing the deviation between simulation and measured data, the turbulent kinetic energy transport equation is optimized, which in turn feeds back into the flow field simulation in steps S2-S4, updates the dynamic stress field of the runner blades, and forms a closed loop of "physical modeling → data optimization → model iteration" to improve prediction accuracy.

[0015] Further optimization is achieved in step S1, where the geometric parameters of the pumped storage unit include the runner diameter D, the number of blades Z, the opening angle of the movable guide vanes α, and the installation angle of the fixed guide vanes β; the real-time operating parameters of the unit include the head H ∈ [200m, 800m], the flow rate Q ∈ [0.5Q]. design 1.2Q design ] and rotational speed n∈[90%n rated ,110%n rated ];n rated Indicates the rated speed.

[0016] Further optimization involves constructing a fourth-order curvature gradient tensor C in step S2, specifically targeting the dynamic curvature variation characteristics of the turbine blades. ijkl :

[0017]

[0018] In the above formula, Represents the velocity component U m The third partial derivative with respect to Cartesian coordinates; where U m (m = 1, 2, 3; corresponding to the velocity components in the x, y, and z directions respectively) represents the velocity of a fluid particle. This third-order partial derivative describes the rate of change of the velocity field in three-dimensional space, reflecting the deformation and rotation characteristics of the flow field.

[0019] Represents the Levi-Civita notation; R(t) is the real-time radius of curvature, calculated by inversion from the instantaneous deformation of the impeller; Where is the hydraulic characteristic length, Q is the flow rate, n is the rotational speed, and D is the impeller diameter;

[0020] For the tensor correction term in the rotating coordinate system; δ np It is the Kronecker symbol; The Levi-Civita notation is primarily related to the dynamic characteristics in a rotating coordinate system. Combined with physical quantities such as vorticity, it reflects the influence of the direction and intensity of vortex structures in a rotating flow field on tensor corrections, thus providing a more accurate description of the physical mechanisms of rotating flow fields. ω rLet ω be the vorticity component, and ||ω| be the vorticity modulus. Represents the vorticity component ω n For spatial coordinates x p The partial derivatives of .

[0021] Further optimization involves using tensor invariants Γ in step S3. c Dynamically corrected eddy viscosity coefficient ν t Specifically:

[0022]

[0023] Dynamic coefficient C μ satisfy:

[0024]

[0025] In the above formula, For the hydraulic Reynolds number Re h =U h D h The sigmoid function of / ν, U h For characteristic velocity, D h ν is the characteristic length, k is the kinematic viscosity, k represents the turbulent kinetic energy, and ε represents the turbulent kinetic energy dissipation rate, which refers to the amount of turbulent kinetic energy dissipated per unit mass of fluid per unit time; C u ‖S‖ represents the empirical coefficients associated with the turbulence model; ‖S‖ represents the strain rate tensor, reflecting the deformation rate of fluid particles in the flow field and embodying the tensile, shear, and other deformation characteristics of the flow field; ‖Ω‖ represents the rotation rate tensor, reflecting the rotation rate of fluid particles in the flow field and embodying the rotational characteristics of the flow field; ‖C ijkl || F Represents the fourth-order curvature gradient tensor C ijkl The Frobenius norm, U tip The impeller blade tip velocity is represented by fμ; fμ represents a function term related to turbulence characteristics; ρ represents fluid density; and δij represents the Kronecker symbol. Eddy viscosity coefficient ν t In turbulence models, it is used to characterize the viscous properties of turbulence, reflect the momentum diffusion capacity in turbulence, and its value affects the calculation of turbulent stress, which in turn affects the solution of parameters such as flow field velocity and pressure.

[0026] Further optimization is achieved in step S3, where the curvature tensor calculation satisfies real-time constraints: 1) the curvature feature update delay within a single time step is ≤10Δt; 2) the local mesh refinement level in the rotating region is based on Γ. c Gradient adaptive adjustment, with a maximum encryption ratio of 8:1.

[0027] Further optimization is achieved in step S4, where the cavitation number σ is:

[0028]

[0029] In the above formula, U ref The reference velocity is often chosen because the runner blade inlet velocity is a core component, and its inlet velocity significantly affects the flow characteristics of the entire flow field, effectively reflecting the initial motion state of the fluid after entering the unit. Even under different operating conditions, where the actual velocity varies greatly, the cavitation coefficient, after normalization using the reference velocity, accurately reflects the relative state of cavitation in the flow field. p represents the local pressure at a point in the flow field. v This represents the saturated vapor pressure.

[0030] Cavitation-Rotation Coupling Criterion Qcav:

[0031]

[0032] When Q cav >0.5Q thres At that time, activate cavitation source term correction:

[0033]

[0034] In the above formula, The term is a correction for the bubble growth rate, where Q is the turbulent Reynolds number. thres The cavitation-rotational coupling criterion Q represents cav The critical value, α v ρ represents the cavitation volume fraction; l ρ represents the density of a liquid. v This indicates the density of the steam.

[0035] Further optimization, step S5 specifically includes:

[0036] Step S5.1: Obtain training data, including:

[0037] High-frequency pressure pulsation data: High-frequency pressure pulsation data of 16 typical working conditions with 4 heads × 4 loads in the impeller-guide vane interference zone are collected by pressure sensor array, with a sampling rate ≥ 10kHz to ensure the capture of high-frequency vibration characteristics of 200-800Hz.

[0038] Cavitation observation images: Cavitation images of the rotor surface acquired by a high-speed camera with a resolution ≥2000fps, recording the morphology of cavitation vortex bands; used to train the ability to recognize cavitation vortex band morphology.

[0039] Transitional operating condition data: Data is collected synchronously by a torque sensor and a tachometer to obtain torque-speed characteristic curves and capture the dynamic characteristics of transient processes such as pumping to power generation.

[0040] Step S5.2: Construct the HPINN neural network:

[0041] Input layer: Contains 32-dimensional multi-scale features, including curvature features calculated by a fourth-order tensor and cavitation volume fraction α output by the cavitation model. v As a key input;

[0042] Output layer: The single output is the turbulent kinetic energy correction coefficient β. NN This coefficient is used to adjust the source or dissipation terms of the turbulent kinetic energy transport equation.

[0043] Network structure: It consists of 5 residual blocks, each of which integrates spectral normalization and multi-head attention mechanism; spectral normalization is used to stabilize the training process, while the multi-head attention mechanism enhances the ability to associate multi-scale features;

[0044] Step S5.3: Train the HPINN neural network: Input the acquired data into the constructed HPINN neural network for training, with the iterative objective of minimizing the deviation between the measured data and the simulation results. sim′ Compared with measured data p exp′ The pressure pulsation, cavitation volume fraction, and other indicators are substituted into the loss function, and the parameters are adjusted through backpropagation. The parameter frequency is synchronized with the CFD time step, and the network parameters are updated once every 10 time steps through MPI parallel communication to ensure consistency with the dynamic changes of the flow field. The engineering verification is carried out through the turbine operating efficiency curve and the pump operating head-flow characteristics.

[0045] Further optimization resulted in the HPINN neural network input layer containing 32-dimensional multi-scale features, specifically:

[0046]

[0047] Output:

[0048]

[0049] In the above formula, P k σ represents the turbulent kinetic energy generation term. k The Prandtl number represents the turbulent kinetic energy k. FFT(p', 200Hz-800Hz) performs a Fast Fourier Transform on the pressure pulsation signal p' and extracts the spectral information within the frequency range of 200Hz-800Hz. The FFT transform converts the time-domain pressure pulsation signal to the frequency domain, facilitating the analysis of pressure pulsation characteristics within a specific frequency range.

[0050] Further optimization involves forcibly satisfying the physical constraint L. phy :

[0051]

[0052] An electronic device, comprising: one or more processors;

[0053] Memory, used to store one or more programs;

[0054] When one or more programs are executed by the processor, the processor performs the above-described method.

[0055] A computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the steps of the above-described method.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] This invention significantly improves the prediction accuracy of pressure pulsation, cavitation vortex instability, and turbine dynamic stress of the unit under complex operating conditions such as pumping, power generation, phase adjustment, and rapid load change by integrating high-order tensor coupling, multi-scale memory effect, and physical-data hybrid correction technology, providing technical support for safe operation and optimized design of the unit. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the coupling mechanism of a fourth-order curvature tensor.

[0059] Figure 2 This is a diagram of the HPINN neural network architecture;

[0060] Figure 3 The results show the prediction of cavitation vortex morphology and the experimental comparison (100% load condition).

[0061] Figure 4 The pressure pulsation spectrum characteristic curve under transient operating conditions;

[0062] Figure 5 The results show the comparison between the model's prediction efficiency and measured data (hydro turbine operating conditions). Detailed Implementation

[0063] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to more clearly understand the present invention. Obviously, the present invention is not limited to the scope of the embodiments. For those skilled in the art, any modifications within the spirit and scope of the present invention as defined and determined by the appended claims are considered non-creative and all inventions utilizing the inventive concept of this method are protected.

[0064] Taking a 350MW reversible pumped storage unit as an example, a multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect includes the following steps:

[0065] Step S1: Acquisition of operating parameters and generation of geometric model mesh:

[0066] Based on the geometric parameters of the pumped storage unit, a three-dimensional geometric model of the pumped storage unit is constructed. The geometric parameters include the runner diameter D, the number of blades Z, the opening angle of the movable guide vanes α, and the installation angle of the fixed guide vanes β. Real-time operating parameters of the unit are obtained, including the head H ∈ [200m, 800m] and the flow rate Q ∈ [0.5Q]. design 1.2Q design ] and rotational speed n∈[90%n rated ,110%n rated ];n rated Indicates the rated speed.

[0067] The three-dimensional geometric model of the pumped storage unit was imported into CFD preprocessing software. The entire flow channel region of the pumped storage unit was then meshed to generate an unstructured dynamic mesh. The characteristic curvature C of the turbine blade mesh was then calculated. ijkl Distance y from the dimensionless wall + ≤5, boundary layer mesh growth rate ≤1.2.

[0068] Regarding the dynamic variation characteristics of the runner blade curvature, such as Figure 1 As shown, a fourth-order curvature gradient tensor C is constructed. ijkl :

[0069]

[0070] In the above formula, Represents the velocity component U m The third partial derivative with respect to Cartesian coordinates; Represents the Levi-Civita notation; R(t) is the real-time radius of curvature, calculated by inversion from the instantaneous deformation of the impeller;

[0071] Where is the hydraulic characteristic length, Q is the flow rate, n is the rotational speed, and D is the impeller diameter.

[0072] For the tensor correction term in the rotating coordinate system; δ np It is the Kronecker symbol; For Levi-Civita symbol; ω r Let ω be the vorticity component, and ||ω| be the vorticity modulus. Represents the vorticity component ω n For spatial coordinates x p The partial derivatives of .

[0073] Figure 1 The corresponding scheme, "fourth-order curvature-rotation tensor dynamic coupling system," visually demonstrates the fourth-order curvature gradient tensor C. ijkl The construction logic, real-time radius of curvature R(t) and hydraulic characteristic length L bThe spatial distribution of the tensor invariants and their effect on the eddy viscosity coefficient ν t The correction mechanism. Figure 1 The tensor component distributions of the radial and axial positions directly correspond to the technical description of dynamic curvature adaptability in the paragraph, verifying the system's ability to capture dynamic changes in the curvature of the runner blades.

[0074] Step S2: Initialize the multi-scale turbulent field:

[0075] In the CFD software, a solver capable of implementing the hybrid RANS-LES method was selected to solve the transient flow field in the runner region, with a time step of Δt ≤ 10⁻⁴ s. The frequency domain characteristics of the velocity gradient tensor, vorticity, and pressure fluctuations were calculated to provide input for higher-order corrections.

[0076] In this embodiment, the Couple algorithm is used to solve the RANS equations, with a time step of 10. -4 s, convergence residual <1e -5 .

[0077] Step S3: Correct higher-order curvature-rotation tensor coupling:

[0078] Real-time calculation of fourth-order curvature tensor invariants Γ c Update the eddy viscosity coefficient ν t and stress term τ ij Dynamically adjust the mesh topology of the rotating region to ensure C ijkl Spatial resolution error ≤1%.

[0079] Curvature tensor calculation satisfies real-time constraints: 1) Curvature feature update delay within a single time step ≤ 10Δt; 2) Local mesh refinement level in the rotating region is based on Γ. c Gradient adaptive adjustment, with a maximum encryption ratio of 8:1.

[0080] Among them, tensor invariant Γ c for:

[0081]

[0082] Dynamic coefficient C μ satisfy:

[0083]

[0084] In the above formula, For the hydraulic Reynolds number Re h =U h D h The sigmoid function of / ν, U h For characteristic velocity, D hν is the characteristic length, k is the kinematic viscosity, k represents the turbulent kinetic energy, and ε represents the turbulent kinetic energy dissipation rate, which refers to the amount of turbulent kinetic energy dissipated per unit mass of fluid per unit time; C u ‖S‖ represents the empirical coefficients associated with the turbulence model; ‖S‖ represents the strain rate tensor, reflecting the deformation rate of fluid particles in the flow field and embodying the tensile, shear, and other deformation characteristics of the flow field; ‖Ω‖ represents the rotation rate tensor, reflecting the rotation rate of fluid particles in the flow field and embodying the rotational characteristics of the flow field; ‖C ijkl || F Represents the fourth-order curvature gradient tensor C ijkl The Frobenius norm, U tip The impeller blade tip velocity is represented by fμ; fμ represents a function term related to turbulence characteristics; ρ represents fluid density; and δij represents the Kronecker symbol. Eddy viscosity coefficient ν t In turbulence models, it is used to characterize the viscous properties of turbulence, reflect the momentum diffusion capacity in turbulence, and its value affects the calculation of turbulent stress, which in turn affects the solution of parameters such as flow field velocity and pressure.

[0085] Step S4: Prediction of cavitation vortex instability:

[0086] When the local pressure at a certain point in the flow field decreases to the saturated vapor pressure p at the corresponding temperature v When the fluid undergoes a phase change, cavitation bubbles are generated, i.e., cavitation occurs. To identify cavitation in the flow field, when the cavitation number σ < 2, the cavitation phase change model is activated, based on the cavitation-rotation coupling criterion Q. cav Identify the vortex core region and correct the cavitation source term and turbulent kinetic energy dissipation rate ε.

[0087] cavitation number σ:

[0088]

[0089] In the above formula, U ref The reference velocity is often chosen because the runner blade inlet velocity is a core component, and its inlet velocity significantly affects the flow characteristics of the entire flow field, effectively reflecting the initial motion state of the fluid after entering the unit. Even under different operating conditions, where the actual velocity varies greatly, the cavitation coefficient, after normalization using the reference velocity, accurately reflects the relative state of cavitation in the flow field. p represents the local pressure at a point in the flow field. v This represents the saturated vapor pressure.

[0090] Cavitation-Rotation Coupling Criterion Qcav:

[0091]

[0092] When Q cav >0.5Q thres At that time, activate cavitation source term correction:

[0093]

[0094] In the above formula, The term is a correction for the bubble growth rate, where Q is the turbulent Reynolds number. thres The cavitation-rotational coupling criterion Q represents cav The critical value, α v ρ represents the cavitation volume fraction; l ρ represents the density of a liquid. v This indicates the density of the steam.

[0095] In this embodiment, the fourth-order curvature tensor is updated every 10 time steps, and the HPINN parameters are updated synchronously through MPI parallel communication.

[0096] Step S5: Cross-scale data assimilation:

[0097] An HPINN neural network was constructed and trained to perform data-driven optimization of the coupling effect between the fourth-order tensor and the cavitation phase transition model. The trained neural network was then fused with measured pressure sensor data (p) from the impeller-guide vane interferometric region. exp′ Compared with simulation results p sim′ The optimized turbulent kinetic energy transport equation is output, and the dynamic stress field of the turbine blades is updated. Specifically, this includes:

[0098] Step S5.1: Obtain training data, including:

[0099] High-frequency pressure pulsation data: High-frequency pressure pulsation data of 16 typical working conditions with 4 heads × 4 loads in the impeller-guide vane interference region were collected by a pressure sensor array with a sampling rate ≥ 10kHz. The frequency domain features of the pressure pulsation were extracted using Tecplot360 and visualized using Python scripts.

[0100] Cavitation observation images: Cavitation images of the rotor surface acquired by a high-speed camera with a resolution ≥2000fps, recording the morphology of cavitation vortex bands; used to train the ability to recognize cavitation vortex band morphology.

[0101] Transitional operating condition data: Data is collected synchronously by a torque sensor and a tachometer to obtain torque-speed characteristic curves and capture the dynamic characteristics of transient processes such as pumping to power generation.

[0102] Step S5.2: Construct the HPINN neural network, as follows Figure 2 As shown:

[0103] Input layer: Contains 32-dimensional multi-scale features, including curvature features calculated by a fourth-order tensor and cavitation volume fraction α output by the cavitation model. v As the key input X;

[0104]

[0105] Output layer: The single output is the turbulent kinetic energy correction coefficient β. NN This coefficient is used to adjust the source or dissipation terms of the turbulent kinetic energy transport equation.

[0106]

[0107] In the above formula, P k σ represents the turbulent kinetic energy generation term. k Prandtl number represents the turbulent kinetic energy k.

[0108] FFT(p', 200Hz-800Hz) performs a Fast Fourier Transform on the pressure pulsation signal p' and extracts the spectral information within the frequency range of 200Hz-800Hz. The FFT transform converts the time-domain pressure pulsation signal to the frequency domain, facilitating the analysis of pressure pulsation characteristics within a specific frequency range.

[0109] Network structure: It consists of 5 residual blocks, each of which integrates spectral normalization and multi-head attention mechanism; spectral normalization is used to stabilize the training process, while the multi-head attention mechanism enhances the ability to associate multi-scale features;

[0110] Step S5.3: Train the HPINN neural network: Input the acquired data into the constructed HPINN neural network for training, with the iterative objective of minimizing the deviation between the measured data and the simulation results. sim′ Compared with measured data p exp′ The pressure pulsation, cavitation volume fraction, and other indicators are substituted into the loss function, and the parameters are adjusted through backpropagation. The parameter frequency is synchronized with the CFD time step, and the network parameters are updated once every 10 time steps through MPI parallel communication to ensure consistency with the dynamic changes of the flow field. The engineering verification is carried out through the turbine operating efficiency curve and the pump operating head-flow characteristics.

[0111] The loss function is forced to satisfy physical constraint L. phy :

[0112]

[0113] Compared to the traditional SST-CC model, this invention significantly improves the accuracy of pressure pulsation prediction by integrating high-order tensor coupling, multi-scale memory effect, and physical-data hybrid correction techniques. Specifically, under 100% load power generation conditions, the amplitude error of high-frequency pulsations (>200Hz) is reduced from ±25% to ±3.5%, and the phase synchronization rate exceeds 95%. Under 80% load pumping conditions, the frequency error of low-frequency vortex bands (0.5-1Hz) is <2%, and the amplitude prediction deviation is <5%.

[0114] In cavitation prediction, the prediction accuracy of cavitation volume fraction was improved by 42%, and the vortex morphology similarity index (SSIM index) increased from 0.65 to 0.92; the accuracy of cavitation risk area identification (ROC-AUC) reached 0.97, and the false alarm rate was reduced by 60%. Figure 3 As shown in the figure, the comparison of cavitation vortex band morphology under 100% load condition (simulation results and experimental data) directly verifies the effectiveness of the "multi-condition cavitation vortex band topology prediction unit" and proves the cavitation-rotation coupling criterion Q. cav The accuracy of vortex core region identification and the actual effect of cavitation source term correction.

[0115] in, Figure 3 (a) in the figure is the result of CFD numerical simulation. By using the vortex identification method to extract the vortex structure in the tailrace pipe, an S-shaped vortex belt that spirals along the axis can be clearly seen, indicating that a strong vortex structure is formed due to the combined effect of the non-axisymmetry of the impeller wake and the diffusion instability of the tailrace pipe. Figure 3 (b) shows the experimental observation results. Laser-induced imaging technology was used to capture flow field changes in the transparent tailrace model. The green laser clearly illuminated the development path of the vortex bands, and their morphology was highly consistent with the numerical simulation results, verifying the accuracy of the simulation. The comparison shows that the numerical simulation and experimental results exhibit good consistency in terms of vortex band position, structural morphology, and rotation trend, indicating that the numerical model used has strong physical reliability. This provides a reliable basis for further research on the energy loss mechanism, pressure pulsation characteristics, and unsteady flow evolution laws within the tailrace.

[0116] In terms of computational efficiency, the full-condition steady-state simulation time is reduced to 1 / 8 of the traditional LES method (single-condition time < 4 hours, hardware configuration: 128-core CPU cluster), and the transition condition tracking speed is improved by 5 times. For example... Figure 4 As shown in the figure, this diagram illustrates the frequency domain characteristics of pressure pulsations during the pumping-to-power generation transition (high-frequency components from 200-800Hz and low-frequency vortex bands from 0.5-1Hz), including experimentally measured pressure (red line) and numerical simulation results (black line). The blue line indicates the variation in guide vane opening (GVO). It can be seen that throughout the guide vane opening adjustment process, the experimental and simulated pressures maintain good consistency in amplitude variation and overall trend, indicating that the established numerical model can accurately predict the pressure response characteristics during the transition process.

[0117] Engineering verification shows that the efficiency curve error of the turbine is <0.5%, and the head-flow characteristic error of the pump is <1.2%. Figure 5The figure shows the comparison between model-predicted efficiency and measured data (turbine operating condition). The figure illustrates the radial distribution of the velocity coefficient within the draft tube, including the tangential velocity (Cu) and axial velocity (Cm) obtained from experimental measurements and numerical simulations. The horizontal axis represents the dimensionless radial position R0 / R, and the vertical axis represents the velocity coefficient. The blue and green curves represent the experimental and simulated tangential velocity coefficients, respectively, while the red and brown curves represent the experimental and simulated axial velocity coefficients, respectively. Figure 5 As can be seen, the tangential velocity exhibits a significant peak near the central axis, indicating a strong rotating flow in this region and characterizing typical vortex zone features. The tangential velocity gradually decreases with increasing radius, showing a trend of vortex diffusion towards the wall. The axial velocity is negative in the central region, indicating a backflow phenomenon, while it gradually becomes positive near the wall. Overall, the numerical simulation and experimental results show good agreement in most regions, especially in the prediction of tangential velocity, verifying the numerical model's good predictive ability for complex flow structures in the tailrace pipe.

[0118] An electronic device, comprising: one or more processors;

[0119] Memory, used to store one or more programs;

[0120] When one or more programs are executed by the processor, the processor performs the above-described method.

[0121] A computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the steps of the above-described method.

[0122] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect, characterized in that, Includes the following steps: Step S1: Based on the geometric parameters of the pumped storage unit, construct a three-dimensional geometric model of the pumped storage unit and obtain the real-time operating parameters of the unit; The entire flow channel region of the three-dimensional geometric model of the pumped storage unit is meshed to generate an unstructured dynamic mesh; and the mesh curvature characteristic C of the runner blades is calculated. ijkl ; Step S2: Solve the transient flow field in the runner region using the hybrid RANS-LES method, setting the time step; calculate the frequency domain characteristics of the velocity gradient tensor, vorticity, and pressure fluctuations; Step S3: Based on the basic flow field data calculated in Step S2, calculate the fourth-order curvature tensor invariant Γ in real time. c Update the eddy viscosity coefficient ν t and stress term τ ij Dynamically adjust the mesh topology of the rotating region to ensure C ijkl Spatial resolution error ≤1%; Step S4: Based on the velocity gradient tensor, vorticity, and pressure fluctuation frequency domain characteristics calculated in Step S2, the corrected eddy viscosity coefficient ν in Step S3 is... t Stress term τ ij The optimized flow field mesh topology is used to identify cavitation phenomena in the flow field and calculate the cavitation number. When the cavitation number σ < 2, the cavitation phase transition model is activated, based on the cavitation-rotation coupling criterion Q. cav Identify the vortex core region and correct the cavitation source term and turbulent kinetic energy dissipation rate ε. Step S5: Using the basic flow field simulation data generated in steps S2-S4, namely the coupling results of the fourth-order tensor and cavitation model, and fusing the measured data pexp′ and simulation results psim′ of the pressure sensor in the impeller-guide vane interference region, as training data, construct the HPINN neural network. By minimizing the deviation between simulation and measured data, the turbulent kinetic energy transport equation is optimized, which in turn feeds back into the flow field simulation in steps S2-S4, updating the dynamic stress field of the runner blades.

2. The multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect as described in claim 1, is characterized in that... In step S1, the geometric parameters of the pumped storage unit include the runner diameter D, the number of blades Z, the opening degree of the movable guide vane α, and the installation angle of the fixed guide vane β. Real-time operating parameters of the unit, including head H∈[200m,800m], flow rate Q∈[0.5Q], etc. design 1.2Q design ] and rotational speed n∈[90%n rated ,110%n rated ];n rated Indicates the rated speed.

3. The multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect as described in claim 2, is characterized in that... In step S1, a fourth-order curvature gradient tensor C is constructed based on the dynamic change characteristics of the runner blade curvature. ijkl : In the above formula, Represents the velocity component U m The third partial derivative with respect to Cartesian coordinates; mkl Represents the Levi-Civita notation; R(t) is the real-time radius of curvature, calculated by inversion from the instantaneous deformation of the impeller; Where is the hydraulic characteristic length, Q is the flow rate, n is the rotational speed, and D is the impeller diameter; For the tensor correction term in the rotating coordinate system; δ np It is the Kronecker symbol; ò npr For Levi-Civita symbol; ω r Let ω be the vorticity component, and ||ω| be the vorticity modulus. Represents the vorticity component ω n For spatial coordinates x p The partial derivatives of .

4. The multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect as described in claim 3, is characterized in that... In step S3, through the tensor invariant Γ c Dynamically corrected eddy viscosity coefficient ν t Specifically: Dynamic coefficient C μ satisfy: In the above formula, For the hydraulic Reynolds number Re h =U h D h The sigmoid function of / ν, U h For characteristic velocity, D h ν is the characteristic length, k is the kinematic viscosity, k represents the turbulent kinetic energy, and ε represents the turbulent kinetic energy dissipation rate; C u Represents the empirical coefficients associated with the turbulence model; ||S|| represents the strain rate tensor magnitude; ||Ω|| represents the rotation rate tensor magnitude; ||C|| represents the coefficients associated with the turbulence model. ijkl || F Represents the fourth-order curvature gradient tensor C ijkl The Frobenius norm, U tip ρ represents the tip velocity of the impeller blades; fμ represents a function term related to the characteristics of turbulence; ρ represents the fluid density; and δij represents the Kronecker symbol.

5. The multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect as described in claim 4, is characterized in that... In step S3, the curvature tensor calculation satisfies real-time constraints: 1) the curvature feature update delay within a single time step is ≤10Δt; 2) the local mesh refinement level of the rotating region is based on Γ. c Gradient adaptive adjustment, with a maximum encryption ratio of 8:

1.

6. The multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect as described in claim 5, is characterized in that... In step S4, the cavitation number σ is: In the above formula, U ref p represents the reference velocity; p represents the local pressure at a point in the flow field. v Indicates saturated vapor pressure; Cavitation-Rotation Coupling Criterion Qcav: When Q cav >0.5Q thres At that time, activate cavitation source term correction: In the above formula, The term is a correction for the bubble growth rate, where Q is the turbulent Reynolds number. thres The cavitation-rotational coupling criterion Q represents cav The critical value, α v ρ represents the cavitation volume fraction; l ρ represents the density of a liquid. v This indicates the density of the steam.

7. The multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect as described in claim 6, is characterized in that... Step S5 specifically includes: Step S5.1: Obtain training data, including: High-frequency pressure pulsation data: High-frequency pressure pulsation data of 16 typical working conditions with 4 heads × 4 loads in the impeller-guide vane interference zone are collected by pressure sensor array, with a sampling rate ≥ 10kHz to ensure the capture of high-frequency vibration characteristics of 200-800Hz. Cavitation observation images: Cavitation images of the rotor surface acquired by a high-speed camera with a resolution ≥2000fps, recording the morphology of cavitation vortex zones; Transitional operating condition data: Data is collected synchronously by a torque sensor and a tachometer to obtain torque-speed characteristic curves and capture the dynamic characteristics of transient processes such as pumping to power generation. Step S5.2: Construct the HPINN neural network: Input layer: Contains 32-dimensional multi-scale features, including curvature features calculated by a fourth-order tensor and cavitation volume fraction α output by the cavitation model. v As a key input; Output layer: The single output is the turbulent kinetic energy correction coefficient β. NN ; Network structure: It consists of 5 residual blocks, each of which integrates spectral normalization and multi-head attention mechanism; spectral normalization is used to stabilize the training process, while the multi-head attention mechanism enhances the ability to associate multi-scale features; Step S5.3: Train the HPINN neural network: Input the acquired data into the constructed HPINN neural network for training, with the iterative objective of minimizing the deviation between the measured data and the simulation results. sim′ Compared with measured data p exp′ The pressure pulsation, cavitation volume fraction, and other indicators are substituted into the loss function, and the parameters are adjusted through backpropagation. The parameter frequency is synchronized with the CFD time step, and the network parameters are updated once every 10 time steps through MPI parallel communication to ensure consistency with the dynamic changes of the flow field. The engineering verification is carried out through the turbine operating efficiency curve and the pump operating head-flow characteristics.

8. The multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect as described in claim 7, is characterized in that... The input layer of the HPINN neural network contains 32-dimensional multi-scale features, specifically: Output: In the above formula, P k σ represents the turbulent kinetic energy generation term. k Prandtl number represents the turbulent kinetic energy k.

9. The multi-scale turbulence modeling method for wide-load pumped storage units based on high-order tensor coupling and dynamic memory effect as described in claim 8, is characterized in that... The loss function is forced to satisfy physical constraint L. phy :

10. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When one or more programs are executed by the processor, the processor performs the method as described in any one of claims 1-9.

11. A computer-readable storage medium storing computer instructions thereon, characterized in that, When executed by the processor, this instruction implements the steps of the method as described in any one of claims 1-9.

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