A method for constructing a long-distance gravity flow pipeline water hammer calculation model

Abstract

This invention discloses a method for constructing a water hammer calculation model for a long-distance gravity flow pipeline, comprising the following steps: obtaining basic pipeline information and boundary point information as input parameters for model calculation; dividing the pipeline into N integer segments based on the basic pipeline information and assuming a calculation time step Δt; calculating the flow rate from the first segment to the Nth segment of the pipeline according to the simple free outflow formula for pipelines; calculating the head loss along the pipeline from the first segment to the Nth segment, and calculating the head H at N+1 nodes. i Save H i Data; calculate the flow rate and head at the (j+1)th Δt time. Based on the water column separation model, determine whether water column separation has occurred, and calculate the Hmax and Hmin values ​​after water column separation is resolved to obtain the pressure envelope along the pipeline. The method of this invention divides the pipeline into time and space, establishes a water column separation model, and accurately simulates the pressure changes during the valve closure process through iterative calculation.

Description

Technical Field

[0001] This invention relates to a method for constructing a water hammer calculation model, and more particularly to a method for constructing a water hammer calculation model for a long-distance gravity flow pipeline. Background Technology

[0002] With the construction of water conservancy and water supply projects, long-distance water transfer is becoming increasingly common. During normal pipeline operation, it is sometimes necessary to cut off the water flow. If the terminal valve or intermediate maintenance valve is not closed properly, it can cause water column separation in the pipeline. The pressure after the water column separation and reconnection is dozens of times higher than the normal valve closing pressure, which has a significant destructive force on the pipeline and threatens the safe operation of the entire pipeline system. Therefore, water column separation in pipelines should be avoided as much as possible. Currently, the calculation methods for water hammer in long-distance pipelines mainly rely on commercial software such as Kypipe, Pipenet, and Hammer, as well as calculations performed independently by various research institutes. Comparing the calculation results of various software and the calculation results commissioned by various research institutes, there are differences, which may lead to inaccuracies in the selected calculation results. Summary of the Invention

[0003] The purpose of this invention is to provide a method for constructing a calculation model for water hammer in long-distance gravity flow pipelines. This method calculates the characteristic parameters of the pipeline during steady-state operation using basic hydraulic formulas based on the design parameters of the long-distance pipeline; based on the characteristic method, it correctly processes the pipeline characteristic parameters, divides the pipeline into time and space, establishes a water column separation model, and accurately simulates the pressure changes during the valve closure process through iterative calculations.

[0004] The technical solution of this invention: A method for constructing a calculation model of water hammer in a long-distance gravity flow pipeline, comprising the following steps:

[0005] S101: Obtain the basic pipeline information and boundary point information of the calculation project as input parameters for model calculation;

[0006] S102: Based on the basic pipeline information, assume a calculation time step. Divide the pipeline into N integer segments;

[0007] S103: Calculate the flow rate of each section of the pipe from the first section to the Nth section, based on the simple free outflow formula for a pipe. The flow rate of the Nth pipe segment ;

[0008] S104: Calculate the head loss along the pipeline from the first segment to the Nth segment using Darcy's formula and Manning's formula, and calculate the head at N+1 nodes. ,save data;

[0009] S105: The results calculated in steps S103 and S104 , As an initial value, based on the method of characteristics, assume the total calculation time. Time step Then calculate the cycle number. Assuming the initial time j=0, calculate the (j+1)th... The corresponding flow rate and head at any given time , ;

[0010] S106: Based on the initial boundary conditions, replace the first node. = The end node is calculated based on the control valve model to obtain... , Replace each , ;

[0011] S107: Regarding Time calculation , Based on the water column separation model, determine whether water column separation has occurred. If water column separation has occurred, input the results into the model to calculate the water column separation repair. , If no water column separation occurs, then maintain , constant;

[0012] S108: Based on the calculation result of step S107, use it as the next step. The initial value at time step m is used to repeat S105, S106, and S107 m times until... Save all calculation results , Find and The pressure envelope along the pipeline is obtained.

[0013] In the aforementioned method for constructing a water hammer calculation model for long-distance gravity flow pipelines, step S101 specifically includes the following basic pipeline information: the number of pipeline segments N, and the length of each pipeline segment. Diameter of each section of pipe Wave velocity in each section of the pipeline Roughness of each section of the pipeline Elevation of the center point at each bend in the pipeline Basic information about the boundary points includes: inlet water level. , outlet water level , Outlet valve flow characteristics.

[0014] In the aforementioned method for constructing a calculation model for water hammer in long-distance gravity flow pipelines, step S102 specifically includes:

[0015] S201: The wave velocity calculation formula for each pipe segment from the 1st to the Nth is shown in formula (1):

[0016] (1)

[0017] In the above formula, The bulk modulus of the fluid; The diameter of each pipe section; The elastic modulus of the pipe wall material; For pipe wall thickness;

[0018] S202: Assume the computation time step The wave speed calculated based on S201 Calculate the number of segments in each section of the pipeline. Rounded down, length of each segment N= Then, based on the calculated number of pipe sections Back-calculate the wave velocity of this section of the pipeline If there is a short pipe in the pipeline, and the wave velocity change rate exceeds 5%, then take... Repeat the iteration until the wave velocity change rate is less than 5%, and obtain the final time step used for calculation. Update the basic parameters of each pipe section , , .

[0019] In the aforementioned method for constructing a long-distance gravity flow pipeline water hammer calculation model, in step S103, the calculation formula for free outflow in the pipeline is as shown in formula (2):

[0020] (2)

[0021] In the above formula, The cross-sectional area of ​​the pipe. The inner diameter of the pipe. To calculate the length of the pipeline section, The effective head includes the head of the traveling flow velocity. This is the coefficient for head loss along the friction path. This is the sum of the local head loss coefficients in the calculated section of the pipeline;

[0022] In the calculation process, local head loss is ignored, and only friction head loss is calculated. If there are no branch pipes in the pipeline, the flow rate is the same throughout the entire pipeline.

[0023] In the aforementioned method for constructing a calculation model for water hammer in long-distance gravity flow pipelines, step S104 specifically includes:

[0024] S401: Darcy's formula is shown in formula (3), Manning's formula is shown in formula (4), and the formulas for calculating head loss along the friction are shown in formulas (3), (4), and (5):

[0025] (3)

[0026] (4)

[0027] (5)

[0028] In the above formula, For head loss along the pipeline, The flow velocity in the pipe, Given the hydraulic radius, combining (3), (4), and (5), we can obtain the length as... The formula for calculating the head loss along the pipeline is shown in formula (6):

[0029] (6)

[0030] S402: Based on formula S401, calculate the following for each of the N pipe segments: The water head at each node, the entire pipeline is divided into [number] sections. In the small segment, node i has a total of There are several nodes, including the starting node and the ending node, with the first node having a water head. Node 2 to The formula for calculating the head at the node is shown in formula (7):

[0031] (7)

[0032] S403: Calculate the head at each node of the pipeline according to formula S402, and adjust the roughness of the pipeline to make the calculated head... and If the difference between the two is within 0.1%, when adjusting the roughness, if The roughness should be increased, and vice versa. The roughness should be reduced, with the increase or decrease ≤20%. The roughness of each node should be calculated. According to the calculation results of step S103 , will each node , The data, as a steady-state result, serves as the initial data for subsequent calculations.

[0033] In the aforementioned method for constructing a calculation model for water hammer in long-distance gravity flow pipelines, step S105 specifically includes:

[0034] S501: According to step 102 , Let i represent the number of the calculated section on the pipe segment, and j represent the time layer number. The pipeline can be divided into a planar grid diagram in space and time. For the water head of P at any time j+1 in space, and traffic It can be extended through the head and flow parameters of its neighboring points i-1 and i+1 at the previous time step. and Solve the equation;

[0035] S502: The steps described in S501 and The calculation formulas for the equations are shown in formulas (8) and (9):

[0036] (8)

[0037] (9)

[0038] In the above formula, , Let P be the water head and flow rate, respectively. , The head and flow rate at point i-1 above point P are given respectively. , Let i and i be the head and flow rate at point i+1, respectively, in the previous time step P. , These are constants related to pipeline characteristics;

[0039] To simplify the calculation, let , Then equations (8) and (9) can be simplified to equations (10) and (11):

[0040] (10)

[0041] (11)

[0042] By combining equations (10) and (11), the parameters of point P can be obtained. , The calculation formulas are as follows: (12) and (13):

[0043] (12)

[0044] (13)

[0045] S503: Calculation in step 502 , When the pipe is an intermediate node, the calculation can be performed according to the formula. In particular, if the calculation node is the starting node, then... , If the node is an end node, , ;

[0046] S504: Calculate pipeline characteristic parameters in step 502. and When, according to the method of characteristics, if node P is located at an intermediate node, then along... and The characteristic parameters are the same; if the calculation node is located at a pipe bend, for each pipe segment length All calculated , , , ,calculate , Use pipeline data prior to the turning point. , Use pipeline data after the turning point; if the calculation node is a turning point in the pipeline, then , The calculation formula is , ;

[0047] S505: Based on the parameters and pipe characteristic constants calculated in steps S503 and 504 at time j, substitute them into formula (12) to calculate the head at each node on the pipe at time j+1. ;

[0048] S506: In step 502, based on the head calculated in step 505, the flow rate at each node on the pipeline at time j+1 is calculated. If the compute node is an intermediate node in the pipeline, then in the computation Both formulas in formula (13) can be calculated; if the calculation node is the beginning node of the pipeline, then If the compute node is the end node of the pipeline. .

[0049] In the aforementioned method for constructing a calculation model for water hammer in long-distance gravity flow pipelines, step S106 specifically includes:

[0050] S601: Since the first end of the pipe is connected to the inlet pool, the water head at the first node of the pipe is always equal to... It does not change over time;

[0051] S602: Assume the valve closing time is... , < Then, as the valve closes, the head and flow rate at the end node are determined by the valve's characteristics; > , , ;

[0052] S603: In step S602, < When the instantaneous value at the valve end boundary point is calculated, the formulas are as follows: (14) and (15):

[0053] (14)

[0054] (15)

[0055] In the above formula: , , , For step S104, calculate the last node at the initial time. , ;

[0056] S604: In step S603, Let be the dimensionless opening coefficient of the valve. When solving for water hammer when the valve is closed, the valve's opening coefficient is... With time The relationship of change can be determined based on the type of valve. The curve is calculated using the formula shown in formula (16):

[0057] (16).

[0058] In the aforementioned method for constructing a calculation model for water hammer in long-distance gravity flow pipelines, step S107 specifically includes:

[0059] S701: The basic physical model of water column separation is the phenomenon of water column separation and re-merging. During water hammer calculations, when the pressure at any cross-section is equal to or less than the vaporization pressure of water, the pressure remains at the vaporization pressure of water. The cavitation generated at that cross-section causes the water column to separate, forming a vapor column. In subsequent calculations, if the volume of the vapor column between the separated water columns is equal to or less than zero, the two water columns collide, resulting in water column re-merging and a sharp increase in pressure. The specific process of the water column separation model is as follows:

[0060] (1) Determine whether water column separation occurs according to formula (17).

[0061] (17)

[0062] In the above formula: The absolute pressure at point i, Let i be the piezometric head at point i, which is the height of the hydraulic gradient line relative to the reference plane. The height of the reference plane at the vertex of the pipe section is the same as the reference plane for the hydraulic gradient. The height of the water column under atmospheric pressure is taken as 10m. This represents the vaporization pressure of water, taken as 2m; when ≤ At that time, liquid column separation occurs. > At that time, no water column separation occurs, so the calculation is not included in the water column separation model and the result is returned. , ;

[0063] (2) If the conditions in (1) are met ≤ Then, the transient parameters at point i after water column separation are calculated according to formulas (18) to (21):

[0064] (18)

[0065] (19)

[0066] (20)

[0067] (twenty one)

[0068] (3) If during the calculation process It is assumed that the water columns have rejoined and collided at that instant. The pressure rise after rejoining is calculated according to formulas (22) to (24). The transient parameters are calculated as follows:

[0069] (twenty two)

[0070] (twenty three)

[0071] (twenty four)

[0072] S702: In the water column separation principle described in step S701, the first step of determining whether water column separation has occurred should be based on formula (17). If water column separation has already occurred at the interface at the previous moment, then a new variable should be referenced. Whether it is zero is used as the criterion;

[0073] S703: Use the calculation results from step S105 as input data to calculate the water column separation model. For the results at the initial time, let... If so, return the original input data and then determine... If true, then calculate the water column separation and the transient parameters at point i according to formulas (18) to (21), and let ; Input data at subsequent time points, if If , it means that no water column separation occurred at this point in the previous moment; if If the result is , it indicates that water column separation has occurred at the previous moment. Continue to calculate the water column separation and the transient parameters at point i according to formulas (18) to (21). If the calculated result is , , indicating that the water column is closed. The pressure rise after closure is calculated according to formulas (22) to (24) and returned as the calculation result.

[0074] In the aforementioned method for constructing a calculation model for water hammer in long-distance gravity flow pipelines, step S108 involves calculating... The pressure should be less than the design pressure of the pipeline, and water column separation should be avoided in the pipeline. >8m; if the calculated If the pressure exceeds the pipeline's design capacity, the closing time of the end valve should be extended. If water column separation occurs in the pipeline, that is... For sections less than 8m, effective water hammer mitigation measures should be implemented.

[0075] The beneficial effects of the present invention: Compared with the prior art, the present invention has the following advantages:

[0076] 1. By adopting the pipe division method in step S102, the deviation of the pipe wave velocity is controlled, so that the pipe wave velocity will not be distorted and an accurate time step is obtained, thus ensuring the accuracy of the calculation results.

[0077] 2. Since the steady-state head calculation method in step S104 is adopted, by adjusting the roughness along the pipeline, the head at the end is the same, the range of roughness variation is reasonable, and no erroneous results will be caused. It can also check the rationality of the design flow rate.

[0078] 3. Since the water column separation model construction method in step S107 is adopted, two discrimination conditions are established for whether water column separation occurs during the first iteration and intermediate iterations. That is, first determine whether the cavity is 0 and whether the water pressure is less than -8m, so as to avoid errors caused by a single discrimination condition.

[0079] In summary, this invention provides a water hammer calculation model for long-distance gravity flow pipelines. This model can simulate the real-time water hammer wave propagation process in the pipeline after the valve at the end of the long-distance gravity pipeline is closed. By assuming different valve closing rules, the optimal valve closing time that prevents water column separation in the pipeline can be calculated, thereby ensuring the safe operation of the pipeline system.

[0080] The method of this invention calculates the characteristic parameters of the pipeline during steady-state operation by applying basic hydraulic formulas based on the design parameters of long-distance pipelines; based on the characteristic method, the pipeline characteristic parameters are correctly processed, the pipeline is divided into time and space, a water column separation model is established, and the pressure change during the valve closure process is accurately simulated through iterative calculation. Attached Figure Description

[0081] Appendix Figure 1 Here is a flowchart of the water hammer calculation process;

[0082] Appendix Figure 2 The pressure envelope in the pipeline is closed by the end valve;

[0083] Appendix Figure 3 The transient pressure characteristics at the end valve;

[0084] Appendix Figure 4 This is the computational grid for the method of characteristics. Detailed Implementation

[0085] The following is in conjunction with the appendix Figure 1-3 The embodiments further illustrate the present invention, but are not intended to limit the present invention.

[0086] An embodiment of the present invention: A method for constructing a calculation model for water hammer in a long-distance gravity flow pipeline, comprising the following steps:

[0087] S101: Obtain the basic pipeline information and boundary point information of the calculation project as input parameters for model calculation;

[0088] S102: Based on the basic pipeline information, assume a calculation time step. Divide the pipeline into N integer segments;

[0089] S103: Calculate the flow rate of each section of the pipe from the first section to the Nth section, based on the simple free outflow formula for a pipe. The flow rate of the Nth pipe segment ;

[0090] S104: Calculate the head loss along the pipeline from the first segment to the Nth segment using Darcy's formula and Manning's formula, and calculate the head at N+1 nodes. ,save data;

[0091] S105: The results calculated in steps S103 and S104 , As an initial value, based on the method of characteristics, assume the total calculation time. Time step Then calculate the cycle number. Assuming the initial time j=0, calculate the (j+1)th... The corresponding flow rate and head at any given time , ;

[0092] S106: Based on the initial boundary conditions, replace the first node. = The end node is calculated based on the control valve model to obtain... , Replace each , ;

[0093] S107: Regarding Time calculation , Based on the water column separation model, determine whether water column separation has occurred. If water column separation has occurred, input the results into the model to calculate the water column separation repair. , If no water column separation occurs, then maintain , constant;

[0094] S108: Based on the calculation result of step S107, use it as the next step. The initial value at time step m is used to repeat S105, S106, and S107 m times until... Save all calculation results , Find and The pressure envelope along the pipeline is obtained.

[0095] In step S101, the basic information of the pipeline and boundary points of the calculation project is obtained. The basic information of the pipeline specifically includes: the number of pipeline segments N, and the length of each pipeline segment. Diameter of each section of pipe Wave velocity in each section of the pipeline Roughness of each section of the pipeline Elevation of the center point at each bend in the pipeline Basic information about the boundary points includes: inlet water level. , outlet water level , Outlet valve flow characteristics.

[0096] In step S102, a calculation time step is assumed based on the basic pipeline information. The pipeline is divided into N integer segments, specifically including:

[0097] S201: The wave velocity calculation formula for each pipe segment from the 1st to the Nth segment is shown in formula (1):

[0098] (1)

[0099] In the above formula, The bulk modulus of the fluid; The diameter of each pipe section; The elastic modulus of the pipe wall material; For pipe wall thickness;

[0100] S202: Assume the computation time step The wave speed calculated based on S201 Calculate the number of segments in each section of the pipeline. Rounded down, length of each segment N= Then, based on the calculated number of pipe sections Back-calculate the wave velocity of this section of the pipeline If there is a short pipe in the pipeline, Calculate the value of this segment after rounding. and The difference will be large; when the rate of change of wave velocity exceeds 5%, take... Repeat the iteration until the wave velocity change rate is less than 5%, and obtain the final time step used for calculation. Update the basic parameters of each pipe section , , .

[0101] Step S103 calculates the pipe flow based on the simple free outflow formula, specifically including: the free outflow calculation formula for the pipe is shown in formula (2):

[0102] (2)

[0103] In the above formula, The cross-sectional area of ​​the pipe. The inner diameter of the pipe. To calculate the length of the pipeline section, The effective head includes the head of the traveling flow velocity. This is the coefficient for head loss along the friction path. This is the sum of the local head loss coefficients in the calculated section of the pipeline;

[0104] In the calculation process, since the water transmission pipeline in water conservancy projects is relatively long, local head loss is ignored and only friction head loss is calculated. If there are no branch pipes in the pipeline, the flow rate is the same throughout the pipeline.

[0105] Step S104 specifically includes:

[0106] S401: Darcy's formula is shown in formula (3), Manning's formula is shown in formula (4), and the formulas for calculating head loss along the friction are shown in formulas (3), (4), and (5):

[0107] (3)

[0108] (4)

[0109] (5)

[0110] In the above formula, For head loss along the pipeline, The flow velocity in the pipe, Given the hydraulic radius, combining (3), (4), and (5), we can obtain the length as... The formula for calculating the head loss along the pipeline is shown in formula (6):

[0111] (6)

[0112] S402: Based on formula S401, calculate the following for each of the N pipe segments: The water head at each node, the entire pipeline is divided into [number] sections. In the small segment, node i has a total of There are several nodes, including the starting node and the ending node, with the first node having a water head. Node 2 to The formula for calculating the head at the node is shown in formula (7):

[0113] (7)

[0114] S403: Calculate the head at each node of the pipeline according to formula S402. Since local head losses are not considered, the calculated... and They may not coincide; the roughness of the pipes needs to be adjusted to match the calculated values. and If the difference between the two is within 0.1%, when adjusting the roughness, if The roughness should be increased, and vice versa. The roughness should be reduced, with the increase or decrease ≤20%. The roughness of each node should be calculated. According to the calculation results of step S103 , will each node , The data, as a steady-state result, serves as the initial data for subsequent calculations.

[0115] Step S105 specifically includes:

[0116] S501: The basic principle of the method of characteristics is as follows: Figure 4 As shown: According to step 102 , Let i represent the number of the calculated section on the pipe segment, and j represent the time layer number (e.g., ...). (This represents the pressure head at node i in the pipe segment and at time layer j). The pipe can be divided into a planar grid diagram in space and time. The pressure head at any point P in space at any time is... and traffic It can be extended by the head and flow parameters of its neighboring points A and B at the previous moment. and Solve the equation;

[0117] S502: The steps described in S501 and The calculation formulas for the equations are shown in formulas (8) and (9):

[0118] (8)

[0119] (9)

[0120] In the above formula, , Let P be the water head and flow rate, respectively. , Let the head and flow rate at point B be the same as those at point P at the previous instant. , Let P be the water head and flow rate at point A at the previous moment. , These are constants related to pipeline characteristics;

[0121] To simplify the calculation, let , Then equations (8) and (9) can be simplified to equations (10) and (11):

[0122] (10)

[0123] (11)

[0124] By combining equations (10) and (11), the parameters of point P can be obtained. , The calculation formulas are as follows: (12) and (13):

[0125] (12)

[0126] (13)

[0127] S503: Calculation in step 502 , When the pipe is an intermediate node, the calculation can be performed according to the formula. In particular, if the calculation node is the starting node, then... , If the node is an end node, then , ;

[0128] S504: Calculate pipeline characteristic parameters in step 502. and When, according to the method of characteristics, if node P is located at an intermediate node, then along... and The characteristic parameters are the same on both sides; however, if the calculation node is located at a pipe bend, the characteristic parameters on both sides will not be the same. Therefore, for each pipe segment length... All calculated , , , If the computed node is a turning point in the pipeline, then , The calculation formula is , ;

[0129] S505: Based on the parameters and pipe characteristic constants calculated in steps S503 and 504 at time j, calculate the head at each node on the pipe at time j+1 according to formula (12). ;

[0130] S506: In step 502, based on the head calculated in step 505, the flow rate at each node on the pipeline at time j+1 is calculated. If the calculation node is an intermediate node in the pipeline, then it is during the calculation. Both formulas in formula (13) can be calculated; if the calculation node is the beginning node of the pipeline, then If the compute node is the end node of the pipeline. .

[0131] Step S106 specifically includes:

[0132] S601: Since the first end of the pipe is connected to the inlet pool, the water head at the first node of the pipe is always equal to... It does not change over time;

[0133] S602: Assume the valve closing time is... , < Then, as the valve closes, the head and flow rate at the end node are determined by the valve's characteristics; > , , ;

[0134] S603: In step S602, < When the instantaneous value at the valve end boundary point is calculated, the formulas are as follows: (14) and (15):

[0135] (14)

[0136] (15)

[0137] In the above formula: , , , For step S104, calculate the last node at the initial time. , ;

[0138] S604: In step S603, Let be the dimensionless opening coefficient of the valve. When solving for water hammer when the valve is closed, the valve's opening coefficient is... With time The relationship of change can be determined based on the type of valve. The curve is calculated using the formula shown in formula (16):

[0139] (16).

[0140] Step S107 specifically includes:

[0141] S701: The basic physical model of water column separation is the phenomenon of water column separation and re-merging. During water hammer calculations, when the pressure at any cross-section is equal to or less than the vaporization pressure of water, the pressure remains at the vaporization pressure of water. The cavitation generated at that cross-section causes the water column to separate, forming a vapor column. In subsequent calculations, if the volume of the vapor column between the separated water columns is equal to or less than zero, the two water columns collide, resulting in water column re-merging and a sharp increase in pressure. The specific process of the water column separation model is as follows:

[0142] (1) Determine whether water column separation occurs according to formula (17).

[0143] (17)

[0144] In the above formula: The absolute pressure at point i, Let i be the piezometric head at point i, which is the height of the hydraulic gradient line relative to the reference plane. The height of the reference plane at the vertex of the pipe section is the same as the reference plane for the hydraulic gradient. The height of the water column under atmospheric pressure is taken as 10m. This represents the vaporization pressure of water, taken as 2m; when ≤ At that time, liquid column separation occurs. > At that time, no water column separation occurs, so the calculation is not included in the water column separation model and the result is returned. , .

[0145] (2) If the conditions in (1) are met ≤ Then, the water column separation and the transient parameters at point i are calculated according to formulas (18) to (21):

[0146] (18)

[0147] (19)

[0148] (20)

[0149] (twenty one)

[0150] (3) If during the calculation process If the water columns have rejoined and collided at that instant, the pressure rise after rejoining is calculated according to formulas (22) to (24). If the water columns have already rejoined and collided at that instant, the transient parameters are calculated as follows:

[0151] (twenty two)

[0152] (twenty three)

[0153] (twenty four)

[0154] S702: In the water column separation principle described in step S701, the first step is to determine whether water column separation has occurred. In actual calculations, if water column separation has already occurred at the interface in the previous moment, a new variable is used. Whether it is zero is used as the criterion.

[0155] S703: Use the calculation results from step S105 as input data to calculate the water column separation model. For the results at the initial time, let... If so, return the original input data and then determine... If true, then calculate the water column separation and the transient parameters at point i according to formulas (18) to (21), and let ; Input data at subsequent time points, if If , it means that no water column separation occurred at this point in the previous moment; if If the result is , it indicates that water column separation has occurred at the previous moment. Continue to calculate the water column separation and the transient parameters at point i according to formulas (18) to (21). If the calculated result is , , indicating that the water column is closed. The pressure rise after closure is calculated according to formulas (22) to (24) and returned as the calculation result.

[0156] In step S108, since steps S103 and S104 are steady-state calculation results, and steps S105, S106, and S107 are transient calculation results at the same moment, the process needs to be performed m times to obtain the result. Each moment within the time period The flow rate and head parameters of the N+1 nodes.

[0157] Calculated The pressure should be less than the design pressure of the pipeline, and water column separation should be avoided in the pipeline. >8m; if the calculated If the pressure exceeds the pipeline's design capacity, the closing time of the end valve should be extended. If water column separation occurs in the pipeline, that is... For sections less than 8m, effective water hammer mitigation measures should be implemented.

[0158] This invention has been applied to the water hammer calculation of a long-distance water conveyance project in Yunnan. The total length of the water conveyance pipeline is 10360m, the water level in the inlet pool is 1520.484m, the water level in the outlet pool is 1501.061m, the pipe material is ductile iron pipe, the pipe radius is 1.40m, a branch pipe is set at chainage G4+797, and a maintenance valve is set at the bifurcation point. The branch pipe has a radius of 0.40m and a length of 1482.00m, and a control valve is set at the end of the branch pipe.

[0159] First, the steady-state flow rate was calculated. By inputting the basic information of the pipeline into the program and considering the friction loss and local head loss, the steady-state main flow rate was calculated to be 2.6 m³ / s. 3 / s, branch pipe flow rate 0.3m³ / s 3 / s. The flow rate and pressure head obtained from steady-state calculations are used as initial values ​​for unsteady flow calculations.

[0160] Using the steady-state calculation results as initial values, iterative time-based calculations were performed. The calculation showed that the minimum valve-closing time to prevent liquid column separation in the pipeline after the main pipe's end valve is closed is 65 seconds. Considering the need for the valve to achieve a throttling effect as quickly as possible after closure and to avoid excessive water hammer pressure, a two-stage valve-closing scheme was adopted: 60% closure in the first 5 seconds, followed by a slow closure in the next 60 seconds. The total calculation time was 150 seconds, yielding the pressure envelope along the pipeline as shown below. Figure 2 As shown in the figure This is the maximum pressure envelope of the pipeline. This is the minimum pressure envelope of the pipeline. This is the center elevation line of the pipeline. ,if > If this occurs, then water column separation is considered to have taken place. Figure 2 See the minimum pressure throughout the process All are above the vaporization pressure line of water. Therefore, water column separation will not occur within the pipeline. The points most prone to liquid column separation in the entire pipeline are near the pipeline inlet and sections protruding from the mountainside. This is because these sections have higher elevations, resulting in very small head in the piezometer during steady-state operation. Under the same pressure reduction, they are more susceptible to liquid column separation and damage compared to other sections. The pressure envelope after valve closure shows that no liquid column separation or damage occurs throughout the entire pipeline. The maximum pressure the pipeline withstands is 1.67 MPa, and the maximum pressure change is 0.79 MPa, which is within the pipeline's allowable pressure range. This indicates that the planned valve closure time can ensure that water column separation does not occur in the pipeline, ensuring safe pipeline operation. The pressure change at the end valve over time is as follows: Figure 3 As shown, according to the calculation results, the pressure in front of the valve continues to rise during the valve closing process. After the valve is fully closed, the pressure changes periodically. Due to energy loss caused by pipeline friction, the pressure peak gradually decreases. The valve can withstand a maximum pressure of 0.89 MPa. Within the valve's design pressure range, the valve can operate safely.

Claims

1. A method for constructing a calculation model for water hammer in a long-distance gravity flow pipeline, characterized in that: It includes the following steps: S101: Obtain the basic pipeline information and boundary point information of the calculation project as input parameters for model calculation; S102: Based on the basic pipeline information, assume a calculation time step. Divide the pipeline into N integer segments; S103: Calculate the flow rate of each section of the pipe from the first section to the Nth section, based on the simple free outflow formula for a pipe. The flow rate of the Nth pipe segment ; S104: Calculate the head loss along the pipeline from the first segment to the Nth segment using Darcy's formula and Manning's formula, and calculate the head at N+1 nodes. ,save data; S105: The results calculated in steps S103 and S104 , As an initial value, based on the method of characteristics, assume the total calculation time. Time step Then calculate the cycle number. Assuming the initial time j=0, calculate the (j+1)th... The corresponding flow rate and head at any given time , ; S106: Based on the initial boundary conditions, replace the first node. = The end node is calculated based on the control valve model to obtain... , Replace each , ; S107: Regarding Time calculation , Based on the water column separation model, determine whether water column separation has occurred. If water column separation has occurred, input the results into the model to calculate the water column separation repair. , If no water column separation occurs, then maintain , constant; S108: Based on the calculation result of step S107, use it as the next step. The initial value at time step m is used to repeat S105, S106, and S107 m times until... Save all calculation results , Find and The pressure envelope along the pipeline is obtained.

2. The method for constructing a calculation model for water hammer in a long-distance gravity flow pipeline according to claim 1, characterized in that: In step S101, the basic pipeline information specifically includes: the number of pipeline segments N, and the length of each pipeline segment. Diameter of each section of pipe Wave velocity in each section of the pipeline Roughness of each section of the pipeline Elevation of the center point at each bend in the pipeline Basic information about the boundary points includes: inlet water level. , outlet water level , Outlet valve flow characteristics.

3. The method for constructing a calculation model for water hammer in a long-distance gravity flow pipeline according to claim 1, characterized in that: Step S102 specifically includes: S201: The wave velocity calculation formula for each pipe segment from the 1st to the Nth is shown in formula (1): （1） In the above formula, The bulk modulus of the fluid; The diameter of each pipe section; The elastic modulus of the pipe wall material; For pipe wall thickness; S202: Assume the computation time step The wave speed calculated based on S201 Calculate the number of segments in each section of the pipeline. Rounded down, length of each segment N= Then, based on the calculated number of pipe sections Back-calculate the wave velocity of this section of the pipeline If there is a short pipe in the pipeline, and the wave velocity change rate exceeds 5%, then take... Repeat the iteration until the wave velocity change rate is less than 5%, and obtain the final time step used for calculation. Update the basic parameters of each pipe section , , .

4. The method for constructing a calculation model for water hammer in a long-distance gravity flow pipeline according to claim 1, characterized in that: In step S103, the formula for calculating the free outflow of the pipe is shown in formula (2): （2） In the above formula, The cross-sectional area of ​​the pipe. The inner diameter of the pipe. To calculate the length of the pipeline section, The effective head includes the head of the traveling flow velocity. This is the coefficient for head loss along the friction path. This is the sum of the local head loss coefficients in the calculated section of the pipeline; In the calculation process, local head loss is ignored, and only friction head loss is calculated. If there are no branch pipes in the pipeline, the flow rate is the same throughout the entire pipeline.

5. The method for constructing a calculation model for water hammer in a long-distance gravity flow pipeline according to claim 1, characterized in that: Step S104 specifically includes: S401: Darcy's formula is shown in formula (3), Manning's formula is shown in formula (4), and the formulas for calculating head loss along the friction are shown in formulas (3), (4), and (5): （3） （4） （5） In the above formula, For head loss along the pipeline, The flow velocity in the pipe, Given the hydraulic radius, combining (3), (4), and (5), we can obtain the length as... The formula for calculating the head loss along the pipeline is shown in formula (6): （6） S402: Based on formula S401, calculate the following for each of the N pipe segments: The water head at each node, the entire pipeline is divided into [number] sections. In the small segment, node i has a total of There are several nodes, including the starting node and the ending node, with the first node having a water head. Node 2 to The formula for calculating the head at the node is shown in formula (7): （7） S403: Calculate the head at each node of the pipeline according to formula S402, and adjust the roughness of the pipeline to make the calculated head... and If the difference between the two is within 0.1%, when adjusting the roughness, if The roughness should be increased, and vice versa. The roughness should be reduced, with the increase or decrease ≤20%. The roughness of each node should be calculated. According to the calculation results of step S103 , will each node , The data, as a steady-state result, serves as the initial data for subsequent calculations.

6. The method for constructing a calculation model for water hammer in a long-distance gravity flow pipeline according to claim 3, characterized in that: Step S105 specifically includes: S501: According to step 102 , Let i represent the number of the calculated section on the pipe segment, and j represent the time layer number. The pipeline can be divided into a planar grid diagram in space and time. For the water head of P at any time j+1 in space, and traffic It can be extended through the head and flow parameters of its neighboring points i-1 and i+1 at the previous time step. and Solve the equation; S502: The steps described in S501 and The calculation formulas for the equations are shown in formulas (8) and (9): （8） （9） In the above formula, , Let P be the water head and flow rate, respectively. , The head and flow rate at point i-1 above point P are given respectively. , Let i and i be the head and flow rate at point i+1, respectively, in the previous time step P. , These are constants related to pipeline characteristics; To simplify the calculation, let , Then equations (8) and (9) can be simplified to equations (10) and (11): （10） （11） By combining equations (10) and (11), the parameters of point P can be obtained. , The calculation formulas are as follows: (12) and (13): （12） （13） S503: Calculation in step 502 , When the pipe is an intermediate node, the calculation can be performed according to the formula. In particular, if the calculation node is the starting node, then... , If the node is an end node, , ; S504: Calculate pipeline characteristic parameters in step 502. and When, according to the method of characteristics, if node P is located at an intermediate node, then along... and The characteristic parameters are the same; if the calculation node is located at a pipe bend, for each pipe segment length All calculated , , , ,calculate , Use pipeline data prior to the turning point. , Use pipeline data after the turning point; if the calculation node is a turning point in the pipeline, then , The calculation formula is , ; S505: Based on the parameters and pipe characteristic constants calculated in steps S503 and 504 at time j, substitute them into formula (12) to calculate the head at each node on the pipe at time j+1. ; S506: In step 502, based on the head calculated in step 505, the flow rate at each node on the pipeline at time j+1 is calculated. If the compute node is an intermediate node in the pipeline, then in the computation Both formulas in formula (13) can be calculated; if the calculation node is the beginning node of the pipeline, then If the compute node is the end node of the pipeline. .

7. The method for constructing a calculation model for water hammer in a long-distance gravity flow pipeline according to claim 1, characterized in that: Step S106 specifically includes: S601: Since the first end of the pipe is connected to the inlet pool, the water head at the first node of the pipe is always equal to... It does not change over time; S602: Assume the valve closing time is... , < Then, as the valve closes, the head and flow rate at the end node are determined by the valve's characteristics; > , , ; S603: In step S602, < When the instantaneous value at the valve end boundary point is calculated, the formulas are as follows: (14) and (15): （14） （15） In the above formula: , , , For step S104, calculate the last node at the initial time. , ; S604: In step S603, Let be the dimensionless opening coefficient of the valve. When solving for water hammer when the valve is closed, the valve's opening coefficient is... With time The relationship of change can be determined based on the type of valve. The curve is calculated using the formula shown in formula (16): （16）。 8. The method for constructing a calculation model for water hammer in a long-distance gravity flow pipeline according to claim 1, characterized in that: Step S107 specifically includes: S701: The basic physical model of water column separation is the phenomenon of water column separation and re-merging. During water hammer calculations, when the pressure at any cross-section is equal to or less than the vaporization pressure of water, the pressure remains at the vaporization pressure of water. The cavitation generated at that cross-section causes the water column to separate, forming a vapor column. In subsequent calculations, if the volume of the vapor column between the separated water columns is equal to or less than zero, the two water columns collide, resulting in water column re-merging and a sharp increase in pressure. The specific process of the water column separation model is as follows: (1) Determine whether water column separation occurs according to formula (17). （17） In the above formula: The absolute pressure at point i, Let i be the piezometric head at point i, which is the height of the hydraulic gradient line relative to the reference plane. The height of the reference plane at the vertex of the pipe section is the same as the reference plane for the hydraulic gradient. The height of the water column under atmospheric pressure is taken as 10m. This represents the vaporization pressure of water, taken as 2m; when ≤ At that time, liquid column separation occurs. > At that time, no water column separation occurs, so the calculation is not included in the water column separation model and the result is returned. , ; (2) If the conditions in (1) are met ≤ Then, the transient parameters at point i after water column separation are calculated according to formulas (18) to (21): （18） （19） （20） （21） (3) If during the calculation process It is assumed that the water column reassembles and collides with each other when the volume of the steam column formed by the water column separation is equal to or less than zero. The pressure rise after reassembly is calculated according to formulas (22) to (24). The transient parameters are calculated as follows: （22） （23） （24） S702: In the water column separation principle described in step S701, the first step of determining whether water column separation has occurred should be based on formula (17). If water column separation has already occurred at the interface where the absolute pressure is less than or equal to the vaporization pressure at the previous moment, then a new variable should be used. Whether it is zero is used as the criterion; S703: Use the calculation results from step S105 as input data to calculate the water column separation model. For the results at the initial time, let... If so, return the original input data and then determine... If true, then calculate the water column separation and the transient parameters at point i according to formulas (18) to (21), and let ; Input data at subsequent time points, if If , it means that no water column separation occurred at this point in the previous moment; if If the result is , it indicates that water column separation has occurred at the previous moment. Continue to calculate the water column separation and the transient parameters at point i according to formulas (18) to (21). If the calculated result is , , indicating that the water column is closed. The pressure rise after closure is calculated according to formulas (22) to (24) and returned as the calculation result.

9. The method for constructing a calculation model for water hammer in a long-distance gravity flow pipeline according to claim 1, characterized in that: In step S108, the calculated The pressure should be less than the design pressure of the pipeline, and water column separation should be avoided in the pipeline. >8m; if the calculated If the pressure exceeds the pipeline's design capacity, the closing time of the end valve should be extended. If water column separation occurs in the pipeline, that is... For sections less than 8m, effective water hammer mitigation measures should be implemented.

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