Simulation method suitable for dynamic characteristics of introduced gas of large-scale water delivery system

Abstract

The invention discloses a simulation method suitable for dynamic characteristics of gas contained in a large-scale water delivery system. According to the method, a continuity equation and a momentum equation of gas are deduced, and correlation of density, wave velocity, flow velocity and parameters representing dynamic characteristics of the gas is constructed; transforming a gas control quasi-linear hyperbolic partial differential equation by adopting a characteristic line method, converting the gas control quasi-linear hyperbolic partial differential equation into an ordinary differential equation, and solving a characteristic value; and carrying out water filling pipeline global solution on a water-gas interface by combining a deduced water body and gas total differential equation. According to the invention, a pressure elastic water column filling model considering gas dynamic characteristics is developed for a gas-water transient flow phenomenon in a rapid filling process, and a provided model simulation result considering gas characteristics is compared with a model simulation result considering correlation between gas pressure change and gas volume change; the gas-water transient flow model can reflect the difference of pressure changes of different nodes in the gas, the gas-water transient flow model only considers that the pressures of all areas in the gas are consistent, and comparison between simulation results of the two models and experimental data shows that the gas-water transient flow model incorporating the gas characteristics is more accurate, and especially in a large-scale pipeline system, the gas-water transient flow model is more accurate. A model that does not consider gas characteristics will underestimate pressure peaks during pressure transients.

Description

Technical Field

[0001] The present invention relates to numerical simulation calculation technology in the field of hydraulics of hydropower stations (pumping stations), and specifically to a simulation method suitable for incorporating gas dynamic characteristics into large-scale water delivery systems, aiming at the transient flow process of gas and water in long-distance water delivery pipelines. Background Art

[0002] Developing a robust water system is essential to addressing the unequal distribution of water resources and promoting national economic growth. The extremely long length and complex design of long-distance water transmission systems pose unique challenges. Pipelines undergo changes in operating conditions, filling and draining processes during maintenance and repair, which can cause complex air-water two-phase flow and entrained large amounts of air. The presence of air can either mitigate the effects of pressure waves or cause extreme destructive pressures, leading to catastrophic pipe bursts or damage to facilities. In addition, entrained air reduces the effective water flow area of ​​the pipeline, thereby reducing engineering benefits. Therefore, it is necessary to accurately simulate the transient pressure during the rapid filling process of long-distance large-scale water transmission pipelines.

[0003] Currently, one-dimensional models for simulating fast-filling pipeline problems are generally divided into two categories:

[0004] The first type applies pressurized flow equations and open flow equations to different flow regions respectively, which are collectively called interface tracking mixed flow models;

[0005] The second is to use a set of equations to simulate the pressurization effect of the flow area.

[0006] The above models often ignore the properties of gas or assume that air is uniform and variable. Due to the lack of consideration of gas space discretization, the dynamic characteristics of gas compression and expansion cannot be fully reflected, which is a knowledge gap in existing models. Summary of the invention

[0007] In order to solve the problem of inaccurate simulation of gas-water transient flow in large-scale water delivery systems due to ignoring the dynamic characteristics of gas, the present invention provides a simulation method suitable for large-scale water delivery systems that incorporates the dynamic characteristics of gas, introduces the control equation of air, and combines it with the water control equation and the interface continuity equation during the rapid filling process to derive the proposed model that incorporates air characteristics. The knowledge gap about the appropriate method for incorporating pressurized air characteristics into the development of numerical models for water filling modeling is solved, and a pressurized elastic water column filling model considering air effects is established, which is compared with the uniform air model and experimental results to evaluate the accuracy of the proposed model.

[0008] The present invention provides a simulation method for incorporating gas dynamic characteristics into a large-scale water delivery system, comprising the following steps:

[0009] S1: Derive the continuity equation and momentum equation of the gas, and construct the correlation relationship between the density, wave velocity, and flow velocity parameters representing the dynamic characteristics of the gas;

[0010] S2: Use the characteristic line method to transform the gas control quasi-linear hyperbolic partial differential equation into an ordinary differential equation and solve the eigenvalue;

[0011] S3: The total differential equations for water and gas are derived simultaneously at the water-gas interface to solve the entire water-filled pipe.

[0012] Furthermore, in the derivation of the gas continuity and momentum control equations in step S1, the continuity and momentum equations of the air in the derivation process can be written as:

[0013]

[0014] In the formula, subscript g is gas; ρ g is the air density; u g is the air speed; P g It's the air pressure.

[0015] The relationship between air wave speed and air density is as follows:

[0016]

[0017] In the formula, c g is the air wave speed; m is the constant multidirectional index; c g0 ,P g0 It is c g and P g The initial value of .

[0018] The following equation (5) is derived from the joint solution of equation (3) and equation (4).

[0019]

[0020] Where k is a constant,

[0021] Substituting equation (5) into equations (3) and (4), we can obtain the derived gas continuity and momentum control equations:

[0022]

[0023] Furthermore, in the transformation process of the gas control quasi-linear hyperbolic partial differential equation in step S2, for the water-filled pipe section, the positive and negative characteristic lines of the standard one-dimensional unsteady flow are integrated to obtain the following formula:

[0024] C + :

[0025] C- : Where i is the location of the current solution node, t+Δt is the next solution time, D is the pipe diameter, A is the pipe area, and subscript w is water; H w is the pressure measuring head; a w is the wave speed; G is the acceleration due to gravity; Δx is the unit distance along the pipe.

[0026] The air momentum equation and the continuity equation (6) and equation (7) form a pair of quasi-linear hyperbolic partial differential equations, with the two dependent variables being the velocity u and g and air density c g , the two independent variables are the distance x on the pipeline and the time t. The characteristic line is used to transform the equation into an ordinary differential equation. The simplified gas control motion equation and continuity equation can be identified as L by equations (8) and (9) respectively. 1 and L 2 :

[0027]

[0028] Furthermore, in step S2, these equations are linearly combined with an unknown multiplier λ:

[0029]

[0030] Any two real numbers, with different input values, will again produce two dependent variables u g and c g The two equations are equivalent in all aspects. Equations (10) and (11) can be simplified to equation (12) by properly selecting two specific λ values. In general, the variable u g and c g is a function of x and t, then, from calculus:

[0031]

[0032] Combining equations (11) and (13), we can see that:

[0033]

[0034] Formula (12) becomes an ordinary differential equation:

[0035]

[0036] The solution of equation (14) yields two special values ​​of λ:

[0037]

[0038] Furthermore, in step S2, the wave propagation speed c g and speed ug It shows the relationship between the position change of the wave and the time change. When a positive value is taken in equation (16), a positive value λ must be taken in equation (15). Similar parallelism exists for negative λ. Substituting these values ​​of λ into equation (15) yields two pairs of equations. This pressure elastic water column filling model that introduces the dynamic characteristics of gas can be derived as C + and C － equation.

[0039] C + :

[0040] C - :

[0041] Furthermore, the step S3 is specifically as follows:

[0042] The simultaneous equations of total differential equations for water and gas at the water-gas interface are:

[0043]

[0044] Q w =u g A (22)

[0045] In the formula, Z interface is the height of the air-water interface.

[0046] The present invention provides a simulation method suitable for incorporating gas dynamic characteristics into large-scale water delivery systems to simulate rapid filling processes, addressing the knowledge gap regarding appropriate methods for water filling modeling that incorporate pressurized air characteristics into mathematical model development.

[0047] The simulation results of the model proposed by the invention which takes into account gas properties are compared with the simulation results of the model which takes into account the correlation between gas pressure change and gas volume change. The former can reflect the difference in pressure changes at different nodes in the gas, while the latter only assumes that the pressure in all areas inside the gas is consistent. Comparison of the simulation results of the two models with the experimental data shows that the gas-water transient flow model which takes into account gas properties proposed by the invention more accurately represents the pressure change process of the rapid filling process.

[0048] Importantly, the present invention provides a method for processing the dynamic characteristics of air based on a pressurized elastic water body model to establish a rapid water filling process for a large-scale pipeline system. Models that do not consider gas characteristics will underestimate the pressure peak during pressure transients.

[0049] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0050] 1. The gas control equation is incorporated into the pressurized elastic water column filling model, and a numerical model of the rapid filling process considering the gas characteristics is proposed. Due to the representation of the gas continuity equation and momentum equation, the simulation results can show that the pressure of the gas at different positions changes with time, and the gas characteristic parameters density, wave velocity, flow rate, and temperature can all be reflected.

[0051] 2. The gas control quasi-linear hyperbolic partial differential equation was transformed and converted into an ordinary differential equation, which is beneficial for solving the eigenvalue. The change reduces the complexity of the solution and simplifies the gas density and velocity as functions of two dependent variables, distance and time. It is beneficial to analyze the availability of solutions for the pressure gradient of the filling water column over time and obtain specific solutions. Therefore, the mature solution of the converted equation is used to solve the practical problem of water-gas two-phase transient flow in the rapid filling process.

[0052] 3. The derived water-gas two-phase transient flow equation is used for the gas region, combined with the wave propagation and reflection characteristics in the gas, to improve the transient pressure curve due to the cumulative effect of compression and expansion of the air column over time. In addition, in the case of a higher gas content, the importance of gas determines the need for a new method to accurately predict the transient generation process. The gas characteristic numerical model improved by combining gas characteristics has been verified to be a feasible method. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the implementation of the present invention;

[0054] Figure 2 It is a comparison diagram of the simulation results of the numerical model applicable to the present invention that incorporates gas characteristics and the original numerical model and experimental results that do not incorporate gas characteristics;

[0055] Figure 3 These are the simulation results of the numerical model of the present invention that incorporates the gas dynamic characteristics and the numerical model that does not incorporate the gas characteristics into consideration in a large-scale pipeline system (L=2400). Implementation

[0057] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0058] The present invention provides a simulation method suitable for incorporating gas dynamic characteristics into a large-scale water delivery system, such as Figure 1 As shown, the following steps are included:

[0059] S1: Derive the continuity equation and momentum equation of the gas, and construct the correlation relationship between density, wave velocity, flow rate and other parameters representing the dynamic characteristics of the gas;

[0060] S2: Use the characteristic line method to transform the gas control quasi-linear hyperbolic partial differential equation into an ordinary differential equation and solve the eigenvalue;

[0061] S3: The total differential equations of water and gas are derived simultaneously at the water-gas interface to solve the entire water-filled pipeline. In this embodiment, the above method is applied as follows:

[0062] In order to verify and analyze the simulation effect of the fast charging process considering the dynamic characteristics of the air mass in the present invention, this embodiment uses the pipeline hydraulic transient experimental device designed by Zhou in 2018 for verification. The system parameters of the experimental device are as follows: pipeline length 8.862 meters, diameter 0.04 meters, upstream water tank head constant 0.08MPa, wave velocity 850m / s, initial static state, initial air mass length 0.4 meters, initial air mass pressure 9.794 meters, valve instantaneous opening. The system parameters adopted by the proposed large-scale pipeline system are: pipeline length 2400m, diameter 24m, upstream water tank head constant 0.392MPa, wave velocity 850m / s, initial static state, initial air mass length 2390 meters

[0063] The specific implementation steps are as follows:

[0064] S1: Derivation process The continuity and momentum equations of air can be written as:

[0065]

[0066] In the formula, subscript g is gas; ρ g is the air density; u g is the air speed; P g It's the air pressure.

[0067] The relationship between air wave speed and air density is as follows:

[0068]

[0069] In the formula, c g is the air wave speed; m is the constant multidirectional index; c g0 ,P g0 It is c g and P g The initial value of .

[0070] The following equation (5) is derived from the joint solution of equation (3) and equation (4).

[0071]

[0072] Where k is a constant,

[0073] Substituting equation (5) into equations (3) and (4), we can obtain the derived gas continuity and momentum control equations:

[0074]

[0075] S2: Based on the derived process air continuity and momentum equations, the gas control quasi-linear hyperbolic partial differential equations are transformed to construct the positive and negative gas characteristic equations of the standard one-dimensional unsteady flow in the characteristic line format of the water-filled pipe section:

[0076] C + :

[0077] C - : Where i is the location of the current solution node, t+Δt is the next solution time, D is the pipe diameter, A is the pipe area, and subscript w is water; H w is the pressure measuring head; a w is the wave speed; G is the acceleration due to gravity; Δx is the unit distance along the pipe.

[0078] The air momentum equation and the continuity equation (6) and equation (7) form a pair of quasi-linear hyperbolic partial differential equations, with the two dependent variables being the velocity u and g and air density c g , the two independent variables are the distance x on the pipeline and the time t. The characteristic line is used to transform the equation into an ordinary differential equation. The simplified gas control motion equation and continuity equation can be identified as L by equations (8) and (9) respectively. 1 and L 2 :

[0079]

[0080] These equations are linear combinations with unknown multipliers λ:

[0081]

[0082] Any two real numbers, with different input values, will again produce two dependent variables u g and c g The two equations are equivalent in all aspects. Equations (10) and (11) can be simplified to equation (12) by properly selecting two specific λ values. In general, the variable u g and c g is a function of x and t, then, from calculus:

[0083]

[0084] Combining equations (11) and (13), we can see that:

[0085]

[0086] Formula (12) becomes an ordinary differential equation:

[0087]

[0088] The solution of equation (14) yields two special values ​​of λ:

[0089]

[0090] The wave propagation speed c g and speed u g It shows the relationship between the position change of the wave and the time change. When a positive value is taken in equation (16), a positive value λ must be taken in equation (15). Similar parallelism exists for negative λ. Substituting these values ​​of λ into equation (15) yields two pairs of equations. This pressure elastic water column filling model that introduces the dynamic characteristics of gas can be derived as C + and C － equation.

[0091] C + :

[0092] C - :

[0093] S3: Combine the constructed gas energy and momentum control equations and solve them in the characteristic numerical format, and solve the water body and gas total differential equations at the water-gas interface to calculate the full-domain water-gas simulation results:

[0094]

[0095] Q w =u g A (22)

[0096] In the formula, Z interface is the height of the air-water interface.

[0097] The derived and simplified gas control equations can be combined with the water control equations under the characteristic scheme at the boundary to solve the global water-gas transient flow phenomenon. Since the propagation and reflection characteristics of waves in the air column are considered, the numerical model combined with the mature solution of the transformed equations is a proven feasible method to solve the practical problem of water-gas two-phase transient flow in the rapid filling process.

[0098] Through the above method, in order to reflect the effect of the method of the present invention, the calculation results of the fast charging process numerical simulation method taking into account the gas characteristics are compared with the experimental results of the embodiment and the original model without considering the gas characteristics. The pressure change curve is as follows: Figure 2As shown in the figure, the calculation results of the fast filling process numerical model taking into account the gas characteristics are compared with the original model without considering the gas characteristics in the long pipeline large-scale system. The pressure curve is shown in Figure 3 shown.

[0099] Depend on Figure 2 It can be seen that compared with the model that does not take gas characteristics into consideration, the numerical model of the fast charging process that takes gas characteristics into consideration provided by the present invention can accurately describe the transient pipeline pressure amplitude and attenuation.

[0100] Depend on Figure 3 It can be seen that when the pressure results of the fast charging process numerical model that takes into account the gas characteristics provided by the present invention are applied to a large-scale pipeline system, the gas characteristics are more obvious, and the original model tends to underestimate the pressure peak when transients occur.

[0101] Therefore, the numerical model calculation that incorporates gas characteristics can be well applied to large-scale water transmission systems and solve the problem of accuracy of numerical simulation of water-gas transient flow during fast filling. The proposed scheme can better predict the experimental pressure fluctuations of large air masses and reflect the influence of large air masses on the transient pressure fluctuations of pipelines.

Claims

1. A simulation method for incorporating gas dynamic characteristics into a large-scale water delivery system, characterized in that: The steps include: S1: Derive the continuity equation and momentum equation of the gas, and construct the correlation relationship between the density, wave velocity, and flow velocity parameters representing the dynamic characteristics of the gas; S2: Use the characteristic line method to transform the gas control quasi-linear hyperbolic partial differential equation, convert it into an ordinary differential equation and solve the eigenvalue; S3: The total differential equations for water and gas are derived simultaneously at the water-gas interface to solve the entire water-filled pipe.

2. A simulation method for incorporating gas dynamic characteristics into a large-scale water delivery system according to claim 1, characterized in that: The gas continuity and momentum control equations in step S1 are derived as follows: The continuity and momentum equations for air are written as: In the formula, subscript g is gas; ρ g is the air density; u g is the air speed; P g is the air pressure; The relationship between air wave speed and air density is as follows: c g 2 JP g ρ g -1 (3) In the formula, c g is the air wave speed; m is the constant multidirectional index; c g0 ,P g0 It is c g and P g The initial value of The following equation (5) is derived from the joint solution of equation (3) and equation (4): Where k is a constant, Substituting equation (5) into equations (3) and (4), we can obtain the derived gas continuity and momentum control equations:

3. A simulation method for incorporating gas dynamic characteristics into a large-scale water delivery system according to claim 2, characterized in that: The transformation process of the gas-controlled quasi-linear hyperbolic partial differential equation, for the water-filled pipe section, integrates the positive and negative characteristic lines of the standard one-dimensional unsteady flow, and the following equation can be obtained: Where i is the location of the current solution node, t+Δt is the next solution time, D is the pipe diameter, A is the pipe area, and subscript w is water; H w is the pressure measuring head; a w is the wave speed; G is the acceleration due to gravity; Δx is the unit distance along the pipe; The air momentum equation and the continuity equation (6) and equation (7) form a pair of quasi-linear hyperbolic partial differential equations, with the two dependent variables being the velocity u and g and air density c g , the two independent variables are the distance x on the pipeline and the time t. The characteristic line is used to transform the equation into an ordinary differential equation. The simplified gas control motion equation and continuity equation can be identified as L1 and L2 respectively by equations (8) and (9):

4. A simulation method for incorporating gas dynamic characteristics into a large-scale water delivery system according to claim 2, characterized in that: Linear combination with unknown multiplier λ: Any two real numbers, with different input values, will again produce two dependent variables u g and c g The two equations represented by are equivalent in all aspects. Equations (10) and (11) can be simplified to equation (12) by appropriately selecting two specific λ values. In general, the variable u g and c g is a function of x and t, then, from calculus: Combining equations (11) and (13), we can see that: Equation (12) becomes an ordinary differential equation: The solution of equation (14) yields two special values ​​of λ:

5. A simulation method for incorporating gas dynamic characteristics into a large-scale water delivery system according to claim 2, characterized in that: The wave propagation speed c g and speed u g It shows the relationship between the position change of the wave and the time change. When a positive value is taken in equation (16), a positive value λ must be taken in equation (15). Similar parallelism also exists for negative λ. Substituting these values ​​of λ into equation (15) yields two pairs of equations. This pressure elastic water column filling model that introduces the dynamic characteristics of gas can be derived as C + and C － equation:

6. A simulation method for incorporating gas dynamic characteristics into a large-scale water delivery system according to claim 3, characterized in that: The simultaneous equations of the water and gas total differential equations at the water-gas interface are: Q w =u g A (22) In the formula, Z interface is the height of the air-water interface.

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