Improved mixed flow simulation method considering large multi-shaft pipeline

Abstract

The invention discloses an improved mixed flow simulation method considering a large multi-shaft pipeline, and provides an improved mixed flow model, a two-phase component method of a water body and discrete gas are combined, a random selection method and a Godeov finite volume method are combined for solving, and the applicability of actual multi-shaft layout and large-size engineering cases is considered. Accuracy, stability and practical applicability of mixed flow simulation can be improved, dynamic pressure characteristics of water-gas two-phase flow in mixed flow simulation can be accurately and quantitatively represented, and the influence effect of multi-shaft layout and scale effect on mixed flow simulation is revealed in detail. The method is of great significance to mixed flow simulation and hydraulic safety guidance considering large-scale multi-shaft complex layout in actual engineering.

Description

Technical Field

[0001] The invention relates to the technical field of hydraulic numerical simulation calculation of a hydropower station (pump station), and in particular to an improved mixed flow simulation method considering large multi-shaft pipelines. Background Art

[0002] In recent years, rapid flow conversion often occurs in large-scale stormwater drainage systems and water diversion projects due to heavy rainfall or large inflows from upstream. This flow pattern is characterized by the initial compression of long-distance gas pockets and subsequent irregular intermittent flow pattern transitions. Due to the actual engineering layout requirements, these pipeline systems involve multi-shaft gas discharge problems. These complex flows pose a great threat to the safe operation of the pipeline system, so it is necessary to develop corresponding mixed flow models.

[0003] In the current research, one-dimensional and three-dimensional numerical methods have been developed for mixed flow simulation. The high computational requirements of three-dimensional methods make them impractical, considering that large pipelines require a large number of grid cells and long simulation times. In contrast, one-dimensional methods are more suitable for large pipelines, including rigid column method, shock capture method and shock fitting method. Among the one-dimensional shock wave capture methods, the two-component pressure method (TPA) is widely used because it effectively solves the mixed flow simulation problem without tracking the air-water interface, so this model is also applied to the water body part of the present invention.

[0004] In addition, in order to solve the problem of trapped air pockets in mixed flow, the two-component pressure method needs to be combined with the air model. The air model is based on the ideal gas law and mainly includes the uniform air pressure head model and the discrete air model. Traditional methods: 1. It is mainly a uniform air pressure head model, which simply assumes that the air pressure in a single air bag is uniform, and cannot accurately consider the problem of trapped air pockets; 2. In addition, the traditional method ignores the mutual influence between the actual multiple vertical shafts, and cannot consider the staged characteristics of gas emission during the mixed flow process. The transient coupling effect of water-gas two-phase pressure, density, and flow rate of the gas-liquid two-phase mixed flow is poor; 3. The size effect of the large-scale prototype and the large-distance air bag between the model is ignored, and there is a lack of quantitative research and verification on the applicability of the water-gas two-phase mixed flow model in actual large-scale projects; 4. The traditional solution method has inherent defects of low resolution and poor conservation for shock wave capture and wave velocity adjustment of multi-phase and transient flows.

[0005] Therefore, the present invention aims to address these gaps by establishing an improved mixed flow model. The model combines a two-component pressure method for the water part simulation and a discrete Euler method for the gas part. The numerical solution is a Godunov type finite volume method combined with a random selection method (RCM) to improve numerical stability. Further emphasis is placed on applicability in large airbags, and multiple shafts and size effect problems are analyzed. Summary of the invention

[0006] The purpose of this section is to summarize some aspects of embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and the invention title of this application to avoid blurring the purpose of this section, the specification abstract and the invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

[0007] In view of the above-mentioned existing gas-liquid two-phase transient flow in the water supply system, the present invention is proposed to solve the problems of dynamically coupled gas and fluid transient parameters, multi-well gas emission, system size effect, and low reproduction accuracy and poor stability of traditional models.

[0008] Therefore, the technical problem solved by the present invention is: to improve the mixed flow model, combine the two-phase component method of water body and discrete gas, and solve it by combining the random selection method and the Godnov type finite volume method, and consider the applicability of actual multi-shaft layout and large-scale engineering cases, so as to improve the accuracy, stability and practical applicability of mixed flow simulation, accurately and quantitatively characterize the dynamic pressure characteristics of water-gas two-phase flow in mixed flow simulation, and reveal in detail the influence of multi-shaft layout and scale effect on mixed flow simulation.

[0009] In order to solve the above technical problems, the present invention provides the following technical solutions: an improved mixed flow simulation method considering large multi-shaft pipelines, including dynamically coupling gas and fluid transient parameters, quantitatively analyzing multi-shaft gas emissions and system size effects, and improving the accuracy and stability of model reproduction, and the specific steps are as follows: S1: constructing a two-phase component model of a water body and calculating the mass and momentum flux of the pipeline body; S2: dynamically coupling a discrete gas model and combining the discrete gas Euler method; S3: introducing a random selection method and a Godnov-type finite volume method to achieve accurate and stable solution of the model; S4: processing the calculation results, and verifying the predicted results of the proposed model with experimental data; S5: quantitatively considering the influencing effects of multi-shaft gas emissions and system scale.

[0010] As a preferred solution of the present invention, a two-phase component simulation model is established for the water body:

[0011]

[0012] Where:

[0013]

[0014]

[0015] Among them, U is the vector of conserved variables; F is the vector of conserved variable fluxes; S is the vector of source terms; x is the distance along the pipe axis; t is time; A is the flow cross-sectional area; Q is the flow rate; g is the gravitational acceleration; hu is the distance between the center of mass of the cross section and the free surface; hp is the additional pressure head; hair is the pressurized air pressure head; θ = π-arccos[(yD / 2)D / 2]; D is the pipe diameter; Apipe is the cross-sectional area; a is the wave speed in the pressurized flow.

[0016] As a preferred solution of the present invention, a gas model is dynamically coupled to establish a discrete Euler gas model:

[0017]

[0018] Among them, is the air density; u is the air velocity; p is the air pressure head, α is the speed of sound waves in air; S d1 , S d2 and S fa They are the source terms in the continuity equation, momentum equation and the loss between the airflow and the pipe wall.

[0019] As a preferred solution of the present invention, the state is assigned to the next time level based on a random sampling process:

[0020]

[0021] Where, the superscript n represents the nth computation time step; the subscript i represents the i-th computation control volume; β n For random numbers, due to the advantages of low variance and uniform distribution, the Van der Korput number pseudo-random sequence is suggested as the best random sequence in the sampling process. The Van der Korput sequence is expressed as:

[0022]

[0023] Where k1 and k2 are two relatively prime numbers, k1>k2>0; mod represents the remainder function; m, a i , A i These are all intermediate generated parameters.

[0024] Among them, the discontinuity problem is handled by using the Godnov type finite volume method with an exact Riemann solver:

[0025] f(A * )≡f L (A * ,A L )+f R (A * ,A R )+u R -uL =0

[0026]

[0027] Among them, u R and u L are the velocity variables on the left and right sides of the node respectively; f K (K=L or R) is the expression that passes through the left or right nonlinear wave and establishes the relationship between the two sides and the middle state; the superscript * is the solution value of the discontinuity area (i.e., the asterisk area) in the Riemann problem; A K (K=L or R) is the area in the flux on the left and right sides; I1 is the integral form of the pressure term of the interface of any shape; is a function of area and can be calculated using existing literature.

[0028] Among them, the expression of the flow Q* in the asterisk area in the Riemann problem is:

[0029]

[0030] Among them, the flow area solution A at the discontinuity is obtained by iteration of the Newton-Raphson method * :

[0031]

[0032] Where f' represents the flux derivative.

[0033] As a preferred solution of the present invention, the gas release effect of multiple shaft discharge is considered: the shaft exhaust boundary condition applies the continuity equation and the orifice equation, and the continuity equation of the boundary condition is:

[0034]

[0035] Wherein, the subscript air represents the corresponding variable of the gas; the subscript 1 represents the first computational control volume of the boundary; Mairout = the mass of air discharged through the vent, calculated using equation (15), using the Riemann invariant to solve the isothermal, one-dimensional, original format Euler equations

[0036] u air1 =u air2 -α(logρ2-logρ1) (15)

[0037] The subscript 2 represents the second control volume adjacent to the first calculation control volume.

[0038] Considering the size effect of the system quantitatively, the original and model Frode numbers are designed to be the same, then:

[0039]

[0040] Among them, Fr is the Froude number; U represents the water flow velocity; g is the gravitational acceleration; L is the system length; λ represents the similarity ratio of the prototype to the model of each variable; Q is the flow rate; p is the pressure; H is the pressure head; ρ is the density; subscript Y represents the prototype, subscript M represents the model, subscript u represents the velocity variable, subscript l represents the length variable, subscript t represents the time variable, subscript r represents the characteristic physical quantity, subscript Q represents the flow variable, and subscript H represents the pressure head variable.

[0041] Beneficial effects of the present invention:

[0042] 1. Establish a high-precision one-dimensional multiphase model, combine the two-phase component water simulation method and the discrete gas Euler simulation method to simulate the water-gas two-phase transient flow, and realize the accurate simulation of the mixed flow in the water pipeline.

[0043] 2. Importantly, the influence of the multi-shaft layout on the water-filled two-phase flow and the influence of the system size effect on the model applicability are carefully explored.

[0044] 3. In addition, the random selection method is combined with the Godnov-type finite volume method to achieve accurate and stable solution of the model, which is conducive to ensuring hydraulic safety prediction, operation scheduling and prevention and control in water pipelines. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0046] Figure 1 The present invention provides an implementation flow chart.

[0047] Figure 2 Schematic diagram of the experimental system provided by the present invention.

[0048] Figure 3 A comparison chart of the multi-well mixed flow model and the gas-free model provided by the present invention and the experimental results.

[0049] Figure 4 This is a multi-shaft exhaust effect analysis diagram of the model working condition in the multi-shaft mixed flow model provided by the present invention.

[0050] Figure 5 This is a size effect analysis diagram of the large-scale prototype working condition of the multi-shaft mixed flow model provided by the present invention. DETAILED DESCRIPTION

[0051] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0052] The improved mixed flow simulation method considering large multi-shaft pipelines is carried out in the following steps:

[0053] S1. Construct a two-phase component model of the water body and calculate the mass and momentum flux of the pipeline body. Calculate the mass and momentum flux of the pipeline body, where the traditional pressure head is subdivided into the pressure head between the centroid of the cross section and the free surface, the additional pressure head above the cross section, and the pressurized air pressure head;

[0054] S2. Dynamically coupled discrete gas model, combined with discrete gas Euler method to solve the mass and momentum flux of the gas separately, where the source terms in the continuity equation, momentum equation and loss between the gas flow and the pipe wall are considered simultaneously;

[0055] S3. The random selection method and the Godnov type finite volume method are introduced to achieve accurate and stable solution of the model. The random selection method mainly allocates the state to the next time level based on the random sampling process through the van der Korput number, and the Godnov type finite volume method uses an exact Riemann solver to deal with discontinuity problems.

[0056] S4. Process the calculation results and verify the prediction results of the proposed model with experimental data. The verification case and verification results can be found in Example 1 below. Figure 2 and Figure 3 ;

[0057] S5. Quantitatively consider the influencing effects of multi-shaft gas emissions and system scale. The continuity equation and orifice equation are applied to the gas emission effect, and the scale conversion relationship of each variable is quantitatively considered in the system scale effect.

[0058] Example:

[0059] In order to verify and analyze the simulation effect of the improved mixed flow simulation method considering large multi-shaft pipelines of the present invention, Example 1 selects Figure 2The experimental system shown in the figure. The experimental system is derived from an actual long-distance large-scale water transmission and diversion project. The main part of the actual pipeline is converted into a typical local pipeline at a standard ratio of 1:34. In the experimental system, the pipeline length is 2243.82m, the pipe diameter is 0.3m, the upstream water level is constant, and there is an initial submergence depth at the downstream end with a constant water level. The remaining part of the pipeline is an initial empty pipe with six vertical shafts with the same diameter as the main pipe. In addition, seven pressure sensors are installed at the intersection of each shaft and the main pipe and at the downstream outlet, all located at the top of the pipe; four flow sensors are installed in the main pipe, located at Q1 (x=8m), Q2 (x=790m), Q3 (x=1598.20m) and Q4 (x=2446.82m). Based on this Figure 2 The experimental system of Example 1 uses the multi-well mixed flow model of the present invention to simulate, and compares the experimental results with the traditional gas-free model and experimental results. The data comparison diagram is shown in FIG. Figure 3 .

[0060] Example 2 uses an actual large-scale project corresponding to the above case to analyze the impact of system size on the model. In the actual project, the pipeline length is 194.3 km, the pipe diameter is 10.2 m, the highest operating water level at the inlet is 173.3 m, and the downstream design water level is 88.3 m. Based on this actual large-scale project, Example 2 uses the multi-shaft mixed flow model of the present invention to simulate the exhaust effect. Figure 4 Data display and analysis, size effect Figure 5 data display and analysis.

[0061] The specific implementation steps are as follows:

[0062] Step 1:

[0063] Construct the water body part to establish a two-phase component simulation model and calculate the mass and momentum flux of the pipeline body:

[0064]

[0065] In the formula

[0066]

[0067] Where U is the vector of conserved variables; F is the vector of conserved variable fluxes; S is the vector of source terms; x is the distance along the tube axis; t is time; A is the flow cross-sectional area; Q is the flow rate; g is the gravitational acceleration; h u is the distance between the centroid of the cross section and the free surface; h p is the additional pressure head; h air is the pressurized air head; θ = π-arccos[(yD / 2)D / 2]; D is the pipe diameter; Apipe is the cross-sectional area; a is the wave velocity in the pressurized flow.

[0068] Step 2:

[0069] Dynamically couple the gas model to establish a discrete Euler gas model:

[0070]

[0071] Among them, ρ is the air density; u is the air velocity; p is the air pressure head, α is the speed of sound waves in air; S d1 , S d2 and Sf a They are the source terms in the continuity equation, momentum equation and the loss between the airflow and the pipe wall.

[0072] Step 3:

[0073] In order to achieve accurate and stable solution of the model, random selection method and Godnov type finite volume method are introduced: random selection method is used to solve the discontinuity problem in complex wave interaction. Different from the integral averaging in Godnov method, the random selection method mainly allocates the state to the next time level based on the random sampling process through the Van der Corput number:

[0074]

[0075] Where, the superscript n represents the nth computation time step; the subscript i represents the i-th computation control volume; β n is a random number. Due to the advantages of low variance and uniform distribution, the Van der Korput number pseudo-random sequence is suggested as the best random sequence in the sampling process. The Van der Korput sequence is expressed as:

[0076]

[0077] Where k1 and k2 are two relatively prime numbers, k1>k2>0; mod represents the remainder function; m, a i , A i These are all intermediate generated parameters.

[0078] Using the Godnov type finite volume method, the discontinuity problem is treated with an exact Riemann solver, which is formulated as follows:

[0079] f(A * )≡f L (A * ,A L )+f R (A * ,A R )+u R -uL =0

[0080]

[0081] Among them, u R and u L are the velocity variables on the left and right sides of the node respectively; f K (K=L or R) is the expression that passes through the left or right nonlinear wave and establishes the relationship between the two sides and the middle state; the superscript * is the solution value of the discontinuity area (i.e., the asterisk area) in the Riemann problem; A K (K=L or R) is the area in the flux on the left and right sides; I1 is the integral form of the pressure term of the interface of any shape; is a function of area.

[0082] Then we can get the expression of the flow Q* in the asterisk area in the Riemann problem:

[0083]

[0084] The Newton-Raphson method is further used to iterate the flow area solution A at the discontinuity. * :

[0085]

[0086] Where f' represents the flux derivative.

[0087] Step 4:

[0088] The calculation results were processed and the prediction results of the proposed model were verified with experimental data. Figure 2 and Figure 3 .

[0089] Step 5:

[0090] Quantitatively consider the impact of multiple shaft gas emissions and system scale:

[0091] The continuity equation and orifice equation are applied to the vertical shaft exhaust boundary condition. The continuity equation of this boundary condition is:

[0092]

[0093] Where, the subscript air represents the corresponding variable of the gas; the subscript 1 represents the first computational control volume on the boundary; Mairout = the mass of air discharged through the vent, calculated using equation (15). Using the Riemann invariant to solve the isothermal, one-dimensional, original format Euler equations

[0094] u air1 =u air2-α(logρ2-logρ1) (15)

[0095] The subscript 2 represents the second control volume adjacent to the first calculation control volume.

[0096] Considering the size effect of the system quantitatively, the original and model Frode numbers are designed to be the same, and the formula is:

[0097]

[0098] Among them, Fr is the Froude number; U represents the water flow velocity; g is the gravitational acceleration; L is the system length; λ represents the similarity ratio of the prototype to the model of each variable; Q is the flow rate; p is the pressure; H is the pressure head; ρ is the density; subscript Y represents the prototype, subscript M represents the model, subscript u represents the velocity variable, subscript l represents the length variable, subscript t represents the time variable, subscript r represents the characteristic physical quantity, subscript Q represents the flow variable, and subscript H represents the pressure head variable.

[0099] Calculated by the above formula, calculated by the above method, based on this Figure 2 The experimental system of Example 1 uses the multi-well mixed flow model of the present invention to simulate, and compares the experimental results with the traditional gas-free model and experimental results. The data comparison diagram is shown in FIG. Figure 3 . Based on a certain scale corresponding to Figure 2 In the actual large-scale project, Example 2 uses the multi-shaft mixed flow model of the present invention to simulate, and discusses the influence of multi-shaft gas emission and system scale in the improved mixed flow model. Figure 4 Data display and analysis, size effect Figure 5 Data display and analysis. Figure 3 It can be seen that the improved mixed flow simulation method considering large multi-shaft pipelines has satisfactory accuracy in the complex layout of actual engineering. Figure 4 , Figure 5 It can be seen that the layout of multiple shafts will cause the pipeline mixed flow to have a staged exhaust phenomenon, which has a great impact on the mixed flow simulation. The volume, pressure, and density of the air mass show dynamic stage changes. Compared with large-scale actual engineering cases, it can be seen that this model takes into account the scale effect of the water and gas phases, and is also applicable to large-scale mixed flow cases. Therefore, the improved mixed flow simulation considering large multi-shaft pipelines has satisfactory accuracy in the simulation of actual engineering mixed flows with complex layouts.

[0100] Technical effects:

[0101] 1. Establish a high-precision one-dimensional multiphase model, combine the two-phase component water simulation method and the discrete gas Euler simulation method to simulate the water-gas two-phase transient flow, and realize the accurate simulation of the mixed flow in the water pipeline.

[0102] 2. Importantly, the influence of the multi-shaft layout on the water-filled two-phase flow and the influence of the system size effect on the model applicability are carefully explored.

[0103] 3. In addition, the random selection method is combined with the Godnov-type finite volume method to achieve accurate and stable solution of the model, which is conducive to ensuring hydraulic safety prediction, operation scheduling and prevention and control in water pipelines.

[0104] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. An improved mixed flow simulation method considering large multi-shaft pipelines, characterized in that: It includes dynamically coupling gas and fluid transient parameters, quantitatively analyzing multi-shaft gas emissions and system size effects, and improving the model's reproduction accuracy and stability. The specific steps are as follows: S1: Construct a two-phase component model of the water body and calculate the mass and momentum flux of the pipeline body; S2: Dynamically coupled discrete gas model combined with discrete gas Euler method; S3: Introduce random selection method and Godnov type finite volume method to achieve accurate and stable solution of the model; S4: Process the calculation results and verify the prediction results of the proposed model with experimental data; S5: Quantitatively consider the impact of multiple shaft gas emissions and system scale.

2. The improved mixed flow simulation method considering large multi-shaft pipelines according to claim 1 is characterized in that: A two-phase component simulation model is established for the water part: Where: Among them, U is the vector of conserved variables; F is the vector of conserved variable fluxes; S is the vector of source terms; x is the distance along the pipe axis; t is time; A is the flow cross-sectional area; Q is the flow rate; g is the gravitational acceleration; hu is the distance between the center of mass of the cross section and the free surface; hp is the additional pressure head; hair is the pressurized air pressure head; θ = π-arccos[(yD / 2)D / 2]; D is the pipe diameter; Apipe is the cross-sectional area; a is the wave speed in the pressurized flow.

3. The improved mixed flow simulation method considering large multi-shaft pipelines according to claim 2 is characterized in that: Dynamically couple the gas model to establish a discrete Euler gas model: in, is the air density; u is the air velocity; p is the air pressure head, α is the speed of sound waves in air; S d1 , S d2 and S fa They are the source terms in the continuity equation, momentum equation and the loss between the airflow and the pipe wall.

4. The improved mixed flow simulation method considering large multi-shaft pipelines according to claim 3 is characterized in that: A random selection method is adopted to resolve discontinuities in complex wave interactions, assigning states to the next time level based on a random sampling process: Where, the superscript n represents the nth computation time step; the subscript i represents the i-th computation control volume; β n For random numbers, the van der Korput number pseudo-random sequence is used as the best random sequence in the sampling process due to its advantages of low variance and uniform distribution; The van der Korput sequence is expressed as: A i =k2a i (modk1) (9) Where k1 and k2 are two relatively prime numbers, k1>k2>0; mod represents the remainder function; m, ai, A i All are intermediate generated parameters; Among them, the discontinuity problem is handled by using the Godnov type finite volume method with an exact Riemann solver: f(A * )≡f L (A * ,A L )+f R (A * ,A R )+u R -u L =0 Among them, u R and u L are the velocity variables on the left and right sides of the node respectively; f K (K=L or R) is the expression that passes through the left or right nonlinear wave and establishes the relationship between the two sides and the middle state; the superscript * is the solution value of the discontinuity area (i.e., the asterisk area) in the Riemann problem; A K (K=L or R) is the area in the flux on the left and right sides; I1 is the integral form of the pressure term of the interface of any shape; is a function of area; Among them, the expression of the flow Q* in the asterisk area in the Riemann problem is: Among them, the flow area solution A at the discontinuity is obtained by iteration of the Newton-Raphson method * : Where f' represents the flux derivative.

5. The improved mixed flow simulation method considering large multi-shaft pipelines according to claim 4 is characterized in that: Considering the impact of gas release from multiple shafts: The shaft exhaust boundary condition applies the continuity equation and the orifice equation. The continuity equation of this boundary condition is: Where, the subscript air represents the corresponding variable of the gas; the subscript 1 represents the first computational control volume on the boundary; Mairout = the mass of air discharged through the vent, calculated using equation (15). Using the Riemann invariant to solve the isothermal, one-dimensional, original format Euler equations you air1 =u air2 -α(logρ2-logρ1) (15) The subscript 2 represents the second control volume adjacent to the first calculation control volume. Considering the size effect of the system quantitatively, the original and model Frode numbers are designed to be the same, then: Among them, Fr is the Froude number; U represents the water flow velocity; g is the gravitational acceleration; L is the system length; λ represents the similarity ratio of the prototype to the model of each variable; Q is the flow rate; p is the pressure; H is the pressure head; ρ is the density; subscript Y represents the prototype, subscript M represents the model, subscript u represents the velocity variable, subscript l represents the length variable, subscript t represents the time variable, subscript r represents the characteristic physical quantity, subscript Q represents the flow variable, and subscript H represents the pressure head variable.

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