Numerical simulation method, device and medium for filling process of pressurized pipeline with air valve

Abstract

This invention discloses a numerical simulation method, equipment, and medium for the water filling process of pressurized pipelines with air valves, belonging to the field of engineering technology for long-distance pressurized water transmission systems. The method includes the following steps: by constructing a three-in-one coupled control equation for pipeline water flow, air masses within the pipe, and air inlet and outlet of the air valve, combined with a gas-liquid interface tracking algorithm adapted to open-full transition flow and a refined dynamic model of the air valve, accurate numerical simulation of the entire process of a pressurized pipeline from empty pipe filling to full pipe operation is achieved. This invention, employing the aforementioned numerical simulation method, equipment, and medium for the water filling process of pressurized pipelines with air valves, improves the simulation accuracy of hydraulic parameters during water filling, enhances computational stability and engineering applicability under complex working conditions, and can accurately identify dangerous conditions such as air blockage, pressure anomalies, and water hammer, providing reliable support for the design, safety assessment, and protection optimization of water filling schemes for long-distance water transmission pipelines.

Description

Technical Field

[0001] This invention belongs to the field of engineering technology for long-distance pressurized water transmission systems, specifically relating to a numerical simulation method, equipment, and medium for the water filling process of pressurized pipelines with air valves. Background Technology

[0002] Long-distance pressurized water pipelines are widely used in inter-basin water transfer projects, urban water supply networks, pressure water diversion systems of water conservancy projects, and industrial circulating water transportation systems. During initial water supply, post-maintenance water replenishment, water pressure testing, and emergency water replenishment, the pipeline is initially filled with air. During the filling process, the water flow pushes and compresses the air inside the pipe. If the air cannot be smoothly discharged through the air valve, it can easily lead to airlock, localized high pressure, negative pressure, or even water hammer caused by a liquid column. Due to limitations such as high cost, long cycle time, and difficulty in reproducing dangerous conditions, physical model testing has become a core technical means for pipeline water filling scheme design, safety assessment, and water hammer protection.

[0003] However, the existing technology has the following shortcomings: the simulation accuracy of the numerical simulation technology for pressurized pipeline water filling is low and the deviation from the actual engineering is large. Most models only calculate the water flow separately and do not achieve strong coupling solution of water flow, air mass in the pipe and air valve intake and exhaust. At the same time, the air valve model is simplified by using a fixed flow coefficient and cannot accurately track the gas-liquid interface movement under the full flow state of water filling, making it difficult to truly reflect the actual hydraulic characteristics of pipeline water filling.

[0004] Secondly, existing numerical algorithms struggle to balance accuracy and stability. They are prone to numerical oscillations and calculation divergences in areas with sudden pressure changes and gas-liquid interfaces. Furthermore, they are only suitable for simple straight pipe scenarios and have poor versatility for complex pipeline systems with multiple humps, varying slopes, and multiple air valves. They also lack supporting program execution schemes and storage media, resulting in insufficient engineering implementation and software integration capabilities.

[0005] In addition, existing simulation methods cannot accurately identify dangerous conditions such as air blockage, pressure abnormality and water hammer during the water filling process. The simulation results are difficult to effectively guide water filling commissioning, air valve arrangement and water hammer protection scheme design, and the ability to predict safety risks of pipeline water filling operation is insufficient.

[0006] Therefore, a new method is urgently needed. Summary of the Invention

[0007] The purpose of this invention is to provide a numerical simulation method, equipment, and medium for the water filling process of pressurized pipelines with air valves. This method improves the simulation accuracy of hydraulic parameters during water filling, enhances the calculation stability and engineering applicability under complex working conditions, and can accurately identify dangerous working conditions such as air blockage, pressure anomalies, and water hammer. It provides reliable support for the design, safety assessment, and protection optimization of water filling schemes for long-distance water transmission pipelines.

[0008] To achieve the above objectives, the present invention provides a numerical simulation method, equipment, and medium for the water filling process of a pressurized pipeline with an air valve, comprising the following steps:

[0009] S1. Obtain the pipeline geometric topology parameters, fluid property parameters, air valve operating parameters and initial and boundary conditions, perform one-dimensional meshing on the pipeline computational domain, and generate and output standardized parameter datasets, discrete mesh information and initial flow field parameters.

[0010] S2. Receive the output data from S1 and establish a closed coupled equation set containing the dynamic flow equations of water flow, air mass and air valve based on the one-dimensional bright full transition flow theory, gas thermodynamic laws and dynamic characteristics of air valve.

[0011] S3 receives the coupled equations output by S2, uses a weighted implicit scheme to discretize the space and time, adaptively determines the computation time step based on the Courant stability criterion, and generates and outputs the discrete algebraic equations and coefficient matrix.

[0012] S4 receives the discrete format, time step and flow field physical quantities output by S3, calculates and updates the gas-liquid interface position, determines the flow regime type based on the pipe section filling degree, outputs the gas-liquid interface and flow regime parameters, and synchronously feeds them back to S2 to update the coupled model.

[0013] S5 receives the air mass pressure, interface position and flow parameters output by S4, calculates the real-time air intake and exhaust flow of the air valve in combination with the valve opening and closing hysteresis model, updates the air mass state and corrects the nonlinear boundary conditions, and outputs the corrected boundary and air mass parameters.

[0014] S6 receives the boundary conditions and discrete equations output from S5, uses the Newton-Raphson method to synchronously iterate the coupled variables across the entire field and determines the convergence; if converged, the flow field and air mass parameters are output to the post-processing step; if not converged, the residual parameters are sent back to S3 to adjust the time step and recalculate.

[0015] S7 receives the time-series flow field and air mass motion parameters output by S6, identifies dangerous conditions such as overpressure, negative pressure and air blockage during the water filling process based on preset safety thresholds, and outputs simulation results and engineering support data.

[0016] Preferably, in S1, the pipeline geometric topology parameters include the pipe segment number and the pipe segment length. Pipe diameter D, pipe bottom slope Pipe wall roughness and the elastic modulus E of the pipe wall;

[0017] Air valve operating parameters include air valve installation location and effective flow area of ​​valve port. Critical pressure threshold for opening and closing and the opening and closing response time constant ;

[0018] The initial operating condition is set to the initial pressure inside the pipeline. Initial flow velocity And the entire area is inflatable.

[0019] Preferably, the flow control equations in S2 include the flow continuity equations:

[0020] ;

[0021] In the formula, The flow area of ​​the pipe, in units ; For time, in units ; The flow rate of water within the pipe, in units of ; For the axial spatial coordinates of the pipeline, in units ;

[0022] Water flow equation:

[0023] ;

[0024] In the formula, For gravitational acceleration, in units ; The pressure head of the water flow in the pipeline, in units ; This represents the friction gradient along the pipeline, without units.

[0025] The governing equations for air masses include the air mass conservation equation:

[0026] ;

[0027] In the formula, For the mass of the air mass within the pipe, in units ; The mass flow rate of the air valve's inlet and outlet is expressed in units of... Positive values ​​indicate exhaust, and negative values ​​indicate replenishment.

[0028] Equation of state for polytropic processes of air masses:

[0029] ;

[0030] In the formula, The pressure of the air mass within the pipe, in units ; The volume of the air mass inside the tube, in units ; The gas polyvariance index has no unit. It is a constant;

[0031] The dynamic flow equation for the air valve is:

[0032] ;

[0033] In the formula, The flow coefficient is a dimensionless coefficient that adapts to the ratio of air mass pressure to atmospheric pressure. Atmospheric pressure, unit ; The effective flow area of ​​the air valve orifice, per unit ; The density of the gas inside the pipe, in units .

[0034] Preferably, in S3, the Preissmann weighted implicit scheme is used for time discretization, as follows:

[0035] ;

[0036] In the formula, The physical quantity to be discretized has no unit; These are weighting coefficients, dimensionless, and range from 0.5 to 1.0. For time step, unit ; This is a spatial computing node number, without units. These are time step numbers, without units;

[0037] Numerical calculations satisfy the Courant number stability constraint:

[0038] ;

[0039] In the formula, This is the Courant number, which has no unit. The water hammer wave velocity, in units ; Spatial step size, unit ;

[0040] The time step is adaptively adjusted using the adaptive time step calculation formula and joint constraints, expressed as:

[0041] ;

[0042] In the formula, For the time step of the next moment, the unit ; This is a safety factor, dimensionless, and ranges from 0.5 to 0.8. For the maximum permissible time step, the unit .

[0043] Preferably, in S4, the formula for calculating the gas-liquid interface propulsion velocity is:

[0044] ;

[0045] In the formula, For the first The propulsion velocity of a gas mass at the gas-liquid interface, per unit ; For the first Water flow rate per spatial node, unit ; For the first The water flow area of ​​each spatial node, in units ;

[0046] The formula for updating the interface position step by step over time is:

[0047] ;

[0048] In the formula, For the first Time step The interface space coordinates of an air mass, in units ; For the first Time step The interface space coordinates of an air mass, in units ; For the first Time step size, in units ;

[0049] The formula for calculating the pipe section fill degree is:

[0050] ;

[0051] In the formula, For the first The pipe segment fill degree of each spatial node, without unit, with a value range of 0 to 1; The full-pipe flow area, unit ;

[0052] Based on pipe segment fill degree Adaptively distinguishes between unpressurized flow, transitional flow, and pressurized flow.

[0053] Preferably, in S5, the formula for determining the opening and closing of the air valve is:

[0054] ;

[0055] ;

[0056] In the formula, The pressure of the air mass inside the tube at a certain moment, in units ; The critical pressure threshold for opening and closing the air valve, in units of ; This is the pressure threshold deviation, in units. This is used to prevent valves from being opened and closed frequently. The air valve opening and closing response time constant, in units of ; This represents the relative opening degree of the air valve. It has no unit and its value ranges from 0 to 1, where 0 indicates fully closed and 1 indicates fully open.

[0057] The formula for calculating the mass increment of an air mass is:

[0058] ;

[0059] In the formula, The mass increment of an air mass within a given time step, in units of ; The real-time intake and exhaust mass flow rate of the air valve, in units ; For the current time step, in units Update the mass, volume, and pressure parameters of the air mass based on the intake and exhaust flow rates.

[0060] Preferably, in S6, the Newton-Raphson iterative scheme is used to solve the discrete equation system:

[0061] ;

[0062] In the formula, It is a Jacobian matrix with no unit; This is the correction vector for the physical quantity to be determined, and it has no unit. This is the residual vector of the system of equations, and it has no unit.

[0063] The global convergence residual uses the infinite norm of the relative residual of the physical quantity as the convergence criterion, expressed as:

[0064] ;

[0065] In the formula, is the infinite norm of the residual vector, and has no unit; For the first The physical quantity to be determined in the next iteration is dimensionless. For the first The physical quantity to be determined in the next iteration is dimensionless. This is a preset convergence precision, and has no unit.

[0066] Preferably, in S7, the overpressure condition determination formula is expressed as:

[0067] ;

[0068] In the formula, For the first The pressure inside the pipe at each spatial node, in units ; For the allowable pressure of the pipeline design, the unit ;

[0069] ;

[0070] In the formula, For the minimum safe pressure of the pipeline, unit ;

[0071] Airlock condition determination is based on interface propulsion speed And the pipe section is full Identify airlock conditions; among them, This represents the critical degree of airlock filling; it has no unit.

[0072] Therefore, the present invention employs the above-mentioned numerical simulation method, equipment, and medium for the water filling process of a pressurized pipeline with an air valve. Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0073] (1) This invention solves the problems of excessive simplification assumptions and distortion of gas-liquid motion in traditional simulation by constructing a strongly coupled mathematical model of water flow-air mass-air valve inlet and outlet, a refined dynamic model of air valve, and a full-flow interface tracking method for open flow; and achieves high-precision simulation of pressure, flow rate and exhaust process of the entire water filling process.

[0074] (2) This invention solves the problems of pressure sudden change is prone to numerical oscillation, poor versatility of complex pipelines and weak engineering integration by optimizing numerical solution algorithm and complex pipeline network adaptation model; adapts to the simulation requirements of complex pipeline systems with multiple humps, variable slope and multiple air valves in combination.

[0075] (3) This invention solves the problem of difficulty in predicting dangerous conditions such as air blockage, high pressure negative pressure and water hammer by accurately identifying transient hydraulic anomalies during the water filling process; and meets the safety design requirements for pipeline water filling and debugging, air valve layout optimization and water hammer protection.

[0076] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0077] Figure 1 This is a flowchart illustrating an embodiment of the numerical simulation method, equipment, and medium for the water filling process of a pressurized pipeline with an air valve according to the present invention.

[0078] Figure 2 This is a flowchart illustrating the construction of the fully coupled equation set of water flow-air mass-air valve for a numerical simulation method, equipment and medium embodiment of the water filling process of a pressurized pipeline with an air valve according to the present invention.

[0079] Figure 3 This is a flowchart illustrating the multi-air mass interface tracking and flow regime adaptive discrimination process of a numerical simulation method, equipment, and medium for the water filling process of a pressurized pipeline with an air valve, as described in this invention.

[0080] Figure 4 This is a flowchart illustrating the coupled calculation and boundary update process of the dynamic characteristics of the air valve in a numerical simulation method, equipment, and medium embodiment of the pressurized pipeline water filling process with an air valve according to the present invention.

[0081] Figure 5 This is a flowchart illustrating the fully coupled system iterative solution and convergence determination process of the numerical simulation method, equipment, and medium embodiment of the pressurized pipeline water filling process with air valve of the present invention. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Unless otherwise defined, the technical or scientific terms used in the present invention should have the ordinary meaning understood by those skilled in the art.

[0083] Example 1

[0084] like Figures 1-5 As shown, this embodiment provides a numerical simulation method, equipment, and medium for the water filling process of a pressurized pipeline with an air valve. It should be understood that the specific parameters, models, and protocols mentioned in this embodiment are merely examples to help those skilled in the art understand the present invention, and are not intended to limit the present invention.

[0085] The present invention provides a numerical simulation method, equipment, and medium for the water filling process of a pressurized pipeline with an air valve, comprising the following steps:

[0086] S1. Obtain pipeline geometric topology parameters, fluid property parameters, air valve operating parameters, and initial and boundary conditions. The process involves structuring the parameters and performing one-dimensional mesh generation on the pipeline computational domain. Generate a standardized parameter dataset, spatial discrete mesh information, and initial flow field parameters. Transfer the data uniformly to the coupled equation system construction step as the basic input for subsequent mathematical modeling and numerical calculation.

[0087] In this step, the pipe segment number and pipe segment length are collected and stored. Pipe diameter D, pipe bottom slope Pipe wall roughness The pipeline topology and geometry parameters, such as the pipe wall elastic modulus E, were collected, along with the air valve installation location and effective flow area at the valve port. Critical pressure threshold for opening and closing and the opening and closing response time constant The air valve characteristic parameters are set such that the pipeline is initially in an atmospheric state, and the initial pressure is... Initial flow velocity Furthermore, the entire pipe is in an inflated state, and the pipe computational domain is divided into a one-dimensional uniform mesh to generate spatial computational nodes. Establish the topological relationships between computing nodes, pipe segments, and air valves to ensure spatial matching for subsequent calculations.

[0088] S2 receives the standardized parameter dataset and discrete grid information transmitted by S1. Based on the one-dimensional bright full transition flow theory, gas thermodynamics, and the dynamic characteristics of the air valve, it constructs a unified closed-loop coupled control equation set for the water flow, air mass, and air valve. This closed-loop coupled control equation set is then transmitted to the numerical discretization step, providing a complete mathematical model foundation for subsequent equation discretization and iterative solutions.

[0089] In this step, a unified flow control equation applicable to unpressurized flow, transitional flow, and pressurized flow is established based on the one-dimensional open-circuit transitional flow theory. The flow continuity equation is shown below:

[0090] ;

[0091] In the formula, The flow area of ​​the pipe, in units It dynamically adjusts according to changes in the water flow pattern; For time, in units ; The flow rate of water within the pipe, in units of ; For the axial spatial coordinates of the pipeline, in units .

[0092] The equation for water flow is shown below:

[0093] ;

[0094] In the formula, For gravitational acceleration, in units ; The pressure head of the water flow in the pipeline, in units ; This is the friction gradient along the pipe, without units, and is related to the pipe wall roughness and water flow velocity.

[0095] Simultaneously, an air mass control model is established, and the air mass mass conservation equation is shown below, which is used to describe the change law of air mass mass in the pipe with the air valve intake and exhaust process:

[0096] ;

[0097] In the formula, For the mass of the air mass within the pipe, in units ; The mass flow rate of the air valve's inlet and outlet is expressed in units of... Positive values ​​indicate exhaust, while negative values ​​indicate replenishment.

[0098] The equation of state for the polytropic process of an air mass is shown below. It describes the relationship between the air mass pressure and volume and the water filling process, and is suitable for the adiabatic compression and expansion process of the air mass:

[0099] ;

[0100] In the formula, The pressure of the air mass within the pipe, in units ; The volume of the air mass inside the tube, in units ; The gas polyvariance index has no unit. It is a constant, determined by the initial state of the air mass.

[0101] The dynamic mass flow equation for the air valve is shown below:

[0102] ;

[0103] In the formula, The flow coefficient is a dimensionless coefficient that adapts to the ratio of air mass pressure to atmospheric pressure. Atmospheric pressure, unit ; The effective flow area of ​​the air valve orifice, per unit ; The density of the gas inside the pipe, in units .

[0104] By embedding the change in air mass mass as a source-sink term into the water flow control equation, a strong coupling relationship between air mass motion and water flow motion is achieved. The air valve's inlet and outlet flow rates and opening and closing characteristics are coupled into the overall control equation set as nonlinear boundary conditions. Finally, a fully coupled mathematical model of water flow-air mass-air valve with self-consistent physical quantities and no redundant assumptions is formed, covering the flow regime changes and coupling laws of the entire water filling process.

[0105] S3 receives the fully coupled control equations transmitted from S2, performs spatial and temporal discretization on the control equations using a weighted implicit scheme, calculates and determines the adaptive time step based on the Courant stability criterion, and generates a discrete algebraic equation set and corresponding coefficient matrix. The discrete algebraic equation set, coefficient matrix, and adaptive time step are then transmitted to the multi-mass interface tracking step, simultaneously providing a stable numerical calculation format for subsequent iterative calculations.

[0106] In this step, the finite difference method is used to spatially discretize the fully coupled control equations, and the Preissmann weighted implicit scheme is used for time-domain discretization. This scheme can be expressed as follows:

[0107] ;

[0108] In the formula, The physical quantity to be discretized (which can represent pressure, flow rate, flow area, etc.) has no unit; This is a weighting coefficient, without units, with a value range of 0.5 to 1.0. In this embodiment, it is set to 0.6 to balance calculation accuracy and stability. For time step, unit ; This is a spatial computing node number, without units. This is a time step number, without units.

[0109] The numerical calculation process satisfies the Courant number stability constraint, as shown in the following equation:

[0110] ;

[0111] In the formula, The Courant number is a unitless number, and its value is no greater than 1 to ensure computational stability. The water hammer wave velocity, in units It is determined by the pipe's elastic modulus, fluid density, and pipe geometric parameters; Spatial step size, unit The length is determined by the pipe length and the number of grid nodes.

[0112] The time step is adaptively determined according to the following formula:

[0113] ;

[0114] In the formula, For the time step of the next moment, the unit ; This is a safety factor, dimensionless, ranging from 0.5 to 0.8, used to reserve stability redundancy. For the maximum permissible time step, the unit The efficiency requirements of engineering simulation are set.

[0115] The time step is adaptively adjusted based on the water hammer wave velocity and pressure change rate to improve the computational stability under large gradient hydraulic conditions while ensuring computational accuracy and grid adaptability. On this basis, the overall discrete algebraic equation system is assembled to complete the assignment of boundary conditions and the setting of iterative initial vectors.

[0116] S4 receives the discrete calculation format, adaptive time step, and previous flow field physical quantities transmitted by S3, calculates the gas-liquid interface motion parameters, updates the interface spatial coordinates, and determines the flow regime type based on the pipe segment filling degree. The gas-liquid interface parameters, flow regime type, and pipe segment filling degree are synchronously fed back to S2 to dynamically update the coupled model parameters, and simultaneously transmitted the parameters to the air valve dynamic characteristic calculation step.

[0117] In this step, interface position tracking is performed on multiple independent gas masses existing within the multi-hump pipe section, and the gas-liquid interface propulsion velocity is calculated according to the following formula:

[0118] ;

[0119] In the formula, For the first The propulsion velocity of a gas mass at the gas-liquid interface, per unit ; For the first Water flow rate per spatial node, unit ; For the first The water flow area of ​​each spatial node, in units .

[0120] The interface position is updated step-by-step according to the following formula:

[0121] ;

[0122] In the formula, For the first Time step The interface space coordinates of an air mass, in units ; For the first Time step The interface space coordinates of an air mass, in units ; For the first Time step size, in units .

[0123] The fill factor of the pipe section is determined by the following formula:

[0124] ;

[0125] In the formula, For the first The pipe segment fill degree of each spatial node, without unit, with a value range of 0 to 1; The full-pipe flow area, unit , by pipe diameter Calculated.

[0126] Based on the obtained pipe segment fill degree The flow regime is adaptively determined, and the threshold for distinguishing between unpressurized flow, transitional flow, and pressurized flow can be adaptively adjusted within the range of 0.9 to 1.1. In this embodiment, unpressurized flow is selected. Transitional flow ( ) and pressurized flow ( The flow state is recorded, and the flow state information and flow area parameters are synchronously fed back to the coupled control equations to achieve adaptive matching between the flow state and the control equations, so that the model can adapt to complex terrain pipeline conditions.

[0127] S5 receives the gas mass pressure, gas-liquid interface position, and flow parameters transmitted from S4. It then calculates the real-time air intake and exhaust flow rates of the air valve using the valve opening and closing hysteresis dynamics model, updates the gas mass, volume, and pressure parameters, and corrects the nonlinear boundary conditions. The corrected nonlinear boundary conditions and gas mass state parameters are then transmitted to the fully coupled iterative solution step as boundary inputs for the iterative calculation.

[0128] In this step, the opening and closing state and real-time relative opening of the air valve are determined based on the air mass pressure and the opening and closing hysteresis model. The valve opening and closing criteria are shown in the following formula, which is used to accurately describe the opening and closing characteristics and hysteresis effect of the air valve triggered by pressure:

[0129] ;

[0130] ;

[0131] In the formula, The pressure of the air mass inside the tube at a certain moment, in units ; The critical pressure threshold for opening and closing the air valve, in units of ; This is the pressure threshold deviation, in units. This is used to prevent valves from being opened and closed frequently. The air valve opening and closing response time constant, in units of ; This represents the relative opening degree of the air valve. It has no unit and its value ranges from 0 to 1, where 0 indicates fully closed and 1 indicates fully open.

[0132] The mass increment of an air mass is calculated using the following formula:

[0133] ;

[0134] In the formula, The mass increment of an air mass within a given time step, in units of ; The real-time intake and exhaust mass flow rate of the air valve, in units ; For the current time step, in units ;

[0135] The dynamic flow coefficient that varies with pressure ratio is substituted into the dynamic mass flow equation of the air valve to calculate the actual inlet and outlet mass flow of the air valve. Based on the inlet and outlet flow and time step, the mass, volume and pressure parameters of the air mass are updated. The air valve flow is used as the boundary flux to couple and update the boundary terms of the discrete algebraic equation system, thus completing the dynamic correction of the boundary conditions.

[0136] S6 receives the updated boundary conditions and discrete algebraic equations transmitted from S5, and performs full-field synchronous iterative calculations on the coupled variables of water flow, air mass, and air valve using the Newton-Raphson method, determining whether the iterative residuals meet the convergence accuracy. If the convergence conditions are met, the pressure field, flow field, and air mass parameters at the current time are output to the post-processing step; if the convergence conditions are not met, the iterative residual parameters are sent back to S3, and the discretization and iterative calculations are re-executed after adaptively reducing the time step.

[0137] In this step, the water flow field, air mass parameter field, and air valve boundary conditions are solved synchronously and uniformly to avoid error accumulation caused by step-by-step solutions. The Newton-Raphson iterative correction scheme, as shown in the following equation, is used to quickly solve the discretized nonlinear algebraic equations:

[0138] ;

[0139] In the formula, is a Jacobian matrix, without a unit, and is composed of the partial derivatives of the discrete system of equations; This is the correction vector for the physical quantity to be determined, and it has no unit. This is the residual vector of the system of equations, which is unitless and reflects the calculation error of the current iteration step.

[0140] The global convergence residual criterion is shown in the following formula, which is used to determine whether the iterative calculation has reached the preset accuracy requirement:

[0141] ;

[0142] In the formula, is the infinite norm of the residual vector, and has no unit; For the first The physical quantity to be determined in the next iteration is dimensionless. For the first The physical quantity to be determined in the next iteration is dimensionless; the convergence accuracy ranges from [value missing]. In this embodiment, Unitless, meeting the accuracy requirements of engineering simulation;

[0143] By calculating the relative residuals of the physical quantities to be solved in adjacent iteration steps and determining whether the preset convergence accuracy has been reached, if the convergence accuracy is met, the hydraulic parameters and air mass motion parameters of the whole field at the current moment are stored. If the convergence accuracy is not met, the time step is automatically reduced and the calculation is returned to S3 to perform numerical discretization and iteration again, thus avoiding the accumulation of errors caused by step-by-step solution.

[0144] S7 receives the full-time series flow field data and air mass motion parameters transmitted by S6, performs statistical analysis on hydraulic parameters such as pressure, flow rate, and gas-liquid interface position, identifies hazardous conditions based on preset engineering safety thresholds, and locates their spatiotemporal positions. Finally, it outputs the simulation results of the entire water filling process, a list of hazardous conditions, and engineering design support data, completing the overall numerical simulation process.

[0145] In this step, hydraulic parameters such as pressure, flow rate, air valve opening, and air mass location are extracted from the time series of the entire water filling process. Overpressure conditions are determined according to the following formula to identify dangerous situations where the pressure inside the pipeline exceeds the design allowable value:

[0146] ;

[0147] In the formula, For the first The pressure inside the pipe at each spatial node, in units ; For the allowable pressure of the pipeline design, the unit The strength is determined by the pipe material.

[0148] The following formula is used to determine negative pressure conditions, identifying dangerous situations where the pressure inside the pipeline is lower than the minimum safe pressure, and preventing the pipeline from being sucked down due to negative pressure:

[0149] ;

[0150] In the formula, For the minimum safe pressure of the pipeline, unit It is usually taken as 0.1 times the atmospheric pressure.

[0151] According to the interface progression speed And the pipe section is full Identifying airlock conditions is used to recognize dangerous situations where air masses inside the pipe cannot escape, hindering water flow; among them... The critical degree of air blockage is unitless and ranges from 0.2 to 0.5 in engineering applications. In this embodiment, it is set to 0.3. It is used to identify dangerous conditions in which air masses in the pipe cannot be discharged and obstruct the flow of water.

[0152] Based on preset safety thresholds such as allowable pressure, minimum safe pressure, and critical filling degree of air lock in pipeline design, the system intelligently identifies dangerous working conditions such as overpressure, negative pressure, air lock, and water hammer and locates their spatiotemporal locations. Finally, it generates simulation results of the entire water filling process and engineering design support data, providing a reliable basis for pipeline water filling commissioning and safety protection design.

[0153] Example 2

[0154] As a first modified embodiment of the present invention, the Preissmann weighted implicit scheme is removed from the numerical discretization stage and replaced with the method of characteristics for spatial and temporal discretization of the control equations. The characteristic line equation is determined based on the propagation characteristics of water hammer waves, and the hydraulic parameters are solved by integration along the characteristic line. The other parameter settings, coupled model construction, gas-liquid interface tracking, dynamic calculation of air valves, and iterative solution rules are all consistent with the embodiment. It can be adapted to the transient flow simulation requirements of steep slopes and long-distance pipelines, verifying the versatility of the numerical method of the present invention.

[0155] Example 3

[0156] As a second modified embodiment of the present invention, the Newton-Raphson method is eliminated in the full-field iterative solution stage and replaced by the PISO algorithm to perform pressure-velocity coupled iteration. The nonlinear equation system is solved in three steps: prediction, correction, and secondary correction, which improves the computational efficiency under complex multi-gas-mass conditions. The other parameter settings, coupled model construction, gas-liquid interface tracking, and dynamic calculation rules of air valves are consistent with the preferred embodiment, which can be adapted to the simulation of complex pipeline systems with multiple air valves arranged together.

[0157] Therefore, the present invention adopts the above-mentioned numerical simulation method, equipment and medium for the water filling process of pressurized pipelines with air valves. This method improves the simulation accuracy of water filling hydraulic parameters, improves the calculation stability and engineering applicability under complex working conditions, and can accurately identify dangerous working conditions such as air blockage, pressure abnormality and water hammer, providing reliable support for the design, safety assessment and protection optimization of water filling schemes for long-distance water transmission pipelines.

[0158] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0159] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A numerical simulation method for the water filling process of a pressurized pipeline with an air valve, characterized in that, Includes the following steps: S1. Obtain the pipeline geometric topology parameters, fluid property parameters, air valve operating parameters and initial and boundary conditions, perform one-dimensional meshing on the pipeline computational domain, and generate and output standardized parameter datasets, discrete mesh information and initial flow field parameters. Pipeline geometric topology parameters include pipe segment number and pipe segment length. Pipe diameter D, pipe bottom slope Pipe wall roughness and the elastic modulus E of the pipe wall; Air valve operating parameters include air valve installation location and effective flow area of ​​valve port. Critical pressure threshold for opening and closing and the opening and closing response time constant ; The initial operating condition is set to the initial pressure inside the pipeline. Initial flow rate And the entire area is inflatable, including, Atmospheric pressure, unit ; S2. Receives the output data from S1. Based on the one-dimensional bright full transition flow theory, gas thermodynamics, and the dynamic characteristics of the air valve, establishes a closed coupled equation set including the dynamic flow equations of water flow, air mass, and air valve, specifically: Continuity equation for water flow: ； In the formula, The flow area of ​​the pipe, in units ; For time, in units ; The flow rate of water within the pipe, in units of ; For the axial spatial coordinates of the pipeline, in units ; Water flow equation: ； In the formula, For gravitational acceleration, in units ; The pressure head of the water flow in the pipeline, in units ; This represents the friction gradient along the pipeline, without units. The governing equations for air masses include the air mass conservation equation: ； In the formula, For the mass of the air mass within the pipe, in units ; The mass flow rate of the air valve's inlet and outlet is expressed in units of... Positive values ​​indicate exhaust, and negative values ​​indicate replenishment. Equation of state for polytropic processes of air masses: ； In the formula, The pressure of the air mass within the pipe, in units ; The volume of the air mass inside the tube, in units ; The gas polyvariance index has no unit. It is a constant; The dynamic flow equation for the air valve is: ； In the formula, The flow coefficient is a dimensionless coefficient that adapts to the ratio of air mass pressure to atmospheric pressure. The effective flow area of ​​the air valve orifice, per unit ; The density of the gas inside the pipe, in units of ; S3 receives the coupled equations output by S2, uses a weighted implicit scheme to discretize the space and time, adaptively determines the computation time step based on the Courant stability criterion, and generates and outputs the discrete algebraic equations and coefficient matrix. S4 receives the discrete format, time step and flow field physical quantities output by S3, calculates and updates the gas-liquid interface position, determines the flow regime type based on the pipe section filling degree, outputs the gas-liquid interface and flow regime parameters, and synchronously feeds them back to S2 to update the coupled model. S5 receives the air mass pressure, interface position and flow parameters output by S4, calculates the real-time air intake and exhaust flow of the air valve in combination with the valve opening and closing hysteresis model, updates the air mass state and corrects the nonlinear boundary conditions, and outputs the corrected boundary and air mass parameters. S6 receives the boundary conditions and discrete equations output from S5, uses the Newton-Raphson method to synchronously iterate the coupled variables across the entire field and determines the convergence; if converged, the flow field and air mass parameters are output to the post-processing step; if not converged, the residual parameters are sent back to S3 to adjust the time step and recalculate. S7 receives the time-series flow field and air mass motion parameters output by S6, identifies dangerous conditions such as overpressure, negative pressure and air blockage during the water filling process based on preset safety thresholds, and outputs simulation results and engineering support data.

2. The numerical simulation method for the water filling process of a pressurized pipeline with an air valve according to claim 1, characterized in that, In S3, the Preissmann weighted implicit scheme is used for time discretization, represented as: ； In the formula, The physical quantity to be discretized has no unit; These are weighting coefficients, dimensionless, and range from 0.5 to 1.

0. For time step, unit ; This is a spatial computing node number, without units. These are time step numbers, without units; Numerical calculations satisfy the Courant number stability constraint: ； In the formula, This is the Courant number, which has no unit. The water hammer wave velocity, in units ; Spatial step size, unit ; The time step is adaptively adjusted using the adaptive time step calculation formula and joint constraints, expressed as: ； In the formula, For the time step of the next moment, the unit ; This is a safety factor, dimensionless, and ranges from 0.5 to 0.

8. For the maximum permissible time step, the unit .

3. The numerical simulation method for the water filling process of a pressurized pipeline with an air valve according to claim 2, characterized in that, In S4, the formula for calculating the gas-liquid interface propulsion velocity is: ； In the formula, For the first The propulsion velocity of a gas mass at the gas-liquid interface, per unit ; For the first Water flow rate per spatial node, unit ; For the first The water flow area of ​​each spatial node, in units ; The formula for updating the interface position step by step over time is: ； In the formula, For the first Time step The interface space coordinates of an air mass, in units ; For the first Time step The interface space coordinates of an air mass, in units ; For the first Time step size, in units ; The formula for calculating the pipe section fill degree is: ； In the formula, For the first The pipe segment fill degree of each spatial node, without unit, with a value range of 0 to 1; The full-pipe flow area, unit ; Based on pipe segment fill degree Adaptively distinguishes between unpressurized flow, transitional flow, and pressurized flow.

4. The numerical simulation method for the water filling process of a pressurized pipeline with an air valve according to claim 3, characterized in that, In S5, the formula for determining the opening and closing of the air valve is: ； ； In the formula, The pressure of the air mass inside the tube at a certain moment, in units ; The critical pressure threshold for opening and closing the air valve, in units of ; This is the pressure threshold deviation, in units. This is used to prevent valves from being opened and closed frequently. The air valve opening and closing response time constant, in units of ; This represents the relative opening degree of the air valve. It has no unit and its value ranges from 0 to 1, where 0 indicates fully closed and 1 indicates fully open. The formula for calculating the mass increment of an air mass is: ； In the formula, The mass increment of an air mass within a given time step, in units of ; The real-time intake and exhaust mass flow rate of the air valve, in units ; For the current time step, in units Update the mass, volume, and pressure parameters of the air mass based on the intake and exhaust flow rates.

5. The numerical simulation method for the water filling process of a pressurized pipeline with an air valve according to claim 4, characterized in that, In S6, the Newton-Raphson iterative scheme is used to solve the discrete equation system: ； In the formula, It is a Jacobian matrix with no unit; This is the correction vector for the physical quantity to be determined, and it has no unit. This is the residual vector of the system of equations, and it has no unit. The global convergence residual uses the infinite norm of the relative residual of the physical quantity as the convergence criterion, expressed as: ； In the formula, is the infinite norm of the residual vector, and has no unit; For the first The physical quantity to be determined in the next iteration is dimensionless. For the first The physical quantity to be determined in the next iteration is dimensionless. This is a preset convergence precision, and has no unit.

6. The numerical simulation method for the water filling process of a pressurized pipeline with an air valve according to claim 5, characterized in that, In S7, the overpressure condition judgment formula is expressed as: ； In the formula, For the first The pressure inside the pipe at each spatial node, in units ; For the allowable pressure of the pipeline design, the unit ; ； In the formula, For the minimum safe pressure of the pipeline, unit ; Airlock condition determination is based on interface propulsion speed And the pipe section is full Identify airlock conditions; among them, This represents the critical degree of airlock filling; it has no unit.

7. A computer device, characterized in that, include: A processor configured to be coupled to memory, read and execute instructions and / or program code in the memory to perform the method as described in any one of claims 1-6.

8. A computer-readable medium, characterized in that, The computer-readable medium stores computer program code that, when executed on a computer, causes the computer to perform the method as described in any one of claims 1-6.

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