A method for simulating fast-filling vertical pipes considering energy dissipation of trapped air

Abstract

The present invention discloses a method for simulating a fast-filling vertical pipeline considering the energy dissipation of trapped air, including: establishing a continuity equation and a pressure balance equation of a moving air-water interface; building a heat transfer model based on the water hammer theory and combining the heat transfer principle of a closed airbag and the equation of an ideal gas; using a first-order local MOC interpolation interface tracking method to solve the filling water column control equation and the air heat transfer equation considering unsteady friction, and calculating and obtaining the air pressure, velocity and position of the moving air-water interface; using the Runge-Kutta fourth-order numerical integration method to solve; simulating according to the solution result to obtain the simulation result. The present invention studies a heat transfer model considering the energy dissipation of trapped air, which can explain the white fog and hot pipe wall phenomena in related experiments and solve the accuracy problem of traditional models. It is of great significance for the heat transfer of trapped air pockets in actual fast-filling vertical pipelines and the energy consumption simulation of violent air-water interactions.

Description

Technical Field

[0001] The invention belongs to the technical field of hydraulic numerical simulation calculation of hydropower stations (pump stations), and in particular relates to a fast filling vertical pipeline simulation method taking into account the energy dissipation of trapped air. Background Art

[0002] The presence of trapped air pockets in pressurized water and urban sewer systems can pose serious operational challenges and may even lead to the formation of geysers or damage to system components. Recently, a series of experiments have been conducted to carefully study the interaction of fluid transients with cavitation, such as the dynamic behavior of online and offline cavitation in horizontal pipes, transient pressures caused by confined cavitation and air expulsion during rapid filling, and the dynamic mechanisms and air-water interactions during geysers. These latest studies have further revealed the dangers and complexity of transient flows with cavitation. Importantly, accurate numerical simulations of all such air-water transient events will help to better understand the relevant physical mechanisms and enable safe operations.

[0003] Various one-dimensional (1D) numerical models have been developed to simulate the hydraulic transients caused by trapped air pockets in rapidly filling pipes, based on some common modeling assumptions: (1) an empirical multivariate relationship approach is used for the trapped air pockets, and (2) a well-defined air-water interface is assumed between the air and water phases, and the fluid-structure interaction (FSI) in the pipe material is neglected. The existing theoretical frameworks generally use a rigid column method to fill the water and an empirical multivariate relationship to calculate the trapped air pockets. To further improve the accuracy of the models, other factors including the change in filling water length, system elasticity, and instability friction have been gradually added to the available models. However, it is worth noting that 1D models tend to underestimate the pressure decay rate, although they usually predict the first cycle - the air compression-expansion cycle - well.

[0004] One-dimensional transient flow simulation of fast-filling pipeline systems with trapped air is an effective means to explore the flow state of pipeline systems. Previous one-dimensional transient flow models mostly used a rigid column method to fill water, an empirical polynomial relationship to calculate trapped air pockets, and a characteristic line method to solve the transient pipeline pressure and flow changes containing both water and air phases. This method has the following defects: 1) It underestimates the pressure decay rate, although they can usually predict the first cycle - air compression-expansion cycle well; 2) It cannot explain the white fog and hot pipe wall phenomenon in fast-filling horizontal and vertical pipelines with trapped air pockets; 3) It does not consider the heat transfer of trapped air pockets and the energy loss caused by the violent air-water interaction.

[0005] Recent experiments have observed white fog and hot pipe wall phenomena in rapidly filling horizontal vertical pipes with trapped air pockets, and these observations indicate the possible importance of thermal processes on the dynamics of trapped air pockets. In addition, high-speed photographs taken during the experiments indicate several important factors: (1) for air pockets trapped in horizontal or horizontal vertical pipes, the air-water interaction and mixing become extremely complex, and (2) in contrast, when the air pocket is completely trapped in the vertical pipe segment, the air-water interface in the vertical pipe segment is essentially stable and nearly perpendicular to the pipe centerline during the entire filling process when the driving pressure is relatively small; however, even in the case of vertical pipes, violent air-water interactions and intensive mixing are observed under certain air pocket sizes and relatively large pressurization conditions. These facts imply that during the rapid filling process, both heat transfer of trapped air pockets and violent air-water interactions can lead to important energy losses, factors that are rarely considered in existing one-dimensional models. Summary of the invention

[0006] Purpose of the invention: In order to overcome the deficiencies in the prior art, a method for simulating the heat transfer of trapped air pockets in a rapidly filled vertical pipeline, the white fog and hot pipe wall phenomena in related experiments, and the accuracy of existing models are provided. The method studies the heat transfer model considering the energy dissipation of trapped air, which is of great significance for the simulation of the heat transfer of trapped air pockets and the energy consumption of violent air-water interaction in an actual rapidly filled vertical pipeline, and can explain the white fog and hot pipe wall phenomena in related experiments, solve the accuracy problem of traditional models, and accurately simulate the efficient air-water transient events.

[0007] Technical solution: To achieve the above purpose, the present invention provides a method for simulating a rapid filling vertical pipeline taking into account the energy dissipation of trapped air, comprising the following steps:

[0008] S1: Establish the continuity equation and pressure balance equation of the moving air-water interface;

[0009] S2: Based on the water hammer theory, the heat transfer model is constructed by combining the heat transfer principle of the closed airbag and the ideal gas equation. The unsteady friction in the liquid-filled water column is considered to study the energy loss in the fast-filled pipe.

[0010] S3: The first-order local MOC interpolation interface tracking method is used to solve the filling water column control equation (Eq. 1, 2) and the air heat transfer equation (Eq. 10) considering unsteady friction, and the air pressure, velocity and position of the moving air-water interface are calculated;

[0011] S4: Derivation of variables (pressure, velocity) of gas-water phases at time step using Runge-Kutta fourth-order numerical integration method;

[0012] S5: Perform simulation according to the solution result of step S4 to obtain simulation results.

[0013] Furthermore, the process of establishing the continuity equation and pressure balance equation of the moving air-water interface in step S1 is as follows:

[0014] Since the air-water interface in the vertical pipe segment is almost perpendicular to the centerline of the pipe during the entire filling process, the one-dimensional numerical simulation includes three parts: the water column with varying length, the well-defined air-water interface, and the trapped air pockets. The continuity and momentum equations of the filled water column can be expressed as:

[0015]

[0016] Where H is the water head; t is the time; a is the wave speed; Q is the flow rate; g is the gravitational acceleration; A is the cross-sectional area of ​​the pipe; x is the calculated distance; F s is the constant friction; F u is unsteady friction;

[0017] Establish the continuity equation and pressure balance equation of the moving air-water interface:

[0018]

[0019] H wa =H a +Z wa (4)

[0020] Where, L w is the initial water column length; L w0 is the initial water column length; l is the calculated pipe length; H wa , V wa and Z wa are the velocity and elevation of the pressure head and position head at the water-air interface, respectively; H a is the relative pressure head of the trapped air bag.

[0021] Furthermore, the step S2 is specifically as follows:

[0022] The heat transfer of the trapped air pocket is considered in the development of the 1D rapid filling model. The energy conservation principle for the closed air pocket gives:

[0023] dU=dN-dW (5)

[0024] Where dU is the energy change of internal energy; dN is the heat energy flowing out of the trapped air pocket by heat transfer; and dW is caused by the work done by the gas. P a * and are the absolute pressure and volume of the trapped air pocket;

[0025] The ideal gas equation is:

[0026]

[0027] R a =C P -C V (7

[0028]

[0029] Where M a is the mass of the air mass; R a is the gas constant; T a is the air temperature; C p is the specific heat at constant pressure; C v is the specific heat at constant volume; γ is the specific heat ratio;

[0030] Substituting the ideal gas equation into equation (5), the energy conservation equation can be written as

[0031]

[0032] The heat transfer rates applicable to air in a rapidly filling pipe are complex and current literature does not provide reliable methods for inclusion. Possible modes of energy exchange, including conduction, convection, radiation, and phase change, are simultaneously involved in a rapidly filling pipe with a closed trapped air pocket. In general, conduction, radiation, and phase change are relatively negligible for modeling the behavior of trapped air, and convection heat transfer dominates.

[0033] Convective heat transfer is often represented assuming a steady-state assumption, a simplification driven by the practical complexity of convective heat transfer. Convective heat transfer in a closed air pocket can be represented by the free convection coefficient.

[0034] The present invention considers that when air pockets are trapped only in vertical pipes, the air-water interface moves vertically throughout the rapid filling process. For a well-defined air-water interface, the heat transfer term dN / dt can be used for quasi-steady flow or low-frequency conditions.

[0035]

[0036] In the formula, A q is the contact area between the trapped air and the tube wall; T in is the temperature of the trapped air; T ex is the external temperature; α is the heat transfer coefficient.

[0037] Furthermore, in step S3, the first-order local MOC interpolation interface tracking method is used to solve the filling water column control equation (Equation 1, 2) and the air heat transfer equation (Equation 10) considering unsteady friction, which is specifically:

[0038] Unsteady friction F u and the unsteady shear stress τ u Introducing the TVB model for efficient and accurate simulation:

[0039]

[0040] In the formula, f s is the Darcy-Weisbach stable friction coefficient; D is the pipe diameter; ρ is the fluid density; v is the fluid viscosity coefficient; i=1~N is the calculation time step; Y ai is the weighted function integral of the current calculation time step; R is the hydraulic radius; n i and m i The specific value of the universal weighting coefficient for the current calculation time step can be found in the literature.

[0041] The positive MOC characteristic equation, the continuity equation, the pressure balance equation at the air-water interface (Eqs. (3) and (4)), and the energy conservation equation of cavitation (Eqs. (10) and (11)) constitute a well-posed problem.

[0042] Considering the elasticity and length change of the filled water, the continuity and momentum equations are applied to the water region, and the standard orifice equation is used to express the valve boundary conditions. Due to the air-water movement during the transient process, the length of the filled water will change. When the characteristic line method is used to solve the water continuity and momentum equations, the filled column can be regarded as two sections at time t+Δt, as follows:

[0043] (1) Fixed grid area L w -ΔL wi =(N-1)Δx, where pressure and flow can be calculated by a fixed MOC grid;

[0044] (2) Water body ΔL wi The changing mesh region can be solved by combining MOC and moving boundary equations.

[0045] Furthermore, the calculation method of the air pressure, speed and position of the moving air-water interface in step S3 is:

[0046] Water head H at point P P and flow rate Q P It can be obtained by combining equations, that is, according to the characteristic equation, ΔL wi The hydraulic head at the upstream point P can be expressed as C of point A–P + Characteristic equation and C of point C–P - Characteristic equation:

[0047] C + :H P -C P +R P Q P=0 (14)

[0048]

[0049] In the formula, H P is the water head at point P; Q P is the flow rate at point P; C P is the characteristic constant at P; H c is the water head at point c; Q c is the flow rate at point C; ΔL wi is the calculated distance moved by the air column;

[0050] The pressure head and flow value at point D cannot be directly calculated by fixed grid. Auxiliary point G is introduced to obtain the value at point D by connecting the air control equation. For 0<ΔL wi ≤Δx, the head and flow at point G are based on the interpolation between points P and E; when Δx<ΔL wi When ≤2Δx, the head and flow at point G are based on the interpolation between points E and F;

[0051] C from point G–D + Characteristics obtained:

[0052]

[0053] Starting from point C–D, the distance the air-water interface moves from t to t+Δt is:

[0054]

[0055] In the formula, H D is the water head at point D; Q D is the flow rate at point D; t D is the time at point D; t c is the time at point C; Δt is the time difference.

[0056] The present invention studies a heat transfer model that takes into account the energy dissipation of trapped air, which can solve the problems of insufficient consideration of factors, low solution accuracy, poor versatility and difficulty in real-time monitoring in existing one-dimensional transient flow models.

[0057] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0058] (1) The proposed model with air heat transfer can almost perfectly reproduce the experimental pressure oscillation patterns, pressure decay, and oscillation period in a rapidly filling vertical pipe with trapped air pockets.

[0059] (2) The kinetic and thermodynamic behaviors of trapped cavitation are used to explain the white fog and hot pipe wall phenomena observed in the experiment.

[0060] (3) The simulation method that considers the energy dissipation of trapped air can well solve the transient simulation problem of rapidly filling vertical pipes. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a flow chart of the implementation of the present invention;

[0062] Figure 2 is a schematic diagram of rapid pipe filling with trapped air of the present invention;

[0063] Figure 3 is a schematic diagram of a MOC fixed grid xt of the present invention;

[0064] Figure 4 is a comparison diagram of the heat transfer model of the present invention and the experimental pressure prediction results of Example 1;

[0065] Figure 5 It is a pressure oscillation comparison diagram of the heat transfer model of the present invention and the empirical polynomial relationship model in Example 2. DETAILED DESCRIPTION

[0066] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0067] The present invention provides a method for simulating a fast filling vertical pipe taking into account the energy dissipation of trapped air, such as Figure 1 As shown, the following steps are included:

[0068] S1: Establish the continuity equation and pressure balance equation of the moving air-water interface:

[0069] Reference Figure 2 , since the air-water interface in the vertical pipe segment is almost perpendicular to the centerline of the pipe during the entire filling process, the one-dimensional numerical simulation includes three parts: the water column with varying length, the well-defined air-water interface, and the trapped air pockets. The continuity and momentum equations of the filled water column can be expressed as:

[0070]

[0071] Where H is the water head; t is the time; a is the wave speed; Q is the flow rate; g is the gravitational acceleration; A is the cross-sectional area of ​​the pipe; x is the calculated distance; F s is the constant friction; F u is unsteady friction;

[0072] Establish the continuity equation and pressure balance equation of the moving air-water interface:

[0073]

[0074] H wa =H a +Z wa (4)

[0075] Where, L w is the initial water column length; L w0 is the initial water column length; l is the calculated pipe length; H wa , V wa and Z wa are the velocity and elevation of the pressure head and position head at the water-air interface, respectively; H a is the relative pressure head of the trapped air bag.

[0076] S2: Based on the water hammer theory, the heat transfer model is constructed by combining the heat transfer principle of the closed airbag and the ideal gas equation. The unsteady friction in the liquid-filled water column is considered to study the energy loss in the fast-filled pipe:

[0077] The heat transfer of the trapped air pocket is considered in the development of the 1D rapid filling model. The energy conservation principle for the closed air pocket gives:

[0078] dU=dN-dW (5)

[0079] Where dU is the energy change of internal energy; dN is the heat energy flowing out of the trapped air pocket by heat transfer; and dW is caused by the work done by the gas. P a * and are the absolute pressure and volume of the trapped air pocket;

[0080] The ideal gas equation is:

[0081]

[0082] R a =C P -C V (7

[0083]

[0084] Where M a is the mass of the air mass; R a is the gas constant; T a is the air temperature; C p is the specific heat at constant pressure; C v is the specific heat at constant volume; γ is the specific heat ratio;

[0085] Substituting the ideal gas equation into equation (5), the energy conservation equation can be written as

[0086]

[0087] The heat transfer rates applicable to air in a rapidly filling pipe are complex and current literature does not provide reliable methods for inclusion. Possible modes of energy exchange, including conduction, convection, radiation, and phase change, are simultaneously involved in a rapidly filling pipe with a closed trapped air pocket. In general, conduction, radiation, and phase change are relatively negligible for modeling the behavior of trapped air, and convection heat transfer dominates.

[0088] Convective heat transfer is often represented assuming a steady-state assumption, a simplification driven by the practical complexity of convective heat transfer. Convective heat transfer in a closed air pocket can be represented by the free convection coefficient.

[0089] The present invention considers that when air pockets are trapped only in vertical pipes, the air-water interface moves vertically throughout the rapid filling process. For a well-defined air-water interface, the heat transfer term dN / dt can be used for quasi-steady flow or low-frequency conditions.

[0090]

[0091] In the formula, A q is the contact area between the trapped air and the tube wall; T in is the temperature of the trapped air; T ex is the external temperature; α is the heat transfer coefficient.

[0092] S3: The first-order local MOC interpolation interface tracking method is used to solve the filling water column control equation (Eq. 1, 2) and the air heat transfer equation (Eq. 10) considering unsteady friction, and the air pressure, velocity and position of the moving air-water interface are calculated:

[0093] Unsteady friction F u and the unsteady shear stress τ u Introducing the TVB model for efficient and accurate simulation:

[0094]

[0095] In the formula, f s is the Darcy-Weisbach stable friction coefficient; D is the pipe diameter; ρ is the fluid density; v is the fluid viscosity coefficient; i=1~N is the calculation time step; Y ai is the weighted function integral of the current calculation time step; R is the hydraulic radius; n i and m i The specific value of the universal weighting coefficient for the current calculation time step can be found in the literature.

[0096] The positive MOC characteristic equation, the continuity equation, the pressure balance equation at the air-water interface (Eqs. (3) and (4)), and the energy conservation equation of cavitation (Eqs. (10) and (11)) constitute a well-posed problem.

[0097] Considering the elasticity and length change of the filled water, the continuity and momentum equations are applied to the water region, and the standard orifice equation is used to express the valve boundary condition. Due to the air-water motion during the transient process, the length of the filled water will change. When the characteristic line method is used to solve the water continuity and momentum equations, refer to Figure 3 , the filled column can be regarded as two cross sections at time t+Δt, as follows:

[0098] (1) Fixed grid area L w -ΔL wi =(N-1)Δx, where pressure and flow can be calculated by a fixed MOC grid;

[0099] (2) Water body ΔL wi The changing mesh region can be solved by combining MOC and moving boundary equations.

[0100] Water head H at point P P and flow rate Q P It can be obtained by combining equations, that is, according to the characteristic equation, ΔL wi The hydraulic head at the upstream point P can be expressed as C of point A–P + Characteristic equation and C-characteristic equation of point C–P:

[0101] C + :H P -C P +R P Q P =0 (14)

[0102]

[0103] In the formula, H P is the water head at point P; Q P is the flow rate at point P; C P is the characteristic constant at P; H c is the water head at point c; Q c is the flow rate at point C; ΔL wi is the calculated distance moved by the air column;

[0104] The pressure head and flow value at point D cannot be directly calculated using the fixed grid. Figure 3 , introduce auxiliary point G, and obtain the value at point D by connecting the air control equation. For 0<ΔL wi ≤Δx, the head and flow at point G are based on the interpolation between points P and E; when Δx<ΔLwi When ≤2Δx, the head and flow at point G are based on the interpolation between points E and F;

[0105] C from point G–D + Characteristics obtained:

[0106]

[0107] Starting from point C–D, the distance the air-water interface moves from t to t+Δt is:

[0108]

[0109] In the formula, H D is the water head at point D; Q D is the flow rate at point D; t D is the time at point D; t c is the time at point C; Δt is the time difference.

[0110] S4: The variables (pressure, velocity) of the gas-water phase at the time step are derived and solved using the Runge-Kutta fourth-order numerical integration method;

[0111] S5: Process the calculation results and compare and verify the simulation results with the calculation results of the traditional empirical polynomial model and experimental data.

[0112] Based on the above scheme, in order to verify the simulation effect of the method of the present invention, the following Examples 1 and 2 are carried out:

[0113] Embodiment 1:

[0114] The experimental data measured in a vertical pipeline with a clear air-water interface in the pipeline hydraulic transient experimental device system designed and built by Zhou in 2018 were selected to verify the effectiveness of the present invention in simulating pressure oscillations in a fast-filling pipeline with trapped air bags.

[0115] In this embodiment, the upstream pressure vessel (relative pressure Pr) is connected to the 8.862 m long, 4 cm inner diameter pipeline at the end, which consists of a 8.382 m long horizontal pipe and a 0.48 m long terminal vertical pipe. Initially, the control valve is completely closed, the trapped air cavity La0 is at atmospheric pressure, and the valve opens instantly.

[0116] The simulation results of the method of the present invention are compared with the above simulation results to obtain the following Figure 4 The pressure curve shown is Figure 4It can be seen that compared with the model without considering the trapped cavitation heat transfer, the heat transfer model that simultaneously considers steady friction, unsteady friction and trapped cavitation heat transfer accurately reproduces the experimental pressure oscillation mode, pressure decay and oscillation period; while for the quasi-constant friction model without considering the trapped cavitation heat transfer and the pressure wave simulated by unsteady friction, as the transient events progress and the heat transfer effects accumulate, the numerical errors of pressure peak and timing gradually appear, and the heat transfer effect becomes more and more obvious.

[0117] Embodiment 2:

[0118] The simulation results of the model with the traditional empirical polynomial relationship are selected to verify the effectiveness of the present invention in simulating energy dissipation based on the new heat transfer model.

[0119] In this embodiment, the constant polytropic index m of the adiabatic process (without heat transfer) is 1.4, and the simulation of unsteady friction utilizes the TVB turbulence model.

[0120] The simulation results of the method of the present invention are compared with the above simulation results to obtain the following Figure 5 The pressure curve shown is Figure 5 It can be seen that the heat transfer model provided by the present invention can accurately simulate the energy dissipation of the system; while the empirical polynomial relationship method with adiabatic assumption can only accurately reproduce the pressure and temperature during the first two oscillations of the system test. As the rapid filling event progresses, it will lead to huge differences in the oscillation peak and time.

[0121] According to the experimental results of Examples 1 and 2, the heat transfer model proposed in the present invention can well solve the long-term accuracy problem of the constant heat transfer coefficient of the traditional empirical polynomial relationship in the transient energy consumption process, can accurately consider the two complex influencing factors of air gap heat transfer and transient pipe wall shear stress at the same time, can better reproduce the experimental pressure oscillations and accurately predict the energy dissipation in the fast-filling pipeline with trapped air masses.

Claims

1. A method for simulating rapid filling of a vertical pipe taking into account the energy dissipation of trapped air, characterized in that: The steps include: S1: Establish the continuity equation and pressure balance equation of the moving air-water interface; S2: Based on the water hammer theory, a heat transfer model is constructed by combining the heat transfer principle of a closed air bag and the equation of an ideal gas; S3: The first-order local MOC interpolation interface tracking method is used to solve the filling water column control equation and the air heat transfer equation considering unsteady friction, and the air pressure, velocity and position of the moving air-water interface are calculated; S4: solve the derivation of variables of gas and water phases at the time step; S5: Perform simulation according to the solution result of step S4 to obtain simulation results; The process of establishing the continuity equation and pressure balance equation of the moving air-water interface in step S1 is: The one-dimensional numerical simulation consists of three parts: a water column with varying length, a well-defined air-water interface, and trapped air pockets. The governing equations for filling the water column include continuity and momentum equations, expressed as: Where H is the water head; t is the time; a is the wave speed; Q is the flow rate; g is the gravitational acceleration; A is the cross-sectional area of ​​the pipe; x is the calculated distance; F s is the steady friction; F u is unsteady friction; Establish the continuity equation and pressure balance equation of the moving air-water interface: H wa =H a +Z wa (4) Where, L w is the initial water column length; L w0 is the initial water column length; l is the calculated pipe length; H wa , V wa and Z wa are the velocity and elevation of the pressure head and position head at the water-air interface, respectively; H a is the relative pressure head of the trapped air bag; The step S2 is specifically as follows: The heat transfer of the trapped air pocket is considered in the development of the 1D rapid filling model. The energy conservation principle for the closed air pocket gives: dU=dN-dW (5) Where dU is the energy change of internal energy; dN is the heat energy flowing out of the trapped air pocket by heat transfer; and dW is caused by the work done by the gas. P a * and are the absolute pressure and volume of the trapped air pocket; The ideal gas equation is: R a =C P -V v (7) Where M a is the mass of the air mass; R a is the gas constant; T a is the air temperature; C p is the specific heat at constant pressure; C v is the specific heat at constant volume; γ is the specific heat ratio; Substituting the ideal gas equation into equation (5), the energy conservation equation is written as When air pockets are trapped only in vertical pipes, the air-water interface moves vertically throughout the rapid filling process. For a well-defined air-water interface, the heat transfer term dN / dt is used for quasi-steady flow or low-frequency conditions. In the formula, A q is the contact area between the trapped air and the tube wall; T in is the temperature of the trapped air; T ex is the external temperature; α is the heat transfer coefficient.

2. A method for simulating rapid filling of a vertical pipe taking into account the energy dissipation of trapped air according to claim 1, characterized in that: In step S3, the first-order local MOC interpolation interface tracking method is used to solve the filling water column control equation and the air heat transfer equation considering unsteady friction, specifically: Unsteady friction F u and the unsteady shear stress τ u Introducing the TVB model for efficient and accurate simulation: In the formula, f s is the Darcy-Weisbach stable friction coefficient; D is the pipe diameter; ρ is the fluid density; v is the fluid viscosity coefficient; i=1~N is the calculation time step; Y ai is the weighted function integral of the current calculation time step; R is the hydraulic radius; n i and mi are the general weighting coefficients for the current calculation time step; Considering the elasticity and length change of the filled water, the continuity and momentum equations are applied to the water region, and the standard orifice equation is used to express the valve boundary conditions. When the characteristic line method is used to solve the water continuity and momentum equations, the filled column can be regarded as two sections at time t+Δt, as follows: (1) Fixed grid area L w -ΔL wi =(N-1)Δx, where pressure and flow can be calculated by a fixed MOC grid; (2) Water body ΔL wi The changing mesh region is solved by combining MOC and moving boundary equations.

3. A method for simulating rapid filling of a vertical pipe taking into account the energy dissipation of trapped air according to claim 2, characterized in that: The calculation method of the air pressure, speed and position of the moving air-water interface in step S3 is: Water head H at point P P and flow rate Q P By combining the equations, we can obtain: wi The hydraulic head at the upstream point P is expressed as C of point A–P + Characteristic equation and C of point C–P - Characteristic equation: C + :H P -C P +R P Q P =0 (14) In the formula, H P is the water head at point P; Q P is the flow rate at point P; C P is the characteristic constant at P; H c is the water head at point c; Q c is the flow rate at point C; ΔL wi is the calculated distance moved by the air column; The pressure head and flow value at point D cannot be directly calculated by fixed grid. Auxiliary point G is introduced to obtain the value at point D by connecting the air control equation. For 0<ΔL wi ≤Δx, the head and flow at point G are based on the interpolation between points P and E; when Δx<ΔL wi When ≤2Δx, the head and flow at point G are based on the interpolation between points E and F; C from point G–D + Characteristics obtained: Starting from point C–D, the distance the air-water interface moves from t to t+Δt is: In the formula, H D is the water head at point D; Q D is the flow rate at point D; t D is the time at point D; t c is the time at point C; Δt is the time difference.

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