Water recession model establishment method and system based on long-distance pressure pipeline

Abstract

The invention relates to the technical field of numerical simulation calculation of water conveyance projects, in particular to a water recession model establishment method and system based on a long-distance pressure pipeline. The method comprises the steps that a rigid water column model is constructed based on deformation of a motion equation and a continuity equation in the non-constant flowing process of fluid in a pressure pipeline, and a water column flow velocity equation and a water column length equation are established to describe liquid phase changes in the non-air-valve water recession process by combining change analysis of hydraulic parameters in the pressure pipeline on the time scale. The pressure intensity in a hollow pipe section at the upstream end of a pressure pipeline without an air valve is analyzed to describe the volume change in the hollow pipe section to construct an air-valve-free water recession model, the change of gas parameters of air passing through the air valve in the hollow pipe section at the upstream end of the pressure pipeline on the time scale is analyzed to construct an air-valve water recession model, and simulation is solved through the model. And predicting the change trend and fluctuation condition of the pressure water head in the upstream end hollow pipe section in the water recession process of the pressure pipeline. The method can accurately predict the recession process of the long-distance water delivery pipeline.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical simulation calculation of water delivery projects, and in particular to a method and system for establishing a water withdrawal model based on a long-distance pressurized pipeline. Background Art

[0002] Long-distance water transmission projects are the most direct and effective way to address the current problems of uneven temporal and spatial distribution of water resources and insufficient urban water supply. Pressurized water pipelines are widely used in long-distance water transmission projects and urban water transmission and distribution network systems due to their high efficiency and low leakage. With the development of cities and the acceleration of urbanization, water transmission projects are becoming increasingly large-scale and multi-branched. As a result, the non-constant flow problem of the water withdrawal process during the inspection and maintenance of pressurized pipelines has become more complex and variable. The pipeline withdrawal process refers to the process in which, when a certain section of the pipeline needs to be inspected and maintained in a water transmission project, the upstream flow needs to be cut off, the withdrawal valve at the downstream withdrawal outlet needs to be opened, and the water in the pipeline needs to be emptied.

[0003] The water withdrawal process generates negative pressure, especially in extreme cases, such as when the air valve fails to function properly or the water withdrawal valve operates too quickly. This can cause the withdrawal pipeline to fail to replenish air in time, resulting in extreme negative pressure and causing pipeline collapse and damage. Furthermore, trapped air masses in the pipeline can expand, rupture, and mix with the fluid, creating an extremely complex gas-liquid two-phase flow, increasing the pipeline's flow resistance and pressure pulsation, leading to extremely serious engineering accidents.

[0004] Therefore, there is an urgent need to improve the research on the water withdrawal process of long-distance pressurized pipelines in order to achieve accurate prediction of the water withdrawal process of long-distance water transmission pipelines and provide a theoretical basis for ensuring their water withdrawal safety. Summary of the Invention

[0005] The technical problem to be solved by the embodiments of the present invention is to provide a method and system for establishing a water withdrawal model based on a long-distance pressurized pipeline, so as to solve the problem in the prior art that the water withdrawal process of a long-distance water transmission pipeline cannot be accurately predicted.

[0006] The present invention discloses a method for establishing a water withdrawal model based on a long-distance pressurized pipeline, comprising: Based on the assumption that the fluid is incompressible, a rigid water column model is constructed based on the deformation of the motion equation and continuity equation of the unsteady flow process of the fluid in the pressurized pipeline. Assuming that there is no air valve at the upstream end of the pressurized pipeline, based on the rigid water column model and combined with the analysis of the changes in hydraulic parameters in the pressurized pipeline on a time scale, the water column velocity equation and the water column length equation are established to describe the liquid phase changes during the water withdrawal process without an air valve. The pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve is analyzed to describe the volume change in the empty pipe section, and the water column velocity equation and the water column length equation are combined to construct a water withdrawal model for the air valve; Assuming that there is an air valve at the upstream end of the pressurized pipeline, the time-scale changes in gas parameters of the air in the empty pipe section at the upstream end of the pressurized pipeline passing through the air valve are analyzed, and the water column velocity equation and the water column length equation are simultaneously established to construct a water withdrawal model with an air valve; By solving the water withdrawal model without an air valve and the water withdrawal model with an air valve respectively and performing simulations based on the solution results, the changing trend and fluctuation of the pressure head in the empty pipe section at the upstream end during the water withdrawal process of the pressurized pipeline are predicted.

[0007] Optionally, the step of constructing a rigid water column model based on the deformation of the motion equation and the continuity equation of the unsteady flow process of the fluid in the pressurized pipeline includes: The motion equation describing the unsteady flow process of fluid in a pressurized pipeline based on the law of conservation of momentum is expressed as follows:

[0008] The continuity equation based on the law of conservation of momentum describes the unsteady flow process of fluid in a pressurized pipeline. The functional expression of the continuity equation is:

[0009] Based on the assumption that the fluid is incompressible, the motion equation and the continuity equation are simplified; The simplified function expression of the continuity equation is:

[0010] The simplified functional expression of the motion equation is:

[0011] In the formula, in the formula, is the instantaneous flow velocity, H is the instantaneous water head, D is the diameter of the pressurized pipe, is the spatial coordinate of the axis of the pressurized pipeline, t is the water withdrawal time, g is the local gravity acceleration, is the water hammer propagation velocity, f is the hydraulic friction coefficient of the unsteady flow in the pipeline, is the upstream head, is the lower water head, is the pipeline resistance loss, is the length of the pressurized pipeline.

[0012] Optionally, establishing a water column velocity equation and a water column length equation to describe the liquid phase changes during the airless valve water withdrawal process includes: The basic conditions for the water withdrawal process in a pressurized pipeline without an air valve are set. The entire water body in the pressurized pipeline is used as the control volume, and it is assumed that the axis direction of the pressurized pipeline is consistent with the direction of the fluid. According to the simplified motion equation, the force analysis of the water column in the pressurized pipe is carried out. Combined with the density and flow velocity of the water column after analysis, and the analysis of the change of the pressure of the gas in the empty pipe section at the upstream end on the time scale, the water column flow velocity equation is established to describe the water column flow velocity during the water withdrawal process of the airless valve. The functional expression of the water column flow velocity equation is:

[0013] According to the simplified continuity equation, combined with the analysis of the change of the length of the water column on the time scale during the water withdrawal process of the pressurized pipeline, the water column length equation is established to describe the water column length during the water withdrawal process of the airless valve. The functional expression of the water column length equation is:

[0014] Where, is the absolute pressure of the gas in the empty pipe section during the water withdrawal process, is the interfacial area, is the angle between the pressurized pipe and the horizontal plane, is the standard atmospheric pressure, is the friction coefficient of the pipe wall, is the total length of the pressurized pipeline, is the length of the water column, is the density of water, is the acceleration due to gravity, is the water flow velocity, is the differential per unit time.

[0015] Optionally, analyzing the pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve to describe the volume change in the empty pipe section includes: According to the absolute pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve, the absolute pressure change equation in the empty pipe section of the pressurized pipeline from the beginning of water withdrawal is established to describe the volume change in the empty pipe section. The function expression of the absolute pressure change equation is:

[0016] Where, is the absolute pressure in the empty pipe section at the initial moment, is the initial length of the empty pipe segment, is the volume of the empty pipe section during the water withdrawal process.

[0017] Optionally, the analyzing the time-scale changes of gas parameters of air in the empty pipe section at the upstream end of the pressurized pipeline passing through the air valve includes: The basic conditions of the water withdrawal process in the pressurized pipeline with an air valve are set to be the same as those in the pressurized pipeline without an air valve, and the water column velocity equation and the water column length equation are used to describe the liquid phase change in the water withdrawal process with the air valve; The gas mass flow equation entering the air valve per unit time is established to describe the volume change of the air in the empty pipe section. The function expression of the gas mass flow equation is:

[0018] By simplifying the gas mass flow equation, the air density change equation is obtained to describe the change of air density in the empty pipe section on a time scale. The functional expression of the air density change equation is:

[0019] Based on the adiabatic compression equation and the ideal gas state equation, the air pressure change equation is established to describe the change of air pressure in the empty pipe section on a time scale. The functional expression of the air pressure change equation is:

[0020] Where, is the atmospheric density, is the flow rate of gas into the air valve, is the air valve inlet area, is the density of the gas in the empty pipe section, is the mass of the gas in the empty pipe section, and k is a constant.

[0021] Optionally, the analyzing the time-scale changes of gas parameters of air in the empty pipe section at the upstream end of the pressurized pipeline passing through the air valve further includes: Assuming the basic conditions for air to pass through the air valve, an air flow equation group is established to describe the changes when air flows into and out of the pressurized pipe through the air valve. The functional expression of the air flow equation group is:

[0022] Where, is the flow rate of air entering the pressurized pipeline, is the flow rate of air flowing out of the pressurized pipe, is the volume of the empty pipe section, is the absolute temperature, is the gas constant, is the absolute pressure of the atmosphere in the empty pipe section; According to the air flow equations, when the air valve is installed and the pressure in the pressurized pipeline is discharged, the atmospheric pressure in the pressurized pipeline is lower than the external atmospheric pressure. An air flow velocity equation is established based on the subsonic air flow and the critical sonic air flow to describe the change in air mass passing through the air valve. The functional expression of the air flow velocity equation is:

[0023] Where: is the flow coefficient when air flows into the air valve, is the opening area of ​​the air valve intake hole, is the atmospheric density.

[0024] Optionally, solving the water withdrawal model without an air valve and the water withdrawal model with an air valve separately includes: The water column flow rate equation, the water column length equation, and the absolute pressure change equation are combined to construct the water withdrawal model without an air valve, and the water column flow rate equation, the water column length equation, the air density change equation, the air pressure change equation, and the air flow rate equation group are combined to construct the water withdrawal model with an air valve; The mass matrix is ​​obtained by deforming the singular mass matrix based on the Runge-Kutta method. The mass matrix is ​​used to solve the water withdrawal model without air valve and the water withdrawal model with air valve, respectively, to obtain the solution results of the water withdrawal model without air valve and the water withdrawal model with air valve. The function expression of the mass matrix is:

[0025] Where M represents the mass matrix.

[0026] The present invention also discloses a model building system, which adopts the above-mentioned method for building a water withdrawal model based on a long-distance pressurized pipeline, and includes: A rigid water column model construction module is used to construct a rigid water column model based on the deformation of the motion equation and continuity equation of the non-steady flow process of the fluid in the pressurized pipe, assuming that the fluid is incompressible; The water withdrawal liquid phase description module is used to assume that there is no air valve at the upstream end of the pressurized pipeline. Based on the rigid water column model and combined with the analysis of the changes in the hydraulic parameters in the pressurized pipeline on the time scale, the water column velocity equation and the water column length equation are established to describe the liquid phase changes during the water withdrawal process without an air valve. An airless valve water withdrawal model establishment module is used to analyze the pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve to describe the volume change in the empty pipe section, and to jointly construct the airless valve water withdrawal model by combining the water column velocity equation and the water column length equation; A module for establishing a water withdrawal model with an air valve is used to assume that there is an air valve at the upstream end of the pressurized pipeline, analyze the changes in gas parameters of the air in the empty pipe section at the upstream end of the pressurized pipeline passing through the air valve on a time scale, and jointly establish the water column velocity equation and the water column length equation to construct a water withdrawal model with an air valve; The model solving simulation module is used to solve the airless valve water withdrawal model and the air valve water withdrawal model respectively, and perform simulation based on the solution results to predict the change trend and fluctuation of the pressure head in the empty pipe section at the upstream end during the water withdrawal process of the pressurized pipeline.

[0027] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the above-mentioned method for establishing a water withdrawal model based on a long-distance pressurized pipeline.

[0028] The present invention also discloses a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. The device is characterized in that when the processor executes the computer program, the method for establishing a water withdrawal model based on a long-distance pressurized pipeline is implemented.

[0029] Compared with the prior art, the method and system for establishing a water withdrawal model based on a long-distance pressurized pipeline provided by the embodiments of the present invention have the following advantages: By constructing a rigid water column model based on an incompressible fluid, and accurately distinguishing between two operating conditions, with and without an air valve at the upstream end, a separate mathematical model for water withdrawal is established. For the case without an air valve, a nonlinear water withdrawal model is constructed, coupling water column velocity, length, and pressure, combining water column motion with the volumetric pressure changes within the empty pipe section. For the case with an air valve, the gas dynamics equations for air valve intake are additionally introduced to comprehensively describe the dynamic interaction between the gas and liquid phases. This modeling approach enables highly accurate simulation of the transient trends, fluctuation amplitudes, and frequency characteristics of the pressure head in the empty upstream pipe section of the pipeline throughout the water withdrawal process. It accurately captures critical risk factors such as strong negative pressure shocks caused by insufficient air supply or rapid valve opening and closing, as well as abnormal pressure pulsations caused by air mass movement under extreme conditions. The prediction results provide a key theoretical basis for optimizing water withdrawal valve operating procedures, verifying air valve selection and placement, and preventing pipeline collapse and damage. These results significantly improve the safety and reliability of large-scale water transmission project maintenance and inspection, avoiding secondary hazards caused by water hammer and gas-liquid two-phase flow. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments, in which: Figure 1 A schematic block diagram of the steps of a method for establishing a water withdrawal model provided in an embodiment of the present invention; Figure 2A schematic diagram of water withdrawal from a pressurized pipeline without an air valve provided in an embodiment of the present invention; Figure 3 A schematic diagram of water withdrawal from a pressurized pipeline with an air valve provided in an embodiment of the present invention; Figure 4 A schematic diagram of air flowing through an air valve provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0031] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. Now, in conjunction with the accompanying drawings, the preferred embodiments of the present invention will be described in detail.

[0032] The present invention discloses a method for establishing a water withdrawal model based on a long-distance pressurized pipeline. Figure 1 As shown, including: S1. Based on the assumption that the fluid is incompressible, a rigid water column model is constructed based on the deformation of the motion equation and continuity equation of the unsteady flow process of the fluid in the pressurized pipeline; S2. Assuming that there is no air valve at the upstream end of the pressurized pipeline, based on the rigid water column model and combined with the analysis of the changes in hydraulic parameters in the pressurized pipeline on a time scale, the water column velocity equation and the water column length equation are established to describe the liquid phase changes during the water withdrawal process without an air valve; S3. Analyze the pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve to describe the volume change in the empty pipe section, and construct a water withdrawal model without an air valve by combining the water column velocity equation and the water column length equation; S4. Assuming that there is an air valve at the upstream end of the pressurized pipeline, analyze the time-scale changes in the gas parameters of the air in the empty pipe section at the upstream end of the pressurized pipeline as it passes through the air valve. Construct a water withdrawal model with the air valve by combining the water column velocity equation and the water column length equation in parallel. S5. By solving the water withdrawal model without an air valve and the water withdrawal model with an air valve respectively, and performing simulations based on the solution results, the changing trend and fluctuation of the pressure head in the empty pipe section at the upstream end during the water withdrawal process of the pressurized pipeline are predicted.

[0033] By implementing the aforementioned water withdrawal modeling method, refined water withdrawal models were established for both air-valve-free and air-valve-supported operating conditions. First, a model derived based on the rigid water column assumption effectively simplifies the complexity of fluid dynamics, ensuring computational efficiency and capturing the core characteristics of the overall water column motion during the initial water withdrawal phase. The water withdrawal model without an air valve simulates water withdrawal when the air valve is not functioning properly. Specifically, targeting the most dangerous air valve failure scenario, the model focuses on the negative pressure formation caused by the volume expansion of the empty pipe section. The water column velocity equation and the water column length equation are used to describe the liquid phase changes during water withdrawal without an air valve. Furthermore, the model is deeply coupled to the volume changes within the empty pipe section at the upstream end of the pressurized pipeline. This allows for precise quantification of the negative feedback relationship between water column velocity decay and the length expansion of the empty pipe section. This captures the extreme negative pressure and abrupt pressure gradient changes caused by the isothermal expansion of the enclosed gas, providing a clear warning of the critical conditions for pipe wall collapse caused by the formation of a vacuum zone due to the unlimited volume expansion of the gas at the top of the pipeline. Furthermore, for operating conditions where the air valve is functioning properly, the water withdrawal model with an air valve further analyzes the complex interaction between the gas and liquid phases. By characterizing the flow rate and pressure characteristics of air flowing through the valve and their temporal variations, the changes in these gas parameters are dynamically coupled with the motion equations of the liquid water column. This allows for the simultaneous simulation of a series of complex transient phenomena, including the accelerated filling of the cavity by the airflow, its mixing with residual water to form a gas-liquid two-phase flow, the work done by gas expansion to counteract the inertia of the water column, and the resulting pressure pulsations. This enables the model to accurately predict the combined impact of design parameters such as valve specifications and opening and closing speeds on system stability, energy dissipation, and water hammer intensity during the water withdrawal process, providing an accurate decision-making tool for the scientific selection of air valves and the optimized control of opening and closing procedures. By establishing refined water withdrawal models for both air valve-free and air valve-containing working conditions, the potential minimum pressure point at any location in the pipeline and its evolution process can be clearly predicted, significantly reducing the risk of physical damage to the pipeline and systemic hydraulic imbalance caused by water withdrawal operations, and ensuring the safe and stable operation of major water transmission infrastructure throughout its life cycle.

[0034] Furthermore, a rigid water column model is constructed based on the deformation of the motion equation and continuity equation of the unsteady flow process of the fluid in the pressurized pipeline, including: The motion equation based on the law of conservation of momentum describes the unsteady flow process of fluid in a pressurized pipe. The functional expression of the motion equation is:

[0035] The continuity equation based on the law of conservation of momentum describes the unsteady flow process of fluid in a pressurized pipeline. The functional expression of the continuity equation is:

[0036] Based on the assumption that the fluid is incompressible, the equations of motion and continuity are simplified; The simplified function expression of the continuity equation is:

[0037] The simplified function expression of the motion equation is:

[0038] In the formula, in the formula, is the instantaneous flow velocity, H is the instantaneous water head, D is the diameter of the pressurized pipe, is the spatial coordinate of the axis of the pressurized pipeline, t is the water withdrawal time, g is the local gravity acceleration, is the water hammer propagation velocity, f is the hydraulic friction coefficient of the unsteady flow in the pipeline, is the upstream head, is the lower water head, is the pipeline resistance loss, is the length of the pressurized pipeline.

[0039] By implementing the aforementioned method for establishing a water-relief model, the equations of motion and continuity are simplified based on the assumption of incompressible fluids. This effectively removes unnecessary complexity associated with the overall migration of the water column during the initial stages of the water-relief process, thereby constructing a basic framework for a rigid water column model that combines critical physical fidelity with engineering practicality. Specifically, the equation of motion, based on the law of conservation of momentum, states that the difference in transient head at each end of the pipe is equal to the sum of the fluid's acceleration head (inertia) and the pipe's resistance loss head, thus forming the rigid water column model. Leveraging this rigid water column model, the original system of partial differential equations describing unsteady flow in a pressurized pipe is transformed into a system of ordinary differential equations that consider only the time scale. This ensures computational accuracy while reducing the difficulty of solving the model. Consequently, based on the rigid water column model, the changes in hydraulic parameters such as velocity, flow rate, and pressure in the pipe can be more easily captured. During the water withdrawal process of a pressurized pipeline, the elasticity of the water body and the pipeline is ignored, only the inertia of the water body is considered, and the focus is on the changes in the hydraulic parameters of the water body in the pipeline over time, rather than the pressure changes at the nodes inside the pipeline. This makes it highly compatible with the calculation and analysis of unsteady flows during the water withdrawal process.

[0040] Furthermore, the water column velocity equation and water column length equation are established to describe the liquid phase changes during the airless valve withdrawal process, including: The basic conditions for the water withdrawal process in a pressurized pipeline without an air valve are set. The entire water body in the pressurized pipeline is used as the control volume, and it is assumed that the axis direction of the pressurized pipeline is consistent with the direction of the fluid. According to the simplified motion equation, the force analysis of the water column in the pressurized pipe is carried out. Combined with the density and flow velocity of the water column after analysis, and the analysis of the change of the pressure of the gas in the empty pipe section at the upstream end on the time scale, the water column flow velocity equation is established to describe the water column flow velocity during the water withdrawal process of the airless valve. The functional expression of the water column flow velocity equation is:

[0041] Based on the simplified continuity equation and the analysis of the change of the water column length on the time scale during the water withdrawal process of the pressurized pipeline, a water column length equation is established to describe the water column length during the water withdrawal process of the airless valve. The functional expression of the water column length equation is:

[0042] Where, is the absolute pressure of the gas in the empty pipe section during the water withdrawal process, is the interfacial area, is the angle between the pressurized pipe and the horizontal plane, is the standard atmospheric pressure, is the friction coefficient of the pipe wall, is the total length of the pressurized pipeline, is the length of the water column, is the density of water, is the acceleration due to gravity, is the water flow velocity, is the differential per unit time.

[0043] By implementing the above-mentioned method for establishing the water withdrawal model, the basic conditions for the water withdrawal process in the pressurized pipeline without an air valve are set as follows: 1) The rapid water withdrawal process is considered to be a constant entropy process, and there is no energy exchange between the gas in the air valve and cavity and the pipe wall and the outside world; 2) The water withdrawal process only considers the inertia of the water body, without considering the elasticity of the pipe and the water body; 3) The friction force of the pipe wall on the fluid is calculated using the Darcy-Weisbach formula; 4) The drain valve is located at the end of the pipe. The water flow rate is determined by its opening. The loss of the drain valve is calculated using the valve resistance coefficient. 5) The behavior of volume change in the empty pipe section is expressed by the ideal gas state equation; 6) The water-air interface is a clear phase interface parallel to the horizontal plane.

[0044] like Figure 2 As shown in the figure, in the case of single-pipe water withdrawal without an air valve, the upstream end of the pipe is closed and there is an empty pipe section. The water withdrawal valve in the downstream section is used to control the opening and closing state of the pipe water withdrawal. The liquid phase description of the water withdrawal process, that is, the description of the water column, is described by the momentum equation and continuity equation of the fluid, respectively, and derived by conservation of momentum and conservation of mass, respectively. Since the water withdrawal process adopts the assumption of a rigid water column, the entire water body of the pipe is selected as the control body, and it is assumed that the axial direction of the pressurized pipe is consistent with the direction of the fluid. The force on the upstream end of the control body is ; The force on the downstream valve side is The force between the fluid and the pipe is ; The component of the water body's own gravity along the x-axis is ;Introduce the resistance term of the valve , the influence of valve resistance is quantitatively described by local loss.

[0045] First, analyze the force on the water column in the pipe. According to the law of conservation of momentum, we can get:

[0046] Divide both sides of the equation by have to:

[0047] Where friction stress τ The Darcy-Weisbach formula is used for calculation. The Darcy-Weisbach formula is: .because τ The direction of the flow is opposite to the direction of the flow, so it is represented by a negative sign in the formula. τ Substituting it into the above formula and simplifying it, we can get the water column flow rate equation.

[0048] Secondly, the description of the length of the water column is obtained from the conservation of mass:

[0049] Differentiating both sides of the above equation with respect to time yields the equation for the length of the water column.

[0050] Furthermore, the pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve is analyzed to describe the volume change in the empty pipe section, including: According to the absolute pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve, the absolute pressure change equation in the empty pipe section of the pressurized pipeline from the beginning of water withdrawal is established to describe the volume change in the empty pipe section. The function expression of the absolute pressure change equation is:

[0051] Where, is the absolute pressure in the empty pipe section at the initial moment, is the initial length of the empty pipe segment, is the volume of the empty pipe section during the water withdrawal process.

[0052] By implementing the above-mentioned method for establishing a water withdrawal model, during the water withdrawal process, the gas within the upstream cavity is stretched, generating negative pressure. The absolute pressure of the cavity determines the boundary conditions at the upstream end of the water withdrawal model when no air valve is present. Introducing a description of the cavity allows for a more accurate description of the water withdrawal process. Since there is no air intake during the water withdrawal process without an air valve, the changes in the cavity within the empty pipe section can be considered a constant entropy process (adiabatic process), that is, the cavity of the empty pipe section can be described using the equation for the change in absolute pressure.

[0053] Furthermore, the time-scale changes of gas parameters of the air in the empty pipe section at the upstream end of the pressurized pipeline passing through the air valve are analyzed, including: The basic conditions for the water withdrawal process in a pressurized pipeline with an air valve are assumed to be the same as those in the process without an air valve, and the water column velocity equation and water column length equation are used to describe the liquid phase changes during the water withdrawal process with an air valve. The gas mass flow equation entering the air valve per unit time is established to describe the volume change of air in the empty pipe section. The function expression of the gas mass flow equation is:

[0054] The air density change equation is obtained by simplifying the gas mass flow equation to describe the change of air density in the empty pipe section on a time scale. The functional expression of the air density change equation is:

[0055] Based on the adiabatic compression equation and the ideal gas state equation, the air pressure change equation is established to describe the change of air pressure in the empty pipe section on a time scale. The functional expression of the air pressure change equation is:

[0056] Where, is the atmospheric density, is the flow rate of gas into the air valve, is the air valve inlet area, is the density of the gas in the empty pipe section, is the mass of the gas in the empty pipe section, and k is a constant.

[0057] Through the implementation of the above-mentioned dewatering model establishment method, such as Figure 3 As shown, an air valve is installed at the upstream end of the water withdrawal pipe with an air valve to replenish air to the empty pipe section during the water withdrawal process. The basic assumptions are consistent with those of the water withdrawal model without an air valve. For the water withdrawal process with an air valve, since downstream air intake and branch pipes are not considered, the water column velocity equation and water column length equation are used to describe the liquid phase changes during the water withdrawal process with an air valve.

[0058] During the water withdrawal process, the water body is regarded as an incompressible fluid. Therefore, the increase in the volume of the empty pipe section per unit time t is equal to the volume of the discharged water, and the increase in the volume of the empty pipe section also depends only on the drainage volume, but it is not necessarily equal to the air intake of the air valve during the time. This is because the pressure in the cavity is lower than the local atmospheric pressure during the water withdrawal process, and the cavity is in a stretched state. During the time, the air intake flowing through the air valve should be less than the increase in the cavity volume. The air intake of the air valve can be described by the mass of the gas entering the air valve per unit time, that is, the mass flow rate of the gas entering the air valve per unit time is the change in the cavity gas volume:

[0059] in, is the mass of the gas in the empty pipe section, which can be expressed as:

[0060] By combining the above two equations, the gas mass flow equation can be obtained.

[0061] Furthermore, the analysis of the time-scale changes in gas parameters of the air in the empty pipe section at the upstream end of the pressurized pipeline passing through the air valve also includes: Assuming the basic conditions for air to pass through the air valve, establish an air flow equation group to describe the changes when air flows into and out of the pressurized pipe through the air valve. The function expression of the air flow equation group is:

[0062] Where, is the flow rate of air entering the pressurized pipeline, is the flow rate of air flowing out of the pressurized pipe, is the volume of the empty pipe section, is the absolute temperature, is the gas constant, is the absolute pressure of the atmosphere in the empty pipe section; According to the air flow equations, when the air valve is installed and the pressure in the pressurized pipe is discharged, the atmospheric pressure in the pressurized pipe is lower than the external atmospheric pressure. The air flow velocity equations are established based on the subsonic air flow and the critical sonic air flow to describe the change in air mass through the air valve. The function expression of the air flow velocity equations is:

[0063] Where: is the flow coefficient when air flows into the air valve, is the opening area of ​​the air valve intake hole, is the atmospheric density, is the absolute pressure of the atmosphere, is the absolute pressure in a pressurized pipe.

[0064] Through the implementation of the above-mentioned dewatering model establishment method, such as Figure 4 As shown, in order to describe the process of air flowing into and out of the pipe through the air valve through-hole, the basic conditions for air passing through the air valve are first set as follows: 1) Air flows isentropically into the air valve; 2) The air temperature in the tube is close to the liquid temperature and follows the isothermal change law; 3) The change in the volume of air in the pipe depends only on the outflow of water in the pipe; 4) The air in the pipe section is retained near the air valve and can be completely discharged.

[0065] When air flows into or out of the pipe section, Figure 4 It can be seen that the unknown parameters are (absolute pressure of the atmosphere in the air traffic control section), (the flow rate of air entering the pressurized pipeline), (the flow rate of air flowing out of the pressurized pipe) and V (the volume of the empty pipe section). This establishes a set of air flow equations to describe the changes in air as it flows into (C+) and out of (C-) the pressurized pipe through the air valve.

[0066] The air mass flow rate through the air valve (the rate of change of air mass) ) depends on the absolute pressure of the atmosphere outside the pipe , absolute temperature , as well as the absolute pressure p and absolute temperature T within the pipeline, typically require consideration of both air inflow and outflow. However, due to the water withdrawal process, the air is stretched, and the atmospheric pressure within the pipeline is lower than the external atmospheric pressure. Therefore, only the air mass change when air flows into the air valve is considered. Therefore, in this embodiment of the present invention, a set of air flow velocity equations is established using subsonic air inflow and critical sonic air inflow to describe the air mass change through the air valve.

[0067] Furthermore, the water withdrawal model without air valve and the water withdrawal model with air valve are solved separately, including: The water column velocity equation, water column length equation, and absolute pressure change equation are combined to construct a water withdrawal model without an air valve. The water column velocity equation, water column length equation, air density change equation, air pressure change equation, and air velocity equation group are combined to construct a water withdrawal model with an air valve. The mass matrix is ​​obtained by deforming the singular mass matrix based on the Runge-Kutta method. The mass matrix is ​​used to solve the water withdrawal model without air valve and the water withdrawal model with air valve respectively. The solution results of the water withdrawal model without air valve and the water withdrawal model with air valve are obtained. The function expression of the mass matrix is:

[0068] Where M represents the mass matrix.

[0069] Through the implementation of the above-mentioned water withdrawal modeling method, due to the assumption of a rigid water column, the mathematical model of the water withdrawal process only considers the changes in various parameters on a temporal scale, not on a spatial scale. The water column velocity equation and water column length equation describe the water column velocity and length during the water withdrawal process in a pressurized pipeline, forming a set of ordinary differential equations. The absolute pressure change equation describes the gas state within the empty pipe section during the water withdrawal process. Assuming the process is a constant entropy process, the algebraic relationship for the gas state equation for a constant entropy process is satisfied. The simultaneous water column velocity equation, water column length equation, and absolute pressure change equation form a set of differential algebraic equations. Similarly, in the water withdrawal model with an air valve, the description of the air valve's air intake velocity is also an algebraic relationship, so the water withdrawal model with an air valve is also a set of differential algebraic equations.

[0070] Differential algebraic equations are a class of differential equations in which one or more dependent variables do not appear in the equation. Variables that appear in the equation without their derivatives are called algebraic variables. The presence of algebraic variables means that not all equations can be written as differential equations in explicit form. form.

[0071] This type of differential equations can be solved using the Runge-Kutta method combined with the singular mass matrix to solve linear implicit problems with differential index 1, including semi-explicit differential algebraic equations of the form:

[0072]

[0073] In this form, the presence of algebraic variables leads to a singular mass matrix due to the presence of one or more zeros on the main diagonal. The singular mass matrix is ​​expressed as:

[0074] The mass matrix M is obtained by transforming the singular mass matrix based on the Runge-Kutta method. The derivative vector of After linear combination and the right function The equation relationship is formed, and the water withdrawal model without air valve and the water withdrawal model with air valve are solved by mass matrix. The effect is similar to the substitution method. The dependent variable without differential form is replaced by an equation with similar algebraic form. When solving the differential algebraic equation system, it can be and At the same time, specify the initial conditions, that is, substitute the initial values ​​of the first-order differentials of the variables to be solved during the solution process and The initial value at the moment can be used to solve the change of the variable over time.

[0075] The present invention also discloses a model building system, which adopts the above-mentioned method for building a water withdrawal model based on a long-distance pressurized pipeline, and includes: A rigid water column model construction module is used to construct a rigid water column model based on the deformation of the motion equation and continuity equation of the non-steady flow process of the fluid in the pressurized pipe, assuming that the fluid is incompressible; The water withdrawal liquid phase description module is used to assume that there is no air valve at the upstream end of the pressurized pipeline. Based on the rigid water column model and combined with the analysis of the time-scale changes in the hydraulic parameters in the pressurized pipeline, the water column velocity equation and water column length equation are established to describe the liquid phase changes during the water withdrawal process without an air valve. The airless valve water withdrawal model establishment module is used to analyze the pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve to describe the volume change in the empty pipe section. The airless valve water withdrawal model is constructed by combining the water column velocity equation and the water column length equation. The module for establishing a water-relief model with an air valve assumes that there is an air valve at the upstream end of a pressurized pipeline. It analyzes the time-scale changes in gas parameters of the air in the empty pipe section at the upstream end of the pressurized pipeline as it passes through the air valve. It also constructs a water-relief model with an air valve by combining the water column velocity equation and the water column length equation in parallel. The model solving simulation module is used to solve the water withdrawal model without air valve and the water withdrawal model with air valve respectively, and simulate according to the solution results to predict the change trend and fluctuation of the pressure head in the empty pipe section at the upstream end during the water withdrawal process of the pressurized pipeline.

[0076] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, wherein the computer program is characterized in that when executed by a processor, the computer program implements the above-mentioned method for establishing a water withdrawal model based on a long-distance pressurized pipeline.

[0077] The present invention also discloses a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. The device is characterized in that when the processor executes the computer program, the method for establishing a water withdrawal model based on a long-distance pressurized pipeline is implemented.

[0078] The present invention is described based on flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to specific embodiments. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0079] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0080] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0081] It should be understood that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Those skilled in the art may modify the technical solutions described in the above embodiments, or replace some of the technical features therein with equivalents; and all these modifications and replacements should fall within the scope of protection of the present invention.

Claims

1. A method for establishing a water withdrawal model based on a long-distance pressurized pipeline, characterized in that: The method for establishing the water withdrawal model comprises: Based on the assumption that the fluid is incompressible, a rigid water column model is constructed based on the deformation of the motion equation and continuity equation of the unsteady flow process of the fluid in the pressurized pipeline. Assuming that there is no air valve at the upstream end of the pressurized pipeline, based on the rigid water column model and combined with the analysis of the changes in hydraulic parameters in the pressurized pipeline on a time scale, the water column velocity equation and the water column length equation are established to describe the liquid phase changes during the water withdrawal process without an air valve. The pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve is analyzed to describe the volume change in the empty pipe section, and the water column velocity equation and the water column length equation are combined to construct a water withdrawal model for the air valve; Assuming that there is an air valve at the upstream end of the pressurized pipeline, the time-scale changes in gas parameters of the air in the empty pipe section at the upstream end of the pressurized pipeline passing through the air valve are analyzed, and the water column velocity equation and the water column length equation are simultaneously established to construct a water withdrawal model with an air valve; By solving the water withdrawal model without an air valve and the water withdrawal model with an air valve respectively and performing simulations based on the solution results, the changing trend and fluctuation of the pressure head in the empty pipe section at the upstream end during the water withdrawal process of the pressurized pipeline are predicted.

2. The method for establishing a water withdrawal model based on a long-distance pressurized pipeline according to claim 1, characterized in that: The rigid water column model is constructed by deforming the motion equation and continuity equation of the non-steady flow process of the fluid in the pressurized pipeline, including: The motion equation describing the unsteady flow process of fluid in a pressurized pipeline based on the law of conservation of momentum is expressed as follows: The continuity equation based on the law of conservation of momentum describes the unsteady flow process of fluid in a pressurized pipeline. The functional expression of the continuity equation is: Based on the assumption that the fluid is incompressible, the motion equation and the continuity equation are simplified; The simplified function expression of the continuity equation is: The simplified functional expression of the motion equation is: In the formula, in the formula, is the instantaneous flow velocity, H is the instantaneous water head, D is the diameter of the pressurized pipe, is the spatial coordinate of the axis of the pressurized pipeline, t is the water withdrawal time, g is the local gravity acceleration, is the water hammer propagation velocity, f is the hydraulic friction coefficient of the unsteady flow in the pipeline, is the upstream head, is the lower water head, is the pipeline resistance loss, is the length of the pressurized pipeline.

3. The method for establishing a water withdrawal model based on a long-distance pressurized pipeline according to claim 2, characterized in that: The establishment of the water column velocity equation and the water column length equation to describe the liquid phase changes during the airless valve water withdrawal process includes: The basic conditions for the water withdrawal process in a pressurized pipeline without an air valve are set. The entire water body in the pressurized pipeline is used as the control volume, and it is assumed that the axis direction of the pressurized pipeline is consistent with the direction of the fluid. According to the simplified motion equation, the force analysis of the water column in the pressurized pipe is carried out. Combined with the density and flow velocity of the water column after analysis, and the analysis of the change of the pressure of the gas in the empty pipe section at the upstream end on the time scale, the water column flow velocity equation is established to describe the water column flow velocity during the water withdrawal process of the airless valve. The functional expression of the water column flow velocity equation is: According to the simplified continuity equation, combined with the analysis of the change of the length of the water column on the time scale during the water withdrawal process of the pressurized pipeline, the water column length equation is established to describe the water column length during the water withdrawal process of the airless valve. The functional expression of the water column length equation is: Where, is the absolute pressure of the gas in the empty pipe section during the water withdrawal process, is the interfacial area, is the angle between the pressurized pipe and the horizontal plane, is the standard atmospheric pressure, is the friction coefficient of the pipe wall, is the total length of the pressurized pipeline, is the length of the water column, is the density of water, is the acceleration due to gravity, is the water flow velocity, is the differential per unit time.

4. The method for establishing a water withdrawal model based on a long-distance pressurized pipeline according to claim 3, characterized in that: The analysis of the pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve to describe the volume change in the empty pipe section includes: According to the absolute pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve, the absolute pressure change equation in the empty pipe section of the pressurized pipeline from the beginning of water withdrawal is established to describe the volume change in the empty pipe section. The function expression of the absolute pressure change equation is: Where, is the absolute pressure in the empty pipe section at the initial moment, is the initial length of the empty pipe segment, is the volume of the empty pipe section during the water withdrawal process.

5. The method for establishing a water withdrawal model based on a long-distance pressurized pipeline according to claim 3, characterized in that: The analysis of the time-scale changes in gas parameters of air in the empty pipe section at the upstream end of the pressurized pipeline passing through the air valve includes: The basic conditions of the water withdrawal process in the pressurized pipeline with an air valve are set to be the same as those in the pressurized pipeline without an air valve, and the water column velocity equation and the water column length equation are used to describe the liquid phase change in the water withdrawal process with the air valve; The gas mass flow equation entering the air valve per unit time is established to describe the volume change of the air in the empty pipe section. The function expression of the gas mass flow equation is: By simplifying the gas mass flow equation, the air density change equation is obtained to describe the change of air density in the empty pipe section on a time scale. The functional expression of the air density change equation is: Based on the adiabatic compression equation and the ideal gas state equation, the air pressure change equation is established to describe the change of air pressure in the empty pipe section on a time scale. The functional expression of the air pressure change equation is: Where, is the atmospheric density, is the flow rate of gas into the air valve, is the air valve inlet area, is the density of the gas in the empty pipe section, is the mass of the gas in the empty pipe section, and k is a constant.

6. The method for establishing a water withdrawal model based on a long-distance pressurized pipeline according to claim 5, characterized in that: The analysis of the time-scale changes in gas parameters of the air in the empty pipe section at the upstream end of the pressurized pipeline passing through the air valve also includes: Assuming the basic conditions for air to pass through the air valve, an air flow equation group is established to describe the changes when air flows into and out of the pressurized pipe through the air valve. The functional expression of the air flow equation group is: Where, is the flow rate of air entering the pressurized pipeline, is the flow rate of air flowing out of the pressurized pipe, is the volume of the empty pipe section, is the absolute temperature, is the gas constant, is the absolute pressure of the atmosphere in the empty pipe section; According to the air flow equations, when the air valve is installed and the pressure in the pressurized pipeline is discharged, the atmospheric pressure in the pressurized pipeline is lower than the external atmospheric pressure. An air flow velocity equation is established based on the subsonic air flow and the critical sonic air flow to describe the change in air mass passing through the air valve. The functional expression of the air flow velocity equation is: Where: is the flow coefficient when air flows into the air valve, is the opening area of ​​the air valve intake hole, is the atmospheric density, is the absolute pressure of the atmosphere, is the absolute pressure in a pressurized pipe.

7. The method for establishing a water withdrawal model based on a long-distance pressurized pipeline according to claim 6, characterized in that: The step of solving the water withdrawal model without an air valve and the water withdrawal model with an air valve respectively includes: The water column flow rate equation, the water column length equation, and the absolute pressure change equation are combined to construct the water withdrawal model without an air valve, and the water column flow rate equation, the water column length equation, the air density change equation, the air pressure change equation, and the air flow rate equation group are combined to construct the water withdrawal model with an air valve; The mass matrix is ​​obtained by deforming the singular mass matrix based on the Runge-Kutta method. The mass matrix is ​​used to solve the water withdrawal model without air valve and the water withdrawal model with air valve, respectively, to obtain the solution results of the water withdrawal model without air valve and the water withdrawal model with air valve. The function expression of the mass matrix is: Where M represents the mass matrix.

8. A model building system, using the method for building a water withdrawal model based on a long-distance pressurized pipeline according to any one of claims 1 to 7, characterized in that: The model building system includes: A rigid water column model construction module is used to construct a rigid water column model based on the deformation of the motion equation and continuity equation of the non-steady flow process of the fluid in the pressurized pipe, assuming that the fluid is incompressible; The water withdrawal liquid phase description module is used to assume that there is no air valve at the upstream end of the pressurized pipeline. Based on the rigid water column model and combined with the analysis of the changes in the hydraulic parameters in the pressurized pipeline on the time scale, the water column velocity equation and the water column length equation are established to describe the liquid phase changes during the water withdrawal process without an air valve. An airless valve water withdrawal model establishment module is used to analyze the pressure in the empty pipe section at the upstream end of the pressurized pipeline when there is no air valve to describe the volume change in the empty pipe section, and to jointly construct the airless valve water withdrawal model by combining the water column velocity equation and the water column length equation; A module for establishing a water withdrawal model with an air valve is used to assume that there is an air valve at the upstream end of the pressurized pipeline, analyze the changes in gas parameters of the air in the empty pipe section at the upstream end of the pressurized pipeline passing through the air valve on a time scale, and jointly establish the water column velocity equation and the water column length equation to construct a water withdrawal model with an air valve; The model solving simulation module is used to solve the airless valve water withdrawal model and the air valve water withdrawal model respectively, and perform simulation based on the solution results to predict the change trend and fluctuation of the pressure head in the empty pipe section at the upstream end during the water withdrawal process of the pressurized pipeline.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for establishing a water withdrawal model based on a long-distance pressurized pipeline according to any one of claims 1 to 7 is implemented.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the method for establishing a water withdrawal model based on a long-distance pressurized pipeline according to any one of claims 1 to 7 is implemented.

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