A Calculation Method for Transient Flow in Pipe

Abstract

The present invention discloses a method for calculating transient flow in a pipeline, comprising: step S1: designing an efficient wave tracking equation group based on a non-constant flow resistance model; step S2: determining a short pipe division standard, performing pipeline node division and determining a time step; step S3: given initial conditions and boundary conditions, performing steady-state calculations; step S4: specifically performing calculations using the efficient wave tracking method. In the process of dividing pipeline nodes in the technical solution of the present invention, the short pipe division proportional coefficient and the wave velocity adjustment coefficient will affect the calculation accuracy and efficiency. The smaller the two coefficients, the higher the calculation accuracy, but the calculation efficiency will be reduced. The efficient wave tracking method used in the present invention can solve this problem, because the calculation time of the efficient wave tracking method is not sensitive to the number of pipeline segments, so it is possible to meet the accuracy requirements as much as possible and select a small short pipe division proportional coefficient and wave velocity adjustment coefficient.

Description

Technical Field

[0001] The invention relates to the technical field of energy power engineering simulation, and in particular to a method for calculating pipeline transient flow. Background Art

[0002] Pipeline transient flow is also often called water hammer. The water hammer process is often accompanied by huge noise and violent vibration. In severe cases, it will cause pipeline fatigue fracture and equipment failure. Commonly used pipeline transient flow calculation methods include characteristic line method based on Euler format, finite volume method, finite difference method, etc. These calculation methods are currently commonly used transient flow calculation methods, but there is a common problem, that is, the calculation efficiency of complex pipeline transient flow is low, and it is difficult to achieve real-time calculation. Another type is the wave characteristic method based on Lagrangian format, Lagrangian method, wave tracking method, etc. The biggest feature of this type of method is to track the propagation process of the pressure wave and update the flow field information where the wave passes, so it has the advantage of high calculation efficiency.

[0003] Theoretically, the numerical method based on the Lagrangian format has the advantage of high computational efficiency. However, due to the immaturity of the implementation plan of the computational method, the computational efficiency of this type of method is not significantly superior to that of the numerical method based on the Euler format. There are problems such as the exponential growth of the number of pressure waves and the selection of the threshold for the disappearance of pressure waves. These problems will lead to low computational accuracy and efficiency, and the computational efficiency can only be improved by 60% at most at the expense of a certain degree of computational accuracy. Using quasi-steady-state friction or constant flow friction for transient flow calculations will also lead to low computational accuracy.

[0004] The current transient flow calculation technology solution is mainly based on the characteristic line method, which means that some calculation accuracy must be sacrificed in order to improve calculation efficiency. For example, a larger wave velocity adjustment coefficient and short pipe division ratio coefficient are used when dividing pipeline nodes. Although this can reduce the total number of pipeline node divisions, it will introduce significant calculation errors.

[0005] Therefore, it is necessary to provide a new method for calculating pipeline transient flow to overcome the problems of low calculation efficiency or low calculation accuracy in existing methods for calculating pipeline transient flow. Summary of the invention

[0006] The present invention provides a method for calculating transient flow in a pipeline, so as to overcome at least one technical problem existing in the prior art.

[0007] According to the technical solution of the embodiment of the present invention, a method for calculating pipeline transient flow is provided, comprising:

[0008] Step S1, designing an efficient wave tracking equation group based on a non-constant flow resistance model, wherein the expression of the efficient wave tracking equation group specifically includes:

[0009]

[0010]

[0011] Among them, the symbol f A represents the downstream wave at the end point A of the pipeline, f B represents the downstream wave at the end point B of the pipeline, symbol L AB represents the distance between the end point A of the pipeline and the end point B of the pipeline; the symbol g represents the acceleration of gravity; the symbol J represents the current friction loss of the pipeline, and the symbol J 0 represents the initial friction loss of the pipeline; the subscripts A and B represent the upstream and downstream endpoints of a single pipeline, (JJ 0 ) A represents the pressure wave loss from the end point A to the end point B, (JJ 0 ) B represents the pressure wave loss from end point B to end point A. The terms in equations (1) and (2) can be calculated by the following equations:

[0012]

[0013]

[0014]

[0015] Wherein, symbol f represents the downstream wave in the positive direction of the initial flow velocity; symbol F represents the upstream wave in the negative direction of the initial flow velocity; symbol H represents the static pressure head, symbol Q represents the volume flow rate; symbol a represents the wave velocity; symbol D represents the diameter of the pipe; symbol A c represents the cross-sectional area of ​​the pipeline; the symbol λ represents the resistance coefficient along the pipeline, and the symbol C * Indicates the Brunone drag coefficient, whose value is related to the flow state; symbol Q 0 Indicates the flow rate in the pipeline at steady state; symbol Q A represents the flow velocity at the end point A, symbol Q B The flow velocity at the end point B, symbol λ A represents the drag coefficient along the path at the end point A, symbol λ B represents the drag coefficient along the path at the end point B, Q A,0 The initial steady-state flow rate at endpoint A, Q B,0 The initial steady-state flow rate at endpoint B, symbol λ A,0 represents the initial steady-state drag coefficient at the end point A, symbol λ B,0 represents the initial steady-state drag coefficient along the path at the end point B;

[0016] Step S2, determining the short pipe division standard, dividing the pipeline nodes and determining the time step;

[0017] Step S3: Given initial conditions and boundary conditions, steady-state calculation is performed;

[0018] Step S4: Calculation of the high-efficiency wave tracking method is specifically performed, including:

[0019] Step S41, a pressure wave library based on the space domain is established for each pipeline, and the pressure wave library consists of two arrays storing the upstream wave F and the downstream wave f of the pipeline respectively, and the array size is N+1; the elements 0, 1...N in the downstream wave array correspond one-to-one to the spatial node positions of the pipeline, and the corresponding relationship between the elements of the upstream wave array and the pipeline node positions is opposite, and the array elements store the pressure wave amplitude at the corresponding position of the pipeline; the pressure wave N represents the pressure wave entering the end point of the pipeline, and the pressure wave 0 represents the pressure wave transmitted from the end point of the pipeline;

[0020] Step S42, at each time step, call the pressure wave N propagated to the boundary node, and solve the boundary node equation. The direction of the pressure wave generated at the boundary is opposite to that of the incident wave. The pressure wave entering the upstream boundary node A is the pressure wave N in the upstream pressure wave library F, and the pressure wave generated is the pressure wave 0 in the downstream pressure wave library. Before the newly generated pressure wave 0 is inserted into the array, the pressure wave attenuation calculation from node A to node B is performed first. The newly generated pressure wave is recorded as F 0 , f 0 , the attenuation is calculated by equation (6) and equation (7):

[0021]

[0022]

[0023] For the newly generated pressure wave 0, it is directly inserted into the array from array element 0, so that the elements in the array move forward one position in the direction of pressure wave propagation; array element N is directly deleted after being called;

[0024] Step S43, tracking the pressure waves f and F during the calculation process, obtaining the pressure head and volume flow rate of the boundary nodes by the following formula, updating the instantaneous hydraulic state of the pipe end point, and returning to step S2 at the next time step until the transient calculation is completed;

[0025]

[0026] Preferably, the pipeline node division specifically includes:

[0027] Step S21, sorting the pipes in the pipe system from long to short;

[0028] Step S22: Select the longest pipeline Lmax , according to the formula L<δL max Determine the division standard of the short pipe length L, and the symbol δ represents the proportional coefficient used to determine the length standard of the short pipe; Step S23, after the short pipe division is completed, the short pipes in the pipeline system are eliminated, and the shortest pipe L is selected from the remaining pipes min ;

[0029] Step S24: Set the number of shortest pipeline segments N min = 1, the time step is calculated based on the wave velocity of the shortest tube

[0030] Step S25: Use the time step in step S24 and the wave speed of each remaining pipe to divide the nodes. When the calculated number of segments is not an integer, adjust the wave speed to obtain an integer number of segments, and record the wave speed adjustment coefficient of each pipeline.

[0031] Step S26: Determine the wave speed adjustment coefficients of all pipelines Is it less than the maximum wave speed adjustment coefficient? If the condition is met, the pipeline division ends; otherwise, the number of the shortest pipeline segments is increased by 1, and step S24 is continued until the condition is met.

[0032] Preferably, the initial conditions include pressure, flow rate, wave velocity and cross-sectional area at each node of the pipeline.

[0033] Preferably, the boundary conditions include but are not limited to valves and reservoirs.

[0034] One embodiment of this specification can achieve at least the following beneficial effects:

[0035] 1. In the process of dividing pipeline nodes, the short pipe division ratio coefficient and the wave speed adjustment coefficient will affect the calculation accuracy and efficiency. The smaller the two coefficients are, the higher the calculation accuracy is, but the calculation efficiency will be reduced. The efficient wave tracking method used in the present invention can solve this problem, because the calculation time of the efficient wave tracking method is not sensitive to the number of pipeline segments, so the short pipe division ratio coefficient and wave speed adjustment coefficient can be selected as small as possible to meet the accuracy requirements.

[0036] 2. The computational implementation scheme of the efficient wave tracking method can simulate the propagation process of pressure waves in the pipeline as time goes by, and can also update the instantaneous hydraulic state of the pipeline at every moment. It combines the advantages of the Lagrangian format and the Euler format, greatly improving the operability and computational efficiency of the efficient wave tracking method.

[0037] 3. The pipeline transient flow calculation technology solution based on the efficient wave tracking method proposed in the present invention effectively improves the efficiency and accuracy of the wave tracking method in pipeline transient flow calculation. In the case calculated according to the present invention, it has the same accuracy as the characteristic line method, and the calculation efficiency is improved by more than 90% compared with the characteristic line method. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 paying creative work.

[0039] Figure 1 It is a flow chart of a calculation technology method of pipeline transient flow provided by the present invention;

[0040] Figure 2 It is a diagram of a calculation implementation scheme based on a high-efficiency wave tracking method proposed in the technical solution of the present invention;

[0041] Figure 3 It is a comparison diagram between the calculation results of the pipeline transient flow calculation technical solution based on the efficient wave tracking method proposed by the technical solution of the present invention and the experimental values;

[0042] Figure 4 It is a comparison chart of the computational efficiency of the pipeline transient flow calculation technical solution based on the efficient wave tracking method proposed in the technical solution of the present invention and the characteristic line method. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of one or more embodiments of this specification clearer, the technical solutions of one or more embodiments of this specification will be clearly and completely described below in combination with the specific embodiments of this specification and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of this specification, not all of the embodiments. Based on the embodiments in this specification, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of one or more embodiments of this specification.

[0044] It should be understood that although the terms first, second, third, etc. may be used in this application document to describe various information, this information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other.

[0045] like Figure 1 As shown, the pipeline transient flow calculation technical solution based on the efficient wave tracking method provided by the present invention includes the following steps:

[0046] Step S1: using an efficient wave tracking equation set based on a non-steady flow resistance model;

[0047] The expression of the efficient wave tracking equations based on the unsteady flow resistance model is:

[0048]

[0049]

[0050] in

[0051]

[0052]

[0053]

[0054] In the formula, the symbol f A represents the downstream wave at the end point A of the pipeline, f B represents the downstream wave at the end point B of the pipeline, symbol L AB represents the distance between the end point A of the pipeline and the end point B of the pipeline; the symbol g represents the acceleration of gravity; the symbol J represents the current friction loss of the pipeline, and the symbol J 0 represents the initial friction loss of the pipeline; the subscripts A and B represent the upstream and downstream endpoints of a single pipeline, (JJ 0 ) A represents the pressure wave loss from the end point A to the end point B, (JJ 0 ) B It represents the pressure wave loss from end point B to end point A. Symbol f A represents the downstream wave at the end point A of the pipeline, f B represents the downstream wave at the end point B of the pipeline, symbol L AB represents the distance between the end point A of the pipeline and the end point B of the pipeline; the symbol g represents the acceleration of gravity; the symbol J represents the current friction loss of the pipeline, and the symbol J 0 represents the initial friction loss of the pipeline; the subscripts A and B represent the upstream and downstream endpoints of a single pipeline, (JJ 0 ) A represents the pressure wave loss from the end point A to the end point B, (JJ 0 ) B Represents the pressure wave loss from end point B to end point A.

[0055] Step S2: Determine the short pipe division standard, divide the pipeline nodes and determine the time step.

[0056] The node division process is as follows:

[0057] Step S21, sorting the pipes in the pipe system from long to short;

[0058] Step S22: Select the longest pipeline L max , according to the formula L<δL max Determine the division standard of the short pipe length L, and the symbol δ represents the proportional coefficient used to determine the length standard of the short pipe; Step S23, after the short pipe division is completed, the short pipes in the pipeline system are eliminated, and the shortest pipe L is selected from the remaining pipes min ;

[0059] Step S24: Set the number of shortest pipeline segments N min = 1, the time step is calculated based on the wave velocity of the shortest tube

[0060] Step S25: Use the time step in step S24 and the wave speed of each remaining pipe to divide the nodes. When the calculated number of segments is not an integer, adjust the wave speed to obtain an integer number of segments, and record the wave speed adjustment coefficient of each pipeline.

[0061] Step S26: Determine the wave speed adjustment coefficients of all pipelines Is it less than the maximum wave speed adjustment coefficient? If the condition is met, the pipeline division ends; otherwise, the number of the shortest pipeline segments is increased by 1, and step S24 is continued until the condition is met.

[0062] In the process of dividing pipeline nodes, the short pipe division ratio coefficient and the wave speed adjustment coefficient will affect the calculation accuracy and efficiency. The smaller the two coefficients are, the higher the calculation accuracy is, but the calculation efficiency will be reduced. The efficient wave tracking method used in the present invention can solve this problem. Because the calculation time of the efficient wave tracking method is not sensitive to the number of segments, it can meet the accuracy requirements as much as possible and select a small short pipe division ratio coefficient and wave speed adjustment coefficient. After calculation, δ = 0.01 is generally selected. Can meet the accuracy requirements.

[0063] Step S3: Given initial conditions and boundary conditions, perform steady-state calculations

[0064] The efficient wave tracking equations based on the non-constant flow resistance model in step S1 are all related to the initial parameters of the pipeline, so a steady-state calculation needs to be performed based on the initial conditions and boundary conditions before performing transient calculations. The initial conditions include the pressure, flow, wave velocity and cross-sectional area at each node of the pipeline; the boundary conditions include several commonly used boundary conditions, such as valves, reservoirs, etc.

[0065] Step S4: Computational implementation of the efficient wave tracking method

[0066] (1) A pressure wave library based on the spatial domain is established for each pipeline. The pressure wave library consists of two arrays that store the upstream wave F and the downstream wave f of the pipeline respectively. The array size is N+1. The elements 0, 1...N in the downstream wave array correspond one-to-one to the spatial node positions of the pipeline. The correspondence between the elements of the upstream wave array and the pipeline node positions is exactly the opposite. The array elements store the pressure wave amplitude at the corresponding position of the pipeline. Pressure wave N represents the pressure wave entering the pipeline endpoint, and pressure wave 0 represents the pressure wave transmitted from the pipeline endpoint;

[0067] (2) At each time step, the pressure wave N propagated to the boundary node is called to solve the boundary node equation. The direction of the pressure wave generated at the boundary is opposite to that of the incident wave. For example, the pressure wave entering the upstream boundary node A is the pressure wave N in the upstream pressure wave library F, and the pressure wave generated is the pressure wave 0 in the downstream pressure wave library. Before the newly generated pressure wave 0 is inserted into the array, the pressure wave attenuation calculation from node A to node B must be performed. The newly generated pressure wave is recorded as, F 0 , f 0 , then the attenuation calculation can be expressed by equation (6) and equation (7):

[0068]

[0069]

[0070] For the newly generated pressure wave 0, it is directly inserted into the array from array element 0, so that the elements in the array move forward one position in the direction of pressure wave propagation. Array element N is directly deleted after being called. This process just describes the disappearance and generation of pressure waves at the boundary and the propagation and attenuation process between the two ends of the pipeline;

[0071] (3) During the calculation process, only the pressure waves f and F need to be tracked, that is, the pressure head and volume flow rate of the boundary nodes are obtained by the following formula to update the instantaneous hydraulic state of the pipe end point. Return to step (2) at the next time step until the transient calculation is completed.

[0072]

[0073] The above technical solution can simulate the propagation process of pressure waves in the pipeline as time goes by, and can also update the instantaneous hydraulic state of the pipeline at every moment. It combines the advantages of the Lagrangian format and the Euler format, greatly improving the operability and computational efficiency of the efficient wave tracking method.

[0074] Figure 3 and Figure 4 They are respectively the verification results of the calculation accuracy and calculation efficiency of the present invention:

[0075] The experimental data comes from the Soares experiment, which uses a reservoir-pipeline-valve system. The reservoir level is 46m, the pipeline length is 15.22m, the pipeline inner diameter is 0.02m, the pipeline wall thickness is 0.001m, and the volume flow rate is 1.33E-4m 3 / s, valve closing time 0.018s. Figure 3 It can be seen that the calculated maximum pressure head is about 2% larger than the experimental value, which is conservative. At the same time, the calculated pressure wave attenuation curve is highly consistent with the experimental value, indicating that the calculation accuracy of the present invention is relatively high. Figure 4 As can be seen from the left figure in , as the number of segments increases, the characteristic line calculation time is always greater than the calculation time of the efficient wave tracking method, while the calculation time of the efficient wave tracking method is not sensitive to the number of segments. Figure 4 In the right figure, the calculation efficiency improvement rate increases with the increase of the number of segments. When the number of segments is less than 10, the calculation efficiency improvement rate changes significantly, with the lowest being 25%. When the number of segments is greater than 20, the calculation time efficiency of the efficient wave tracking method is improved by more than 90%.

[0076] Those skilled in the art can understand that the accompanying drawings are only schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0077] Finally, 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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating transient flow in a pipeline, characterized in that: The method comprises: Step S1, designing an efficient wave tracking equation group based on a non-constant flow resistance model, wherein the expression of the efficient wave tracking equation group specifically includes: Among them, the symbol f A represents the downstream wave at the end point A of the pipeline, f B represents the downstream wave at the end point B of the pipeline, symbol L AB represents the distance between the endpoint A of the pipeline and the endpoint B of the pipeline; the symbol g represents the acceleration of gravity; the symbol J represents the current friction loss of the pipeline, and the symbol J0 represents the initial friction loss of the pipeline; the subscripts A and B represent the upstream and downstream endpoints of a single pipeline, (J-J0) A represents the pressure wave loss from the end point A to the end point B, (J-J0) B represents the pressure wave loss from end point B to end point A. The terms in equations (1) and (2) can be calculated by the following equations: Wherein, symbol f represents the downstream wave in the positive direction of the initial flow velocity; symbol F represents the upstream wave in the negative direction of the initial flow velocity; symbol H represents the static pressure head, symbol Q represents the volume flow rate; symbol a represents the wave velocity; symbol D represents the diameter of the pipe; symbol A c represents the cross-sectional area of ​​the pipeline; the symbol λ represents the resistance coefficient along the pipeline, and the symbol C * Indicates the Brunone resistance coefficient whose value is related to the flow state; the symbol Q0 indicates the flow velocity in the steady state of the pipeline; the symbol Q A represents the flow rate at the end point A, symbol Q B The flow velocity at the end point B, symbol λ A represents the drag coefficient along the path at the end point A, symbol λ B represents the drag coefficient along the path at the end point B, Q A,0 The initial steady-state flow rate at endpoint A, Q B,0 The initial steady-state flow rate at endpoint B, symbol λ A,0 represents the initial steady-state drag coefficient at the end point A, symbol λ B,0 represents the initial steady-state drag coefficient along the path at the end point B; Step S2, determining the short pipe division standard, dividing the pipeline nodes and determining the time step; Step S3: Given initial conditions and boundary conditions, steady-state calculation is performed; Step S4: Calculation of the high-efficiency wave tracking method is specifically performed, including: Step S41, a pressure wave library based on the space domain is established for each pipeline, and the pressure wave library consists of two arrays storing the upstream wave F and the downstream wave f of the pipeline respectively, and the array size is N+1; the elements 0, 1...N in the downstream wave array correspond one-to-one to the spatial node positions of the pipeline, and the corresponding relationship between the elements of the upstream wave array and the pipeline node positions is opposite, and the array elements store the pressure wave amplitude at the corresponding position of the pipeline; the pressure wave N represents the pressure wave entering the end point of the pipeline, and the pressure wave 0 represents the pressure wave transmitted from the end point of the pipeline; Step S42, at each time step, call the pressure wave N propagated to the boundary node, and solve the boundary node equation. The pressure wave generated at the boundary is opposite to the direction of the incident wave. The pressure wave entering the upstream boundary node A is the pressure wave N in the upstream pressure wave library F, and the pressure wave generated is the pressure wave 0 in the downstream pressure wave library. Before the newly generated pressure wave 0 is inserted into the array, the pressure wave attenuation calculation from node A to node B is performed. The newly generated pressure wave is recorded as F0, f0, and the attenuation calculation is performed by equations (6) and (7): For the newly generated pressure wave 0, it is directly inserted into the array from array element 0, so that the elements in the array move forward one position in the direction of pressure wave propagation; array element N is directly deleted after being called; Step S43, tracking the pressure waves f and F during the calculation process, obtaining the pressure head and volume flow rate of the boundary nodes by the following formula, updating the instantaneous hydraulic state of the pipe end point, and returning to step S2 at the next time step until the transient calculation is completed; 2. The method for calculating pipeline transient flow according to claim 1, characterized in that: The pipeline node division specifically includes: Step S21, sorting the pipes in the pipe system from long to short; Step S22: Select the longest pipeline L max , according to the formula L<δL max Determine the division standard of the short pipe length L, and the symbol δ represents the proportional coefficient used to determine the length standard of the short pipe; Step S23, after the short pipe division is completed, the short pipes in the pipeline system are eliminated, and the shortest pipe L is selected from the remaining pipes min ; Step S24: Set the number of shortest pipeline segments N min = 1, the time step is calculated based on the wave velocity of the shortest tube Step S25: Use the time step in step S24 and the wave speed of each remaining pipe to divide the nodes. When the calculated number of segments is not an integer, adjust the wave speed to obtain an integer number of segments, and record the wave speed adjustment coefficient of each pipeline. Step S26: Determine the wave speed adjustment coefficients of all pipelines Is it less than the maximum wave speed adjustment coefficient? If the condition is met, the pipeline division ends; otherwise, the number of the shortest pipeline segments is increased by 1, and step S24 is continued until the condition is met.

3. The method for calculating pipeline transient flow according to claim 1, characterized in that: The initial conditions include pressure, flow rate, wave velocity and cross-sectional area at each node of the pipeline.

4. The method for calculating pipeline transient flow according to claim 1, characterized in that: The boundary conditions include but are not limited to valves and reservoirs.

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