Pipeline multi-flow-state FVM simulation method based on one-dimensional gas-water fluid model

Abstract

The invention discloses a pipeline multi-flow-state FVM simulation method based on a one-dimensional gas-water fluid model, and the method comprises the following steps: constructing and improving a one-dimensional control equation of a pipeline unsteady gas-water fluid model, so that the equation can meet the requirements of plug-shaped transient flow, pressurized water hammer transient flow and free surface transient flow at the same time; and seamless connection among different flow states is realized through a unified solution framework. A finite volume method (FVM method) in a Rohl-Philip format is adopted to solve the three flow states in a unified manner, the challenge that different flow states are suitable for thermodynamic basic relations and wave velocity equation differences is overcome, and the improved one-dimensional multi-equation fluid model can simulate multiple flow states at the same time. And finally, performing model evaluation verification on simulation of three flow states by using the model. The method provides stability and precision guarantee for real-time control simulation of an actual long-distance water delivery system, a rainfall flood system and a long-distance water supply system, and is of great significance in improving simulation precision and reliability of complex water conservancy projects.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydraulic numerical simulation and calculation, and specifically relates to a unified numerical simulation method based on a multi-equation fluid model, which can simulate various flow states such as plug-shaped transient flow, pressurized water hammer flow, free surface transient flow, etc., and is suitable for complex water conservancy projects such as long-distance water transmission systems, rainwater and flood systems, and long-distance water supply systems. Background Art

[0002] Existing hydraulic numerical simulation methods have limitations and it is difficult to accurately simulate the various flow states in complex water conservancy and water supply pipeline projects, especially the coexistence of plug transient flow, water hammer flow, and free surface transient flow.

[0003] Secondly, existing methods usually adopt simplified models for specific flow states. For example, existing multi-equation fluid models are mainly suitable for pressure flow scenarios and it is difficult to accurately simulate open channel flow and transient flow; existing single-phase flow models can often only simulate transient flow with water hammer and free surface transient flow.

[0004] However, so far, there are few models that can simulate multiple flow states at the same time. In addition, in the solution methods of mathematical models, the existing solvers are often targeted at specific basic thermodynamic relationships, lack universality, and are difficult to apply to the simulation of multiple flow states in practice. Therefore, it is crucial to develop a unified model that can simulate multiple flow states at the same time, and use a unified solver that can adapt to the solution under different flow state characteristics. Summary of the invention

[0005] In order to solve the problem that the existing models are difficult to accurately simulate various flow states in complex water conservancy water pipeline projects, this paper proposes a pipeline multi-flow state FVM simulation method based on a one-dimensional gas-water fluid model, which can effectively simulate various flow states such as plug transient flow, water hammer flow, free surface transient flow, etc., and uses the same solver for unified solution, and has the following characteristics:

[0006] Unified model: This model can uniformly handle plug transient flow, water hammer flow, and free surface transient flow, simplifying the simulation process.

[0007] High precision: This model improves the one-dimensional multi-equation fluid model and can more accurately simulate the changes in the air-water interface, thereby improving the simulation accuracy.

[0008] High efficiency: The model uses the "Rod-Phillips" format to solve the gas-water fluid model, which improves the calculation efficiency.

[0009] Universality: This model can be applied to a variety of basic thermodynamic relationships and has stronger universality.

[0010] Technical solution: To achieve the above purpose, the present invention provides a pipeline multi-flow state FVM simulation method based on a one-dimensional gas-water fluid model, comprising the following steps:

[0011] S1: Construct the one-dimensional control equation of the unsteady gas-water fluid model and improve the control equation to adapt to the simulation of plug transient flow, water hammer transient flow and free surface transient flow;

[0012] S2: Solving the eigenvalues ​​and eigenvectors of the system of equations;

[0013] S3: The FVM method of Rowe-Phillips format is used to uniformly solve the three flow regimes;

[0014] S4: Based on the calculation results of step S3, the model is evaluated and verified to ensure its accuracy and reliability.

[0015] Furthermore, the step S1 constructs a one-dimensional control equation of an unsteady gas-water fluid model:

[0016]

[0017] In the above formula: subscripts a and w represent the gas phase and water phase respectively. For the sake of simplicity, subscript p is used to represent p = a, w; interface variable: j; wall-related variable: b; pre p Indicates pressure; jp Indicates the pressure at the air-water interface; v p Indicates speed; Den p Indicates density; Represents the volume fraction of a phase, satisfying represents the inclination angle of the pipeline; F represents the friction force, and g represents the acceleration of gravity;

[0018] For circular cross-section pipes ( Figure 1 ), the water phase area is recorded as Area w , water phase volume fraction It is expressed as:

[0019] Area w =D 2 / 8(θ-sinθ) (5)

[0020]

[0021] Where D represents the diameter of the pipe; θ represents the center angle of the water level; Area full Represents the area of ​​the pipe when it is full.

[0022] In step S1, the plug transient flow, water hammer transient flow, and free surface transient flow are specifically:

[0023] A1: Plug transient flow:

[0024] Equations (1)-(4) contain five unknowns: Water phase volume fraction, v w Water phase velocity, v a Gas phase velocity, pre w Water phase pressure, pre a Gas phase pressure, four equations cannot solve five unknowns, so by deriving the topological equation describing the gas evolution process, it is added to the above four equations, and its expression is as follows:

[0025]

[0026] Among them, v j Represents the velocity between gas and water. The velocity is approximated by the velocity of the center of mass, that is:

[0027]

[0028] In formula (7), γ pre represents the pressure relaxation coefficient, when γ pre When it approaches infinity, it means that the pressure reaches equilibrium instantly. If the tension between the gas and water fluid is not considered, then formula (7) ja -pre jw = 0, if the tension between air and water is considered, then the pre in formula (7) ja -pre jw ≠0,

[0029] The pressure term in formula (2) and formula (4) is written as:

[0030]

[0031] In the formula, h w Indicates the depth of the aqueous phase.

[0032] Since both the water phase and the gas phase in this multi-equation fluid equation are contractible, equations (1)-(4) complement the basic thermodynamic relationship that relates pressure to density. jp It is expressed as:

[0033]

[0034] In the formula, Cel p is the wave speed, Den p0 Represents the base density of each phase, per 0 represents the base pressure,

[0035] By combining equations (1), (2), (3), (4) and (7), the five unknowns of the plug transient flow ( v w 、v a 、per w and per a ).

[0036] A2: Transient flow with water hammer:

[0037] When the long-distance water pipeline contains only water, it is relatively simple to simulate using the improved one-dimensional gas-water fluid model proposed in the present invention. The gas rate in the five equations of the plug transient flow is set to zero, indicating that there is no gas phase:

[0038]

[0039] In the transient flow field, the transient flow phenomenon of water hammer is simulated, where h w Represents the pressure head of each section. Usually, D≤h w , the hydrostatic pressure per section w Expressed as per w＝ Den w gh w However, in the patent model, the water depth h of each section in the case of pure water hammer flow is w is equal to the pipe diameter D, and in this patent model, water is regarded as a contractible fluid, so the hydrostatic pressure per cross section is w It is expressed as:

[0040]

[0041] A3: Free surface transient flow:

[0042] The derivation of the air-water fluid model relies on its contractibility. In a pressurized transient flow, the waves are contractile waves, and the wave speed in water is usually 1000m / s. In contrast, in the case of a free surface transient flow, the waves are gravity waves, and the wave speed of gravity waves is usually expressed as:

[0043]

[0044] When the long-distance water pipeline is a free surface transient flow, the water density Den w Keep at 1000m 3 / s is a constant value, however, the basic thermodynamic relationship in the multi-equation fluid model uses formula (10), which is not applicable to free surface transient flow. In order to adapt to the characteristics of free surface transient flow, the following basic thermodynamic relationship is used for this flow state:

[0045] per w=Den w h w g (14)

[0046] Among them, h w represents the water depth at each cross section under free surface transient flow conditions, usually satisfying h w ≤D.

[0047] A4: Source term:

[0048] The present invention considers the multi-equation fluid model of water and gas, and the water-wall force F wb , air-wall force F ab and the air-water interface force F j Defined as:

[0049]

[0050] Among them, Cir w Represents the perimeter wetted by the water phase, Cir a Represents the perimeter wetted by the gas phase, Cir j Represents the width of the air-water interface. The three stresses in the one-dimensional system are derived from the free surface flow model:

[0051] τ wb =0.5f w Den w v w |v w |, τ ab =0.5f a Den a v a |v a |, τ j =0.5f j Den g (v g -v w )|v g -v w |(16)

[0052] In this equation, f w 、f a and f j The friction coefficient of each item is expressed by the following formula:

[0053]

[0054] Where, Reynolds number Re a ,Re j ,Re w and Re sw It can be expressed by the following formula:

[0055]

[0056] Among them, Area a represents the gas phase area; v sw represents the surface water velocity, v sa represents the surface air velocity, μ p Represents dynamic viscosity.

[0057] Furthermore, the step S2: solving the eigenvalues ​​and eigenvectors of the equation system:

[0058] The matrix form of the improved one-dimensional gas-water fluid model in this paper can be expressed as:

[0059]

[0060] The matrix U, flux G and source matrix S can be written as follows:

[0061]

[0062]

[0063] The eigenvalue λ of matrix B is:

[0064] λ=[v j v a -Cel a v a +Cel a v w -Cel w v w +Cel w ] (25)

[0065] The eigenvector R is:

[0066]

[0067] Furthermore, the step S3 adopts the FVM method of Rowe-Philippe format to uniformly solve the three flow states.

[0068] The operator solution method based on the Luo-Phillips format is as follows:

[0069]

[0070] In the formula, Represents the variable value on grid i at time n and n+1, the variable update and operator from time n to n+1 and source term operator related.

[0071] The solution for the Luo-Philip format specifically includes the following three steps, including: A1: Hyperbolic operator Solution; A2: Source operator Solution: A3: Philipp linearization. The following is a detailed description of each step:

[0072] A1: Hyperbolic Operator Solution: Hyperbolic Operator Expand using the high-precision Godunov format:

[0073]

[0074] In the formula, Δx is the length of the calculation unit, Δt is the calculation time step, Represents a high-precision correction value of the flux, They represent the waves propagating from grids i+1 and i-1 to grid i. These two parts can be obtained by the following calculation:

[0075]

[0076] here, represents the kth wave, is its velocity, and the superscript is the propagation direction. Depending on the propagation direction, its expression is:

[0077]

[0078] in is the right eigenvector of the kth wave.

[0079] In formula (28), It can be expressed as:

[0080]

[0081] Where: is the smoothness of the kth wave:

[0082]

[0083] Where “·” represents the dot product, and I is determined by the direction of wave propagation:

[0084]

[0085] Use high-precision limiter To achieve second-order accuracy, the expression is:

[0086]

[0087] A2: Source operator solution

[0088] The source term is considered in the multi-equation fluid model, and the final expression of the variable is obtained by using the source term operation:

[0089]

[0090] A3: Philipp Linearization

[0091] The linearized format is obtained by Luo Philip averaging:

[0092]

[0093] The boundary conditions of the water delivery system are complex, and it is easy to produce various complex flow states, or even a mixture of multiple flow states, which makes the design and simulation of the water delivery system very difficult. Most of the existing numerical simulation models can only simulate a single flow state, and the existing gas-water fluid model can only simulate the pressurized state. In order to improve the accuracy of data calculation, combined with the above scheme, the present invention improves the existing one-dimensional gas-water fluid model so that the model can simultaneously meet the requirements of plug transient flow, pressurized water hammer transient flow, and free surface transient flow. Although these flow states have large differences in characteristics, the three flow states are uniformly solved by adopting the "Rod-Philippe" format.

[0094] Beneficial effects: Compared with the prior art, the model of the present invention can simultaneously simulate three different flow states, namely, plug transient flow, water hammer transient flow, and free surface transient flow. There is no need to use specific models for different flow states, which simplifies the simulation process and improves the versatility of the model.

[0095] More accurately predict transient flow events in hydraulic systems, such as water hammer, to provide early warning and take measures to reduce engineering risks and ensure safe system operation.

[0096] It can more effectively optimize water resource utilization, improve water resource management efficiency, and provide better support for the operation and management of water conservancy projects.

[0097] Through more accurate simulation results, the engineering design scheme can be optimized more effectively and the construction and operation costs of the project can be reduced. The introduction of this model provides new methods and ideas for the field of hydraulic numerical simulation and promotes the development of this discipline. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 It is a flow chart of the implementation of the present invention;

[0099] Figure 2 is a cross-sectional parameter diagram of a circular pipe of the present invention;

[0100] Figure 3 It is the water depth map along the pipeline of plug-shaped transient flow at t = 9.3s;

[0101] Figure 4 It is the water depth map along the pipeline of plug-shaped transient flow at t = 9.39s;

[0102] Figure 5 This is a diagram of pressure fluctuation before the valve in a pressurized transient flow pipeline;

[0103] Figure 6 This is a dynamic diagram of the water depth changes at different positions in the free surface transient flow pipeline. Implementation

[0105] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0106] The present invention is a pipeline multi-flow state FVM simulation method based on a one-dimensional gas-water fluid model, referring to Figure 1 , which includes the following steps: S1 constructs the one-dimensional control equation of the unsteady gas-water fluid model:

[0107]

[0108] In the above formula: subscripts a and w represent the gas phase and water phase respectively. For the sake of simplicity, subscript p is used to represent it, p = a, w. Interface variables: j; wall-related variables: b; pre p Indicates pressure; jp Indicates the pressure at the air-water interface; v p Indicates speed; Den p Indicates density; Represents the volume fraction of a phase, satisfying represents the inclination angle of the pipeline; F represents the friction force, and g represents the acceleration due to gravity.

[0109] For circular cross-section pipes ( Figure 1 ), the water phase area is recorded as Area w , water phase volume fraction It is expressed as:

[0110] Area w =D 2 / 8(θ-sinθ) (5)

[0111]

[0112] Where D represents the diameter of the pipe; θ represents the center angle of the water level; Area full Represents the area of ​​the pipe when it is full.

[0113] Step S1 constructs a one-dimensional control equation of an unsteady gas-water fluid model and improves the control equation to adapt to the simulation of plug-shaped transient flow, water hammer transient flow, and free surface transient flow, specifically including the following aspects: A1: Plug-shaped transient flow:

[0114] Equations (1)-(4) contain five unknowns: Water phase volume fraction, v w Water phase velocity, v a Gas phase velocity, pre w Water phase pressure, pre a Gas phase pressure, four equations cannot solve five unknowns. Therefore, by deriving the topological equation describing the gas evolution process, it is added to the above four equations, and its expression is as follows:

[0115]

[0116] Among them, v j Represents the velocity between gas and water. The velocity is approximated by the velocity of the center of mass, that is:

[0117]

[0118] In formula (7), γ pre represents the pressure relaxation coefficient, when γ pre When it approaches infinity, it means that the pressure reaches equilibrium instantly. If the tension between the gas and water fluid is not considered, then formula (7) ja -pre jw = 0, if the tension between air and water is considered, then the pre in formula (7) ja -pre jw ≠0.

[0119] The pressure term in formula (2) and formula (4) is written as:

[0120]

[0121] In the formula, h w Indicates the depth of the aqueous phase.

[0122] Since both the water phase and the gas phase in this multi-equation fluid equation are contractible, equations (1)-(4) complement the basic thermodynamic relationship that relates pressure to density. jp It is expressed as:

[0123]

[0124] In the formula, Cel p is the wave speed, Den p0Represents the base density of each phase, per 0 Represents the base pressure.

[0125] By combining equations (1), (2), (3), (4) and (7), the five unknowns of the plug transient flow ( v w 、v a 、per w and per a ).

[0126] A2: Transient flow with water hammer:

[0127] When the long-distance water pipeline contains only water, it is relatively simple to simulate using the improved one-dimensional gas-water fluid model proposed in the present invention. The gas rate in the five equations of the plug transient flow is set to zero, indicating that there is no gas phase:

[0128]

[0129] In the transient flow field, the transient flow phenomenon of water hammer is simulated, where h w Represents the pressure head of each section. Usually, D≤h w , the hydrostatic pressure per section w Expressed as per w＝ Den w gh w However, in the patent model, the water depth h of each section in the case of pure water hammer flow is w is equal to the pipe diameter D, and in this patent model, water is regarded as a contractible fluid, so the hydrostatic pressure per cross section is w It is expressed as:

[0130]

[0131] A3: Free surface transient flow:

[0132] The derivation of the air-water fluid model relies on its contractibility. In a pressurized transient flow, the waves are contractile waves, and the wave speed in water is usually 1000m / s. In contrast, in the case of a free surface transient flow, the waves are gravity waves, and the wave speed of gravity waves is usually expressed as:

[0133]

[0134] When the long-distance water pipeline is a free surface transient flow, the water density Den w Keep at 1000m 3 / s is a constant value, however, the basic thermodynamic relationship in the multi-equation fluid model uses formula (10), which is not applicable to free surface transient flow. In order to adapt to the characteristics of free surface transient flow, the following basic thermodynamic relationship is used for this flow state:

[0135] per w =Den w h w g (14)

[0136] Among them, h w represents the water depth at each cross section under free surface transient flow conditions, usually satisfying h w ≤D.

[0137] A4: Source term:

[0138] The present invention considers the multi-equation fluid model of water and gas, and the water-wall force F wb , air-wall force F ab and the air-water interface force F j Defined as:

[0139]

[0140] Among them, Cir w Represents the perimeter wetted by the water phase, Cir a Represents the perimeter wetted by the gas phase, Cir j Represents the width of the air-water interface. The three stresses in the one-dimensional system are derived from the free surface flow model:

[0141] τ wb =0.5f w Den w v w |v w |, τ ab =0.5f a Den a v a |v a |, τ j =0.5f j Den g (v g -v w )|v g -v w |(16)

[0142] In this equation, f w 、f a and f j The friction coefficient of each item is expressed by the following formula:

[0143]

[0144] Where, Reynolds number Re a ,Re j ,Re w and Re sw It can be expressed by the following formula:

[0145]

[0146] Among them, Area a represents the gas phase area; v sw represents the surface water velocity, v sa represents the surface air velocity, μ p Represents dynamic viscosity.

[0147] S2: Solving the eigenvalues ​​and eigenvectors of the system of equations:

[0148] The matrix form of the improved one-dimensional gas-water fluid model in this paper can be expressed as:

[0149]

[0150] The matrix U, flux G and source matrix S can be written as follows:

[0151]

[0152]

[0153]

[0154] The eigenvalue λ of matrix B is:

[0155] λ=[v j v a -Cel a v a +Cel a v w -Cel w v w +Cel w ] (25)

[0156] The eigenvector R is:

[0157]

[0158] S3: The FVM method of Rowe-Philippe format is used to uniformly solve the three flow states.

[0159] The operator solution method based on the Luo-Phillips format is as follows:

[0160]

[0161] In the formula, Represents the variable value on grid i at time n and n+1 respectively. Variable update and operator from time n to n+1 and source term operator related.

[0162] The solution for the Luo-Philip format specifically includes the following three steps, including: A1: Hyperbolic operator Solution; A2: Source operator Solution: A3: Philipp linearization. The following is a detailed description of each step:

[0163] A1: Hyperbolic Operator Solution: Hyperbolic Operator Expand using the high-precision Godunov format:

[0164]

[0165] In the formula, Δx is the length of the calculation unit, Δt is the calculation time step, Represents a high-precision correction value of the flux, They represent the waves propagating from grids i+1 and i-1 to grid i. These two parts can be obtained by the following calculation:

[0166]

[0167] here, represents the kth wave, is its velocity, and the superscript is the propagation direction. Depending on the propagation direction, its expression is:

[0168]

[0169] in is the right eigenvector of the kth wave.

[0170] In formula (28), It can be expressed as:

[0171]

[0172] Where: is the smoothness of the kth wave:

[0173]

[0174] Where “·” represents the dot product, and I is determined by the direction of wave propagation:

[0175]

[0176] Use high-precision limiter To achieve second-order accuracy, the expression is:

[0177]

[0178] A2: Source operator solution

[0179] The source term is considered in the multi-equation fluid model, and the final expression of the variable is obtained by using the source term operation:

[0180]

[0181] A3: Philipp Linearization

[0182] The linearized format is obtained by Luo Philip averaging:

[0183]

[0184] S4: Conduct model evaluation and verification.

[0185] Based on the above scheme, in order to verify the actual simulation effect of the method of the present invention, Examples 1, 2 and 3 were carried out respectively, which were slug transient flow, water hammer transient flow and free surface transient flow, respectively. Through the three examples, the ability of the model in this paper to simulate the above multiple flow states was verified. The details are as follows:

[0186] Example 1: Slug transient flow

[0187] Davies 1992 experiment, the pipe is 10 meters long and has an inner diameter of 0.074 meters. By using a special inlet device, the water and gas flow is divided at the inlet. The initial gas surface velocity is 1.84 meters per second, and the initial water surface velocity is 0.295 meters per second. The water depth at the upstream boundary is kept constant, and the downstream boundary is free outflow. In the simulation, the initial density of water is set to 1000kg / m 3 , the initial density of the gas is set to 1.0 kg / m3, the initial wave velocity of water is 1000 m / s, and the initial wave velocity of the gas is 100000 0.5 m / s. The viscosity of water is μ w =1.14·10 -3 Pascal seconds, the viscosity of the gas is μ a =1.79·10 -5 Pascal seconds.

[0188] The solution obtained by the method of the present invention is compared with the experimental results of Davies 1992, and the following results are obtained respectively: Figure 3 and Figure 4 The water depth comparison curve along the pipeline is shown. Figure 3 This is the water depth map along the pipeline at 9.30s. Figure 4 This is the water depth map along the pipeline after another 0.09s. According to the results in the figure, it can be seen that the method proposed in this patent can accurately simulate the plug flow occurring in the pipeline at different times.

[0189] Example 2: Transient flow with water hammer

[0190] Take a pipe with a length of 500m and a diameter of 0.021m. The pipe is filled with water. The initial upstream water level is 0.35m, the initial flow velocity is 2.8872m / s, the wave velocity is 1000m / s, and the downstream valve is suddenly closed to simulate the water head before the pipeline valve.

[0191] Comparing the calculation results of the method of the present invention with the results of water hammer simulation in 2004 by Zhao et al., we can obtain the following: Figure 5 The comparison curve shown is Figure 5 It can be seen that the present invention can accurately simulate transient flow with water hammer, which is highly consistent with the simulation results of Zhao in 2004.

[0192] Example 3: Free Surface Transient Flow

[0193] In order to verify the effectiveness of the present invention in simulating free surface transient flow, we selected the free surface pipe transient simulation experimental results conducted by Ackers (1964) for comparison.

[0194] Experimental parameters:

[0195] Pipeline length: 304.80 meters; Pipeline inner diameter: 0.3048 meters; Manning roughness coefficient: 0.0115; Pipeline slope: 0.001; Initial water depth: 0.0768 meters; Initial flow rate: 0.004984 cubic meters per second

[0196] Upstream boundary flow changes: trapezoidal form, duration 132 seconds, maximum flow 0.018689 cubic meters / second, maximum flow duration 12 seconds.

[0197] Experimental conditions: Under the above experimental conditions, transient flow occurs in the free surface pipe due to the variation of upstream inflow.

[0198] The calculation results of the method of the present invention are compared with the transient simulation experimental results of free surface pipeline by Ackers in 1964, and a comparison curve is drawn ( Figure 6 ), the results show that the proposed method can accurately simulate the transient flow on the free surface. Figure 6The comparison curves of the calculation results of the method of the present invention and the Ackers experimental results at 8.66m, 77.94m, 147.22m, and 216.46m are shown. The two are highly consistent in pressure amplitude and attenuation trend, proving the accuracy of the model. This shows that the method of the present invention can effectively simulate the pressure change trend of transient flow in a free surface pipeline. According to the results of Examples 1, 2, and 3, the results of the three embodiments show that the method of the present invention can effectively simulate the slug transient flow, the pressure water hammer transient flow, and the free surface transient flow that appear in the pipeline, showing the powerful ability of the method in hydraulic system simulation.

Claims

1. A pipeline multi-flow state FVM simulation method based on a one-dimensional gas-water fluid model is used to simulate three typical transient flow states in the pipeline: plug transient flow, water hammer transient flow and free surface transient flow. The method comprises the following steps: S1: Construct the one-dimensional control equation of the unsteady gas-water fluid model and improve the control equation to make it adapt to the simulation of plug transient flow, water hammer transient flow and free surface transient flow; S2: Solving the eigenvalues ​​and eigenvectors of the system of equations; S3: The FVM method of Rowe-Phillips format is used to uniformly solve the three flow regimes; S4: Based on the calculation results of step S3, the model is evaluated and verified.

2. The pipeline multi-flow state FVM simulation method based on a one-dimensional gas-water fluid model according to claim 1 is characterized in that: The step S1 constructs a one-dimensional control equation of an unsteady gas-water fluid model: In the above formula: subscripts a and w represent gas phase and water phase respectively; subscript p represents p = a, w; interface variable: j; Wall-related variables: b; pre p Indicates pressure; jp Indicates the pressure at the air-water interface; v p Indicates speed; Den p Indicates density; Represents the volume fraction of a phase, satisfying represents the inclination angle of the pipeline; F represents the friction force, and g represents the acceleration of gravity; For a circular cross-section pipe, the water phase area is recorded as Area w , water phase volume fraction It is expressed as: Area w =D 2 / 8(θ-sinθ) (5) Where D represents the diameter of the pipe; θ represents the center angle of the water level; Area full Represents the area of ​​the pipe when it is full.

3. The pipeline multi-flow state FVM simulation method based on a one-dimensional gas-water fluid model according to claim 1 is characterized in that: In step S1, A1: Plug transient flow: Equations (1)-(4) contain five unknowns: Water phase volume fraction, v w Water phase velocity, v a Gas phase velocity, pre w Water phase pressure, pre a Gas phase pressure, four equations cannot solve five unknowns, so by deriving the topological equation describing the gas evolution process, it is added to the above four equations, and its expression is as follows: Among them, v j Represents the velocity between gas and water, and the velocity is approximately expressed and calculated using the velocity of the center of mass, that is: In formula (7), γ pre represents the pressure relaxation coefficient, when γ pre When it approaches infinity, it means that the pressure reaches equilibrium instantly. If the tension between the gas and water fluid is not considered, then formula (7) ja -pre jw = 0, if the tension between air and water is considered, then the pre in formula (7) ja -pre jw ≠0, The pressure term in formula (2) and formula (4) is written as: In the formula, h w represents the depth of the water phase, Since both the water phase and the gas phase in this multi-equation fluid equation are shrinkable, equations (1)-(4) supplement the basic thermodynamic relationship, which relates pressure to density, per jp It is expressed as: In the formula, Cel p is the wave speed, Den p0 represents the base density of each phase, per0 represents the base pressure, By combining equations (1), (2), (3), (4) and (7), the five unknowns of the plug transient flow ( v w 、v a 、per w and per a ); A2: Transient flow with water hammer: When the long-distance water pipeline contains only water, the gas rate in the five equations of the plug transient flow is set to zero, indicating that there is no gas phase: In the transient flow field, the transient flow phenomenon of water hammer is simulated, where h w Represents the pressure head of each section. Usually, D≤h w , the hydrostatic pressure per section w Expressed as per w =Den w gh w ; However, in the case of pure water hammer flow, the water depth h of each section w is equal to the pipe diameter D, and water in the model is considered as a shrinkable fluid, so the hydrostatic pressure per cross section is w It is expressed as: A3: Free surface transient flow: The derivation of the air-water fluid model relies on its contractibility. In the pressurized transient flow, the waves are contractile waves, and the wave speed in water is usually 1000m / s. In contrast, in the case of free surface transient flow, the waves are gravity waves, and the wave speed of gravity waves is usually expressed as: When the long-distance water pipeline is a free surface transient flow, the water density Den w Keep at 1000m 3 / s is a constant value. However, the basic thermodynamic relationship in the multi-equation fluid model adopts formula (10), which is not applicable to the free surface transient flow. In order to adapt to the characteristics of the free surface transient flow, the following basic thermodynamic relationship is adopted for this flow state: per w =The w h w g (14) Among them, h w represents the water depth at each cross section under free surface transient flow conditions, usually satisfying h w ≤D; A4: Source term: The multi-equation fluid model considering water and gas, the water-wall force F wb , air-wall force F ab and the air-water interface force F j Defined as: Among them, Cir w Represents the perimeter wetted by the water phase, Cir a Represents the perimeter wetted by the gas phase, Cir j Represents the width of the air-water interface. The three stresses in the one-dimensional system are derived from the free surface flow model: τ wb =0.5f w Den w v w v w |, τ ab =0.5f a Den a v a v a |, τ j =0.5f j Den g (v g -v w )|v g -v w | (16) In this equation, f w 、f a and f j The friction coefficient of each item is expressed by the following formula: Where, Reynolds number Re a ,Re j ,Re w and Re sw It can be expressed by the following formula: Among them, Area a represents the gas phase area; v sw represents the surface water velocity, v sa represents the surface air velocity, μ p Represents dynamic viscosity.

4. The pipeline multi-flow state FVM simulation method based on a one-dimensional gas-water fluid model according to claim 1 is characterized in that: Step S2: solving the eigenvalues ​​and eigenvectors of the equation system: The matrix form of the one-dimensional gas-water fluid model can be expressed as: The matrix U, flux G and source matrix S can be written as follows: The eigenvalue λ of matrix B is: λ=[v j in a -Cell a in a +Tel a in w -Cell w in w +Tel w ] (25) The eigenvector R is:

5. The pipeline multi-flow state FVM simulation method based on a one-dimensional gas-water fluid model according to claim 1 is characterized in that: The step S3: using the FVM method of the Rowe-Phillips format to uniformly solve the three flow states, the operator solution method based on the Rowe-Phillips format is as follows: In the formula, and Represents the variable value on grid i at time n and n+1, the variable update and operator from time n to n+1 and source term operator related; The solution for the Luo-Philip format specifically includes the following three steps, including: A1: Hyperbolic operator Solution; A2: Source operator Solution; A3: Luo Philip linearization, each step is described in detail below: A1: Hyperbolic Operator Solution: Hyperbolic Operator Expand using the high-precision Godunov format: In the formula, Δx is the length of the calculation unit, Δt is the calculation time step, Represents a high-precision correction value of the flux, and They represent the waves propagating from grids i+1 and i-1 to grid i respectively. These two parts can be obtained by the following calculation: Here, W k i-1 / 2 represents the kth wave, λ k i-1 / 2 is its speed and the superscript is the propagation direction. Depending on the propagation direction, the expression is: where r k i-1 / 2 is the right eigenvector of the kth wave, In formula (28), It can be expressed as: Where: k i-1 / 2 is the smoothness of the kth wave: Where "·" represents the dot product, and I is determined by the direction of wave propagation: Use high-precision limiter To achieve second-order accuracy, the expression is: A2: Source operator solution The source term is considered in the multi-equation fluid model, and the final expression of the variable is obtained by using the source term operation: A3: Philipp Linearization The linearized format is obtained by Luo Philip averaging:

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