Equivalent calculation method and system for pressure wave of train meeting in tunnel

Abstract

The application relates to the field of railway tunnel aerodynamics, and provides a tunnel train meeting pressure wave equivalent calculation method and system, the method comprising the following steps: establishing a two-dimensional axisymmetric overlapping grid model of two trains running towards each other in a tunnel, monitoring the axial distance between the two train head end surfaces in real time, switching the second train into a hidden state when the distance is less than a critical value to avoid geometric overlap, while retaining virtual motion information of the second train and constructing a local moving momentum source term to be applied to an axial momentum equation to equivalently compensate for meeting additional disturbance; after the meeting is completed, the entity state of the second train is restored to continue solving, and the pressure wave fluctuation results of the surfaces of the two trains and the tunnel wall are output. In this way, the calculation precision of the pressure wave is effectively improved.

Description

Technical Field

[0001] This application relates to the field of railway tunnel aerodynamics technology, specifically to an equivalent calculation method and system for pressure waves caused by trains passing each other in a tunnel. Background Technology

[0002] When a high-speed train travels through a tunnel, the train's front entering the tunnel generates a compression wave at the tunnel entrance, while the rear generates an expansion wave. These compression and expansion waves propagate at the speed of sound within the tunnel and are reflected and superimposed at the tunnel entrance and exit sections, forming a complex vehicle-tunnel coupled pressure wave system. When two high-speed trains travel towards each other and meet in a tunnel, in addition to the compression and expansion waves generated by each train entering the tunnel and the reflected waves at the tunnel entrance, localized additional pressure disturbances are generated between the trains and between the trains and the tunnel walls at the moment of meeting. These additional disturbances, superimposed on the aforementioned propagating wave system, jointly determine the full-time pressure fluctuation characteristics of the train body surface and the tunnel walls. Accurately predicting tunnel meeting pressure waves is of great significance for assessing train aerodynamic loads, designing car body strength, ensuring tunnel structural safety, and optimizing passenger comfort.

[0003] Currently, numerical studies on pressure wave problems caused by train encounters in long tunnels mainly employ one-dimensional unsteady methods. While one-dimensional unsteady methods offer extremely high computational efficiency and can quickly obtain pressure variation trends along the tunnel, they simplify the tunnel into an axial one-dimensional pipe, failing to accurately capture the waveform structure of the pressure wave, the radial flow field distribution, and the local flow details around the train. Consequently, their computational accuracy and waveform resolution are insufficient.

[0004] It is evident that the calculation scheme for the pressure wave of trains meeting in tunnels in the relevant technologies suffers from poor calculation accuracy. Summary of the Invention

[0005] This application aims to address the problem of poor calculation accuracy in the calculation schemes for pressure waves of trains meeting in tunnels in related technologies, and to provide an equivalent calculation method and system for pressure waves of trains meeting in tunnels.

[0006] To solve the above problems, this application is implemented as follows:

[0007] Firstly, this application provides an equivalent calculation method for pressure waves caused by trains meeting in a tunnel, including: A two-dimensional axisymmetric overlapping mesh numerical model is established for two trains running towards each other in a tunnel. The two-dimensional axisymmetric overlapping mesh numerical model includes a tunnel background mesh, a first train motion overlapping mesh, and a second train motion overlapping mesh. The positions of the first and second trains along the tunnel axis are acquired in real time, and the axial distance between the head end face of the first train and the head end face of the second train is calculated. When the axial spacing is less than the preset critical distance, the second train is switched from the solid calculation state to the hidden state; in the hidden state, the solid wall boundary of the second train and the overlapping mesh of the second train motion no longer participate in the overlapping mesh interpolation and flow field solution; While the second train is in a hidden state, the virtual trajectory, virtual head position, virtual tail position, and running speed of the second train are preserved; and based on the relative speed between the first train and the second train, as well as the train blockage ratio, meeting position, and meeting disturbance correction coefficient, a local moving momentum source term is constructed and applied to the tunnel axial momentum equation. When the first train and the second train have completed their intersection and no longer have geometric overlap, the second train is restored from the hidden state to the solid calculation state, so that the solid wall boundary of the second train and the motion overlap mesh of the second train participate in the calculation again. Continue solving until the transient pressure wave propagation process of the train passing through the tunnel is completed, and output the pressure fluctuation results of the first train surface, the second train surface, and the tunnel wall.

[0008] Secondly, this application provides an equivalent calculation system for pressure waves from train encounters within a tunnel, comprising: A module is established to create a two-dimensional axisymmetric overlapping mesh numerical model of two trains running towards each other in a tunnel. The two-dimensional axisymmetric overlapping mesh numerical model includes a tunnel background mesh, a first train motion overlapping mesh, and a second train motion overlapping mesh. The acquisition module is used to acquire the positions of the first train and the second train in the tunnel axis in real time, and to calculate the axial distance between the head end face of the first train and the head end face of the second train. The switching module is used to switch the second train from the solid calculation state to the hidden state when the axial spacing is less than a preset critical distance; in the hidden state, the solid wall boundary of the second train and the overlapping mesh of the second train motion no longer participate in the overlapping mesh interpolation and flow field solution; An application module is constructed to retain the virtual trajectory, virtual head position, virtual tail position, and running speed of the second train while the second train is in a hidden state; and to construct a local moving momentum source term based on the relative speed between the first train and the second train, as well as the train blocking ratio, meeting position, and meeting disturbance correction coefficient, and to apply the local moving momentum source term to the tunnel axial momentum equation. The recovery module is used to restore the second train from the hidden state to the solid calculation state when the first train and the second train have completed their intersection and no longer have geometric overlap, so that the solid wall boundary of the second train and the motion overlap mesh of the second train can re-participate in the calculation. The solution output module is used to continue solving until the transient pressure wave propagation process of the train passing through the tunnel is completed, and outputs the pressure fluctuation results of the first train surface, the second train surface, and the tunnel wall.

[0009] Thirdly, this application provides a terminal device including a processor and a memory, wherein the memory stores a program or instructions executable on the processor, and the program or instructions, when executed by the processor, implement the steps of the method described in the first aspect.

[0010] Fourthly, this application provides a readable storage medium on which a program or instructions are stored, which, when executed by a processor, implement the steps of the method described in the first aspect.

[0011] Fifthly, this application provides a chip including a processor and a communication interface, the communication interface being coupled to the processor, the processor being used to run programs or instructions to implement the steps of the method described in the first aspect.

[0012] In a sixth aspect, this application provides a computer program product stored in a storage medium, the program product being executed by at least one processor to implement the steps of the method described in the first aspect.

[0013] Compared with the prior art, this application has the following beneficial effects: By switching the two trains to a hidden state at the critical distance of their intersection, the geometric conflict problem that the two-dimensional axisymmetric overlapping mesh method cannot calculate the intersection due to the two trains sharing the same axis is solved. On this basis, the additional disturbance of the hidden train during the intersection is equivalently compensated by the local moving momentum source term. Thus, while maintaining the high efficiency advantage of the two-dimensional axisymmetric method, the complete capture of the compression wave of the train entering the tunnel, the expansion wave at the tail, the reflected wave at the tunnel entrance, and the local disturbance of the intersection is achieved. This effectively improves the calculation accuracy of the pressure wave while taking into account the calculation efficiency, and provides a reliable calculation method for the rapid evaluation of pressure wave engineering in tunnel intersections. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a flowchart illustrating an embodiment of the equivalent calculation method for pressure waves from train encounters within a tunnel provided in this application. Figure 2 This is a schematic diagram of a model showing the intersection of two train tunnels according to an embodiment of this application; Figure 3 This is a schematic diagram comparing the simulation results of the pressure wave from a two-dimensional axisymmetric method and a conventional three-dimensional numerical method provided in an embodiment of this application; Figure 4 This is a schematic diagram of the equivalent calculation system for pressure waves of trains meeting in a tunnel according to an embodiment of this application; Figure 5 This is a schematic diagram of the structure of a terminal device provided in an embodiment of this application. Detailed Implementation

[0016] The technical solutions of this application will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0017] The terms "first," "second," etc., used in this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products, or apparatuses. Additionally, the use of "and / or" in this application indicates at least one of the connected objects, such as A and / or B and / or C, representing seven possibilities: including A alone, B alone, C alone, and the presence of both A and B, both B and C, both A and C, and the presence of A, B, and C.

[0018] In this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" or "for example" in this application should not be construed as being more preferred or advantageous than other embodiments or designs. Rather, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0019] The equivalent calculation method for the pressure wave of trains meeting in a tunnel provided in this application is explained below.

[0020] See Figure 1 , Figure 1 This is a flowchart illustrating an embodiment of the equivalent calculation method for pressure waves during train encounters in a tunnel provided in this application. Figure 1 The equivalent calculation method for the pressure wave of trains meeting in the tunnel shown can be executed by terminal equipment such as computers.

[0021] like Figure 1 As shown, the equivalent calculation method for the pressure wave of trains meeting in a tunnel provided in this application may include the following steps: Step 101: Establish a two-dimensional axisymmetric overlapping grid numerical model of two trains running towards each other in a tunnel. The two-dimensional axisymmetric overlapping grid numerical model includes a tunnel background grid, a first train motion overlapping grid, and a second train motion overlapping grid.

[0022] In this embodiment, the three-dimensional train shape can be equivalently represented as a two-dimensional axisymmetric shape rotating around the tunnel axis, based on the distribution of the train's cross-sectional area along its length. That is, non-axisymmetric details of the train's cross-section are ignored, such as pantographs, bogies, and car body edges, retaining only the curve of the equivalent cross-sectional area's variation along the axial direction. This allows the train model to have the same blockage ratio distribution characteristics as a real train in a two-dimensional axisymmetric coordinate system. Simultaneously, the actual tunnel can also be equivalently represented as a two-dimensional axisymmetric circular tube with an equal cross-sectional area, based on the tunnel's cross-sectional area.

[0023] Since the initial compression wave amplitude generated when a train passes through a tunnel mainly depends on the train blockage ratio and the rate of change of the train head volume as it enters the tunnel, the local asymmetric features of the car body have little impact on the principal components of the pressure wave. Therefore, using an axisymmetric body with an equivalent cross-sectional integral distribution to replace the actual train shape has sufficient engineering accuracy.

[0024] In some embodiments, the tunnel background mesh covers the entire interior region of the tunnel, as well as local atmospheric regions outside the tunnel entrance and exit. The tunnel background mesh is a static mesh, which can be divided using structured quadrilateral meshes and can be fined near the tunnel walls to capture the pressure gradient at the walls. Moreover, the axial extent of the tunnel background mesh needs to be long enough to ensure that the compression and expansion waves generated at the tunnel entrance do not propagate to the background mesh boundaries and cause non-physical reflections in the computational time domain.

[0025] In some embodiments, a first train motion overlapping mesh is disposed around the first train and moves with the first train along the tunnel axis at a given speed. The first train motion overlapping mesh is a body-fitted mesh that includes the solid wall of the first train, and the train wall is configured with a no-slip wall boundary condition to simulate the obstruction effect of the train surface on the airflow.

[0026] In some embodiments, a second train motion overlapping grid is disposed around the second train and moves in the opposite direction along the tunnel axis with the second train. The structure of the second train motion overlapping grid is the same as that of the first train motion overlapping grid, and includes the solid wall boundary of the second train.

[0027] It is understood that the geometric parameters of the first train and the second train in this application may be the same or different. That is, the geometric parameters such as the length, cross-sectional integral distribution, and head shape characteristics may be the same or different, and can be determined according to the actual calculation conditions.

[0028] In some embodiments, flow field information can be transferred between the tunnel background grid and the first and second train motion overlapping grids through overlapping grid interpolation techniques; specifically, this includes: Within each time step, the solver first determines the current position of each moving overlapping mesh within the background mesh. Then, using a hole-punching technique, it identifies regions within the background mesh covered by the moving overlapping meshes, marking these background mesh cells as holed cells, which do not participate in the flow field solution. Next, an interpolation boundary is established between the outer boundary of the moving overlapping meshes and the live cells of the background mesh. A contributor cell search algorithm is used to determine the donor cells required for interpolation, and the flow field variable values ​​of the donor cells are interpolated and transferred to the recipient mesh cells. If spatial overlap occurs between two sets of moving overlapping meshes, the flow field information transfer in the overlapping region is handled using the same interpolation mechanism.

[0029] In this embodiment, by constructing a two-dimensional axisymmetric overlapping grid numerical model, the calculation accuracy of pressure waves can be effectively improved compared with the conventional one-dimensional unsteady method.

[0030] Step 102: Obtain the positions of the first train and the second train in the tunnel axis in real time, and calculate the axial distance between the head end face of the first train and the head end face of the second train.

[0031] Since the first and second train motion overlapping grids have been established in step 101, each grid has a defined axial position at each time step. Therefore, by querying the current grid position of the first train motion overlapping grid using the solver, the position of the first train along the tunnel axis can be determined; similarly, by querying the current grid position of the second train motion overlapping grid using the solver, the position of the second train along the tunnel axis can be determined. This position information is automatically updated at each time step as the corresponding motion overlapping grid moves, eliminating the need for additional position sensors or monitoring points.

[0032] In some embodiments, the operating speed of the first train can be set to... The second train's operating speed is The two trains are traveling towards each other. Taking the center of the tunnel entrance section as the origin, and the direction along the tunnel axis towards the inside of the tunnel as the positive X-axis, then at any given moment... axial position of the head end face of the first train Axial position of the head end face of the second train They can be represented as:

[0033]

[0034] In the formula, This represents the initial axial position of the head face of the first train. This represents the initial axial position of the head face of the second train. Wherein, and The settings can be configured based on actual application needs, and no specific limitations are made here.

[0035] In some embodiments, the axial spacing is calculated using the following formula:

[0036] In the formula, for The axial distance between the head end face of the first train and the head end face of the second train at any given time. for The position of the head end face of the first train at that moment, i.e. The axial position of the first train at any given time. for The position of the head end face of the second train at that time, i.e. The axial position of the second train at that moment.

[0037] The two trains were moving towards each other before they met. and They are close to each other, therefore It gradually decreases over time. The solver calculates at each time step. The calculation result will be used as the basis for determining whether to perform a state transition in subsequent step 103: when When the distance exceeds the preset critical distance, the two trains continue to maintain the entity calculation state; when When the distance is less than or equal to the preset critical distance, the state switching operation in step 103 is executed.

[0038] In some embodiments, a schematic diagram of the two train tunnels meeting is shown below. Figure 2 As shown.

[0039] Step 103: When the axial spacing is less than the preset critical distance, the second train is switched from the solid calculation state to the hidden state; in the hidden state, the solid wall boundary of the second train and the overlapping mesh of the second train motion no longer participate in the overlapping mesh interpolation and flow field solution.

[0040] In this embodiment, when the axial spacing is less than the preset critical distance, the second train is switched from the solid calculation state to the hidden state, which can avoid the two trains from geometrically overlapping and meshing due to sharing the same axis in the two-dimensional axisymmetric model.

[0041] In some embodiments, the preset critical distance is a distance threshold that triggers state switching, and its value needs to meet the following conditions: when the distance between the head end faces of the two trains is greater than the preset critical distance, the motion overlapping meshes of the two trains do not overlap spatially, and the overlapping mesh interpolation can be performed normally; when the distance between the head end faces of the two trains is less than or equal to the preset critical distance, if the two trains continue to be in the solid calculation state, the motion overlapping meshes of the two trains will spatially intrude and cross, which will cause the overlapping mesh interpolation to fail.

[0042] In some embodiments, the preset critical distance can be determined comprehensively based on the train head length, overlapping mesh size, time step, and computational stability. The longer the train head, the larger the required critical distance; the larger the overlapping mesh size, the larger the required critical distance; the larger the time step, the more the required critical distance should be appropriately increased to ensure that the state switch is completed before a mesh conflict occurs.

[0043] In some embodiments, the preset critical distance ranges from 1m to 2m, such as 1.5m.

[0044] In some embodiments, the preset critical distance can be adjusted within the above range according to the actual grid system and calculation parameters to ensure that the motion overlapping grids of the two trains have not yet spatially overlapped when the state is switched.

[0045] In some embodiments, when the axial spacing is determined to be less than a preset critical distance, the solver performs the following state switching operation: The second train is switched from solid calculation state to hidden state. In solid calculation state, the solid wall boundary of the second train participates in the flow field solution as a no-slip wall boundary, and the moving overlapping mesh of the second train participates in the hole-punching, interpolation, and flow field solution of the overlapping mesh. After switching to hidden state, the solid wall boundary of the second train no longer participates in the flow field solution as a wall boundary, and the moving overlapping mesh of the second train no longer participates in the overlapping mesh interpolation and flow field solution. Specifically, in the overlapping mesh interpolation process, the solver marks all mesh elements of the moving overlapping mesh of the second train as inactive elements, so that they do not participate in hole-punching judgment, donor element search, or interpolation calculation, and at the same time, the solid wall boundary of the second train is removed from the wall boundary conditions.

[0046] In this embodiment, when the axial spacing is less than a preset critical distance, the second train is switched from a solid calculation state to a hidden state. The second train no longer appears as a solid wall in the two-dimensional axisymmetric overlapping mesh numerical model. Therefore, the two trains no longer have the possibility of geometric overlap, and the overlapping mesh interpolation algorithm will not fail due to the spatial intrusion of two sets of moving overlapping meshes. The first train continues to maintain its solid calculation state, and its moving overlapping mesh normally participates in overlapping mesh interpolation and flow field solving. The main pressure waves formed by the compression wave from the train entering the tunnel, the expansion wave at the tail, and the reflection wave at the tunnel entrance continue to propagate in the computational domain.

[0047] It should be noted that although the second train is switched to a hidden state, this step only provides a prerequisite for equivalent compensation using momentum source terms in the subsequent step 104. During the hidden state, the local compression and additional pressure disturbance of the flow field in the intersection area caused by the second train will be equivalently compensated by the locally moving momentum source terms constructed in step 104.

[0048] Step 104: While the second train is in a hidden state, retain the virtual trajectory, virtual head position, virtual tail position and running speed of the second train; and construct a local moving momentum source term based on the relative speed between the first train and the second train, as well as the train blocking ratio, meeting position and meeting disturbance correction coefficient, and apply the local moving momentum source term to the tunnel axial momentum equation.

[0049] In this embodiment, during the period when the second train is hidden, by constructing a local moving momentum source term and applying it to the tunnel axial momentum equation, the additional pressure disturbance missing in the intersection section after the second train is hidden can be equivalently compensated.

[0050] Specifically, after the second train is switched to a hidden state, its physical wall boundaries and moving overlapping meshes no longer participate in the flow field solution. However, the physical impact of the second train on the tunnel flow field during the intersection process needs to be compensated for in other ways. Therefore, during the hidden state, the virtual trajectory, virtual head position, virtual tail position, and running speed of the second train are retained. Specifically, at each time step, the solver still calculates the virtual spatial position of the second train at the current moment, including the virtual head end face position, virtual tail end face position, and virtual trajectory, based on the second train's initial position, running speed, and direction of motion. The above virtual information is only used to determine the location and range of the local moving momentum source term and does not represent the actual existence of the second train entity in the flow field.

[0051] In some embodiments, during the period when the second train is concealed, its local compression and additional pressure disturbance effects on the tunnel flow field can be equivalently replaced by a moving momentum source term. Essentially, this source term adds a local, moving momentum source distribution to the tunnel axial momentum equation, simulating the displacement and obstruction of airflow by the second train body in the meeting region. The intensity of this source term is related to factors such as the relative speed of the two trains, the train blockage ratio, and the meeting position. Its spatial distribution exhibits a Gaussian concentration along the tunnel axial direction and moves with the virtual trajectory of the second train.

[0052] In some embodiments, the expression for the local moving momentum source term is:

[0053]

[0054] In the formula, for The spatial coordinates of the tunnel axis at that time are The corresponding local moving momentum source term, For smooth start-stop function, The source term direction symbol, This is the rendezvous disturbance correction factor. The dynamic pressure is the relative motion pressure between the first train and the second train. air density, The relative speed between the first train and the second train. The train congestion ratio, The length of the source term's action. The virtual rendezvous center location, The width of the source term spatial distribution.

[0055] Among them, the smooth start-stop function is used to control the smooth loading and unloading of source items over time, avoiding pressure surges and numerical divergence caused by sudden increases or decreases in source items.

[0056] In some embodiments, the smooth start-stop function has a smooth rising segment at the moment when the source term begins to be applied and a smooth falling segment at the moment when the source term stops to be applied.

[0057] The direction sign of the source term is consistent with the direction of motion of the second train; specifically, when the second train moves along the positive X-axis, When the second train moves along the negative X-axis, This symbol ensures that the direction of the source term's obstruction of the airflow corresponds to the direction of motion of the second train.

[0058] The intersection perturbation correction coefficient is a dimensionless empirical coefficient used to correct the difference between the two-dimensional axisymmetric model and the actual three-dimensional situation. Its value ranges from 0.01 to 0.30.

[0059] In some embodiments, the rendezvous disturbance correction coefficient can be obtained by calibration using three-dimensional numerical simulation results or actual vehicle test results: using the peak pressure in the rendezvous area measured by three-dimensional numerical simulation or actual vehicle test as a reference, the value of the rendezvous disturbance correction coefficient is adjusted so that the pressure amplitude of the two-dimensional axisymmetric equivalent calculation result is consistent with the reference result near the rendezvous moment.

[0060] The above relative motion dynamic pressure It is used to characterize the dynamic pressure effect of the relative motion of two trains on the airflow.

[0061] In some embodiments, the train blockage ratio is the ratio of the equivalent cross-sectional area of ​​the train to the cross-sectional area of ​​the tunnel.

[0062] In some embodiments, the spatial distribution width of the source terms is used to control the degree of spatial concentration of the source terms near the intersection center. The smaller the value, the more concentrated the source terms are near the intersection center; the larger the value, the wider the influence range of the source terms.

[0063] In some embodiments, to avoid the introduction of non-physical oscillations due to the source terms being confined to a single computational grid, the term space distribution width is not less than 3 times the axial grid size.

[0064] In some embodiments, the range of the source term action length can be set to 2. Up to 4 This ensures that the source terms decay smoothly to a negligible level on both sides of the intersection center.

[0065] In some embodiments, the constructed local moving momentum source term The axial momentum equation is applied to the two-dimensional axisymmetric unsteady compressible governing equations. Specifically, during the solution process at each time step, the solver traverses all computational cells corresponding to the tunnel axial momentum equation, determining whether each computational cell is located within the region of influence of the local source term. When the axial coordinate of a certain computational cell... satisfy At that time, the local moving momentum source term is added to the right-hand side of the axial momentum equation of the unit. When the axial coordinate of the calculation unit If the above conditions are not met, the unit does not apply the intersection momentum source term.

[0066] It should be noted that the local moving momentum source term indirectly induces the pressure disturbance at the intersection by changing the local axial momentum distribution near the intersection region, rather than directly forcing values ​​onto the pressure variables. This approach is consistent with the solution logic of the compressible flow control equations, that is, the source term in the axial momentum equation changes the local velocity and density distribution, and then the pressure response is naturally generated through the coupling solution of the continuity equation and the energy equation, which helps to reduce the risk of numerical divergence that may be caused by direct forced assignment.

[0067] To avoid abrupt changes in the flow field when the second train switches from the physical calculation state to the hidden state, and to prevent pressure abrupt changes and numerical divergences caused by sudden increases or decreases in the source term during the start-up and shutdown of the local moving momentum source term, a smooth start-stop function is adopted for the source term. Control is implemented. Smooth start / stop function. At the moment when the source term begins to be applied The value of the nearby term smoothly increases from 0 to 1 at the moment when the source term stops being applied. The value of the source term smoothly decreases from 1 to 0. After the smooth start-stop process, the source term is complete and continuous in time, without any abrupt changes, thus ensuring computational stability.

[0068] In some embodiments, a transition time is enabled. and closing transition time The relative speed and critical distance between the two trains are determined, and their values ​​are no greater than the time required for the head faces of the two trains to move from the preset critical distance to the meeting position, so as to ensure that the source term smoothly exits after the meeting disturbance completely disappears. In a specific embodiment, the relative speed between the two trains is approximately 194.44 m / s, and the time scale corresponding to a 2 m distance between the head faces of the two trains is approximately 0.010 s. The opening transition time and closing transition time are each taken as no more than 5 to 10 time steps greater than this time scale.

[0069] In some embodiments, smooth start / stop functions It can be represented as:

[0070] in, The time at which the source term begins to be applied. When the source term stops applying, Enable transition time for the source item. The transition time is set to close the source item.

[0071] In this embodiment, through the aforementioned source term construction and application, the local compression and additional pressure disturbance effects on the tunnel flow field within the intersection interval caused by the second train being hidden are effectively compensated. Simultaneously, the stability of the numerical calculation is ensured through smooth start-stop control and indirect induction. While the second train is hidden, the first train continues to participate in the flow field solution as a physical entity. The main pressure wave formed by the compression wave from the two trains entering the tunnel, the expansion wave at the tail, and the reflected wave from the tunnel entrance continues to propagate in the computational domain. The local moving momentum source term is used to supplement the physical effects of the additional disturbance during intersection.

[0072] Step 105: When the first train and the second train have completed their intersection and no longer have geometric overlap, restore the second train from the hidden state to the solid calculation state, so that the solid wall boundary of the second train and the motion overlap mesh of the second train participate in the calculation again.

[0073] In this embodiment, after the second train is restored from the hidden state to the solid calculation state, the solver re-marks all grid cells of the overlapping grid of the second train as active cells, so that they can participate again in the hole-punching judgment, donor cell search and interpolation calculation of the overlapping grid. At the same time, the solid wall boundary of the second train is reset to the no-slip wall boundary condition, so that it can participate again in the flow field solution.

[0074] In some embodiments, to ensure a smooth transition of the flow field during state recovery and to avoid non-physical oscillations in the local flow field caused by the sudden appearance of the second train boundary, a weighted transition processing is performed on the computational region surrounding the second train during the recovery process based on the current flow field. Specifically, within the initial several time steps after the second train recovers to its physical computational state, the flow field variables in the computational region surrounding the second train are spatially weighted and smoothed to ensure a smooth transition between the flow field at the newly recovered physical wall boundary and the surrounding background flow field, with non-physical disturbances gradually attenuating to a negligible level.

[0075] The specific implementation of the weighted transition includes, but is not limited to: in the first time step after recovery, setting the flow field variables such as pressure, density, and velocity components around the second train as a weighted average between the background grid interpolation results and the wall boundary conditions; in subsequent time steps, gradually increasing the weight of the wall boundary conditions to allow the flow field to naturally transition to a steady-state solution. The transition time steps, weighting coefficients, and other parameters of the above transition processing can be adjusted according to the actual calculation conditions and grid system.

[0076] After the second train resumes its solid computation state, both trains participate in the flow field solution using solid wall boundaries. At this point, the two trains have completed their intersection and are moving away from each other. There is no spatial overlap between the motion overlapping meshes of the two trains, and the two-dimensional axisymmetric overlapping mesh model returns to normal operation. The main pressure wave formed by the compression wave from the two trains entering the tunnel, the expansion wave from the tail, and the reflected wave from the tunnel entrance continues to propagate in the computational domain. The additional disturbance from the intersection has been compensated for in step 104 by the local moving momentum source term, and no further source term processing is required in subsequent calculations.

[0077] Step 106: Continue solving until the transient pressure wave propagation process of the train passing through the tunnel is completed, and output the pressure fluctuation results of the first train surface, the second train surface, and the tunnel wall.

[0078] After the second train resumes its solid computation state, both trains are now in solid computation state and have moved away from each other in space. There is no overlapping region between the motion overlapping meshes of the two trains, and the overlapping mesh interpolation algorithm runs normally. The solver continues to solve the two-dimensional axisymmetric unsteady compressible control equations over time until the total computation time reaches the preset termination time.

[0079] During the continued solution phase, the overlapping meshes of the two trains continue to move along the tunnel axis at their respective velocities until each train has completely exited the tunnel. The solver iteratively solves the continuity equation, axial momentum equation, radial momentum equation, and energy equation at each time step to obtain the flow field distribution at each moment within the entire computational domain. As the trains continue to move, the main pressure waves formed by the compression wave upon entering the tunnel, the expansion wave at the tail, and the reflected wave at the tunnel entrance continue to propagate, reflect, and superimpose within the computational domain, forming a complete vehicle-tunnel coupled pressure wave system.

[0080] The equivalent calculation method for pressure waves from train encounters in tunnels provided in this application solves the geometric conflict problem of the two-dimensional axisymmetric overlapping mesh method, which cannot calculate the encounter due to the two trains sharing the same axis, by switching the two trains to a hidden state at the critical distance of the encounter. On this basis, the method compensates for the additional disturbances of the hidden trains during the encounter by using the local moving momentum source term. Thus, while maintaining the high efficiency advantage of the two-dimensional axisymmetric method, it achieves complete capture of the compression wave of the train entering the tunnel, the expansion wave at the tail, the reflected wave at the tunnel entrance, and the local disturbances during the encounter. This effectively improves the calculation accuracy of pressure waves while also taking into account the calculation efficiency, providing a reliable calculation means for the rapid engineering assessment of pressure waves from tunnel encounters.

[0081] Figure 3The results comparing the two-dimensional axisymmetric method for measuring train surface pressure fluctuations provided in this application with conventional three-dimensional numerical methods are presented. It can be seen that the two methods show good consistency in the main peaks, valleys, and overall pressure fluctuation trends, indicating that the two-dimensional axisymmetric equivalent rapid calculation method can effectively capture the main pressure wave characteristics such as train entry compression waves, tail expansion waves, and tunnel entrance reflection waves. Some differences still exist between the two-dimensional axisymmetric method and the three-dimensional method in local time periods. These differences can be used to calibrate the intersection disturbance correction coefficients, thereby further improving the equivalent prediction accuracy of local pressure disturbances during intersections.

[0082] See Figure 4 , Figure 4 This is a schematic diagram of the equivalent calculation system for pressure waves from train encounters within a tunnel, provided in one embodiment of this application. Figure 4 As shown, system 400 includes: Module 401 is used to establish a two-dimensional axisymmetric overlapping mesh numerical model of two trains running towards each other in a tunnel. The two-dimensional axisymmetric overlapping mesh numerical model includes a tunnel background mesh, a first train motion overlapping mesh, and a second train motion overlapping mesh. The acquisition module 402 is used to acquire the positions of the first train and the second train in the tunnel axis in real time, and to calculate the axial distance between the head end face of the first train and the head end face of the second train. The switching module 403 is used to switch the second train from the solid calculation state to the hidden state when the axial spacing is less than the preset critical distance; in the hidden state, the solid wall boundary of the second train and the overlapping mesh of the second train motion no longer participate in the overlapping mesh interpolation and flow field solution; The construction application module 404 is used to retain the virtual motion trajectory, virtual head position, virtual tail position and running speed of the second train while the second train is in a hidden state; and to construct a local moving momentum source term based on the relative speed between the first train and the second train, as well as the train blocking ratio, meeting position and meeting disturbance correction coefficient, and to apply the local moving momentum source term to the tunnel axial momentum equation. The recovery module 405 is used to restore the second train from the hidden state to the solid calculation state when the first train and the second train have completed their intersection and no longer have geometric overlap, so that the solid wall boundary of the second train and the motion overlap mesh of the second train can participate in the calculation again. The solution output module 406 is used to continue solving until the transient pressure wave propagation process of the entire train passing through the tunnel is completed, and outputs the pressure fluctuation results of the first train surface, the second train surface and the tunnel wall.

[0083] Optionally, the axial spacing is calculated using the following formula:

[0084] In the formula, for The axial distance between the head end face of the first train and the head end face of the second train at any given time. for The position of the head end face of the first train at that moment. for The position of the head end face of the second train at that moment.

[0085] Optionally, the expression for the local moving momentum source term is:

[0086]

[0087] In the formula, for The spatial coordinates of the tunnel axis at that time are The corresponding local moving momentum source term, For smooth start-stop function, The source term direction symbol, This is the rendezvous disturbance correction factor. The dynamic pressure is the relative motion pressure between the first train and the second train. air density, The relative speed between the first train and the second train. The train congestion ratio, The length of the source term's action. The virtual rendezvous center location, The width of the source term spatial distribution.

[0088] Optionally, the spatial distribution width of the source term is not less than three times the axial grid size, and the range of the effective length of the source term is 2. Up to 4 .

[0089] Optionally, the smooth start-stop function has a smooth rising segment when the source term begins to be applied and a smooth falling segment when the source term stops being applied.

[0090] The equivalent calculation system for pressure waves during train encounters in tunnels provided in this application can achieve the calculation of the pressure waves described in this application. Figure 1 The various processes in the method embodiments, and the ways to achieve the same beneficial effects, will not be repeated here to avoid repetition.

[0091] like Figure 5As shown, this application also provides a terminal device, including a processor 501 and a memory 502. The memory 502 stores a program or instructions that can run on the processor 501. When the program or instructions are executed by the processor 501, they implement the various steps of the above-described equivalent calculation method embodiment for the pressure wave of trains meeting in the tunnel, and can achieve the same technical effect. To avoid repetition, they will not be described again here.

[0092] It should be noted that the terminal device in this application can be a terminal or other devices besides a terminal. For example, the terminal device can be a tablet computer, a laptop computer, etc., and this application does not make any specific limitation.

[0093] This application also provides a readable storage medium storing a program or instructions that, when executed by a processor, implements the various processes of the above-described equivalent calculation method embodiment for the pressure wave of trains meeting in a tunnel, and achieves the same technical effect. To avoid repetition, these will not be described again here.

[0094] The processor is the processor in the terminal device described in the above embodiments. The readable storage medium includes a computer-readable storage medium, such as a computer read-only memory (Read-Only Memory). Only memory (ROM), random access memory (RAM), magnetic disks or optical disks, etc.

[0095] This application also provides a chip, which includes a processor and a communication interface. The communication interface is coupled to the processor. The processor is used to run programs or instructions to implement the various processes of the above-described equivalent calculation method embodiment for pressure waves of trains meeting in tunnels, and can achieve the same technical effect. To avoid repetition, it will not be described again here.

[0096] It should be understood that the chip mentioned in this application may also be referred to as a system-on-a-chip, system chip, chip system, or system-on-a-chip, etc.

[0097] This application provides a computer program product, which is stored in a storage medium and executed by at least one processor to implement the various processes of the equivalent calculation method embodiment for the pressure wave of trains meeting in a tunnel as described above, and can achieve the same technical effect. To avoid repetition, it will not be described again here.

[0098] It should be noted that, in this document, 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 that element. Furthermore, it should be noted that the scope of the methods and apparatuses in the embodiments of this application is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. Additionally, features described with reference to certain examples may be combined in other examples.

[0099] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a computer software product, which is stored in a storage medium (such as a read-only memory). The device includes a number of instructions in a ROM (random access memory), RAM (magnetic disk), or optical disk to cause a terminal (which may be a computer, server, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0100] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. An equivalent calculation method for pressure waves from train encounters within a tunnel, characterized in that, include: A two-dimensional axisymmetric overlapping mesh numerical model is established for two trains running towards each other in a tunnel. The two-dimensional axisymmetric overlapping mesh numerical model includes a tunnel background mesh, a first train motion overlapping mesh, and a second train motion overlapping mesh. The positions of the first and second trains along the tunnel axis are acquired in real time, and the axial distance between the head end face of the first train and the head end face of the second train is calculated. When the axial spacing is less than the preset critical distance, the second train is switched from the physical calculation state to the hidden state; In the hidden state, the solid wall boundary of the second train and the overlapping mesh of the second train motion no longer participate in the overlapping mesh interpolation and flow field solution; While the second train is in a hidden state, the virtual trajectory, virtual head position, virtual tail position, and running speed of the second train are preserved; and based on the relative speed between the first train and the second train, as well as the train blockage ratio, meeting position, and meeting disturbance correction coefficient, a local moving momentum source term is constructed and applied to the tunnel axial momentum equation. When the first train and the second train have completed their intersection and no longer have geometric overlap, the second train is restored from the hidden state to the solid calculation state, so that the solid wall boundary of the second train and the motion overlap mesh of the second train participate in the calculation again. Continue solving until the transient pressure wave propagation process of the train passing through the tunnel is completed, and output the pressure fluctuation results of the first train surface, the second train surface, and the tunnel wall.

2. The method according to claim 1, characterized in that, The axial spacing is calculated using the following formula: In the formula, for The axial distance between the head end face of the first train and the head end face of the second train at any given time. for The position of the head end face of the first train at that moment. for The position of the head end face of the second train at that moment.

3. The method according to claim 1, characterized in that, The expression for the local moving momentum source term is: In the formula, for The spatial coordinates of the tunnel axis at that time are The corresponding local moving momentum source term, For smooth start-stop function, The source term direction symbol, This is the rendezvous disturbance correction factor. The dynamic pressure is the relative motion pressure between the first train and the second train. air density, The relative speed between the first train and the second train. The train congestion ratio, The length of the source term's action. The virtual rendezvous center location, The width of the source term spatial distribution.

4. The method according to claim 3, characterized in that, The spatial distribution width of the source term is not less than 3 times the axial grid size, and the range of the effective length of the source term is 2. Up to 4 .

5. The method according to claim 3, characterized in that, The smooth start-stop function has a smooth rising segment when the source term begins to be applied and a smooth falling segment when the source term stops being applied.

6. An equivalent calculation system for pressure waves from train encounters within a tunnel, characterized in that, include: A module is established to create a two-dimensional axisymmetric overlapping mesh numerical model of two trains running towards each other in a tunnel. The two-dimensional axisymmetric overlapping mesh numerical model includes a tunnel background mesh, a first train motion overlapping mesh, and a second train motion overlapping mesh. The acquisition module is used to acquire the positions of the first train and the second train in the tunnel axis in real time, and to calculate the axial distance between the head end face of the first train and the head end face of the second train. The switching module is used to switch the second train from the physical calculation state to the hidden state when the axial spacing is less than a preset critical distance; In the hidden state, the solid wall boundary of the second train and the overlapping mesh of the second train motion no longer participate in the overlapping mesh interpolation and flow field solution; An application module is constructed to retain the virtual trajectory, virtual head position, virtual tail position, and running speed of the second train while the second train is in a hidden state; and to construct a local moving momentum source term based on the relative speed between the first train and the second train, as well as the train blocking ratio, meeting position, and meeting disturbance correction coefficient, and to apply the local moving momentum source term to the tunnel axial momentum equation. The recovery module is used to restore the second train from the hidden state to the solid calculation state when the first train and the second train have completed their intersection and no longer have geometric overlap, so that the solid wall boundary of the second train and the motion overlap mesh of the second train can re-participate in the calculation. The solution output module is used to continue solving until the transient pressure wave propagation process of the train passing through the tunnel is completed, and outputs the pressure fluctuation results of the first train surface, the second train surface, and the tunnel wall.

7. The system according to claim 6, characterized in that, The axial spacing is calculated using the following formula: In the formula, for The axial distance between the head end face of the first train and the head end face of the second train at any given time. for The position of the head end face of the first train at that moment. for The position of the head end face of the second train at that moment.

8. The system according to claim 6, characterized in that, The expression for the local moving momentum source term is: In the formula, for The spatial coordinates of the tunnel axis at that time are The corresponding local moving momentum source term, For smooth start-stop function, The source term direction symbol, This is the rendezvous disturbance correction factor. The dynamic pressure is the relative motion pressure between the first train and the second train. air density, The relative speed between the first train and the second train. The train congestion ratio, The length of the source term's action. The virtual rendezvous center location, The width of the source term spatial distribution.

9. The system according to claim 8, characterized in that, The spatial distribution width of the source term is not less than 3 times the axial grid size, and the range of the effective length of the source term is 2. Up to 4 .

10. The system according to claim 8, characterized in that, The smooth start-stop function has a smooth rising segment when the source term begins to be applied and a smooth falling segment when the source term stops being applied.

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