Transient flow simulation method containing retention air mass based on generalized Kelvin-Voigt model

Abstract

The invention discloses a transient flow simulation method containing a retention air mass based on a generalized Kelvin-Voigt model, and the method comprises the following steps: collecting related initial parameters of a pipeline system, including an upstream boundary water level, an initial air mass length and an air mass position; constructing a corresponding control equation for the water body, the air mass and the water-air interface; a generalized Kelvin-Voigt model is introduced, and an air mass pressure-air mass length relational expression is established; a time-domain full-waveform inversion method is adopted to deduce creep compliance and relaxation time in the relational expression; and solving the position and pressure change of the water-gas interface by combining a characteristic line method and a Newton iteration method. The generalized Kelvin-Voigt model is introduced, the gas control equation is improved, the simulation precision of the transient flow containing the retention gas mass is improved, and the applicability under different complex working conditions is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of calculation of transient flow simulation of pressurized water delivery system, and particularly relates to a transient flow simulation method for air mass containing based on a generalized Kelvin-Voigt model. BACKGROUND

[0002] In the numerical simulation method of long-distance water diversion project, pump station, fire-fighting system and other pressurized pipelines, the previous hydraulic calculation usually only considers the conventional water hammer problem in the pipeline, and ignores or underestimates the abnormal pressure caused by the air mass containing in the system start-up water filling. Due to the hydraulic fluctuation, poor exhaust and other reasons, the residual water in the pressurized water delivery system and the air mass containing cannot be completely exhausted, which will lead to the very possible unconventional water-air coupling transient flow phenomenon of water flow impacting air mass in the pressurized pipeline under the water filling condition. In the process of compression and expansion of the air mass containing, the water delivery efficiency is reduced, and a huge pressure enough to cause the structure damage of the water delivery pipeline may be generated.

[0003] In order to deal with the complex transient flow phenomenon of water flow impacting air mass containing in the pipeline system, domestic and foreign scholars use one-dimensional model to study the transient flow containing air mass, which has the characteristics of high calculation efficiency and relatively high model accuracy, and constantly optimizes the scheme for water body and gas model.

[0004] In terms of water body model, it develops from the rigid model of incompressible water body to the elastic water body model considering the compressibility of water body. In terms of gas model, the ideal gas equation of state is often used to deal with gas to reduce the difficulty of model solution, however, the model precision of transient flow containing air mass cannot be further improved due to the reasons such as gas dissolution, water-gas heat transfer, gas-wall heat transfer, water-gas interface vortex and other reasons in the water-air coupling process. An air mass analogy model based on Voigt model, which regards the compression and expansion process of air mass as the compression and extension process of spring-viscous damper system, couples the mechanical properties of Voigt model and the ideal gas equation of state. This analogy model has certain advantages in the numerical simulation of pressure peak value and decay period, however, the applicability of its specific coefficient is relatively narrow, and the coefficient value lacks consideration. Or introduce the law of conservation of energy to simulate pressure fluctuation, but this method needs to retransmit the heat transfer coefficient under different boundary conditions and initial conditions, which is not conducive to the wide application in practical engineering.

[0005] The generalized Kelvin-Voigt model is composed of a spring and a dashpot unit, and can approach the mechanical characteristics of a real system to a certain extent. The whole pipeline is regarded as a single spring and a large number of Voigt models (a unit model in parallel with a spring and a dashpot) in series. Due to the complex changes among the water-gas-solid three phases, there is great uncertainty, and the deformation mechanism of the spring and the dashpot has certain commonality with the compression and expansion characteristics of the gas mass. Therefore, it is of great significance to study the feasibility of applying the generalized Kelvin-Voigt model to the transient flow containing a trapped gas mass, so as to realize high-precision simulation of the transient flow containing a trapped gas mass under complex working conditions and improve the adaptability of the model to complex transient flow phenomena. SUMMARY

[0006] In order to solve the problem that it is difficult to accurately simulate the transient flow containing a trapped gas mass under complex working conditions in actual engineering, the application provides a simulation method for transient flow containing a trapped gas mass based on a generalized Kelvin-Voigt model. The generalized Kelvin-Voigt model is introduced, the gas control equation is improved, the simulation accuracy of the transient flow containing a trapped gas mass is improved, and the applicability under different complex working conditions is improved.

[0007] A simulation method for transient flow containing a trapped gas mass based on a generalized Kelvin-Voigt model, the specific steps are as follows: S1: Collecting relevant initial parameters of the pipeline system, including the upstream boundary water level, the initial gas mass length, and the gas mass position; S2: Constructing a classical model of transient flow containing a trapped gas mass, that is, establishing corresponding control equations for the gas mass, the water-gas interface and the water body; S3: Introducing the generalized Kelvin-Voigt model, comparing the trapped gas mass compression with the hypothetical spring-dashpot damping system stretching, and establishing a gas mass analogy model capable of quantifying the relationship between gas pressure and gas length for accurate simulation; S4: Using the time-domain full waveform inversion method to determine the creep compliance and relaxation time, two characteristic parameters in the generalized Kelvin-Voigt model based on experimental data; S5: For the water body part of the pipeline system, the characteristic line method is used to solve the elastic water body model, the position of the water-gas interface is dynamically tracked, the control equations of the gas, the water-gas interface and the water body end characteristic line are solved simultaneously, and the Newton iteration method is used to solve the position and pressure change of the water-gas interface; S6: Comparing the simulation results of different complex working conditions with the experimental results to verify the accuracy and applicability of the model.

[0008] Further, in S2, the mathematical model for describing the water flow impacting the trapped gas mass in the pipeline includes transient state control equations of three parts of the water body, the gas and the water-gas interface: (1) Water body basic control equation In the process of water flow impacting the stagnant gas mass, the length of water body in the pipeline is constantly changing with the movement of water-gas interface. Considering the compressibility of the whole water body and the elasticity of the pipe wall, the continuity equation and momentum equation are: In the formula: H is the piezometric tube head, m; Q is the water flow, m 3 / s; f is the pipeline friction; D is the pipeline diameter, m; A is the pipeline cross-sectional area, m 2 ; a is the water hammer wave speed, m / s; g is the gravitational acceleration, m / s 2 ; (2) Gas control equation According to the ideal gas state equation, the gas control equation is derived: In the formula: m is the gas polytropic index, usually m =1.4 is taken in the rapid transient process, indicating an adiabatic process; H is the absolute pressure of the gas, m; V is the gas volume, m 3 / s; L is the gas mass length, m; (3) Water-gas interface control equation The position of the water body front: In the formula: x b represents the distance of the water body front from the upstream section, m; v b represents the speed of the water-gas interface movement, m / s; Water-gas interface equilibrium equation: In the formula: H w represents the water body pressure, m; H a represents the gas pressure, m.

[0009] Further, in S3, the generalized Kelvin-Voigt model is introduced, and the energy loss caused by the water-gas coupling process is replaced by mechanical loss by improving the gas control equation; (1) Stress-strain relationship in the generalized Kelvin-Voigt model The total strain expression for the generalized Kelvin-Voigt model is: creep function J ( t The expression is: In the formula: J 0 is the instantaneous creep compliance, m 2 / N; J k It is the first k The creep compliance of the spring in the Voigt model, m 2 / N; τ k It is the first k The relaxation time (s) of the glue pot in the Voigt model; for this model... J 0、 J k , τ k All are unknown quantities. Transform the integral term to obtain make but Approximately solving the integral term yields the recurrence relation: (2) Gas pressure-strain relationship Solving transient flow problems involving stagnant gas masses requires establishing the relationship between gas pressure and gas length. Therefore, it's necessary to analyze step-by-step how to correlate stress and strain with gas pressure and gas length, respectively. Firstly, regarding stress, the initial gas pressure is not zero, but the gas strain is assumed to be zero. Therefore, stress is defined as follows: but This transforms the stress-strain relationship into a gas pressure-strain relationship; remember but remember Then simplify to The gas pressure-strain relationship is obtained as follows: (3) Gas pressure-gas length relationship The hypothetical spring-Voigt damper system is analogous to the compressed trapped air mass. When the spring-Voigt damper system is stretched to infinity, the infinite stress generated is consistent with the infinite gas pressure generated when the trapped air mass is compressed to infinity. Therefore, the expression is: .

[0010] In S3, to achieve accurate simulation of the transient flow model containing trapped air mass, the following three steps are taken: A. Increase the index. According to the ideal gas state equation, the relationship between the air mass pressure and the air mass length is: In the formula: m is the gas polytropic index, generally taking the value of 1.0, 1.2, 1.4, and the strain gas length expression is: B. Difference calculation. To achieve the time step calculation of transient flow, the gas length at the current time is calculated according to the average flow at the previous two times of the water-air interface, and the expression is: C. Adjust the weight. By modifying the 0 term, when the number of hypothetical Voigt models is 0, the gas pressure-gas length relationship is consistent with the gas control equation in the classical model, J Let That is, The final expression of the gas pressure-gas length relationship is: The unknown quantity in this expression is J k , τ k (k represents the total number of hypothetical Voigt models).

[0011] Further, in S5, for the overall pipeline system containing trapped air mass, the corresponding control equation is solved for transient flow; (1) Water body internal calculation node ​For the water part, the method of characteristics is used to solve the continuity and momentum equations. In order to realize the solution of hydraulic transient process step by step, the fixed characteristic grid length is obtained as follows: wherein: , is the characteristic grid length, m; Δ t is the calculation time step, s.

[0012] The flow rate and pressure of the point P to be solved are obtained by simultaneous solution as follows: wherein: C P =H A +BQ A , C M =H B -BQ B , B P =B+RQ A , B M =B+RQ B ; (2) Tracing of the water-air interface The position of the water-air interface in the pipe system changes over time. Dynamic tracing of the position of the water-air interface is the key to the solution of the model. The compression and expansion of the trapped air mass is a variable process, and the pressure inside the air mass is equal everywhere. According to the virtual plug assumption, a micro-section of water body near the water-air interface is taken as Δ L w , and its length is taken as 0.5Δ x ≤Δ L w ≤1.5Δ x . The determination of the position of the water-air interface needs to simultaneously solve the gas control equation, the water-air interface control equation, the water body end C + characteristic equation, and the virtual plug assumption. C + Characteristic equation: Water-air interface control equation: Gas control equation: According to the virtual plug assumption, the following can be obtained: In the formula: subscript P represents the water body end node, subscript WA represents the water-gas interface, subscript a represents the gas, superscript n represents the time to be solved, superscript n -1 and n -2 respectively represent the previous time and the time before the previous time, x is the distance from the water-gas interface to the upstream starting point, V WA is the water-gas interface moving speed, H a0 is the initial pressure of the gas mass, L a0 is the initial length of the gas mass occupying in the pipeline; By simultaneously using the above four formulas, the Newton iteration method can be used to obtain V WA , which is substituted back into the above equation to obtain H WA , x WA , Q WA ; at the same time, the fluid components ɑ of each node are revalued, and the position and length of the trapped gas mass are determined before the next time step calculation.

[0013] Advantages: Compared with the prior art, the simulation method of transient flow containing trapped gas mass based on the generalized Kelvin-Voigt model has the following advantages: (1) Based on the generalized Kelvin-Voigt model, the compression and expansion process of the gas mass is more accurately described by analogy of the trapped gas mass being compressed by the imaginary spring-viscous damper system under tension, and the simulation accuracy of the transient flow containing trapped gas mass is improved; (2) The time-domain full waveform inversion method is used to obtain the creep function, so that the model can adapt to the simulation of transient flow containing trapped gas mass under different working conditions; (3) It has important application value in actual engineering, and numerical simulation research is carried out for various operating conditions of the engineering, which provides guarantee for the hydraulic safety warning work of the pipeline system. DETAILED DESCRIPTION

[0014] Figure 1 is a flow chart of the simulation method of transient flow containing trapped gas mass based on the generalized Kelvin-Voigt model of the application; Figure 2is a schematic diagram of an air mass analogy model based on a generalized Kelvin-Voigt model; Figure 3 is a schematic diagram of a node characteristic line grid division inside a water body; Figure 4 is a schematic diagram of a pipeline system of an embodiment of the present application; Figure 5 is a comparison diagram of end air mass pressure simulated by the model of the present application and two different models for working condition 1.

[0015] Figure 6 is a comparison diagram of end air mass pressure simulated by the model of the present application and two different models for working condition 2.

[0016] Figure 7 is a comparison diagram of end air mass pressure simulated by the model of the present application and two different models for working condition 3.

[0017] Figure 8 is a comparison diagram of end air mass pressure simulated by the model of the present application and two different models for working condition 4. Embodiment

[0018] The principles and technical advantages of the present application will be further illustrated below in combination with specific implementation cases and corresponding drawings. It should be noted that these cases are only used to illustrate the functions of the present application and are not used to limit the application scope of the present application. Any modification of the various equivalent forms of the present application made by those skilled in the art after reading the principles and functions of the present application should be within the scope limited by the claims of the present application.

[0019] As shown in Figure 1 , a simulation method for transient flow containing a trapped air mass based on a generalized Kelvin-Voigt model, a generalized Kelvin-Voigt model is introduced, a gas control equation is improved, the simulation accuracy of transient flow containing a trapped air mass is improved, and the applicability under different complex working conditions is improved. The specific steps are as follows: S1: Collecting relevant initial parameters of the pipeline system, including upstream boundary water level, initial air mass length, and air mass position; S2: Constructing a classical model of transient flow containing a trapped air mass, that is, establishing corresponding control equations for the air mass, the water-air interface, and the water body; In S2, for the classical model of transient flow containing a trapped air mass, the following assumptions are made: (1) the water-air interface is always perpendicular to the central axis of the pipeline; (2) there is no mass exchange between water and air during the transient process; (3) constant friction is used as the pipeline friction during the transient process; (4) the inertia of the trapped air mass in the pipeline is ignored, and the pressure inside the gas is equal everywhere.

[0020] In S2, the mathematical model describing the water flow impacting the trapped air mass in the pipeline includes the transient state control equations of three parts: water body, gas, and water-gas interface: (1) Water body basic control equation During the process of water flow impacting the trapped air mass, the length of the water body in the pipeline is constantly changing with the movement of the water-gas interface. Considering the compressibility of the entire water body and the elasticity of the pipe wall, the continuity equation and momentum equation are: In the formula: H is the pressure tube water head, m; Q is the water body flow, m 3 / s; f is the pipeline friction; D is the pipeline diameter, m; A is the pipeline cross-sectional area, m 2 ; a is the water hammer wave speed, m / s; g is the gravitational acceleration, m / s 2 .

[0021] (2) Gas control equation The gas control equation is derived according to the ideal gas state equation: or In the formula: m is the gas polytropic index, usually m =1.4 is taken in the rapid transient process, indicating an adiabatic process; H is the absolute pressure of the gas, m; V is the gas volume, m 3 / s; L is the length of the air mass, m.

[0022] (3) Water-gas interface control equation The position of the water body front: In the formula: x b represents the distance of the water body front from the upstream section, m; v b represents the speed of the water-gas interface movement, m / s.

[0023] Water-gas interface balance equation: In the formula: H w represents the water body pressure, m; H a represents the gas pressure, m.

[0024] S3: Introducing the generalized Kelvin-Voigt model, analogizing the compression of the trapped air mass to the stretching of the hypothetical spring-damper system, establishing an air mass analog model that can quantify the relationship between gas pressure and gas length for precise simulation; In S3, the generalized Kelvin-Voigt model is introduced, and the gas control equation is improved by replacing the energy loss caused by gas dissolution, water-gas heat transfer, gas-wall heat transfer, and water-gas interface vortex in the water-air coupling process with mechanical loss; (1) Stress-strain relationship in the generalized Kelvin-Voigt model As shown in Figure 2 , the total strain expression of the generalized Kelvin-Voigt model is: The creep function J ( t ) expression is: In the formula: J 0 is the instantaneous creep compliance, m 2 / N; J k is the creep compliance of the spring in the k th Voigt model, m 2 / N; τ k is the relaxation time of the damper in the k th Voigt model, s. For this model, J 0, J k , τ k are unknown quantities.

[0025] Transforming the integral term gives Let Then Approximate solution of the integral term gives the recursive formula: (2) Gas pressure-strain relationship To solve the transient flow problem involving trapped air masses, the relationship between gas pressure and gas length needs to be established, so it is necessary to analyze how to correspond stress and strain to gas pressure and gas length respectively. First, for stress, the initial pressure of the gas is not 0, but it is considered that the gas strain is 0 at this time, so the stress is defined as: Then Thus, the stress-strain relationship is transformed into the gas pressure-strain relationship.

[0026] Let Then Let Then The gas pressure-strain relationship is obtained as follows: (3) Gas pressure-gas length relationship The most critical step in the establishment of the model is to express the strain in terms of the gas length. One approach is to analogize the compression of the spring-Bingham damper system to the compression of the trapped gas mass, resulting in the expression: In the formula: L a0 L0 is the initial length of the trapped gas mass in the pipeline, m; L aN L is the length of the trapped gas mass in the pipeline at a certain calculation time, m.

[0027] Although the compression of the gas mass and the compression of the spring-Bingham damper system have some similarities, there is a significant difference in the stress change during the deformation process. On the one hand, the stress generated by the compression of the latter is approximately proportional to the deformation variable, which leads to a significant difference in the stress change rate during the deformation process. On the other hand, when the compression deformation variable is the initial length, the maximum stress generated by the compression of the spring-Bingham damper system reaches the limit value, while for the gas mass, the gas pressure will reach infinity at this time. In summary, if the above relationship is adopted, it will result in a large deviation in the peak value of the system pressure fluctuation, especially the first phase peak value which is most concerned in the field of transient flow.

[0028] Therefore, the model of the present application proposes another approach: analogizing the compression of the trapped gas mass to the stretching of the hypothetical spring-Bingham damper system. The infinite stress generated by the stretching of the spring-Bingham damper system to infinity is consistent with the infinite gas pressure generated by the compression of the trapped gas mass to infinity. Therefore, the expression is obtained as follows: To achieve accurate simulation of the transient flow model containing trapped gas mass, the following three steps are taken: A. Increase index. According to the ideal gas state equation, the relationship between the gas pressure and the gas length is: In the formula: m is the gas polytropic index, generally taking the value of 1.0, 1.2, 1.4. By slightly adjusting the correlation between the two, the fitting result is better, and the expression of the strained gas length is obtained: B. Difference calculation. In order to realize the time step calculation of transient flow, the gas length at the current time is calculated according to the average flow at the front two times of the water-gas interface. The expression is: C. Adjust the weight. By modifying the 0 term, when the number of imaginary Voigt model is 0, the relationship between gas pressure and gas length is consistent with the gas control equation in the classical model. J

[0029] Let That is, This step is essentially adjusting the weight between the first term and the summation term in the gas pressure strain relationship, trying to avoid the local extremum in the characteristic parameter inversion process, resulting in a large numerical error.

[0030] Finally, the expression of the relationship between the gas pressure and the gas length is obtained: The unknown quantity in the expression is J k , τ k (k represents the total number of imaginary Voigt models).

[0031] S4: Using time domain full waveform inversion method, based on experimental data to solve the creep compliance and relaxation time two kinds of characteristic parameters in the generalized Kelvin-Voigt model; S5: For the water part of the pipeline system, the characteristic line method is used to solve the elastic water body model. The position of the water-gas interface is dynamically tracked, and the control equations of the gas, water-gas interface and water body end characteristic line are solved simultaneously to solve the position and pressure change of the water-gas interface by using Newton iteration method; In S5, for the whole pipeline system containing trapped gas, the corresponding control equations are solved simultaneously to solve the transient flow; (1) Water body internal calculation node ​For the water body portion, the method of characteristics is used to solve the water continuity and momentum equations. To achieve time-step solutions during hydraulic transients, such as... Figure 3 As shown, with the feature line mesh fixed, the feature line equations are obtained as follows: In the formula: , Δ is the feature line grid length, in meters; t Let s be the time step for calculation.

[0032] The flow rate and pressure at the point P to be determined are obtained by combining the following equations: In the formula: C P =H A +BQ A , C M =H B -BQ B , B P =B+RQ A , B M =B+RQ B .

[0033] (2) Tracking of the water-air interface The location of the water-air interface in the pipeline system is constantly changing, and dynamically tracking its position is crucial for solving this model. The compression and expansion of the trapped gas mass are variable processes, and the internal pressure of the gas mass is constant. Based on the virtual plug assumption, a small segment of water near the water-air interface, Δ... L w Its length is taken as 0.5Δ x ≤Δ L w ≤1.5Δ x Determining the location of the water-air interface requires simultaneously solving the gas governing equations, the water-air interface governing equations, and the end-water equations. C + Equations of characteristics and the virtual plug assumption.

[0034] C + Equations of characteristic lines: Water-air interface governing equations: Gas governing equations: According to the virtual plug assumption In the formula: subscript P represents the end node of the water body, subscript WA represents the water-gas interface, subscript a represents the gas, superscript n represents the time to be solved, superscript n -1 and n -2 respectively represent the previous time and the time before the previous time, x is the distance from the water-gas interface to the upstream starting point, V WA is the water-gas interface moving speed, H a0 is the initial pressure of the gas mass, L a0 is the initial length occupied by the gas mass in the pipeline.

[0035] By simultaneously solving the above four formulas, the Newton iteration method can be used to obtain V WA , which is substituted back into the above equation to obtain H WA , x WA , Q WA At the same time, the fluid component ɑ of each node is revalued, and the position and length of the trapped gas mass are determined before the next time step calculation.

[0036] S6: Compare the simulation results of different complex working conditions with the experimental results to verify the accuracy and applicability of the model.

[0037] Based on the above scheme, in order to verify the practicability of the method of the present application, the following embodiment is carried out: Figure 4 The experimental system mainly consists of a pressure tank, a drain valve, a flow meter, an air inlet valve, a ball valve, an organic glass transparent pipe, a pressure sensor and the like. The valve at the downstream end of the pipeline is manually controlled to open and close, thereby generating a transient flow containing a trapped gas mass, and the pressure fluctuation signal is recorded. The horizontal part of the pipeline is 8.382 m long, the vertical part of the closed end of the pipeline is 0.48 m long, the inner diameter of the pipeline is 0.04 m, and the wall thickness of the pipeline is 10 mm. The pressure sensor is arranged at the blind end of the pipeline to measure the pressure change of the impacted gas mass, and Labview software is used for operation with a sampling rate of 250kS / s. In order to prevent the pipeline support from being unstable due to the huge water hammer pressure during the valve closing process, thereby generating fluid-structure coupling and reducing the accuracy of the experiment, stainless steel supports are used to fix each layer of the pipeline.

[0038] Through the measurement and calculation of multiple experimental conditions, the wave velocity of the experimental device is 850 m / s, and the average hydraulic loss coefficient of the pipeline is 0.096.

[0039] In the experiment, the independent variables are the upstream water level and the initial gas length, and by controlling the valve at the corresponding position to be closed, the initial gas with the required length is formed at the end of the pipeline. After the formation of the gas, the water flow impact on the retained gas is generated by quickly opening the ball valve. Four working conditions are set, and each working condition is repeated at least three times to ensure the accuracy of the experimental results, as shown in the following table.

[0040] To verify the applicability of the model in different conditions, only the experimental data of the first 5s of working condition 1 is collected, and the time-domain full waveform inversion method is used to invert the creep compliance and relaxation time; in the transient flow classical model containing retained gas and the gas analogy model based on the generalized Kelvin-Voigt model, the gas polytropic index is taken as 1.4, indicating an adiabatic process; in the heat transfer model considering the thermodynamic effect of gas, the heat transfer coefficient is always taken as 0.015; in order to improve the efficiency of parameter inversion and ensure the accuracy of the model, the number of Voigt models in the generalized Kelvin-Voigt model of the system is given as 3, and the relaxation time is assumed to be: The creep compliance is: For working conditions 1-4, the 10s numerical simulation results obtained by substituting the above parameters into the mathematical model are compared with the transient flow classical model containing retained gas, the heat transfer model considering the thermodynamic effect of gas, and the experimental results, as shown in Figures 5-8

[0041] Through curve comparison, it is found that the transient flow classical model containing retained gas and the heat transfer model considering the thermodynamic effect of gas cannot realize high-precision simulation in terms of pressure fluctuation period and pressure wave peak decay.

[0042] The gas analogy model based on the generalized Kelvin-Voigt model proposed in the present application can accurately predict the gas pressure change of working condition 1 within 10s, realize accurate extrapolation of experimental data under the current working condition, and better simulate the peak value of each pressure wave and the phase of pressure fluctuation in the transient flow experimental system containing retained gas, which proves that the model can accurately simulate the transient flow containing retained gas.

[0043] ​In practical engineering, for example, long distance water diversion project operation period, through the collection of pipeline pressure fluctuation data, inversion of the characteristics of the project specific parameters, will be applied to the gas analogy model, for a variety of operating conditions of the project to carry out numerical simulation research, to provide protection for the hydraulic safety warning work of pipeline system.

Claims

1. A method for simulating transient flows of stagnant air masses based on the generalized Kelvin-Voigt model, characterized in that, The specific steps are as follows: S1: Collect relevant initial parameters of the pipeline system, including upstream boundary water level, initial gas mass length, and gas mass location; S2: Construct a classical transient flow model containing a stagnant air mass, that is, establish corresponding governing equations for the three parts: air mass, water-air interface and water body; S3: Introduce the generalized Kelvin-Voigt model, and use the hypothetical spring-stick pot damping system under tension as an analogy to the compression of the stagnant gas mass to establish a gas mass analogy model that can quantify the gas pressure-gas length relationship for accurate simulation; S4: Using the time-domain full waveform inversion method, the two characteristic parameters of creep compliance and relaxation time in the generalized Kelvin-Voigt model are derived based on experimental data; S5: For the water part of the pipeline system, the method of characteristics is used to solve the elastic water body model, dynamically track the position of the water-air interface, solve the control equations of the gas, water-air interface and the end characteristic line of the water body, and use the Newton iteration method to solve the position and pressure change of the water-air interface. S6: Compare the simulation results with the experimental results under different complex working conditions to verify the accuracy and applicability of the model.

2. The method for simulating transient flow of stagnant gas masses based on the generalized Kelvin-Voigt model as described in claim 1, characterized in that, In S2, the mathematical model describing the impact of water flow on trapped air masses within the pipe includes transient state governing equations for three parts: water, gas, and the water-gas interface. (1) Basic governing equations of water bodies During the process of water flow impacting and trapping air masses, the length of the water body inside the pipe changes continuously with the movement of the water-air interface. Considering the compressibility of the entire water body and the elasticity of the pipe wall, its continuity equation and momentum equation are: In the formula: H For the pressure gauge head; Q Water flow rate; f For pipe friction; D The diameter of the pipe; A This refers to the cross-sectional area of ​​the pipe. a The wave velocity of the water hammer wave; g It is gravitational acceleration; (2) Gas governing equations The governing equations for the gas are derived from the ideal gas law: In the formula: m The gas polytropic index is typically taken as [value missing] during rapid transient processes. m =1.4, indicating an adiabatic process; H This refers to the absolute pressure of the gas. V For gas volume; L The length of the air mass; (3) Governing equations of the water-air interface Location of the water's edge: In the formula: x b Indicates the distance from the water's front edge to the upstream section; v b This indicates the speed at which the water-air interface moves; Water-air interface equilibrium equation: In the formula: H w Indicates water pressure; H a This indicates gas pressure.

3. The method for simulating transient flow of stagnant gas masses based on the generalized Kelvin-Voigt model as described in claim 1, characterized in that, In S3, a generalized Kelvin-Voigt model is introduced, and the energy loss caused by the water-gas coupling process is replaced by mechanical loss in the form of improved gas control equations. (1) Stress-strain relationship in the generalized Kelvin-Voigt model The total strain expression for the generalized Kelvin-Voigt model is: creep function J ( t The expression is: In the formula: J 0 represents instantaneous creep compliance; J k It is the first k Creep compliance of a spring in a Voigt model; τ k It is the first k The relaxation time of the sticky pot in the previous Voigt model, for this model... J 0、 J k , τ k All are unknown quantities. Transform the integral term to obtain make but Approximately solving the integral term yields the recurrence relation: (2) Gas pressure-strain relationship Solving transient flow problems involving stagnant gas masses requires establishing the relationship between gas pressure and gas length. Therefore, it's necessary to analyze step-by-step how to correlate stress and strain with gas pressure and gas length, respectively. Firstly, regarding stress, the initial gas pressure is not zero, but the gas strain is assumed to be zero. Therefore, stress is defined as follows: but This transforms the stress-strain relationship into a gas pressure-strain relationship; remember but remember Then simplify to The gas pressure-strain relationship is obtained: (3) Gas pressure-gas length relationship Using the analogy of a hypothetical spring-sticker damping system under tension and a trapped gas mass under compression, the infinite stress generated when the spring-sticker damping system is stretched to infinity is consistent with the infinite gas pressure generated when the trapped gas mass is compressed to infinity. Therefore, the expression is: 。 4. The method for simulating transient flow of stagnant gas masses based on the generalized Kelvin-Voigt model as described in claim 1, characterized in that, In S3, to achieve accurate simulation of transient flow models containing stagnant air masses, the following three steps are taken: A. Increasing the exponent, according to the ideal gas law, the relationship between gas mass pressure and gas mass length is as follows: In the formula: m is the gas polytropic index, which is generally taken as 1.0, 1.2, or 1.

4. The expression for the strained gas length is obtained as follows: B. Differential calculation: To achieve hourly step-by-hour calculation of transient flow, the gas length at the current moment is estimated based on the average flow rate at the water-gas interface at the previous two moments, resulting in the following expression: C. Adjust the weights by correcting... J The term 0 ensures that when the hypothetical Voigt model has zero elements, the gas pressure-gas length relationship is consistent with the gas governing equations in the classical model. make Even if The final expression for the gas pressure-gas length relationship is: The unknown in this expression is J k , τ k , where k represents the total number of hypothetical Voigt models.

5. A method for simulating transient flow of stagnant gas masses based on the generalized Kelvin-Voigt model as described in claim 1, characterized in that, In S5, for the overall pipeline system containing stagnant gas masses, the corresponding control equations are solved simultaneously for transient flow. (1) Calculation nodes inside the water body For the water body portion, the method of characteristics is used to solve the water continuity and momentum equations. To achieve time-step solutions during hydraulic transients, a fixed characteristic line grid is used to obtain the characteristic line equations as follows: In the formula: Δ x Δ is the feature line grid length; t For calculating time steps; The flow rate and pressure at the point P to be determined are obtained by combining the following equations: In the formula: C P =H A +BQ A , C M =H B -BQ B , B P =B+RQ A , B M =B+RQ B ; (2) Tracking of the water-air interface The position of the water-air interface in the pipeline system is constantly changing. Dynamically tracking the position of the water-air interface is the key to solving this model. The compression and expansion of the trapped gas mass are variable processes, and the internal pressure of the gas mass is equal everywhere. Based on the virtual plug assumption, a small segment of water near the water-air interface is taken as Δ. L w Its length is taken as 0.5Δ x ≤Δ L w ≤1.5Δ x Determining the location of the water-air interface requires simultaneously solving the gas governing equations, the water-air interface governing equations, and the end-water equations. C + Equations of characteristics, virtual plug assumption; C + Equations of characteristic lines: Water-air interface governing equations: Gas governing equations: Based on the virtual plug assumption, we can obtain: In the formula: subscript P Indicates the end node of a water body, subscript WA Indicates the water-air interface, subscript a Indicates gas, superscript n Indicates the time to be requested, indicated by superscript. n -1 and n -2 represents the previous time and the time before that, respectively. x The distance from the water-air interface to the upstream starting point. V WA The velocity at the water-air interface. H a0 The initial pressure of the air mass. L a0 The initial length occupied by the air mass within the pipe; By combining the above four equations, the result can be obtained using Newton's iteration method. V WA Substituting back into the above equation, we can obtain... H WA , x WA , Q WA Simultaneously, the fluid composition of each node is re-evaluated. a Assign values ​​to determine the location and length of the stagnant air mass before the next time step calculation.

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