A numerical simulation method of wind load on bridge structure under tornado action based on CFD

Abstract

The application belongs to the technical field of bridge wind resistance engineering, and discloses a numerical simulation method of bridge structure wind load under the action of tornado based on CFD, which comprises the following steps: referring to the geometric configuration of a tornado laboratory simulation device, a CFD calculation domain model of a three-dimensional tornado generator is established, a speed inlet boundary condition is constructed by using Doppler radar observation data of a real tornado, and a three-dimensional tornado wind field is obtained by numerical solution; a vortex ratio is controlled by an inflow angle, and a tornado intensity is controlled by an inlet wind speed. The numerical simulation method of bridge structure wind load under the action of tornado based on CFD aims to solve the problem that in the existing numerical simulation method of tornado wind field based on CFD, an idealized analytical wind field is used as a boundary condition to drive the generation of a wind field, and there is a lack of quantitative mapping relationship between control parameters and wind field structure characteristic quantities, so that the bridge structure surface wind pressure coefficient cannot be systematically obtained under the working conditions of multiple radial positions and wind direction angles.

Description

Technical Field

[0001] This invention relates to the field of bridge wind-resistant engineering technology, specifically to a numerical simulation method for wind load on bridge structures under tornado action based on CFD. Background Technology

[0002] Tornadoes are extremely destructive weather phenomena in nature, with wind speeds exceeding 420 kilometers per hour. They are characterized by high wind speeds, concentrated areas, and complex vortex structures. Bridges, as crucial transportation infrastructure, face severe wind load threats under tornado influence. The rotating wind field of a tornado generates intense alternating positive and negative pressure distributions on the bridge structure surface. Numerous engineering examples have demonstrated that tornadoes can cause severe damage such as bridge deck displacement, pier cracking, and bearing misalignment. Therefore, accurate simulation of wind loads on bridge structures under tornado influence is a prerequisite for tornado-resistant bridge design. Existing research primarily uses wind tunnel tests or field measurements to obtain wind load data on bridge surfaces. However, wind tunnel tests are constrained by equipment size and similarity criteria, making it difficult to simultaneously satisfy the similarity relationship between the tornado vortex core radius, translational velocity, and structural geometric dimensions. Field measurements, on the other hand, are affected by the randomness of the natural environment, making it impossible to repeatedly obtain wind field data under specified control parameters. Numerical simulation methods based on computational fluid dynamics (CFD) have been introduced into the numerical generation research of tornado wind fields due to their controllable parameters and repeatable operating conditions.

[0003] However, existing CFD-based research generally uses idealized analytical wind fields (such as the Rankine vortex model) as boundary conditions for the computational domain when constructing tornado wind fields, rather than driving the wind field generation with Doppler radar observation data of real tornadoes. At the same time, when simulating wind loads by placing bridge structures into the wind field, a quantitative mapping relationship between the three types of control parameters (vortex ratio, inflow angle, and inlet wind speed) and the structural characteristics of the wind field is not established. This results in a systematic deviation between the simulated tornado wind field and the wind field structure of real tornadoes. The wind pressure coefficients at various pressure measurement points on the bridge surface lack systematic coverage under different radial positions and wind direction angles, making it impossible to form a complete basis for wind load values, which restricts the engineering application of bridge tornado-resistant design. Summary of the Invention

[0004] The purpose of this invention is to solve the problem that existing CFD-based numerical simulation methods for tornado wind fields use idealized analytical wind fields as boundary conditions to drive wind field generation and lack quantitative mapping relationships between control parameters and wind field structural characteristics, resulting in the inability to systematically obtain the wind pressure coefficient on the surface of bridge structures under multiple radial positions and wind direction angles. Therefore, this invention proposes a CFD-based numerical simulation method for wind loads on bridge structures under tornado action.

[0005] The technical solution of the present invention to solve the above-mentioned technical problems is as follows: A CFD-based numerical simulation method for wind loads on bridge structures under tornado conditions includes the following steps: S1: Referring to the geometric configuration of the tornado laboratory simulation device, a CFD computational domain model of the three-dimensional tornado generator is established. The velocity inlet boundary conditions are constructed using Doppler radar observation data of real tornadoes, and the three-dimensional tornado wind field is obtained through numerical solution. S2: Control the eddy ratio by the inflow angle and control the tornado intensity by the inlet wind speed. Perform multi-condition parameterized simulation on the three-dimensional tornado wind field obtained in step S1 to establish a quantitative relationship between the control parameters and the structural characteristics of the wind field. S3: Place the bridge structure model into the tornado wind field obtained in step S2, perform numerical simulation according to the multi-condition combination of radial position and wind direction angle, and extract the wind pressure coefficient of each pressure measurement point on the bridge structure surface. S4: Compare the wind pressure coefficient obtained in step S3 with the pressure test data of the scaled model to complete the verification.

[0006] Based on the above technical solution, the present invention can be further improved as follows.

[0007] Furthermore, the CFD computational domain model adopts a rotationally symmetric cylindrical computational domain; A velocity boundary condition is applied at the lateral inlet of the computational domain, which is a superposition of tangential and radial velocity components. A no-slip wall boundary condition is applied at the bottom of the computational domain, and a pressure outlet boundary condition is applied at the top outlet.

[0008] Furthermore, the construction of velocity inlet boundary conditions using Doppler radar observation data specifically includes: The tangential velocity component and the radial velocity component are separated from the radial velocity field of the Doppler radar, and the two are assigned to the lateral inlet of the computational domain in the form of velocity inlet boundary conditions. The maximum tangential velocity and its corresponding characteristic radius in the numerical wind field are consistent with the radar observation value as the criterion for boundary condition calibration.

[0009] Furthermore, the numerical solution is obtained by simultaneously solving the Reynolds-averaged NS equations and the RNG k-ε turbulence model, or by using the large eddy simulation method. The computational domain grid is divided using a hybrid structured and unstructured method, with local refinement applied to the tornado vortex core region and the near-surface boundary layer region. The radial and vertical grid sizes of the refined regions are no greater than 1 / 20 of the characteristic radius.

[0010] Furthermore, the establishment of a quantitative relationship between control parameters and wind field structural characteristics specifically involves: Under various parameter conditions, the vertical distribution of the tornado's maximum tangential velocity, characteristic radius, maximum radial velocity, and axial velocity was extracted respectively. The extracted data were fitted using the Rankine combined vortex model or the Burgers-Rott vortex model to quantify the sensitivity coefficients of the vortex ratio, inflow angle and inlet wind speed to the above-mentioned characteristic quantities, thus forming a quantitative mapping relationship between control parameters and wind field structural characteristic quantities.

[0011] Furthermore, the eddy ratio ranges from 0.1 to 1.4, the inflow angle ranges from 30° to 75°, and the inlet wind speed is set according to the characteristic wind speed range corresponding to the EF0 to EF5 tornado intensity levels. The combination scheme of control parameters adopts full factorial design or orthogonal experimental design, and each control parameter is iterated one by one at predetermined intervals within the above parameter range.

[0012] Furthermore, the specific method for placing the bridge structure model into the tornado wind field is as follows: keeping the boundary conditions of the tornado computational domain unchanged, embedding the geometric entities of the bridge main beam section and bridge deck at the bottom ground of the computational domain according to preset radial position coordinates, and refining the mesh of the flow field on the bridge surface and surrounding area. After refining, the normal spacing of the first layer of mesh on the bridge surface satisfies the wall function on y. + Value requirements.

[0013] Furthermore, the radial position is taken as multiple discrete values ​​within the range from the center of the tornado vortex core to the edge of the computational domain, including at the characteristic radius, at 2 times the characteristic radius, at 3 times the characteristic radius, and at 4 times the characteristic radius; The wind direction angle is taken at 15° intervals within the range of 0° to 360°. Under the combined conditions of each radial position and wind direction angle, the average wind pressure and pulsating wind pressure at each pressure measurement point on the bridge structure surface are recorded. The wind pressure coefficient is calculated by taking the dynamic pressure value corresponding to the maximum tangential velocity of the tornado at each pressure measurement section as the reference dynamic pressure.

[0014] Furthermore, in S3, the wind pressure coefficient of each pressure measuring section is integrated along the bridge axis to obtain the lift coefficient, drag coefficient, and moment coefficient around the centroid of the section, respectively. The maximum value of the above aerodynamic coefficients under all radial positions and wind direction angles is used as the wind load envelope value to form a set of wind load values ​​for tornado resistance design.

[0015] Furthermore, the verification specifically involves conducting pressure tests under equivalent working conditions using a scaled-down model of the main beam of a bridge that is geometrically similar to that of numerical computation, in a tornado simulator or a boundary layer wind tunnel. The wind pressure coefficients at each pressure measurement point obtained from the experiment were compared with the numerical simulation results point by point. The average relative error of the time-averaged wind pressure coefficient at each pressure measurement point not exceeding 15% was used as the criterion for passing the verification. After verification, the wind pressure coefficient of the untested working conditions in step S3 is calculated by replacing the physical test with numerical simulation results.

[0016] Compared with the prior art, the technical solution of this application has the following beneficial technical effects: This invention constructs velocity inlet boundary conditions using Doppler radar observation data of real tornadoes, replacing the boundary setting method of directly assigning idealized analytical wind fields in existing methods. This ensures that the generated three-dimensional tornado wind field is consistent with real tornadoes in key structural features such as maximum tangential velocity and characteristic radius, eliminating the systematic deviations introduced by the boundary conditions of idealized vortex models. By controlling the vortex ratio through the inflow angle and the tornado intensity through the inlet wind speed, the wind field is simulated under multiple working conditions using parametric methods. The mapping relationship between three types of control parameters and wind field structural characteristics is quantitatively established, providing a traceable wind field input basis for subsequent bridge wind load simulation. The wind pressure coefficients of each pressure measurement point on the bridge structure surface are extracted according to the multi-working-condition combination system of radial position and wind direction angle, achieving full working-condition coverage of wind pressure coefficients under different relative positions of tornadoes and incoming flow directions. This solves the problem of incomplete pressure measurement working condition coverage and inability to form a complete basis for wind load values ​​in existing methods. The numerical simulation results are verified point by point by using pressure measurement test data from scaled models, ensuring the reliability of the above-mentioned wind pressure coefficient data. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a schematic diagram illustrating the CFD model establishment and wind field solution of the present invention; Figure 3 This is a schematic diagram illustrating the establishment of multi-condition parametric simulation and quantitative relationship in this invention; Figure 4 This is a schematic diagram of bridge placement and wind load extraction according to the present invention; Figure 5 This is a schematic diagram illustrating the experimental verification and application of the results of this invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] This invention provides a CFD-based numerical simulation method for wind loads on bridge structures under tornado conditions, using FLUENT software as the solution platform. Figure 1As shown, the overall process includes four interconnected steps: First, referencing the geometric configuration of a tornado laboratory simulation device, a CFD computational domain model of a three-dimensional tornado generator is established. Velocity inlet boundary conditions are constructed using Doppler radar observation data from real tornadoes, and the three-dimensional tornado wind field is obtained through numerical solution. Second, the eddy current ratio is controlled by the inflow angle, and the tornado intensity is controlled by the inlet wind speed. Multi-condition parametric simulations are performed on the obtained three-dimensional tornado wind field to establish a quantitative relationship between control parameters and wind field structural characteristics. Third, a bridge structure model is placed within the tornado wind field, and numerical simulations are performed using multiple combinations of radial position and wind direction angle to extract the wind pressure coefficient at each pressure measurement point on the bridge structure surface. Finally, the obtained wind pressure coefficient is compared with pressure test data from a scaled model to complete the verification. The following details the specific implementation process of each stage.

[0020] Step S1: Establishment of the CFD computational domain model of the three-dimensional tornado generator and numerical generation of the wind field Establishment of the geometric model of the computational domain The CFD computational domain model employs a rotationally symmetric cylindrical computational domain. The design of this cylindrical domain references the geometry of a tornado laboratory simulation device, and its basic structure consists of three parts: a lateral inflow region, a bottom surface region, and a top outflow region. The diameter-to-height ratio of the computational domain is determined based on the geometric proportions of an actual tornado simulator to ensure that the vortex flow field develops fully within the computational domain without being affected by the domain boundary cutoff effect. The technical reason for using a rotationally symmetric cylindrical computational domain instead of a cuboid computational domain is that the tornado vortex itself has an axisymmetric rotating flow field structure. The cylindrical domain can uniformly distribute the lateral inflow in all directions, avoiding numerical diffusion problems caused by geometric abrupt changes in corner regions. It also facilitates the independent extraction and analysis of the tangential, radial, and axial velocity components of the wind field in polar coordinates.

[0021] Apply a velocity boundary condition at the lateral entrance of the computational domain, which is a superposition of tangential and radial velocity components. For example... Figure 1 and Figure 2 As shown, specifically, the airflow velocity at the lateral inlet is composed of two mutually perpendicular components: the tangential velocity component points along the tangent of the cylinder, driving the airflow to rotate around the axis; the radial velocity component points inward along the radius, driving the airflow to converge towards the vortex core. A no-slip wall boundary condition is applied at the bottom of the computational domain to simulate the frictional drag effect of the ground on the near-surface airflow, ensuring accurate reproduction of the velocity gradient within the near-surface boundary layer. A pressure outlet boundary condition is applied at the top outflow, allowing the vortex airflow to freely exit vertically while maintaining a stable static pressure reference value within the computational domain to prevent numerical backflow.

[0022] Boundary condition transformation of Doppler radar observation data Constructing velocity inlet boundary conditions using Doppler radar observation data is one of the core technical features that distinguishes this invention from existing methods. The specific implementation process is as follows: Tangential and radial velocity components are separated from the radial velocity field of the Doppler radar. Doppler radar directly measures the radial velocity along the radar beam direction, which is the superposition of the tornado's tangential and radial velocities projected onto the radar beam direction. Using multiple sets of radar scan data at different azimuth angles, through velocity azimuth display (VAD) technology or dual-Doppler wind field inversion technology, the radar radial velocity field is decomposed into mutually perpendicular horizontal tangential and horizontal radial velocity components, and the height distribution information of the vertical velocity is further extracted. The separated tangential and radial velocity components are assigned to the lateral inlet of the computational domain as velocity inlet boundary conditions, ensuring that the driving conditions of the numerical wind field are consistent with the measured wind field of a real tornado.

[0023] After assigning boundary conditions, the consistency between the maximum tangential velocity and its corresponding characteristic radius in the numerical wind field and radar observations is used as the criterion for boundary condition calibration. The characteristic radius is defined as the radial distance from the point where the maximum tangential velocity occurs to the vortex center, also known as the vortex core radius. During calibration, if the maximum tangential velocity in the numerical wind field deviates from the radar measurement value beyond the allowable error range, the order of magnitude of the inlet velocity is iteratively adjusted; if the vortex core radius does not match the measured value, the radial distribution of the inlet velocity is adjusted until both indicators meet the calibration criteria. This boundary condition construction method, driven by measured data and calibrated with two indicators, fundamentally avoids the systematic bias introduced when using an idealized analytical vortex model as the boundary condition.

[0024] Numerical solution methods and mesh generation Numerical solutions are obtained by simultaneously solving the Reynolds-averaged Navier-Stokes equations and the RNG k-ε turbulence model, or by using Large Eddy Simulation (LES). Each method has its applicable scenarios: when computational resources are limited and rapid extraction of wind field characteristics is required under a large number of parameters, the RANS-RNG k-ε method is used. This method improves the standard k-ε model by introducing a rotational correction term, which can better capture the characteristics of turbulent anisotropy in rotating flow fields. When a refined analysis of the instantaneous vortex structure and turbulence spectrum characteristics of tornado wind fields under specific conditions is required, the LES method is used. LES obtains more physically realistic unsteady flow field information by directly solving large-scale vortices and processing small-scale vortices using a sub-grid model.

[0025] The computational domain mesh is generated using a hybrid structured and unstructured approach. Local refinement is applied to the tornado vortex core region and the near-surface boundary layer region, with the radial and vertical mesh sizes in the refined regions not exceeding 1 / 20 of the characteristic radius. The specific hybrid mesh generation strategy is as follows: Unstructured tetrahedral meshes are used in the outer regions of the computational domain (far from the vortex core center) to reduce the total mesh size and save computational resources; within a radius of approximately 3 times the characteristic radius in the vortex core center region, structured hexahedral meshes are used to reduce numerical dissipation and accurately capture the radial gradient of the tangential velocity; prism-layer meshes are arranged in the bottom near-surface layer of the computational domain (within approximately 1 / 10 of the computational domain height), with the height of the first layer determined by the selected turbulence model based on the wall y-axis. + The required value is determined, and the RNG k-ε model is used with the standard wall function when y + When using LES, the first mesh layer near the wall should be controlled within the range of 30 to 300. + The value should not exceed 5. Mesh independence verification is performed by sequentially refining the global mesh size and comparing the convergence of the maximum tangential velocity and vortex radius in the vortex core region. The criterion for passing mesh independence is that the difference of the above characteristic quantities between two adjacent mesh schemes does not exceed 3%.

[0026] Step S2: Establishment of multi-condition parameterized simulation and quantitative mapping relationship of control parameters Definition and value range setting of control parameters This invention uses three parameters—vortex ratio, inflow angle, and inlet wind speed—as control parameters for the tornado wind field. These three parameters together determine the structural morphology and intensity characteristics of the simulated tornado. For example... Figure 1 and Figure 3 As shown, the vortex ratio ranges from 0.1 to 1.4. The vortex ratio is defined as a dimensionless parameter representing the ratio of the tangential velocity component to the radial velocity component at the lateral inlet of the computational domain. Physically, it represents the ratio of the rotational intensity of the airflow to its centripetal convergence intensity. When the vortex ratio is low (approximately less than 0.3), the vortex exhibits a single-vortex structure with a small vortex core radius and a high maximum tangential velocity. As the vortex ratio increases (approximately 0.4 to 0.7), the vortex may transition from a single-vortex structure to a double-vortex or multi-vortex structure. When the vortex ratio further increases to above 1.0, the vortex exhibits a wide funnel-shaped characteristic, with an increased vortex core radius and a decrease in maximum tangential velocity. The inflow angle ranges from 30° to 75°. The inflow angle is defined as the angle between the velocity vector and the horizontal plane when the airflow enters the lateral inlet of the computational domain. This angle controls the magnitude of the vertical component of the airflow, thus affecting the vertical vortex structure and near-surface inflow thickness of the tornado. The inlet wind speed is set according to the characteristic wind speed range corresponding to the EF0 to EF5 tornado intensity levels. The maximum ground wind speed corresponding to EF0 is about 29 to 38 m / s, and the maximum ground wind speed corresponding to EF5 exceeds 89 m / s. Several representative wind speed values ​​are determined between each level by linear interpolation or logarithmic intervals.

[0027] The combination scheme of control parameters adopts either full factorial design or orthogonal experimental design, and each control parameter is traversed one by one at predetermined intervals within the above parameter range. When the number of levels of the three control parameters are n1, n2, and n3, the full factorial design generates a total of n1×n2×n3 working condition combinations, which can completely cover all interaction effects in the parameter space and is suitable for situations with a small number of parameter levels. When the number of levels of each parameter is large, resulting in an excessively large total number of full factorial working conditions, an orthogonal experimental design scheme is used instead. The parameter space is uniformly sampled through an orthogonal array, which significantly reduces the number of calculated working conditions while retaining the complete ability to distinguish main effects and low-order interaction effects. Each working condition independently completes steady-state or unsteady calculations in the computational domain model established in step S1, and the converged velocity field is extracted as the representative result of the tornado wind field under that working condition.

[0028] Extraction of wind field structural features and establishment of quantitative mapping relationships Under various parameter conditions, the vertical distributions of the tornado's maximum tangential velocity, characteristic radius, maximum radial velocity, and axial velocity were extracted. These four types of characteristic quantities describe the tornado's wind field structure from different perspectives: the maximum tangential velocity directly reflects the tornado's intensity level and serves as the basis for determining the reference dynamic pressure in bridge wind load calculations; the characteristic radius (vortex core radius) determines the spatial range of the maximum wind speed region, affecting the local wind field differences experienced by the bridge structure when placed in different radial positions; the maximum radial velocity characterizes the intensity of the tornado's near-surface inflow and directly contributes to the wind pressure distribution at the bottom of the bridge structure; the vertical distribution of the axial velocity reflects the organization of the tornado's vertical airflow and affects the vertical pressure difference distribution between the upper and lower flanges of the bridge.

[0029] The extracted data were fitted using either the Rankine combined vortex model or the Burgers-Rott vortex model to quantify the sensitivity coefficients of the vortex ratio, inflow angle, and inlet wind speed to these characteristic quantities, thus establishing a quantitative mapping relationship between control parameters and wind field structural characteristics. The Rankine combined vortex model treats the interior of the vortex core (radius smaller than the characteristic radius) as a rigid body rotation region and the exterior of the vortex core as a potential flow rotation region, fitting the radial distribution of tangential velocity with a piecewise linear function, making it suitable for single-vortex conditions with low vortex ratios. The Burgers-Rott vortex model, based on the Rankine model, introduces corrections for axial velocity components and viscous terms, enabling a more accurate description of the vertical attenuation characteristics of tangential velocity within the near-surface frictional boundary layer, making it suitable for conditions with medium to high vortex ratios. The extracted data for each condition were fitted using the aforementioned models, and the fitting parameter values ​​for each condition were recorded. Then, explicit functional relationships between the three control parameters (vortex ratio S, inflow angle α, and inlet wind speed V) and four types of wind field characteristic quantities were established using multiple regression analysis or response surface methodology, forming a control parameter sensitivity coefficient matrix. This matrix quantitatively describes the magnitude of change in each wind field characteristic quantity caused by a unit change in each control parameter, providing a quantitative basis for selecting reasonable wind field parameters for tornadoes of specific intensity levels in subsequent bridge wind load simulations.

[0030] Furthermore, after extracting the tangential velocity characteristics, the effect of ground roughness under various operating conditions needs to be evaluated. When tornadoes pass through different surface types (open plains, mixed urban and suburban terrain, etc.), ground roughness alters the velocity gradient of the airflow within the boundary layer through near-surface friction, thereby affecting the vortex core structure and the height distribution of the maximum tangential velocity. In this step, the equivalent roughness height in the no-slip wall boundary condition at the bottom of the computational domain is used as the control quantity for ground roughness. Representative values ​​of ground roughness are appropriately added to the parametric simulation operating condition matrix to obtain a quantitative understanding of the influence of surface conditions on wind field characteristics, and this is incorporated into the correction term of the quantitative mapping relationship between control parameters and wind field characteristics.

[0031] Step S3: Embedding of the bridge structural model and numerical simulation of multi-condition wind loads Embedding method of bridge structural model Keeping the boundary conditions of the tornado computational domain unchanged, the geometric entities of the bridge main beam section and bridge deck are embedded into the ground at the bottom of the computational domain according to preset radial position coordinates. For example... Figure 1 and Figure 4As shown, the bridge structural model is established using the cross-section of the main girder of a typical long-span bridge as the object. The cross-sectional forms cover two categories: streamlined box girder (suitable for suspension and cable-stayed bridge main girders) and π-shaped composite beam (suitable for high-speed railway continuous beam bridge main girders), to cover the two most common types of main girder forms in engineering. The bridge main girder is modeled as a finite-length three-dimensional solid geometry, and its axial length should be greater than three times the beam height to ensure that the flow field at the middle section of the main girder is not disturbed by end boundary effects. The bridge deck model should include the equivalent geometry of auxiliary components such as crash barriers and wind deflectors, as these detailed components have a significant impact on the local wind pressure distribution on the bridge surface.

[0032] The bridge geometry is subtracted from the computational fluid domain using Boolean operations, making the bridge surface a solid boundary of the fluid domain. The flow field on and around the bridge surface is then meshed, with the normal spacing of the first mesh layer on the bridge surface satisfying the wall function on the y-axis. + The requirements for values ​​are as follows. In specific implementation, prismatic mesh layers are grown in the normal direction of the outer contour of the main beam of the bridge. A total of 10 to 20 prismatic layers are set, with a growth ratio controlled between 1.1 and 1.2. A transition and densification zone is further set around the prismatic layers, within a range of approximately 5 times the beam height, filled with hexahedral or hybrid meshes to ensure a smooth mesh transition from the bridge surface to the far-field tornado wind field, avoiding numerical dissipation caused by abrupt changes in mesh scale. After embedding the bridge model, a comprehensive mesh quality check is performed on the computational domain to ensure that the maximum skewness of all mesh elements does not exceed 0.85 and the minimum orthogonal quality is not less than 0.15, meeting the basic mesh quality requirements of the FLUENT solver.

[0033] Radial position and wind direction angle multi-condition design The radial positions are taken from multiple discrete values ​​within the range from the center of the tornado vortex core to the edge of the computational domain, including the characteristic radius, twice the characteristic radius, three times the characteristic radius, and four times the characteristic radius. The selection of these four radial positions is based on the following criteria: the characteristic radius (vortex core edge) corresponds to the location of the tornado's maximum tangential velocity, representing the highest wind speed condition the bridge structure can encounter; twice the characteristic radius (i.e., twice the vortex core radius) corresponds to the intermediate region where the tangential velocity is still at a high level, but the radial velocity has significantly decreased; the three and four times the characteristic radius represent the outer region of the tornado, where the proportion of the radial velocity component relative to the tangential velocity component increases, and the spatial non-uniformity of the wind field significantly affects the wind pressure differences across the bridge's axial sections. By covering these four radial positions, a complete envelope curve of the wind pressure coefficient as a function of the tornado's relative position can be established.

[0034] The wind direction angle is taken at 15° intervals within the range of 0° to 360°, resulting in 24 discrete wind direction angle values. The wind direction angle is defined as the angle between the direction of the line connecting the centers of the tornado vortex cores (i.e., the normal direction of the bridge axis) and the reference due north direction. Because the rotating wind field of a tornado is asymmetrical in the horizontal plane (tangential velocity is superimposed or canceled with the direction of rotation), the wind pressure distribution on the bridge differs significantly between the downwind and upwind directions. Therefore, it is necessary to traverse all wind direction angles at equal angular intervals throughout the entire range of 0° to 360°, rather than simulating only the half-range of 0° to 180°. Under both clockwise and counterclockwise vortex rotations, the wind field structure at the same wind direction angle exhibits a mirror symmetry relationship. This relationship can be used to verify some operating conditions through interchange, reducing redundant calculations.

[0035] Under each radial position and wind direction angle combination, the hourly average wind pressure and fluctuating wind pressure at each pressure measurement point on the bridge structure surface were recorded. The wind pressure coefficient was calculated using the dynamic pressure value corresponding to the maximum tangential velocity of the tornado at each pressure measurement section as the reference dynamic pressure. The main girder of the bridge structure was divided into several equally spaced pressure measurement sections along the axial direction. On each section, several pressure measurement points were set along the beam height direction on the outer surface of the upper flange, the inner surface of the upper flange (below the box section), the outer side of the web, the inner side of the web, the outer surface of the lower flange, and the upper surface of the bridge deck, to comprehensively describe the annular variation law of wind pressure distribution around the section. The fluctuating wind pressure coefficient was extracted from the unsteady time series data using the root mean square method in the time domain, characterizing the dynamic fluctuation amplitude of wind pressure.

[0036] Extraction of aerodynamic coefficients and formation of wind load envelope values Integrating the wind pressure coefficient at each pressure measurement section along the bridge axis yields the lift coefficient, drag coefficient, and moment coefficient about the centroid of the section. The lift coefficient corresponds to the resultant force perpendicular to the bridge axis and the horizontal plane, characterizing the vertical lifting or pressing effect of the tornado on the bridge deck. The drag coefficient corresponds to the resultant force perpendicular to the bridge axis and parallel to the horizontal plane, characterizing the lateral thrust of the tornado on the main girder. The moment coefficient corresponds to the torsional moment about the centroid of the main girder section, characterizing the torque generated on the section by the asymmetric wind pressure distribution caused by the tornado's rotating wind field. The dimensionless representation of the three aerodynamic coefficients uses the product of the dynamic pressure value corresponding to the maximum tangential velocity of the tornado at each pressure measurement section and the characteristic dimension (girder height or girder width) of the main girder as a reference value.

[0037] The maximum value of the aforementioned aerodynamic coefficients under all radial positions and wind direction angles is used as the wind load envelope value, forming a set of wind load values ​​for tornado-resistant design. The envelope value is determined by taking the maximum and minimum algebraic values ​​(i.e., maximum positive and maximum negative values) of the lift coefficient, drag coefficient, and moment coefficient in the matrix of all radial positions and wind direction angle combinations to form the upper and lower envelopes of each aerodynamic coefficient. For tornado-resistant bridge structure design, both the most unfavorable positive pressure and the most unfavorable negative pressure conditions must be considered simultaneously. The maximum negative value of the lift coefficient (i.e., maximum upward suction) is often a key parameter controlling the torsional resistance design of the bridge deck, while the maximum positive value of the drag coefficient is a key parameter controlling the lateral support design of the bridge. The envelope value of the moment coefficient provides load input for the torsional resistance verification of the bridge cross-section. The above wind load value set, along with the corresponding radial position, wind direction angle, eddy ratio, inflow angle, and inlet wind speed parameters, is recorded to form a structured wind load database for reference in engineering design.

[0038] Step S4: Comparative verification of pressure test on scaled model Scale model making and equivalent working condition setting A scaled-down model of the bridge main girder, geometrically similar to that used in numerical computation, was used to conduct pressure tests under equivalent working conditions in a tornado simulator or boundary layer wind tunnel. The selection of the scale ratio had to simultaneously satisfy the following two constraints: First, the ratio of the characteristic dimension (girder height) of the scaled model to the vortex core radius of the tornado simulator should be the same as the ratio in the numerical simulation, ensuring the geometric similarity of the relative position of the bridge model in the vortex wind field; second, the characteristic Reynolds number of the scaled model (defined as the product of the maximum tangential velocity and the girder height divided by the kinematic viscosity) should be similar to the Reynolds number in the numerical simulation, or the Reynolds number should be increased to a level meeting the self-modeling requirements by increasing the wind speed under test conditions, thus eliminating the influence of the Reynolds number effect on the wind pressure coefficient results. The scaled-down model was manufactured using high-precision CNC machining, with dimensional errors not exceeding ±0.5% of the design value and surface roughness not exceeding 1.6 μm, to avoid interference from surface defects on local wind pressure.

[0039] The tornado simulator used in the pressure test was designed with the same geometric similarity ratio as the numerical simulation, and its eddy ratio and inflow angle adjustment range covered the control parameter range set in step S2. When conducting the equivalent test in the boundary layer wind tunnel, the tornado's rotating wind field effect needed to be converted into the gust coefficient of the equivalent straight wind field for correction. A scaled-down model was fixed at the same radial position as in the numerical simulation, and different wind direction angles were simulated by rotating the model. The arrangement of the pressure measurement points strictly corresponded to the measurement point positions of each pressure measurement section in the numerical simulation. Each measurement point was connected to an electronically scanned valve-type pressure sensor via a narrow-diameter pressure guide tube. The sensor range was selected based on 1.5 times the expected maximum dynamic pressure value, the sampling frequency was not less than 500 Hz, and the sampling duration was not less than 120 s to ensure the convergence of the time-averaged wind pressure coefficient and the pulsating wind pressure coefficient statistics.

[0040] Verification criteria and supplementary calculations for untested operating conditions like Figure 5 As shown, the wind pressure coefficients obtained from the experiment at each pressure measurement point are compared with the numerical simulation results point by point. The criterion for passing the verification is that the average relative error of the time-averaged wind pressure coefficient at each pressure measurement point does not exceed 15%. During the comparison process, in addition to the time-averaged wind pressure coefficient, the distribution trend of the fluctuating wind pressure coefficient (root mean square value) and the amplitude differences of the lift coefficient, drag coefficient, and moment coefficient at key sections must also be compared simultaneously to form a multi-dimensional comprehensive verification and evaluation report. If the relative error of the time-averaged wind pressure coefficient at a specific pressure measurement point under a certain operating condition exceeds 15% but does not exceed 20%, a special analysis must be conducted, taking into account the location of the pressure measurement point on the cross section and the surrounding flow field characteristics, to eliminate systematic factors such as interference from the experimental pressure measurement pipeline or local geometric differences in the model.

[0041] After successful verification, numerical simulation results are used to supplement the calculation of wind pressure coefficients for the untested conditions in step S3, replacing the physical experiments. The verified numerical model has reliable predictive capabilities within the set range of control parameters such as eddy ratio, inflow angle, and inlet wind speed. Following the parametric simulation framework established in steps S2 and S3, batch supplementary calculations can be performed for radial positions, wind direction angles, or combinations of control parameters not covered by the physical experiments. The wind pressure coefficients obtained from the supplementary calculations, along with the results from the physical experiment conditions, are incorporated into the established wind load database, ultimately forming a complete set of bridge tornado-resistant wind load values ​​covering the entire parameter space. This provides a systematic numerical basis for tornado resistance verification during the engineering design phase.

[0042] In the above complete process, the two core links of radar data-driven boundary conditions in step S1 and quantitative mapping of parameterized control parameters in step S2 support each other: the former ensures high-fidelity reproduction of the wind field under a single real tornado event, while the latter expands the system to full parameter space coverage required for engineering design on this basis; the multi-condition wind load extraction in step S3 and the experimental verification in step S4 form a complete numerical-experimental mutual verification closed loop, ensuring the engineering usability of the established wind load database.

[0043] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0044] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A numerical simulation method for wind load on bridge structures under tornado action based on CFD, characterized in that, Includes the following steps: S1: Referring to the geometric configuration of the tornado laboratory simulation device, a CFD computational domain model of the three-dimensional tornado generator is established. The velocity inlet boundary conditions are constructed using Doppler radar observation data of real tornadoes, and the three-dimensional tornado wind field is obtained through numerical solution. S2: Control the eddy ratio by the inflow angle and control the tornado intensity by the inlet wind speed. Perform multi-condition parameterized simulation on the three-dimensional tornado wind field obtained in step S1 to establish a quantitative relationship between the control parameters and the structural characteristics of the wind field. S3: Place the bridge structure model into the tornado wind field obtained in step S2, perform numerical simulation according to the multi-condition combination of radial position and wind direction angle, and extract the wind pressure coefficient of each pressure measurement point on the bridge structure surface. S4: Compare the wind pressure coefficient obtained in step S3 with the pressure test data of the scaled model to complete the verification.

2. The numerical simulation method for wind load on bridge structures under tornado action based on CFD as described in claim 1, characterized in that, The CFD computational domain model adopts a rotationally symmetric cylindrical computational domain; A velocity boundary condition is applied at the lateral inlet of the computational domain, which is a superposition of tangential and radial velocity components. A no-slip wall boundary condition is applied at the bottom of the computational domain, and a pressure outlet boundary condition is applied at the top outlet. The vortex ratio is controlled by adjusting the ratio of tangential velocity to radial velocity, and the inflow angle is controlled by adjusting the inflow direction angle.

3. The numerical simulation method for wind load on bridge structures under tornado action based on CFD according to claim 2, characterized in that, The velocity inlet boundary conditions constructed using Doppler radar observation data are as follows: The tangential velocity component and the radial velocity component are separated from the radial velocity field of the Doppler radar, and the two are assigned to the lateral inlet of the computational domain in the form of velocity inlet boundary conditions. The maximum tangential velocity and its corresponding characteristic radius in the numerical wind field are consistent with the radar observation value as the criterion for boundary condition calibration.

4. The numerical simulation method for wind load on bridge structures under tornado action based on CFD according to claim 2, characterized in that, The numerical solution is obtained by simultaneously solving the Reynolds averaged NS equation and the RNG k-ε turbulence model, or by using the large eddy simulation method. The computational domain grid is divided using a hybrid structured and unstructured method, with local refinement applied to the tornado vortex core region and the near-surface boundary layer region. The radial and vertical grid sizes of the refined regions are no greater than 1 / 20 of the characteristic radius.

5. The numerical simulation method for wind load on bridge structures under tornado action based on CFD as described in claim 1, characterized in that, The establishment of a quantitative relationship between control parameters and wind field structural characteristics specifically involves: Under various parameter conditions, the vertical distribution of the tornado's maximum tangential velocity, characteristic radius, maximum radial velocity, and axial velocity was extracted respectively. The extracted data were fitted using the Rankine combined vortex model or the Burgers-Rott vortex model to quantify the sensitivity coefficients of the vortex ratio, inflow angle and inlet wind speed to the above-mentioned characteristic quantities, thus forming a quantitative mapping relationship between control parameters and wind field structural characteristic quantities.

6. The numerical simulation method for wind load on bridge structures under tornado action based on CFD as described in claim 5, characterized in that, The eddy ratio ranges from 0.1 to 1.4, the inflow angle ranges from 30° to 75°, and the inlet wind speed is set according to the characteristic wind speed range corresponding to the EF0 to EF5 tornado intensity levels. The combination scheme of control parameters adopts full factorial design or orthogonal experimental design, and each control parameter is iterated one by one at predetermined intervals within the above parameter range.

7. The numerical simulation method for wind load on bridge structures under tornado action based on CFD as described in claim 1, characterized in that, The specific method for placing the bridge structure model into the tornado wind field is as follows: Keeping the boundary conditions of the tornado computational domain unchanged, embedding the geometric entities of the bridge main beam section and bridge deck at the bottom ground of the computational domain according to preset radial position coordinates; refining the mesh of the flow field on and around the bridge surface; after refining, the normal spacing of the first layer of mesh on the bridge surface satisfies the wall function on y... + Value requirements.

8. The numerical simulation method for wind load on bridge structures under tornado action based on CFD as described in claim 7, characterized in that, The radial position is taken as multiple discrete values ​​within the range from the center of the tornado vortex core to the edge of the computational domain, including at the characteristic radius, 2 times the characteristic radius, 3 times the characteristic radius, and 4 times the characteristic radius; The wind direction angle is taken at 15° intervals within the range of 0° to 360°. Under the combined conditions of each radial position and wind direction angle, the average wind pressure and pulsating wind pressure at each pressure measurement point on the bridge structure surface are recorded. The wind pressure coefficient is calculated by taking the dynamic pressure value corresponding to the maximum tangential velocity of the tornado at each pressure measurement section as the reference dynamic pressure.

9. The numerical simulation method for wind load on bridge structures under tornado action based on CFD as described in claim 8, characterized in that, In S3, the wind pressure coefficient of each pressure measuring section is integrated along the bridge axis to obtain the lift coefficient, drag coefficient, and moment coefficient around the centroid of the section, respectively. The maximum value of the above aerodynamic coefficients under all radial positions and wind direction angles is used as the wind load envelope value to form a set of wind load values ​​for tornado resistance design.

10. The numerical simulation method for wind load on bridge structures under tornado action based on CFD according to claim 1, characterized in that, The verification specifically involves conducting pressure tests under equivalent working conditions using a scaled-down model of the main beam of a bridge that is similar to numerical computation geometry, in a tornado simulator or a boundary layer wind tunnel. The wind pressure coefficients at each pressure measurement point obtained from the experiment were compared with the numerical simulation results point by point. The average relative error of the time-averaged wind pressure coefficient at each pressure measurement point not exceeding 15% was used as the criterion for passing the verification. After verification, the wind pressure coefficient of the untested working conditions in step S3 is calculated by replacing the physical test with numerical simulation results.

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