Ice surface lake has pressure pipeline flow fast calculation method, system, equipment and storage medium

Abstract

The application discloses an ice surface lake pressure pipeline flow rapid calculation method, system and device, equipment and a storage medium, belongs to the ice lake breaching risk simulation and disaster prevention and mitigation technical field, including: obtaining basic data; constructing temperature-dependent ice creep coefficient, and calculating effective driving water head, overburden ice pressure and water pressure in the pipeline; establishing an ice pipeline pressure flow control equation; forming a coupled ordinary differential equation set, and solving; identifying the main flood discharge termination time and outputting the result. The application simplifies the calculation process of the ice surface lake-ice pipeline coupling system under the premise of ensuring the accuracy of the main physical process description, improves the simulation efficiency and automation degree; at the same time, fully considers the key physical mechanisms such as pressure turbulent flow, ablation expansion, ice creep closure and water balance, can better reflect the evolution law of the ice surface lake discharge process, has high calculation precision, and provides technical support for ice lake disaster risk assessment, monitoring and early warning and rapid simulation analysis of the ice lake discharge process.

Description

Technical Field

[0001] This invention belongs to the field of glacial lake outburst risk simulation and disaster prevention and mitigation technology, and particularly relates to a rapid calculation method, system, equipment and storage medium for pressurized pipeline flow in glacial lakes. Background Technology

[0002] Glacial lake outflow is a typical hydrodynamic process in high-altitude glacial regions and a core mechanism triggering glacial lake outburst floods. Its evolution is controlled by the coupling of three core physical processes: pressurized flow through subglacial channels, frictional thermal erosion of water flow, and ice creep closure. Accurate calculation of glacial lake outflow is of irreplaceable importance for glacial lake stability assessment, dynamic water volume monitoring, outburst risk early warning, and downstream disaster prevention and mitigation.

[0003] Traditional methods for calculating the discharge of glacial lakes mainly rely on empirical formulas, simplified steady-state calculations, or open channel flow assumptions. They do not fully consider the real flow characteristics of pressurized turbulent flow in subglacial pipes, ignore the nonlinear physical mechanism of temperature-dependent ice creep behavior coupled with frictional heat erosion, and cannot automatically identify the termination time of flood discharge. This results in insufficient accuracy in discharge process calculations, distortion of flow process lines, and large errors in determining the start and end times of floods, making it difficult to meet the engineering needs of rapid calculation and real-time disaster early warning in remote glacial lake areas. Summary of the Invention

[0004] The purpose of this invention is to provide a method, system, equipment, and storage medium for rapid calculation of pressurized pipeline flow in icy lakes, in order to solve the problem of insufficient accuracy in the calculation of main outflow in icy lakes in the prior art.

[0005] The embodiments of this application implement a method for rapid calculation of pressurized pipeline flow in an ice-covered lake as follows: S01. Obtain basic data; S02. Construct the temperature-dependent ice creep coefficient and calculate the effective driving head, overlying ice pressure and water pressure inside the pipe; S03. Establish the control equations for pressurized flow in sub-ice pipelines; S04. Establish the dynamic evolution equation of the pipeline; S05. Establish the water balance equation for the ice surface lake; S06. Combine the pressurized flow control equations, pipeline dynamic evolution equations, and water balance equations to form a set of coupled ordinary differential equations, and solve them. S07. Identify the moment when the main flood discharge terminates and output the result.

[0006] Optionally, in some embodiments of this application, basic data of the ice lake, the sub-ice pipeline, and the ice layer are obtained. The basic data includes one or more of the following: ice lake area, initial lake surface water level elevation, initial pipeline radius, pipeline length, inlet elevation, outlet elevation, ice thickness, and ice temperature.

[0007] Optionally, in some embodiments of this application, the temperature-dependent ice creep coefficient is calculated based on Glen's law of ice flow: ; In the formula, The creep coefficient of ice; Glen is the pre-coefficient; The activation energy of ice; It is the gas constant; Kelvin value for ice temperature; and / or The formula for calculating the effective driving head is as follows: ; In the formula, To effectively drive the water head; For the force of the incoming water; For export water power; The density of water; It is the acceleration due to gravity; ; ; In the formula, For the force of the incoming water; For export water power; The density of ice; The density of water; It is the acceleration due to gravity; The ice is thick; This refers to the lake's water level elevation. For the export elevation; and / or The formulas for the pressure of the overlying ice and the water pressure inside the pipe are as follows: ; ; In the formula, The pressure of the overlying ice; The water pressure inside the pipe; The density of ice; The density of water; It is the acceleration due to gravity; The ice is thick; This refers to the lake's water level elevation. This is the entrance elevation.

[0008] Optionally, in some embodiments of this application, the governing equations for pressurized flow in sub-ice pipelines based on the Darcy-Weisbach formula are established as follows: ; ; ; ; In the formula: The flow velocity in the pipe; For pipeline flow rate; It is the Reynolds number; The viscosity of water during motion; It is the acceleration due to gravity; The diameter of the pipe; To effectively drive the water head; The coefficient of friction; This refers to the length of the pipe. For the pipe radius; and / or The dynamic evolution of the pipeline is controlled by the closed-loop coupling of water flow frictional thermal erosion expansion and ice effective pressure creep, as shown in the formula: ; ; ; ; In the formula, This represents the rate of erosion expansion; The creep closure rate; This represents the net rate of change of the pipeline radius. For effective pressure; The hydraulic potential gradient; The density of ice; The latent heat of ice melting; The pressure of the overlying ice; The water pressure inside the pipe; The Glen stress index; For pipeline flow rate; Where the pipe radius is; The creep coefficient of ice; t is the simulation time; and / or The water balance equation for the frozen lake is: ; In the formula, The rate of change of lake surface water level elevation; This refers to the lake's water level elevation. The area of ​​the frozen lake; For pipeline flow rate; t is the simulation time; and / or The compressive flow control equations for the subglacial pipeline, the pipeline dynamic evolution equations, and the ice surface lake water balance equations are coupled to construct the following system with pipeline radius R and lake water level H as variables. l The system consists of a set of coupled ordinary differential equations for the system's state variables: ; In the formula: Where the pipe radius is; This refers to the lake's water level elevation. For pipeline flow rate; The hydraulic potential gradient; The creep coefficient of ice; The pressure of the overlying ice; The water pressure inside the pipe; The Glen stress index; t represents the area of ​​the frozen lake; t represents the simulation time.

[0009] Optionally, in some embodiments of this application, the initial pipe flow velocity is estimated based on the effective driving head, the corresponding Reynolds number is calculated, the friction coefficient is updated based on the Reynolds number, and the pipe flow velocity is recalculated using the updated friction coefficient; the above steps are repeated until the results of two adjacent calculations meet the preset convergence condition. ; in, The flow velocity in the pipe obtained in the k-th iteration is... Let be the pipe flow rate in the (k+1)th iteration. For the preset convergence threshold; and / or Through the above two state variables and The resulting set of binary coupled ordinary differential equations updates intermediate computational quantities in real time at each time step and uses the RK45 adaptive step-size algorithm for numerical integration to obtain time series results including simulation time, pipe radius, lake surface water level elevation, pipe flow rate, pipe velocity, effective driving head, effective pressure, melting expansion rate, creep closure rate, and net change rate of pipe radius. This allows us to obtain the dynamic evolution results of the entire process of ice lake discharge.

[0010] Optionally, in some embodiments of this application, the melting expansion rate and creep closure rate at each time point are compared based on the time series results to determine the termination time of the main flood discharge.

[0011] Optionally, in some embodiments of this application, the criterion for determining the termination time of the main flood discharge is: ; In the formula, Where the pipe radius is; t is the simulation time; This represents the rate of erosion expansion; The creep closure rate; This is the empirical stability coefficient; Based on the above determination, the time when the main flood discharge ends is obtained. And extract the time series and flood feature values ​​corresponding to that moment; The time series includes one or more of the following: simulation time, pipe radius, lake surface elevation, pipe flow rate, pipe velocity, erosion expansion rate, creep closure rate, net pipe change rate, effective pressure, and effective driving head. Flood characteristic values ​​include one or more of the following: peak flow, total discharge, lake level drop, termination time of the main flood discharge, pipe radius at the termination of the main flood discharge, and lake surface elevation at the termination of the main flood discharge.

[0012] Accordingly, embodiments of this application also provide a rapid calculation system for pressurized pipeline flow in ice-covered lakes, including: The basic data module is used to obtain basic data; The ice creep coefficient module is used to construct the temperature-dependent ice creep coefficient and calculate the effective driving head, overlying ice pressure, and water pressure inside the pipe. The module for controlling the compressive flow in sub-ice pipelines is used to establish the control equations for the compressive flow in sub-ice pipelines. The pipeline dynamic evolution equation module is used to establish pipeline dynamic evolution equations. The module for water balance equations of ice-covered lakes is used to establish water balance equations for ice-covered lakes. The solution module is used to simultaneously establish the pressurized flow control equations, pipeline dynamic evolution equations, and water balance equations, forming a coupled set of ordinary differential equations, and then solve them. The identification and output module identifies the termination time of the main flood discharge and outputs the result.

[0013] Accordingly, embodiments of this application also provide a computer device, including a storage device and a processor, wherein the storage device stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method described above.

[0014] Accordingly, embodiments of this application also provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method described above.

[0015] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: This invention, based on fundamental data of ice-covered lakes, subglacial pipelines, and ice layers, and combining Nye pipeline stability theory, the Darcy-Weisbach pressurized flow model, the melting-closure competition mechanism, and lake water balance equations, constructs a coupled computational framework for pressurized pipeline flow in ice-covered lakes. By establishing a physical parameter system, constructing a set of governing equations, employing an adaptive numerical solution method, and automatically identifying the termination time of the main flood discharge, it achieves rapid simulation of the ice-covered lake discharge process and calculation of flood process characteristic parameters. Compared with existing technologies, this invention simplifies the computational process of the ice-covered lake-subglacial pipeline coupled system while ensuring the accuracy of the description of the main physical processes, improving simulation efficiency and automation. Simultaneously, it fully considers key physical mechanisms such as pressurized turbulence, melting expansion, ice creep closure, water balance, and flood termination criteria based on the competitive relationship between melting expansion rate and ice creep closure rate. This allows it to better reflect the evolution of the ice-covered lake discharge process with high computational accuracy, providing technical support for ice-lake disaster risk assessment, monitoring and early warning, and rapid simulation analysis of ice-lake discharge processes.

[0016] In the real world, the discharge process of ice-covered lakes is controlled by the competitive forces of erosion expansion and creep closure in the pipeline, exhibiting significant pressurized flow characteristics driven by water head. The termination time of the main flood discharge is determined by the steady state of the pipeline. This application simulates the discharge of ice-covered lakes by using a flood termination criterion based on the competitive relationship between erosion expansion rate and ice creep closure rate, along with assumptions of coupled physical equations. This allows the calculation results to more closely approximate the actual physical process, avoiding unreasonable flow rate, water level, and pipeline evolution characteristics, thereby improving the stability, reliability, and accuracy of the calculation.

[0017] This application combines physical mechanisms and numerical calculation principles, and through systematic steps, it can effectively simulate the outflow characteristics of ice lakes under different ice temperatures, ice surface lake areas, and pipeline parameters, providing a scientific basis for dynamic monitoring of ice lakes, water resource assessment, and disaster prevention and mitigation.

[0018] Based on the proposed rapid calculation method for pressurized pipeline flow in icy lakes, this application can obtain key parameters such as the time series of icy lake discharge, flood characteristic values, and pipeline evolution patterns. Relevant management departments can formulate icy lake resource management plans and disaster emergency response measures in advance based on the calculation results. Attached Figure Description

[0019] Figure 1 This is a flowchart of the rapid calculation method for pressurized pipeline flow in an ice-covered lake according to the present invention; Figure 2 A flow rate curve of an ice-covered lake, representing an application example of the present invention; Figure 3 This is a diagram showing the water level changes in a lake, representing an application example of the present invention. Figure 4 This is a diagram illustrating the evolution of the radius of an under-ice pipe in an application example of the present invention; Figure 5 This is a comparison chart of the melting rate and closing rate in an application example of the present invention; Figure 6 This is a diagram showing the change in driving head in an application example of the present invention; Figure 7 This is a diagram of the ice-water pressure difference in an application example of the present invention; Figure 8 This is a diagram showing the flow velocity variation in a pipeline, representing an application example of the present invention. Figure 9 This is a water level-flow rate relationship diagram illustrating an application example of the present invention. Figure 10 This is a radius-flow rate relationship diagram for an application example of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0021] The technical solution of this application is as follows: Please see Figure 1 This application provides a method for rapid calculation of pressurized pipeline flow in ice-covered lakes, including: S01. Obtain basic data; S02. Construct the temperature-dependent ice creep coefficient and calculate the effective driving head, overlying ice pressure and water pressure inside the pipe; S03. Establish the control equations for pressurized flow in sub-ice pipelines; S04. Establish the dynamic evolution equation of the pipeline; S05. Establish the water balance equation for the ice surface lake; S06. Combine the pressurized flow control equations, pipeline dynamic evolution equations, and water balance equations to form a set of coupled ordinary differential equations, and solve them. S07. Identify the moment when the main flood discharge terminates and output the result.

[0022] In S01: In some embodiments, basic data on the surface lake, subglacial pipes, and ice layers are obtained.

[0023] Furthermore, the basic data includes one or more of the following: ice surface lake area, initial lake surface water level elevation, initial pipeline radius, pipeline length, inlet elevation, outlet elevation, ice thickness, and ice temperature.

[0024] It is understandable that the basic data serves as input parameters for subsequent calculations. Among them, the surface area of ​​the glacial lake, the initial lake surface elevation, and the initial pipe radius serve as initial conditions for the coupled ordinary differential equation system; the inlet elevation and outlet elevation are used to calculate the effective driving head; the ice thickness is used to calculate the overlying ice pressure and the inlet hydraulic potential; the ice temperature is used to calculate the temperature-dependent ice creep coefficient; the pipe length is used to calculate the pipe flow velocity; and the initial pipe radius is used for both pipe flow rate calculation and pipe dynamic evolution calculation.

[0025] In S02: In some embodiments, the temperature-dependent ice creep coefficient is calculated based on Glen's law of ice flow: ; In the formula, Ice creep coefficient, unit: ; Glen is the pre-coefficient, in units of: ; The activation energy of ice, in units of: ; Gas constant, unit: ; Kelvin value for ice temperature, unit: .

[0026] Furthermore, the formula for calculating the effective driving head is as follows: ; In the formula, To effectively drive the water head, the unit is: ; For inlet water force, unit: ; For water force at the outlet, unit: ; Density of water, unit: ; Acceleration due to gravity, unit: ; ; ; In the formula, For inlet water force, unit: ; For water force at the outlet, unit: ; Ice density, unit: ; Density of water, unit: ; Acceleration due to gravity, unit: ; Ice thickness, unit: ; Lake surface water level elevation, unit: ; Elevation at the exit, unit: .

[0027] Furthermore, the formulas for the pressure of the overlying ice and the water pressure inside the pipe are as follows: ; ; In the formula, The pressure of the overlying ice, in units of: ; Water pressure inside the pipe, unit: ; Ice density, unit: ; Density of water, unit: ; Acceleration due to gravity, unit: ; Ice thickness, unit: ; Lake surface water level elevation, unit: ; The elevation of the entrance is given in units of: .

[0028] In S03: In some embodiments, the governing equations for pressurized flow in sub-ice pipelines are established based on the Darcy-Weisbach formula, as follows: ; ; ; ; In the formula: Pipe flow velocity, unit: ; Pipe flow rate, unit: ; is the Reynolds number, with a dimensionless unit; Kinematic viscosity of water, unit: ; Acceleration due to gravity, unit: ; Pipe diameter, unit: ; To effectively drive the water head, the unit is: ; The coefficient of friction, unit: dimensionless; Pipe length, unit: ; Pipe radius, unit: .

[0029] It is understandable that this is due to the flow velocity in the pipe. With coefficient of friction The two systems are mutually coupled, meaning that the friction coefficient is determined by the Reynolds number, which in turn depends on the flow velocity in the pipe. Therefore, an iterative method is used to solve the problem.

[0030] Furthermore, the initial pipe velocity is estimated based on the effective driving head, the corresponding Reynolds number is calculated, the friction coefficient is updated based on the Reynolds number, and the pipe velocity is recalculated using the updated friction coefficient; the above steps are repeated until the results of two consecutive calculations meet the preset convergence condition. ; in, The flow velocity in the pipe obtained in the k-th iteration is... Let be the pipe flow rate in the (k+1)th iteration. This is the preset convergence threshold.

[0031] For example, Pick .

[0032] Finally, a stable pipe flow rate is achieved. and pipeline flow This serves as the input for subsequent calculations of the pipeline dynamic evolution equation and the ice lake water balance equation.

[0033] In S04: In some embodiments, the dynamic evolution of the pipeline is controlled by a closed-loop coupling of water flow frictional thermal erosion expansion and ice effective pressure creep, as shown in the following formula: ; ; ; ; In the formula, The rate of fusion expansion, in units of: ; Creep closure rate, unit: ; Net rate of change of pipe radius, unit: ; Effective pressure, unit: ; Hydrodynamic potential gradient, unit: ; Ice density, unit: ; The latent heat of ice melting, unit: ; The pressure of the overlying ice, in units of: ; Water pressure inside the pipe, unit: ; Glen stress index, unit: dimensionless; Pipe flow rate, unit: ; Pipe radius, unit: ; Ice creep coefficient, unit: ; t represents the simulation time, in units of s .

[0034] It is understandable that the net rate of change of the pipeline radius is... It is used to characterize the evolution of the pipe radius under the combined influence of erosion expansion and ice creep closure, and serves as the input to the coupled ordinary differential equation system in step S06.

[0035] In S05: In some embodiments, the water balance equation for ice-covered lakes is: ; In the formula, The rate of change of lake surface water level elevation, unit: ; Lake surface water level elevation, unit: ; Area of ​​the frozen lake, unit: ; For pipeline flow rate, in units ; t represents the simulation time, in units of s .

[0036] In S06: In some embodiments, the compressive flow control equation for the sub-ice pipeline, the pipeline dynamic evolution equation, and the ice surface lake water balance equation are coupled to construct the following system based on the pipeline radius. Lake water level The system consists of a set of coupled ordinary differential equations for the system's state variables: ; In the formula: Pipe radius, unit: ; Lake surface water level elevation, unit: ; Pipe flow rate, unit: ; Hydrodynamic potential gradient, unit: ; Ice creep coefficient, unit: ; The pressure of the overlying ice, in units of: ; Water pressure inside the pipe, unit: ; Glen stress index, unit: dimensionless; Area of ​​the frozen lake, unit: t represents the simulation time, in units of s .

[0037] It is understandable that the pipe flow rate is considered during the solution process. Pipeline flow velocity Effectively drive water head Overlying ice pressure Water pressure inside the pipe Effective pressure , fusion expansion rate creep closure rate Net change rate of pipeline radius Based on the current pipe radius With lake water level Obtained through real-time calculation.

[0038] Furthermore, through the two state variables mentioned above and The resulting set of binary coupled ordinary differential equations updates intermediate computational quantities in real time at each time step and uses the RK45 adaptive step-size algorithm for numerical integration to obtain time series results including simulation time, pipe radius, lake surface water level elevation, pipe flow rate, pipe velocity, effective driving head, effective pressure, melting expansion rate, creep closure rate, and net change rate of pipe radius. This allows us to obtain the dynamic evolution results of the entire process of ice lake discharge.

[0039] In S07: In some embodiments, the melting expansion rate and creep closure rate at each time point are compared based on the time series results to determine the termination time of the main flood discharge.

[0040] It is understandable that the evolution of the subglacial channel is jointly controlled by erosion expansion and ice creep closure. When the closure gradually becomes dominant, the flood enters the attenuation stage. In order to improve the stability of the identification of the flood termination time, this application adopts the creep closure rate exceeding the erosion expansion rate by 1.2 times as the criterion for the termination of the main flood discharge stage.

[0041] Furthermore, the criterion for determining the termination time of the main flood discharge is: ; In the formula, Pipe radius, unit: ; t represents the simulation time, in units of s ; The rate of fusion expansion, in units of: ; Creep closure rate, unit: ; Empirical stability coefficient, unit: dimensionless; Based on the above determination, the time when the main flood discharge ends is obtained. And extract the time series and flood feature values ​​corresponding to that moment.

[0042] Furthermore, the time series includes one or more of the following: simulation time, pipe radius, lake surface elevation, pipe flow rate, pipe velocity, erosion expansion rate, creep closure rate, net pipe change rate, effective pressure, and effective driving head. Flood characteristic values ​​include one or more of the following: peak flow, total discharge, lake level drop, termination time of the main flood discharge, pipe radius at the termination of the main flood discharge, and lake surface elevation at the termination of the main flood discharge.

[0043] Furthermore, .

[0044] Understandable. The preferred value for this application is a coefficient of 1.2, which serves as a stability margin to avoid misjudgments caused by short-term fluctuations in the melting rate and closure rate, and to improve the stability of identifying the termination time of the main flood discharge.

[0045] Secondly, embodiments of this application provide a rapid calculation system for pressurized pipeline flow in ice-covered lakes, comprising: The basic data module is used to obtain basic data; The ice creep coefficient module is used to construct the temperature-dependent ice creep coefficient and calculate the effective driving head, overlying ice pressure, and water pressure inside the pipe. The module for controlling the compressive flow in sub-ice pipelines is used to establish the control equations for the compressive flow in sub-ice pipelines. The pipeline dynamic evolution equation module is used to establish pipeline dynamic evolution equations. The module for water balance equations of ice-covered lakes is used to establish water balance equations for ice-covered lakes. The solution module is used to simultaneously establish the pressurized flow control equations, pipeline dynamic evolution equations, and water balance equations, forming a coupled set of ordinary differential equations, and then solve them. The identification and output module identifies the termination time of the main flood discharge and outputs the result.

[0046] In the basic data module: In some embodiments, basic data on the surface lake, subglacial pipes, and ice layers are obtained.

[0047] Furthermore, the basic data includes one or more of the following: ice surface lake area, initial lake surface water level elevation, initial pipeline radius, pipeline length, inlet elevation, outlet elevation, ice thickness, and ice temperature.

[0048] It is understandable that the basic data serves as input parameters for subsequent calculations. Among them, the surface area of ​​the glacial lake, the initial lake surface elevation, and the initial pipe radius serve as initial conditions for the coupled ordinary differential equation system; the inlet elevation and outlet elevation are used to calculate the effective driving head; the ice thickness is used to calculate the overlying ice pressure and the inlet hydraulic potential; the ice temperature is used to calculate the temperature-dependent ice creep coefficient; the pipe length is used to calculate the pipe flow velocity; and the initial pipe radius is used for both pipe flow rate calculation and pipe dynamic evolution calculation.

[0049] In the ice creep coefficient module: In some embodiments, the temperature-dependent ice creep coefficient is calculated based on Glen's law of ice flow: ; In the formula, Ice creep coefficient, unit: ; Glen is the pre-coefficient, in units of: ; The activation energy of ice, in units of: ; Gas constant, unit: ; Kelvin value for ice temperature, unit: .

[0050] Furthermore, the formula for calculating the effective driving head is as follows: ; In the formula, To effectively drive the water head, the unit is: ; For inlet water force, unit: ; For water force at the outlet, unit: ; Density of water, unit: ; Acceleration due to gravity, unit: ; ; ; In the formula, For inlet water force, unit: ; For water force at the outlet, unit: ; Ice density, unit: ; Density of water, unit: ; Acceleration due to gravity, unit: ; Ice thickness, unit: ; Lake surface water level elevation, unit: ; Elevation at the exit, unit: .

[0051] Furthermore, the formulas for the pressure of the overlying ice and the water pressure inside the pipe are as follows: ; ; In the formula, The pressure of the overlying ice, in units of: ; Water pressure inside the pipe, unit: ; Ice density, unit: ; Density of water, unit: ; Acceleration due to gravity, unit: ; Ice thickness, unit: ; Lake surface water level elevation, unit: ; The elevation of the entrance is given in units of: .

[0052] The sub-ice pipeline has a pressure flow control equation module: In some embodiments, the governing equations for pressurized flow in sub-ice pipelines are established based on the Darcy-Weisbach formula, as follows: ; ; ; ; In the formula: Pipe flow velocity, unit: ; Pipe flow rate, unit: ; is the Reynolds number, with a dimensionless unit; Kinematic viscosity of water, unit: ; Acceleration due to gravity, unit: ; Pipe diameter, unit: ; To effectively drive the water head, the unit is: ; The coefficient of friction, unit: dimensionless; Pipe length, unit: ; Pipe radius, unit: .

[0053] It is understandable that this is due to the flow velocity in the pipe. With coefficient of friction The two systems are mutually coupled, meaning that the friction coefficient is determined by the Reynolds number, which in turn depends on the flow velocity in the pipe. Therefore, an iterative method is used to solve the problem.

[0054] Furthermore, the initial pipe velocity is estimated based on the effective driving head, the corresponding Reynolds number is calculated, the friction coefficient is updated based on the Reynolds number, and the pipe velocity is recalculated using the updated friction coefficient; the above steps are repeated until the results of two consecutive calculations meet the preset convergence condition. ; in, The flow velocity in the pipe obtained in the k-th iteration is... Let be the pipe flow rate in the (k+1)th iteration. This is the preset convergence threshold.

[0055] For example, Pick .

[0056] Finally, a stable pipe flow rate is achieved. and pipeline flow This serves as the input for subsequent calculations of the pipeline dynamic evolution equation and the ice lake water balance equation.

[0057] In the pipeline dynamic evolution equation module: In some embodiments, the dynamic evolution of the pipeline is controlled by a closed-loop coupling of water flow frictional thermal erosion expansion and ice effective pressure creep, as shown in the following formula: ; ; ; ; In the formula, The rate of fusion expansion, in units of: ; Creep closure rate, unit: ; Net rate of change of pipe radius, unit: ; Effective pressure, unit: ; Hydrodynamic potential gradient, unit: ; Ice density, unit: ; The latent heat of ice melting, unit: ; The pressure of the overlying ice, in units of: ; Water pressure inside the pipe, unit: ; Glen stress index, unit: dimensionless; Pipe flow rate, unit: ; Pipe radius, unit: ; Ice creep coefficient, unit: ; t represents the simulation time, in units of s .

[0058] It is understandable that the net rate of change of the pipeline radius is... It is used to characterize the evolution of the pipe radius under the combined influence of erosion expansion and ice creep closure, and serves as the input to the coupled ordinary differential equation system in step S06.

[0059] In the ice lake water balance equation module: In some embodiments, the water balance equation for ice-covered lakes is: ; In the formula, The rate of change of lake surface water level elevation, unit: ; Lake surface water level elevation, unit: ; Area of ​​the frozen lake, unit: ; For pipeline flow rate, in units ; t represents the simulation time, in units of s .

[0060] In the solution module: In some embodiments, the compressive flow control equation for the sub-ice pipeline, the pipeline dynamic evolution equation, and the ice surface lake water balance equation are coupled to construct the following system with pipeline radius R and lake water level H as variables. l The system consists of a set of coupled ordinary differential equations for the system's state variables: ; In the formula: Pipe radius, unit: ; Lake surface water level elevation, unit: ; Pipe flow rate, unit: ; Hydrodynamic potential gradient, unit: ; Ice creep coefficient, unit: ; The pressure of the overlying ice, in units of: ; Water pressure inside the pipe, unit: ; Glen stress index, unit: dimensionless; Area of ​​the frozen lake, unit: t represents the simulation time, in units of s .

[0061] It is understandable that the pipe flow rate is considered during the solution process. Pipeline flow velocity Effectively drive water head Overlying ice pressure Water pressure inside the pipe Effective pressure , fusion expansion rate creep closure rate Net change rate of pipeline radius Based on the current pipe radius With lake water level Obtained through real-time calculation.

[0062] Furthermore, through the two state variables mentioned above and The resulting set of binary coupled ordinary differential equations updates intermediate computational quantities in real time at each time step and uses the RK45 adaptive step-size algorithm for numerical integration to obtain time series results including simulation time, pipe radius, lake surface water level elevation, pipe flow rate, pipe velocity, effective driving head, effective pressure, melting expansion rate, creep closure rate, and net change rate of pipe radius. This allows us to obtain the dynamic evolution results of the entire process of ice lake discharge.

[0063] In the recognition and output module: In some embodiments, the melting expansion rate and creep closure rate at each time point are compared based on the time series results to determine the termination time of the main flood discharge.

[0064] Furthermore, the criterion for determining the termination time of the main flood discharge is as follows: ; In the formula, Pipe radius, unit: ; t represents the simulation time, in units of s ; The rate of fusion expansion, in units of: ; Creep closure rate, unit: ; Empirical stability coefficient, unit: dimensionless; Based on the above determination, the time when the main flood discharge ends is obtained. And extract the time series and flood feature values ​​corresponding to that moment.

[0065] Furthermore, the time series includes one or more of the following: simulation time, pipe radius, lake surface elevation, pipe flow rate, pipe velocity, erosion expansion rate, creep closure rate, net pipe change rate, effective pressure, and effective driving head. Flood characteristic values ​​include one or more of the following: peak flow, total discharge, lake level drop, termination time of the main flood discharge, pipe radius at the termination of the main flood discharge, and lake surface elevation at the termination of the main flood discharge.

[0066] Furthermore, .

[0067] Understandable. The preferred value for this application is a coefficient of 1.2, which serves as a stability margin to avoid misjudgments caused by short-term fluctuations in the melting rate and closure rate, and to improve the stability of identifying the termination time of the main flood discharge.

[0068] Thirdly, this application provides a computer device including a storage device and a processor. The storage device stores a computer program, which, when executed by the processor, causes the processor to perform the steps of the above-described method for rapid calculation of pressurized pipeline flow in an ice-covered lake.

[0069] The computer device can be a desktop computer, laptop, handheld computer, or cloud server, etc. The computer device can interact with the user via a keyboard, mouse, remote control, touchpad, or voice control.

[0070] The memory includes at least one type of readable storage medium, including flash memory, hard disk, multimedia card, card-type memory (e.g., SD or D-interface display memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, etc. In some embodiments, the memory may be an internal storage unit of the computer device, such as the hard disk or memory of the computer device. In other embodiments, the memory may also be an external storage device of the computer device, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the computer device. Of course, the memory may include both the internal storage unit and the external storage device of the computer device. In this embodiment, the memory is often used to store the operating system and various application software installed on the computer device, such as the program code of the rapid calculation method for pressurized pipeline flow in the frozen lake. In addition, the memory can also be used to temporarily store various types of data that have been output or will be output.

[0071] In some embodiments, the processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip. The processor is typically used to control the overall operation of the computer device. In this embodiment, the processor is used to run program code stored in the memory or process data, for example, to run the program code for the rapid calculation method of pressurized pipeline flow in the frozen lake.

[0072] Fourthly, this application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the above-described method for rapid calculation of pressurized pipeline flow in an ice-covered lake.

[0073] The computer-readable storage medium stores an interface display program that can be executed by at least one processor to perform the steps of the rapid calculation method for pressurized pipeline flow in an ice lake as described above.

[0074] 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 software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the rapid calculation method for pressurized pipeline flow in ice lakes described in the embodiments of this application.

[0075] The invention will be further described below with reference to application examples.

[0076] Application examples A high-altitude glacial lake in China. The data for the glacial lake was obtained through remote sensing and field measurements, and includes a lake area of ​​5×10. 5 m², lake surface elevation 920m, pipe radius 0.1m, pipe length 1500m, inlet elevation 900m, outlet elevation 895m, ice thickness 100m, ice temperature −5℃; calculation parameter settings: time step 600s, maximum simulation duration 604800s (7 days).

[0077] The ice creep coefficient was calculated using the Arrhenius formula; The pressurized flow is solved iteratively using the Darcy-Weisbach formula; The pipeline evolution coupled with erosion and closure processes; The water balance equation updates the water level in real time; The RK45 method was used to solve the coupled equations. A flood termination criterion based on the competitive relationship between the melting expansion rate and the ice creep closure rate identifies the termination time of the main flood discharge.

[0078] The calculation results are as follows Figures 2-10 As shown, Figure 2 The flow rate curve of the ice lake in this embodiment shows a typical pattern of "slow rise, rapid rise, peak, and steep decline". The peak flow rate is about 1000 m³ / s, and the main flood discharge process lasts for about 4.71 days, which is consistent with the typical evolution pattern of ice lake outburst flood. Figure 3The figure shows the water level change curve of the ice lake in this embodiment. The initial water level elevation was 920m. As the discharge process continued to decrease, the water level dropped to about 805m at the end of the main discharge stage of the flood. The water level drop process was negatively correlated with the flow rate process, which is consistent with the theoretical expectation of the water balance equation. Figure 4 The figure shows the evolution curve of the sub-ice pipe radius in this embodiment. The pipe radius starts from an initial 0.1m and gradually increases with melting and expansion, reaching a maximum of about 4.7m at the peak of the flood. After the flood ends, the pipe gradually closes due to ice creep. The dashed line in the figure marks the time when the main flood discharge terminates, based on the competition between the melting expansion rate and the ice creep closure rate. Figure 5 The diagram shows the decomposition curve of the pipeline radius change rate in this embodiment. The blue curve represents the erosion expansion rate, the red curve represents the creep closure rate, and the black dashed line represents the net change rate. During the flood growth phase, the erosion expansion rate is much greater than the closure rate, resulting in a positive net change rate and continuous pipeline expansion. During the flood decline phase, the closure rate surpasses the erosion expansion rate, the net change rate turns negative, and the pipeline begins to contract. This fully illustrates the competitive mechanism between the pipeline's erosion expansion and ice creep closure evolution. Figure 6 The curve showing the effective driving head change of the sub-ice pipeline in this embodiment is shown. The initial effective driving head is about 120m. As the lake water level drops, the effective driving head gradually decreases, resulting in a continuous weakening of the discharge capacity, which creates conditions for flood attenuation and closure of the sub-ice pipeline. Figure 7 The effective pressure change curve for this embodiment shows that the initial effective pressure is about 0.7 MPa. As the lake water level drops and the water pressure decreases, the effective pressure gradually increases and stabilizes at about 0.9 MPa at the end of the flood, providing a continuous driving force for ice creep closure. Figure 8 The velocity change curve in the pipeline in this embodiment shows that the velocity first increases and then decreases with the expansion of the pipeline and the change of water head. The peak velocity is about 19 m / s, which occurs during the peak flood stage, consistent with the change law of the flow process line. Figure 9 The curve showing the relationship between lake surface water level elevation and pipeline flow rate in this embodiment is a closed loop, reflecting the lag relationship between water level and flow rate during the discharge of the frozen lake. The water level-flow rate relationship does not coincide with the flood rise stage and the decline stage, reflecting the feedback effect of pipeline evolution on the discharge process. Figure 10 The curve showing the relationship between the radius of the sub-ice pipe and the flow rate in this embodiment is also a closed loop. The flow rate increases as the pipe expands and decreases as the pipe contracts, fully demonstrating the coupling relationship between pipe evolution and the discharge process.

[0079] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A rapid calculation method for pressurized pipeline flow in an ice-covered lake, characterized in that, include: Obtain basic data; Construct a temperature-dependent ice creep coefficient and calculate the effective driving head, overlying ice pressure, and water pressure inside the pipe; Establish the governing equations for pressurized flow in sub-ice pipelines; Establish the dynamic evolution equation of the pipeline; Establish the water balance equation for the ice-covered lake; The pressure flow control equation, pipeline dynamic evolution equation, and water balance equation are combined to form a set of coupled ordinary differential equations, which are then solved. Identify the moment when the main flood discharge terminates and output the result.

2. The method for rapid calculation of pressurized pipeline flow in an ice-covered lake according to claim 1, characterized in that, Obtain basic data on the surface lake, the subglacial pipeline, and the ice layer. The basic data includes one or more of the following: surface lake area, initial lake surface elevation, initial pipeline radius, pipeline length, inlet elevation, outlet elevation, ice thickness, and ice temperature.

3. The method for rapid calculation of pressurized pipeline flow in an ice-covered lake according to claim 1, characterized in that, Based on Glen's law of ice flow, calculate the temperature-dependent ice creep coefficient: ； In the formula, The creep coefficient of ice; Glen is the pre-coefficient; The activation energy of ice; It is the gas constant; Kelvin value for ice temperature; and / or The formula for calculating the effective driving head is as follows: ； In the formula, To effectively drive the water head; For the force of the incoming water; For export water power; The density of water; It is the acceleration due to gravity; ； ； In the formula, For the force of the incoming water; For export water power; The density of ice; The density of water; It is the acceleration due to gravity; The ice is thick; This refers to the lake's water level elevation. For the export elevation; and / or The formulas for the pressure of the overlying ice and the water pressure inside the pipe are as follows: ； ； In the formula, The pressure of the overlying ice; The water pressure inside the pipe; The density of ice; The density of water; It is the acceleration due to gravity; The ice is thick; This refers to the lake's water level elevation. This is the entrance elevation.

4. The method for rapid calculation of pressurized pipeline flow in an ice-covered lake according to claim 3, characterized in that, The governing equations for compressible flow in sub-ice pipes, based on the Darcy-Weisbach formula, are established as follows: ； ； ； ； In the formula: The flow velocity in the pipe; For pipeline flow rate; It is the Reynolds number; The viscosity of water at kinematic speed; It is the acceleration due to gravity; The diameter of the pipe; To effectively drive the water head; The coefficient of friction; This refers to the length of the pipe. For the pipe radius; and / or The dynamic evolution of the pipeline is controlled by the closed-loop coupling of water flow frictional thermal erosion expansion and ice effective pressure creep, as shown in the formula: ； ； ； ； In the formula, This represents the rate of erosion expansion. The creep closure rate; This represents the net rate of change of the pipeline radius. For effective pressure; The hydraulic potential gradient; The density of ice; The latent heat of ice melting; The pressure of the overlying ice; The water pressure inside the pipe; The Glen stress index; For pipeline flow rate; Where the pipe radius is; The creep coefficient of ice; t is the simulation time; and / or The water balance equation for the frozen lake is: ； In the formula, The rate of change of lake surface water level elevation; This refers to the lake's water level elevation. The area of ​​the frozen lake; For pipeline flow rate; t is the simulation time; and / or The compressive flow control equations for the subglacial pipeline, the pipeline dynamic evolution equations, and the ice surface lake water balance equations are coupled to construct the following system with pipeline radius R and lake water level H as variables. l The system consists of a set of coupled ordinary differential equations for the system's state variables: ； In the formula: Where the pipe radius is; This refers to the lake's water level elevation. For pipeline flow rate; The hydraulic potential gradient; The creep coefficient of ice; The pressure of the overlying ice; The water pressure inside the pipe; The Glen stress index; t represents the area of ​​the frozen lake; t represents the simulation time.

5. The method for rapid calculation of pressurized pipeline flow in an ice-covered lake according to claim 4, characterized in that, Estimate the initial pipe velocity based on the effective driving head, calculate the corresponding Reynolds number, update the friction coefficient based on the Reynolds number, and recalculate the pipe velocity using the updated friction coefficient; repeat the above steps until the results of two consecutive calculations meet the preset convergence condition. ； in, The flow velocity in the pipe obtained in the k-th iteration is... Let be the pipe flow rate in the (k+1)th iteration. For the preset convergence threshold; and / or pass and The resulting set of binary coupled ordinary differential equations updates intermediate computational quantities in real time at each time step and uses the RK45 adaptive step-size algorithm for numerical integration to obtain time series results including simulation time, pipe radius, lake surface water level elevation, pipe flow rate, pipe velocity, effective driving head, effective pressure, melting expansion rate, creep closure rate, and net change rate of pipe radius. This allows us to obtain the dynamic evolution results of the entire process of ice lake discharge.

6. The method for rapid calculation of pressurized pipeline flow in an ice-covered lake according to claim 5, characterized in that, Based on the time series results, the melting expansion rate and creep closure rate at each time point are compared to determine the termination time of the main flood discharge.

7. The method for rapid calculation of pressurized pipeline flow in an ice-covered lake according to claim 6, characterized in that, The criterion for determining the termination time of the main flood discharge is: ； In the formula, Where the pipe radius is; t is the simulation time; This represents the rate of erosion expansion. The creep closure rate; This is the empirical stability coefficient; Based on the above criteria, the time when the main flood discharge ends is determined. And extract the time series and flood feature values ​​corresponding to that moment; The time series includes one or more of the following: simulation time, pipe radius, lake surface elevation, pipe flow rate, pipe velocity, erosion expansion rate, creep closure rate, net pipe change rate, effective pressure, and effective driving head. Flood characteristic values ​​include one or more of the following: peak flow, total discharge, lake level drop, termination time of the main flood discharge, pipe radius at the termination of the main flood discharge, and lake surface elevation at the termination of the main flood discharge.

8. A rapid calculation system for pressurized pipeline flow in icy lakes, characterized in that, include: The basic data module is used to obtain basic data; The ice creep coefficient module is used to construct the temperature-dependent ice creep coefficient and calculate the effective driving head, overlying ice pressure, and water pressure inside the pipe. The module for controlling the compressive flow in sub-ice pipelines is used to establish the control equations for the compressive flow in sub-ice pipelines. The pipeline dynamic evolution equation module is used to establish pipeline dynamic evolution equations. The module for water balance equations of ice-covered lakes is used to establish water balance equations for ice-covered lakes. The solution module is used to simultaneously establish the pressurized flow control equations, pipeline dynamic evolution equations, and water balance equations, forming a coupled set of ordinary differential equations, and then solve them. The identification and output module identifies the termination time of the main flood discharge and outputs the result.

9. A computer device, characterized in that, It includes a storage device and a processor, the storage device storing a computer program that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The device stores a computer program that, when executed by a processor, causes the processor to perform the steps of the method as described in any one of claims 1-7.

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