CN114460981A - Numerical simulation method for hydraulic control of water distribution hub - Google Patents

Numerical simulation method for hydraulic control of water distribution hub Download PDF

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CN114460981A
CN114460981A CN202210079779.5A CN202210079779A CN114460981A CN 114460981 A CN114460981 A CN 114460981A CN 202210079779 A CN202210079779 A CN 202210079779A CN 114460981 A CN114460981 A CN 114460981A
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water
channel
increment
flow
formula
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刘军
李甲振
王瑞
郭新蕾
叶茂
曾利
陆志华
赵冠亮
仝妍妍
陈敏
王军
周皞
成志超
潘佳佳
路锦枝
谭震
孙亚翡
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Water Conservancy Bureau Of Sucheng District Suqian City
China Institute of Water Resources and Hydropower Research
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Water Conservancy Bureau Of Sucheng District Suqian City
China Institute of Water Resources and Hydropower Research
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    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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Abstract

The invention relates to a numerical simulation method for hydraulic control of a water distribution hub, which comprises the steps of obtaining an increment correlation relation; converting and integrating; deducing a correlation between the flow increment of the inlet node of the water channel and the water level increment; flow increment and water level increment of all nodes of the water outlet channel are solved by back substitution; solving the flow increment and the water level increment of the outlet node of the water inlet channel and the inlet node of the water outlet channel and the water level increment of the distribution pool; flow increment and water level increment of other nodes of each channel are solved in a retrospective mode; and calculating the flow and the water level of each node. The mass and energy conservation equation under the complex operating conditions of inflow, outflow and overflow of the water distribution hub is constructed through theoretical analysis, contents such as a Newton-Simpson discrete algorithm, a coding mode, a calculation program of a Preissmann four-point implicit difference algorithm and the like are provided, and a theoretical model of the water distribution hub is established; a numerical solving method is provided for the working conditions of multiple water inlets, multiple water outlets, pressure-free coupling and the like, and reference is provided for the operation scheduling of the engineering.

Description

Numerical simulation method for hydraulic control of water distribution hub
Technical Field
The invention relates to a numerical simulation method for hydraulic control of a water distribution hub, which is an analysis method for hydraulic engineering and a method for analyzing the hydraulic engineering and assisting operation and scheduling by applying a computer.
Background
Water transfer engineering and large and medium irrigation areas are engineering measures for optimizing water resource space allocation and relieving the problem of water resource shortage in local areas or agricultural irrigation, and safe scheduling and operation are keys for guaranteeing national water resource safety. The control and regulation of engineering usually needs to calculate the hydraulic transition process, analyze the flow, water level and pressure changes of the pipe, culvert, canal and tunnel under certain operation strategies of equipment such as gates, pumps, valves and the like, so that the requirements of standard regulations, pipeline pressure bearing, equipment limit values and the like are met.
The water distribution hub is a common hydraulic building in water distribution projects and large and medium irrigation areas, and is used for connecting a pipe culvert channel tunnel, a main water diversion channel (pipe) and a water distribution trunk and branch channel (pipe) of long-distance water diversion projects and subsequent water distribution projects. If the reservoir is used as a water distribution hub, the water distribution hub can be regarded as a normal water level boundary, and the hydraulic transition processes of the water diversion project and the water distribution project are respectively calculated. Due to the restriction of factors such as overall layout of projects, topographic and geological conditions, relocation and the like, a plurality of projects do not have proper reservoir areas as water distribution hubs, and facilities such as pools, water channels and the like need to be constructed manually. The problems of cost, environment and the like must be considered in manual construction, and the pond and the canal are limited within a certain range. Because the volume of the artificial water pool of the water distribution hub is limited, when the water supply flow or the user demand changes, the on-way flow, the water level and the pressure of the whole water delivery system can be changed along with the change, the water distribution hub is regarded as a normal water level boundary, the real hydraulic characteristics of the water diversion project and the water distribution project cannot be reflected, and the influence degree on the operation scheduling of the project need to be coupled with the water diversion project, the water distribution hub and the water distribution project for simulation analysis. How to carry out simulation analysis to the water distribution hub to provide effective data and ensure the water delivery safety is a problem to be solved.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides a numerical simulation method for hydraulic control of a water distribution hub. The method researches hydraulic characteristics of a limited-volume water distribution hub under the condition of complicated inflow and outflow, provides contents such as a control equation, a discrete method, a solving program and the like, establishes a theoretical model of the water distribution hub, performs simulation analysis on hydraulic control of the water distribution hub by combining a typical example, and solves the model problem of simultaneous solution of a diversion project, the water distribution hub and the water distribution project.
The purpose of the invention is realized as follows: a numerical simulation method of a hydraulic control of a water distribution hub, the analyzed water distribution hub of the method comprising: m water inlet channels, a distribution pool provided with an overflow channel and N water outlet channels; setting m +1 computing nodes along each water inlet channel, and coding the computing nodes of each water inlet channel from upstream to downstream; setting n +1 computing nodes along the 1 st water outlet channel, and coding the computing nodes of the water outlet channel 1 from upstream to downstream; setting N +1 computing nodes along the 2 nd to N th water outlet channels, and coding the computing nodes of the water outlet channels 2 to N from downstream to upstream; namely: the method is characterized in that the tail end calculation nodes of the M water inlet channels, the tail end calculation nodes of the 2-N water outlet channels and the head end calculation nodes of the 1 water outlet channel are calculation nodes at the joint of the water inlet channels or the water outlet channels and the distribution pool, and the method comprises the following steps:
step 1, obtaining an increment correlation: calculating elements of a matrix B and a column vector P of the water inlet channel 1, the water inlet channel 2, the water inlet channel … …, the water inlet channel M, the water outlet channel 2, the water outlet channel … … and the water outlet channel N by using a elimination process of a double-sweep method, and obtaining a correlation relation between a flow increment and a water level increment of a final node, wherein the equation number is M + N-1; the calculation formula is as follows:
X＝BX+P (1)
in the formula:
Figure BDA0003485430910000021
delta Q is the flow increment of the current iteration step, the lower corner mark K represents the number of the calculation node, and the numerical value of the lower corner mark is 0-m for the water inlet channel; for the water outlet channel, the numerical value of the lower corner mark is 0-n; delta h is the water depth increment of the current iteration step; u, W, P is the double sweep coefficient; u, W, P, the lower corner mark represents the row number change of the matrix, and the number of the water inlet channel is 0-2 m < -1 >; numbering the water outlet channels to be 0-2 n-1;
each element is calculated by the following recursion formula:
Figure BDA0003485430910000022
Figure BDA0003485430910000023
Figure BDA0003485430910000024
in the formula: c. b, D, a and e are coefficients; j is a node number, and j is 1,2, … …, K-2;
for the water inlet channel 1, the flow increment and the water quantity increment of the terminal computing node satisfy the following relational expression:
ΔQIn1,m＝UIn1,2m-2ΔyIn1,m+PIn1,2m-2 (5.1)
for water inlet channels 2-M, the flow increment and the water quantity increment of the terminal computing node satisfy the following relational expression:
ΔQIn2,m＝UIn2,2m-2ΔyIn2,m+PIn2,2m-2 (5.2)
……
ΔQInM,m＝UInM,2m-2ΔyInM,m+PInM,2m-2 (5.M)
for the water outlet channels 2-N, the flow increment and the water quantity increment of the tail end computing node satisfy the following relational expression:
ΔQOut2,n＝UOut2,2n-2ΔyOut2,n+POut2,2n-2 (6.2)
……
ΔQOutN,n＝UOutN,2n-2ΔyOutN,n+POutN,2n-2 (6.N)
thus, M + N-1 values of delta Q for the flow rate and the water amount are obtainedIn1,m、ΔyIn1,m、……、ΔQInM,m、ΔyInM,m、ΔQOut2,n、ΔyOut2,n、……、ΔQOutN,n、ΔyOutN,nAn equation of the correlation; in the lower corner mark represents a water inlet channel, Out represents a water outlet channel, the following numbers represent channel numbers, and the numbers after comma represent computing node numbers;
step 2, conversion and integration: all the water inlet, the water outlet and the water level of the distribution pool meet the energy conservation equation, and the dispersion is carried out by utilizing a Newton-Simpson method, wherein the equation quantity is M + N; meanwhile, the mass conservation equation is also met, integration is carried out, second-order approximation is carried out, and the equation quantity is 1;
the energy conservation equation of the outlet node of the water inlet channel 1 and the distribution pool is as follows:
Figure BDA0003485430910000031
in the formula: y isIn1,mA pressure measuring pipe water head which is an outlet node of the water inlet channel 1; qIn1,mThe flow rate of an outlet node of the water inlet channel 1; g is the acceleration of gravity; a. theIn1,mThe flow area of an outlet node of the water inlet channel 1; y issA piezometer tube water head of the distribution pool; zetaIn1The local head loss coefficient of water entering the distribution pool for the water in the water inlet channel 1;
energy conservation equation of 2-M outlet nodes of the water inlet channel and the distribution pool:
Figure BDA0003485430910000032
in the formula: y isIn2,m、……、yInM,mA pressure measuring pipe water head of 2-M outlet nodes of the water inlet channel; qIn2,m、……、QInM,mThe flow rate of 2-M outlet nodes of the water inlet channel; g is the acceleration of gravity; a. theIn2,m、……、AInM,mThe flow area of the outlet node of the water inlet channel is 2-M; zetaIn2、……、ζInMThe local head loss coefficient of water entering the distribution pool from the water inlet channel 2-M;
energy conservation equation of the inlet node of the distribution pool and the water outlet channel 1:
Figure BDA0003485430910000041
in the formula: y isOut1,0Is discharged with waterA piezometer tube water head of an inlet node of the channel 1; qOut1,0Is the flow of the inlet node of the water outlet channel 1; a. theOut1,0The flow area of an inlet node of the water outlet channel 1; zetaOut1The local head loss coefficient of water entering the water outlet channel 1;
energy conservation equation of the inlet nodes 2-N of the distribution pool and the water outlet channel:
Figure BDA0003485430910000042
……
Figure BDA0003485430910000043
in the formula: y isOut2,n、……、yOutN,nA pressure measuring pipe water head with 2-N inlet nodes of the water outlet channel; qOut2,n、……、QOutN,nThe flow rate of the inlet node of the water outlet channel is 2-N; a. theOut2,n、……、AOutN,nThe overflow area of the inlet node of the water outlet channel is 2-N; zetaOut2、……、ζOutNThe local head loss coefficient of water entering the water outlet channel is 2-N;
the mass conservation equation of the distribution pool is as follows:
Figure BDA0003485430910000044
in the formula: a. the0The plane area of the distribution pool; qwThe calculation formula is as follows:
Figure BDA0003485430910000045
in the formula: mu is a flow coefficient; b iswIs the weir width; hwIs the weir elevation;
and (3) equation conversion:
for the water inlet channel 1, it can be obtained from the formula (7.1):
Figure BDA0003485430910000046
by the Newton-Simpson method, formula (11) is converted to:
FIn10+eIn1ΔyIn1,m+aIn1ΔQIn1,m+esΔys＝0 (12.1)
in the formula:
Figure BDA0003485430910000051
Figure BDA0003485430910000052
Δysis the increment of the water level of the water distribution tank;
for water inlet channels 2-M, the following can be obtained:
FIn20+eIn2ΔyIn2,m+aIn2ΔQIn2,m+esΔys＝0 (12.2)
……
FInM0+eInMΔyInM,m+aInMΔQInM,m+esΔys＝0 (12.M)
in the formula:
Figure BDA0003485430910000053
……、
Figure BDA0003485430910000054
……、
Figure BDA0003485430910000055
……、
Figure BDA0003485430910000056
thus, M values of Δ y are obtaineds、ΔQIn1,m、ΔyIn1,m、……、ΔQInM,m、ΔyInM,mThe equation of (c);
for the water outlet channel 1, the following formula (8.1) is obtained:
Figure BDA0003485430910000057
using the Newton-Simpson method, formula (13) is converted to:
FOut10+eOut1ΔyOut1,0+aOut1ΔQOut1,0+esΔys＝0 (14.1)
in the formula:
Figure BDA0003485430910000058
Figure BDA0003485430910000059
for the water outlet channels 2-N, obtaining
FOut20+eOut2ΔyOut2,n+aOut2ΔQOut2,n+esΔys＝0 (14.2)
……
FOutN0+eOutNΔyOutN,n+aOutNΔQOutN,n+esΔys＝0 (14.N)
In the formula:
Figure BDA0003485430910000061
……、
Figure BDA0003485430910000062
……、
Figure BDA0003485430910000063
……、
Figure BDA0003485430910000064
for the mass conservation equation of the distribution pool, the mass conservation equation is obtained by integrating and taking second-order approximation by the formula (9):
Figure BDA0003485430910000065
Figure BDA0003485430910000066
in the formula: Δ t is the time step; suffix 0 represents the value of the physical quantity at the previous time step;
formula (15) can be converted to using the newton-simpson method:
Figure BDA0003485430910000067
in the formula:
Figure BDA0003485430910000068
Figure BDA0003485430910000069
Figure BDA00034854309100000610
thus, 1 for Δ y can be obtaineds、ΔQIn1,m、ΔyIn1,m、……、ΔQInM,m、ΔyInM,m、ΔQOut1,0、ΔyOut1,0、ΔQOut2,n、ΔyOut2,n、……、ΔQOutN,n、ΔyOutN,nThe equation of (c);
step 3, deducing the flow increment of the inlet node of the water outlet channel 1 andcorrelation of water level increment: for the current iteration step, the unknowns include: flow increment and water level increment, delta Q, of the water inlet channel 1, the water inlet channel 2, … …, the water inlet channel M, the water outlet channel 1, the water outlet channel 2, … … and the water outlet channel NIn1,m、ΔyIn1,m、……、ΔQInM,m、ΔyInM,m、ΔQOut1,0、ΔyOut1,0、ΔQOut2,n、ΔyOut2,n、……、ΔQOutN,n、ΔyOutN,nWater level increment of distribution reservoir, Δ ysIn total, 2(M + N) + 1; the quantity of the equation is 2(M + N), and the flow increment delta Q of the inlet node of the water channel 1 can be obtained through derivationOut1,0Increment of water level by delta yOut1,0The correlation of (2);
and 4, solving the flow increment and the water level increment of all the nodes of the water outlet channel 1 by back substitution: solving the flow increment and the water level increment of all the nodes of the water outlet channel 1 by utilizing a back substitution process, wherein the calculation formula is as follows:
Figure BDA0003485430910000071
step 5, solving the flow increment and the water level increment of the outlet node of the water inlet channel and the inlet node of the water outlet channel and the water level increment of the distribution pool: solving the outlet nodes of the water inlet channel 1, the water inlet channel 2, … … and the water inlet channel M, the flow increment and the water level increment of the inlet nodes of the water outlet channel 2, … … and the water outlet channel N and the water level increment of the distribution pool; utilizing the flow increment delta Q of the inlet node of the water outlet channel 1 obtained in the step 4Out1,0Increment of water level by delta yOut1,0Substituting the above-established equation to determine the flow increment and water level increment, delta Q, of the inlet nodes of the inlet water 1, the inlet water 2, … … and the inlet water M, and the inlet nodes of the outlet water 2, … … and the outlet water NIn1,m、ΔyIn1,m、……、ΔQInM,m、ΔyInM,m、ΔQOut2,n、ΔyOut2,n、……、ΔQOutN,n、ΔyOutN,nWater level increment of distribution reservoir, Δ ys；
And 6, solving the flow increment and the water level increment of other nodes of each channel in a back substitution way: respectively solving the flow increment and the water level increment of all nodes of the water inlet channel 1, the water inlet channel 2, the water inlet channel … …, the water inlet channel M, the water outlet channel 2, the water outlet channel … … and the water outlet channel N in a back-substitution mode, wherein the calculation formula is as follows:
Figure BDA0003485430910000072
and 7, calculating the flow and the water level of each node: calculating the flow and the water level of all nodes of the water inlet channel 1, the water inlet channel 2, … …, the water inlet channel M, the water outlet channel 1, the water outlet channel 2, … … and the water outlet channel N in the current iteration step and the water level of the distribution pool in the current iteration step; the flow rate is equal to the value of the previous iteration step plus the flow increment, and the water level is equal to the value of the previous iteration step plus the water level increment.
Further, the water inlet channel or the water outlet channel flows under pressure, a narrow gap method is adopted for solving, and the width of the gap is as follows:
B＝gA/a2 (19)
in the formula: b is the gap width; a is the cross section of pressure flow; and a is the water shock wave speed.
The invention has the advantages and beneficial effects that: the mass and energy conservation equation under the complex operating conditions of inflow, outflow and overflow of the water distribution hub is constructed through theoretical analysis, contents such as a Newton-Simpson discrete algorithm, a coding mode, a calculation program of a Preissmann four-point implicit difference algorithm and the like are provided, and a theoretical model of the water distribution hub is established; a numerical solving method is provided aiming at the possible working conditions of multiple water inlets, multiple water outlets, pressure and non-pressure coupling and the like, and reference can be provided for the operation scheduling of the engineering.
Drawings
The invention is further illustrated by the following figures and examples.
FIG. 1 is a schematic structural diagram of a water distribution hub analyzed by a method according to an embodiment of the present invention;
FIG. 2 is a flow chart of a method according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a water distribution hub with one inlet and two outlets according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a water distribution system according to an example of the present invention;
FIG. 5 is a flow and level process for a typical location of a water distribution system according to one embodiment of the present invention, wherein (a) is a flow process and (b) is a level process;
fig. 6 shows hydraulic characteristics of an upstream tunnel according to an embodiment of the present invention, wherein (a) a flow process and (b) a water level process.
Detailed Description
The first embodiment is as follows:
the embodiment is a numerical simulation method for hydraulic control of a water distribution hub. The analyzed water distribution hub of the method comprises: m water inlet channels, a water distribution pool provided with an overflow channel, and N water outlet channels are shown in figure 1. The arrows in fig. 1 indicate the direction of the water flow.
The water distribution hub is a common hydraulic building in water transfer engineering and large and medium irrigation areas, and is used for connecting a pipe culvert channel tunnel, a main water diversion channel (pipe), a water distribution trunk and branch channels (pipes) of long-distance water diversion engineering and subsequent water distribution engineering. If the reservoir is used as a water distribution hub, the water distribution hub can be regarded as a normal water level boundary, and the hydraulic transition processes of the water diversion project and the water distribution project are respectively calculated. Due to the restriction of factors such as overall project layout, topographic and geological conditions, relocation and the like, a lot of projects do not have proper reservoir areas as water distribution hubs and need to be built. During design, the volume of the water distribution hub is generally selected according to two references: i, the underwater volume of the water inlet pool can be determined according to the design flow of 30-50 times of the water pump sharing the water inlet pool; and ii, when the water delivery scale is not large or the requirement is not high, the volume of the water pool in the middle of the gravity water delivery pipeline can be determined according to the maximum designed water volume not less than 5 min. Therefore, the volume of the built water distribution hub is generally 30-300 times of the design flow. Because the volume of the water distribution hub is small, when the water supply flow or the user demand changes, the on-way flow, the water level and the pressure of the whole water delivery system change along with the change, and the real hydraulic characteristics of the water diversion project and the water distribution project cannot be reflected by regarding the water distribution hub as a normal water level boundary. Improper control can not deliver the required water amount for the user in due time, and engineering accidents such as overflow of the embankment, pipe explosion, structural building damage and the like can be caused. In this case, simulation analysis needs to be performed by coupling the diversion project, the water distribution hub and the water distribution project.
The purpose of this embodiment is to study hydraulic characteristics of a limited-volume water distribution hub under complex inlet and outlet flow conditions, to provide contents such as a control equation, a discrete method, a solving program and the like, to establish a theoretical model of the water distribution hub, to perform simulation analysis on hydraulic control of the water distribution hub by combining a typical example, and to solve a model problem of simultaneous solution of a diversion project, the water distribution hub and the water distribution project.
The water distribution hub described in this embodiment mainly comprises three elements: water inlet channel, water outlet channel and distribution pool. The water inlet channel and the water outlet channel can be open channels or non-pressure culverts or pressure pipelines. The number of the water inlet channels and the number of the water outlet channels can be equal or unequal, and in most cases, the number of the water inlet channels is usually less than that of the water outlet channels. The distribution pool is an artificially constructed pool, and the flow is designed according to 30-300 times.
For convenient calculation, this embodiment has set up the computational node at the water channel of intaking and the channel of going out: and (2) setting m +1 computing nodes along each water inlet channel, and coding the computing nodes of each water inlet channel from upstream to downstream. Setting n +1 computing nodes along the 1 st water outlet channel, and coding the computing nodes of the water outlet channel 1 from upstream to downstream; setting N +1 computing nodes along the 2 nd to N th water outlet channels, and coding the computing nodes of the water outlet channels from the downstream to the upstream; namely: the tail end computing nodes of the M water inlet channels, the tail end computing nodes of the 2-N water outlet channels and the head end computing nodes of the 1 water outlet channel are all computing nodes at the joint of the water inlet channels or the water outlet channels and the distribution pool, and the figure 1 shows that the water inlet channels and the water outlet channels are all the computing nodes.
Water distribution hubs are typically open channel flows with free surfaces. The control equation is a Saint-Vietnam equation and comprises a momentum equation and a continuous equation, and the solving method mainly comprises a characteristic line method, a display difference method, an implicit difference method and the like, wherein the stability of numerical calculation of the implicit difference method is good. Therefore, the research adopts the Preissmann four-point implicit differential format which is widely applied in engineering calculation.
Energy conservation of a water inlet system:
the energy conservation equations of the water inlet channel 1, the water inlet channels 2 and … …, the water inlet channel M and the distribution pool are as follows.
The water coming from the water inlet channel 1 enters the distribution pool, and the energy conservation equation of the last node of the water inlet channel 1 and the distribution pool can be obtained by the unsteady flow Bernoulli energy equation:
the energy conservation equation of the outlet node of the water inlet channel 1 and the distribution pool is as follows:
Figure BDA0003485430910000091
in the formula: y isIn1,mA pressure measuring pipe water head which is an outlet node of the water inlet channel 1; qIn1,mThe flow rate of an outlet node of the water inlet channel 1; g is the acceleration of gravity; a. theIn1,mThe flow area of an outlet node of the water inlet channel 1; y issA piezometer tube water head of the distribution pool; zetaIn1The local head loss coefficient of water entering the distribution pool for the water in the water inlet channel 1; since the cross-sectional area of the distribution basin is generally much greater than the cross-sectional area of the channel, the flow head of the distribution basin is negligible.
The water coming from the water inlet channel 2 enters the distribution pool, and the energy conservation equation of the tail node of the water inlet channel 2 and the distribution pool can be obtained by the unsteady flow Bernoulli energy equation:
Figure BDA0003485430910000092
in the formula: y isIn2,mA pressure measuring pipe water head which is an outlet node of the water inlet channel 2; the flow rate of the outlet node of the water inlet channel 2; a. theIn2,mThe flow area of the outlet node of the water inlet channel 2; the local head loss coefficient of water entering the distribution pool from the water inlet channel 2-M.
… … (energy conservation equation of the end node from the water inlet channel 3 to the water inlet channel M-1 and the distribution pool)
The water coming from the water inlet channel M enters the distribution pool, and the energy conservation equation of the last node of the water inlet channel M and the distribution pool can be obtained by the unsteady flow Bernoulli energy equation:
Figure BDA0003485430910000101
in the formula: y isInM,mA pressure measuring pipe water head of an outlet node of the water inlet channel M; qInM,mThe flow of an outlet node of the water inlet channel M is obtained; a. theInM,mThe flow area of an outlet node of the water inlet channel M is shown; zetaInMThe local head loss coefficient of water entering the distribution pool for the water in the water inlet channel M;
(II) energy conservation of the water outlet system:
the energy conservation equations of the water outlet channel 1, the water outlet channels 2 and … … and the water outlet channel N are as follows:
the water in the distribution pool enters the water outlet channel 1, and an energy conservation equation of the inlet nodes of the distribution pool and the water outlet channel 1 can be obtained by a non-constant flow Bernoulli energy equation:
Figure BDA0003485430910000102
in the formula: y isOut1,0A pressure measuring pipe water head of an inlet node of the water outlet channel 1; qOut1,0Is the flow of the inlet node of the water outlet channel 1; a. theOut1,0The flow area of an inlet node of the water outlet channel 1; zetaOut1Is the local head loss coefficient of water entering the water outlet channel 1.
The water in the distribution pool enters the water outlet channel 2, and the energy conservation equation of the inlet nodes of the distribution pool and the water outlet channel 2 can be obtained by the unsteady flow Bernoulli energy equation
Figure BDA0003485430910000103
In the formula: y isOut2,nA pressure measuring pipe water head of an inlet node of the water outlet channel 2; qOut2,nFor discharging water channelFlow at the inlet node of lane 2; a. theOut2,nThe flow area of the inlet node of the water outlet channel 2; zetaOut2Is the local head loss coefficient of water entering the water outlet channel 2. The computing nodes of the outlet channel 2 are encoded from downstream to upstream.
… … (energy conservation equation of the end node from the channel 3 to the channel M-1 and the distribution pool)
The water in the distribution pool enters the water outlet channel N, and an energy conservation equation of the inlet nodes of the distribution pool and the water outlet channel N can be obtained by a non-constant flow Bernoulli energy equation:
Figure BDA0003485430910000111
in the formula: y isOutN,nA pressure measuring pipe water head of the N inlet nodes of the water outlet channel; qOutN,nThe flow rate of the inlet node of the water outlet channel N is obtained; a. theOutN,nThe flow area of the inlet node of the water outlet channel N is shown; zetaOutNThe local head loss coefficient of water entering the water outlet channel N. The computing nodes of the water outlet channel N are coded from downstream to upstream.
And (III) conservation of mass of the distribution pool:
the increment of the water body of the distribution pool is equal to the sum of inflow, outflow and overflow, and the mass conservation equation is as follows:
Figure BDA0003485430910000112
in the formula: a. the0For the plane area of the distribution basin, m2；QwIs the flow of the spillway, m3S, the calculation formula is
Figure BDA0003485430910000113
In the formula: mu is a flow coefficient; b iswIs the weir width, m; hwIs the weir elevation, m.
(IV) equation conversion:
for the water inlet channel 1, it can be obtained from the formula (7.1):
Figure BDA0003485430910000114
formula (11) can be converted to using the newton-simpson method:
FIn10+eIn1ΔyIn1,m+aIn1ΔQIn1,m+esΔys＝0 (12.1)
in the formula:
Figure BDA0003485430910000115
Figure BDA0003485430910000116
Δysis the increment of the water level of the water distribution tank.
Other water inlet channel equations may be converted in a similar manner.
From the formula (8.1):
Figure BDA0003485430910000117
formula (13) can be converted to using the newton-simpson method:
FOut10+eOut1ΔyOut1,0+aOut1ΔQOut1,0+esΔys＝0 (14.1)
in the formula:
Figure BDA0003485430910000121
Figure BDA0003485430910000122
other outlet channel equations may be converted in a similar manner.
For the mass conservation equation of the distribution pool, the mass conservation equation is obtained by integrating and taking second-order approximation by the formula (9):
Figure BDA0003485430910000123
Figure BDA0003485430910000124
in the formula: Δ t is the time step; the suffix 0 denotes the value of the physical quantity at the preceding time step.
Formula (15) can be converted to using the newton-simpson method:
Figure BDA0003485430910000125
in the formula:
Figure BDA0003485430910000126
Figure BDA0003485430910000127
Figure BDA0003485430910000128
calculation of other nodes:
the continuity equation and momentum equation of one-dimensional unsteady flow of the open channel are as follows:
Figure BDA0003485430910000129
Figure BDA00034854309100001210
in the formula: a is the flow area, m2(ii) a t is a time variable, s; q is the flow，m3S; x is a space variable, m; q is the lateral flow per channel length, m3S; beta is a correction coefficient introduced by uneven cross-section flow velocity distribution; g is the acceleration of gravity, m2S; h is water depth m; s0Is a bottom slope of a riverbed; sfFor the friction specific reduction, the calculation formula is as follows:
Sf＝Q|Q|/K2 (22)
in the formula: k is the flow modulus,
Figure BDA0003485430910000131
n is the roughness of the channel; r is hydraulic radius, m. With the Preissmann implicit format, the continuity and momentum equations are discretized as:
Figure BDA0003485430910000132
Figure BDA0003485430910000133
in the formula: y is the water surface elevation; psiRAre spatial coefficients and are not necessarily the same as ψ.
After the continuity equation (23) is substituted, the result is:
a2j+1Δhj+b2j+1ΔQj+c2j+1Δhj+1+d2j+1ΔQj+1＝D2j+1 (25)
in the formula:
Figure BDA0003485430910000134
b2j+1＝-θ/Δx；
Figure BDA0003485430910000135
d2j+1＝θ/Δx；
Figure BDA0003485430910000136
after the momentum equation (24) is substituted, the following results are obtained:
e2j+2Δhj+a2j+2ΔQj+b2j+2Δhj+1+c2j+2ΔQj+1＝D2j+2 (26)
in the formula:
Figure BDA0003485430910000137
Figure BDA0003485430910000138
Figure BDA0003485430910000139
Figure BDA0003485430910000141
Figure BDA0003485430910000142
boundary conditions:
there are three common boundary conditions:
a.F＝h-h(t)＝0
b.F＝Q-Q(t)＝0
c.F＝Q-f(h)＝0
for class a boundaries, water depth is a function of time; for class b boundaries, traffic is a function of time; for class c boundaries, the flow is a function of the water depth. For example, the downstream of the open channel is a wide top weir, and the flow water level relationship is as follows:
Figure BDA0003485430910000143
in the formula: mu is a flow coefficient; b is the weir top width m; h is weir head, m.
The three types of boundary conditions can be converted into the following conditions by using a Newton-Simpson formula:
FhΔh+FQΔQ＝-F0
for the case of a type a boundary condition,
Figure BDA0003485430910000144
for the case of a boundary condition of the b-type,
Figure BDA0003485430910000145
for the case of a type c boundary condition,
Figure BDA0003485430910000146
discretizing nodes in the channel by a Preissmann four-point implicit difference, and linearizing boundary conditions by a Newton-Simpson formula, wherein a matrix form of the equation is as follows:
AX＝D (31)
in the formula:
Figure BDA0003485430910000151
coefficient b0、c0And D0Determined by channel entry boundary conditions, b0＝Fh、c0＝FQAnd D0＝-F0；a2K-1、b2K-1And D2K-1Determined by the channel exit boundary conditions, a2K-1＝Fh、b2K-1＝FQAnd D2K-1＝-F0。
The coefficient matrix A of the nonlinear equation set is in a strip shape, non-zero elements of the coefficient matrix A are all located near a diagonal line, and the equation set can be solved by adopting a double-scanning method. Let coefficient b be assumed0Not equal to 0, the equation is transformed by using a elimination method:
X＝BX+P (1)
in the formula:
Figure BDA0003485430910000152
each element is calculated by the following recursion formula:
Figure BDA0003485430910000153
Figure BDA0003485430910000154
Figure BDA0003485430910000161
Figure BDA0003485430910000162
since the matrix B of the linear equation set is an upper triangular matrix with 0 element on the diagonal, the solution is recursively performed by using a back-substitution process of the following formula:
Figure BDA0003485430910000163
the specific process of numerical solution can be described as (the flow is shown in fig. 2):
step 1, obtaining increment correlation. And calculating the elements of a matrix B and a column vector P of the inlet water 1, the inlet water 2, the inlet water … …, the inlet water M, the outlet water 2, the outlet water … … and the outlet water N by using the elimination process of a double-sweep method, and obtaining the correlation between the flow increment and the water level increment of the end node, wherein the equation quantity is M + (N-1).
And 2, converting and integrating. All the water inlet, the water outlet and the water level of the distribution pool meet the energy conservation equation, and the dispersion is carried out by utilizing a Newton-Simpson method, wherein the equation quantity is M + N; meanwhile, the mass conservation equation is also satisfied, integration and second-order approximation are taken, and the equation quantity is 1.
And 3, deducing the correlation between the flow increment of the inlet node of the water channel 1 and the water level increment. For a certain iteration, the unknowns include: the flow increment and the water level increment of inlet water 1, inlet water 2, … …, inlet water M, outlet water 1, outlet water 2, … … and outlet water N, and the water level increment of a distribution pool are 2(M + N) +1 in total; the equation quantity is 2(M + N), and the correlation between the flow increment and the water level increment of the inlet node of the water channel 1 can be obtained through derivation.
And 4, solving the flow increment and the water level increment of all the nodes of the water outlet channel 1 by back substitution.
And 5, solving the flow increment and the water level increment of the outlet node of the water inlet channel and the inlet node of the water outlet channel and the water level increment of the distribution pool.
And 6, solving the flow increment and the water level increment of other nodes of each channel in a back substitution manner.
And 7, calculating the flow and the water level of each node.
When the flow increment and the water level increment of the calculation node are smaller than the set error, the calculation of the current time step is finished, the upstream boundary and the downstream boundary are updated, and the simulation calculation of a new time step is started; otherwise, starting a new iteration step by using the new flow and the new water level until the precision requirement is met.
In practice, there is another special case that some inlet water or outlet water flows under pressure. At this time, the solution can be carried out by adopting a narrow slit method or other methods which can be used for changing the pressure into the equivalent pressureless method.
Calculation example:
to further illustrate the method of this embodiment, a water distribution hub with "one inlet, two outlets, and one overflow (discharge)" is shown in fig. 3 for specific description, wherein the water inlet channel is named as channel 1, and the two water outlet channels are named as channels 2 and 3, respectively, for convenience of description. The water from channel 1 enters the distribution pool, and is distributed to channel 2 and channel 3 after being controlled by gate, and overflow channel or emptying pipe is set to avoid overflow. The spillway and the emptying pipe are all boundaries of relation between water level and flow, and the spillway is used for analysis in the embodiment.
The control equation:
the water coming from the channel 1 enters the distribution pool, and the energy conservation equation of the last node of the channel 1 and the distribution pool can be obtained by the unsteady flow Bernoulli energy equation:
Figure BDA0003485430910000171
in the formula: y is1,mA piezometer tube water head m of a channel 1 end node; q1,mIs the flow of channel 1 end node, m3S; g is the acceleration of gravity, m/s2；A1,mIs the flow area, m, of the channel 1 end node2；ysA pressure measuring pipe water head m of the distribution pool; zeta1The loss coefficient of the local water head of water entering the distribution pool comprises section change, a water outlet, a control gate and the like. Since the cross-sectional area of the distribution basin is generally much greater than the cross-sectional area of the channel, the flow head of the distribution basin is negligible.
The water in the distribution pool enters the channel 2, and an energy conservation equation of the distribution pool and the first node of the channel 2 can be obtained by a non-constant flow Bernoulli energy equation:
Figure BDA0003485430910000172
in the formula: y is2,nA piezometer tube water head m of a channel 2 head node; q2,nIs the flow of the channel 2 head node, m3/s；A2,nIs the flow area of the channel 2 head node, m2；ζ2The local head loss coefficient of water entering the channel 2 comprises section change, a water inlet, a control gate and the like. The compute nodes of channel 2 are encoded from downstream to upstream.
The water in the distribution pool enters the channel 3, and an energy conservation equation of the distribution pool and the first node of the channel 3 can be obtained by a non-constant flow Bernoulli energy equation:
Figure BDA0003485430910000173
in the formula: y is3,0A piezometer tube water head m of a channel 3 head node; q3,0Flow of channel 3 head node, m3/s；A3,0Is the flow area of the channel 3 head node, m2；ζ3The local head loss coefficient of water entering the channel 3 comprises section change, a water outlet, a control gate and the like.
The increment of the water body of the distribution pool is equal to the sum of inflow, outflow and overflow, and the mass conservation equation is as follows:
Figure BDA0003485430910000181
in the formula: a. the0For the plane area of the distribution basin, m2；QwIs the flow of the spillway, m3And/s, the calculation formula is as follows:
Figure BDA0003485430910000182
in the formula: mu is a flow coefficient; b iswIs the weir width, m; hwIs the weir elevation, m.
Solving an algorithm:
obtained by the formula (1 a):
Figure BDA0003485430910000183
formula (6a) can be converted to using the newton-simpson method:
F10+e1Δy1,m+a1ΔQ1,m+esΔys＝0(7a)
in the formula:
Figure BDA0003485430910000184
Δ represents the increment of the corresponding physical quantity in a certain iteration step;
Figure BDA0003485430910000185
obtained by the formula (2 a):
Figure BDA0003485430910000186
formula (8a) can be converted to using the newton-simpson method:
F20+e2Δy2,n+a2ΔQ2,n+esΔys＝0 (9a)
in the formula:
Figure BDA0003485430910000187
Figure BDA0003485430910000188
obtained by the formula (3 a):
Figure BDA0003485430910000191
formula (10a) can be converted to using the newton-simpson method:
F30+e3Δy3,0+a3ΔQ3,0+esΔys＝0 (11a)
in the formula:
Figure BDA0003485430910000192
Figure BDA0003485430910000193
integrated and second order approximated by equation (4 a):
Figure BDA0003485430910000194
finishing to obtain:
Figure BDA0003485430910000195
in the formula: Δ t is the time step, s; the subscript 0 indicates the value at the time step preceding the physical quantity.
Formula (13a) can be converted to using the newton-simpson method:
F40+F4,ysΔys+F4,Q1,mΔQ1,m+F4,Q2,nΔQ2,n+F4,Q3,0ΔQ3,0＝0 (14a)
in the formula:
Figure BDA0003485430910000196
Figure BDA0003485430910000197
Figure BDA0003485430910000198
the entrance to channel 1 is usually the flow boundary, which is satisfied by the vanishing process of the double sweep method by the last node:
ΔQ1,m＝U1,2m-2Δy1,m+P1,2m-2 (15a)
in the formula: u shapei,j、Pi,jIs a double sweep coefficient.
When the outlet of the channel 2 is a water level boundary or a water level-flow relation, the elimination element from the outlet to the inlet direction can be obtained:
Δy2,n＝U2,2n-2ΔQ2,n+P2,2n-2 (16a)
obtained by the formula (7 a):
Figure BDA0003485430910000201
formula (17a) is substituted for formula (15 a):
Figure BDA0003485430910000202
obtained by the formula (9 a):
Figure BDA0003485430910000203
substituting formula (19a) into formula (16a) yields:
Figure BDA0003485430910000204
formulae (18a) and (20a) are substituted for formula (14 a):
Figure BDA0003485430910000205
in the formula:
Figure BDA0003485430910000206
Figure BDA0003485430910000207
formula (21a) is substituted into formula (11 a):
b3,0Δy3,0+c3,0ΔQ3,0＝D3,0 (22a)
in the formula: b3,0＝e3；
Figure BDA0003485430910000208
The program for carrying out numerical solution on the whole water delivery system is as follows:
(1) calculating the matrix B of the water inlet channel and the channel water outlet 1 and the element U of the column vector P by using the elimination process of the double-scanning method1,i、W1,i、P1,i、U2,j、W2,jAnd P2,j(i＝0,1,...,2m-2，j＝0,1,...,2n-2)；
(2) Determining the double sweep coefficient of the channel 1 entrance boundary using equation (22a), b3,0、c3,0And D3,0；
(3) Solving the water depth and flow increment of the channel 3 by a double-sweeping method;
(4) Δ y is solved sequentially by equations (21a), (20a), (19a), (18a) and (17a)s、ΔQ2,n、Δy2,n、ΔQ1,mAnd Δ y1,m；
(5) And solving the water depth and flow increment of the channel 1 and the channel 2 by using the back substitution process of the double-sweeping method.
Application example:
one diversion works transfers water to another area through the canal tunnel 1, as shown in fig. 4, the middle distribution pool distributes water to 2 canal tunnels, which are then transported to the receiving area.
The water of the hydro-junction is discharged into a water delivery channel tunnel 1 and then enters a distribution pool, and the designed flow is 70m3And s. The distribution tank is a rectangular tank body with the length of 80m, the width of 46m and the volume of 2.8 ten thousand m3(ii) a The water in the water distribution pond enters the water conveying channel tunnel 2 and the water conveying channel tunnel 3 after being regulated, and flows out through the overflow weir when the water level is high, as shown in figure 4.
The water distribution flow of the water conveying channel tunnel 2 and the water conveying channel tunnel 3 is 47m3/s+23m3S and 40m3/s+30m3Two cases are used per second. The water distribution flow is 47m3/s+23m3The/s is switched to 40m3/s+30m3When the pressure is measured per second, the opening of the canal tunnel 2 gate is reduced to 2.1m from full opening, the opening of the canal tunnel 3 gate is reduced to full opening from 1.7m, the action speed is 0.2m/min, and the hydraulic transition process characteristics of a distribution pool and a distribution project are shown in figure 5. The target flow rate of 40m is reached at the positions of 5km and 10km of the channel 2 after the gate moves for 103min and 136min respectively3S; the water storage tank reaches the target flow of 30m after the gate moves for 15min3And s. The water level of the water distribution pool is stably reduced to 258.74m from 258.88m, the water level of the water after the canal tunnel 2 gate is reduced to 257.78m from 258.33m, and the water level of the water storage pool is increased to 258.10m from 256.79 m. The hydraulic transition process characteristics of the canal tunnel 1 upstream of the distribution basin are shown in fig. 6. In the process of adjusting the flow of water distribution, water is distributedThe flow and water level of the canal tunnel 1 in the range of 15km upstream of the pond are changed. The flow at the upstream 5km is increased to 70.14m3S, then slowly returning to 70.00m3And/s, the water level is reduced from 260.84m to 260.79m, and the change amplitude of the flow and the water level is reduced along with the increase of the distance. In the water distribution flow adjusting process, the flow of the channel tunnel 1, the channel tunnel 2 and the channel tunnel 3 is stably transited, the open flow tunnel does not have a full flow phenomenon, and the water distribution pool does not overflow.
According to an example, in the process of adjusting the water distribution flow, the on-way flow and the water level of the water adjusting project can be changed; similarly, the adjustment of the water diversion project can affect the water supply process, the available water quantity and the like of the user. If the water distribution hub with a limited volume is used as a normal water level boundary, the hydraulic transition process of the whole water delivery system cannot be analyzed, and the real flow, water level and pressure change characteristics are difficult to quantify. The impact on the engineering operation safety and scheduling scheme compilation needs specific problems and specific analysis.
Example two:
the embodiment is an improvement of the above embodiment, and is a refinement of the above embodiment about the water inlet pipe and the water outlet pipe, where the water inlet channel or the water outlet channel described in this embodiment is flowing under pressure, and the solution is performed by using a narrow slit method, where the width of the slit is:
B＝gA/a2 (18)
in the formula: b is the gap width; a is the cross section of pressure flow; and a is the water shock wave speed.
The narrow slit method described in this embodiment is used for solving, that is, assuming that a very narrow slit is formed at the top of the pipeline, the sectional area of the pipeline is not increased, the hydraulic radius is not increased, the method is very simple, and very accurate calculation can be achieved.
Finally, it should be noted that the above is only for illustrating the technical solution of the present invention and not for limiting, although the present invention is described in detail with reference to the preferred arrangement, it should be understood by those skilled in the art that the technical solution of the present invention (such as the form of the water distribution system, the application of various formulas, the sequence of steps, etc.) can be modified or equivalently replaced without departing from the spirit and scope of the technical solution of the present invention.

Claims (2)

1. A numerical simulation method of a hydraulic control of a water distribution hub, the analyzed water distribution hub of the method comprising: m water inlet channels, a distribution pool provided with an overflow channel and N water outlet channels; setting m +1 computing nodes along each water inlet channel, and coding the computing nodes of each water inlet channel from upstream to downstream; setting n +1 computing nodes along the 1 st water outlet channel, and coding the computing nodes of the water outlet channel 1 from upstream to downstream; setting N +1 computing nodes along the 2 nd to N th water outlet channels, and coding the computing nodes of the water outlet channels 2 to N from downstream to upstream; namely: the method is characterized in that the tail end computing nodes of the M water inlet channels, the tail end computing nodes of the 2-N water outlet channels and the head end computing nodes of the 1 water outlet channel are all computing nodes at the joint of the water inlet channels or the water outlet channels and the distribution pool, and the method comprises the following steps:
step 1, obtaining an increment correlation: calculating elements of a matrix B and a column vector P of the water inlet channel 1, the water inlet channel 2, the water inlet channel … …, the water inlet channel M, the water outlet channel 2, the water outlet channel … … and the water outlet channel N by using a elimination process of a double-sweep method, and obtaining a correlation relation between a flow increment and a water level increment of a final node, wherein the equation number is M + N-1; the calculation formula is as follows:
X＝BX+P (1)
in the formula:
Figure FDA0003485430900000011
delta Q is the flow increment of the current iteration step, the lower corner mark K represents the number of a calculation node, and the number of the lower corner mark is 0-m for a water inlet channel; for the water outlet channel, the number of the lower corner mark is 0-n; delta h is the water depth increment of the current iteration step; u, W, P is the double sweep coefficient; u, W, P, the lower corner mark represents the row number change of the matrix, and the number of the water inlet channel is 0-2 m < -1 >; numbering the water outlet channels to be 0-2 n-1;
each element is calculated by the following recursion formula:
Figure FDA0003485430900000012
Figure FDA0003485430900000013
Figure FDA0003485430900000021
in the formula: c. b, D, a and e are coefficients; j is a node number, and j is 1,2, … …, K-2;
for the water inlet channel 1, the flow increment and the water quantity increment of the terminal computing node satisfy the following relational expression:
ΔQIn1,m＝UIn1,2m-2ΔyIn1,m+PIn1,2m-2 (5.1)
for water inlet channels 2-M, the flow increment and the water quantity increment of the terminal computing node satisfy the following relational expression:
ΔQIn2,m＝UIn2,2m-2ΔyIn2,m+PIn2,2m-2 (7.2)
……
ΔQInM,m＝UInM,2m-2ΔyInM,m+PInM,2m-2 (5.M)
for the water outlet channels 2-N, the flow increment and the water quantity increment of the tail end computing node satisfy the following relational expression:
ΔQOut2,n＝UOut2,2n-2ΔyOut2,n+POut2,2n-2 (6.2)
……
ΔQOutN,n＝UOutN,2n-2ΔyOutN,n+POutN,2n-2 (6.N)
thus, M + N-1 values of delta Q for the flow rate and the water amount are obtainedIn1,m、ΔyIn1,m、……、ΔQInM,m、ΔyInM,m、ΔQOut2,n、ΔyOut2,n、……、ΔQOutN,n、ΔyOutN,nAn equation of the correlation; in the lower corner markThe water channel Out represents a water outlet channel, the following numbers represent channel numbers, and the numbers after commas represent calculation node numbers;
step 2, conversion and integration: all the water inlet, the water outlet and the water level of the distribution pool meet the energy conservation equation, and the dispersion is carried out by utilizing a Newton-Simpson method, wherein the equation quantity is M + N; meanwhile, the mass conservation equation is also met, integration is carried out, second-order approximation is carried out, and the equation quantity is 1;
the energy conservation equation of the outlet node of the water inlet channel 1 and the distribution pool is as follows:
Figure FDA0003485430900000022
in the formula: y isIn1,mA pressure measuring pipe water head which is an outlet node of the water inlet channel 1; qIn1,mThe flow rate of an outlet node of the water inlet channel 1; g is the acceleration of gravity; a. theIn1,mThe flow area of an outlet node of the water inlet channel 1; y issA piezometer tube water head of the distribution pool; zetaIn1The local head loss coefficient of water entering the distribution pool for the water in the water inlet channel 1;
energy conservation equation of 2-M outlet nodes of the water inlet channel and the distribution pool:
Figure FDA0003485430900000023
……
Figure FDA0003485430900000031
in the formula: y isIn2,m、……、yInM,mA pressure measuring pipe water head of 2-M outlet nodes of the water inlet channel; qIn2,m、……、QInM,mThe flow rate of 2-M outlet nodes of the water inlet channel; g is the acceleration of gravity; a. theIn2,m、……、AInM,mThe flow area of the outlet node of the water inlet channel is 2-M; zetaIn2、……、ζInMIs a water inlet channel 2-MThe local head loss coefficient of the water entering the distribution pool;
energy conservation equation of the inlet node of the distribution pool and the water outlet channel 1:
Figure FDA0003485430900000032
in the formula: y isOut1,0A pressure measuring pipe water head of an inlet node of the water outlet channel 1; qOut1,0Is the flow of the inlet node of the water outlet channel 1; a. theOut1,0The flow area of an inlet node of the water outlet channel 1; zetaOut1The local head loss coefficient of water entering the water outlet channel 1;
energy conservation equation of the inlet nodes 2-N of the distribution pool and the water outlet channel:
Figure FDA0003485430900000033
……
Figure FDA0003485430900000034
in the formula: y isOut2,n、……、yOutN,nA pressure measuring pipe water head with 2-N inlet nodes of the water outlet channel; qOut2,n、……、QOutN,nThe flow rate of the inlet node of the water outlet channel is 2-N; a. theOut2,n、……、AOutN,nThe overflow area of the inlet node of the water outlet channel is 2-N; zetaOut2、……、ζOutNThe local head loss coefficient of water entering the water outlet channel is 2-N;
the mass conservation equation of the distribution pool is as follows:
Figure FDA0003485430900000035
in the formula: a. the0The plane area of the distribution pool; qwIs the flow of the spillwayThe calculation formula is as follows:
Figure FDA0003485430900000036
in the formula: mu is a flow coefficient; b iswIs the weir width; hwIs the weir elevation;
and (3) equation conversion:
for the water inlet channel 1, it can be obtained from the formula (7.1):
Figure FDA0003485430900000041
by the Newton-Simpson method, formula (11) is converted to:
FIn10+eIn1ΔyIn1,m+aIn1ΔQIn1,m+esΔys＝0 (12.1)
in the formula:
Figure FDA0003485430900000042
Figure FDA0003485430900000043
Δysis the increment of the water level of the water distribution tank;
for water inlet channels 2-M, the following can be obtained:
FIn20+eIn2ΔyIn2,m+aIn2ΔQIn2,m+esΔys＝0 (12.2)
……
FInM0+eInMΔyInM,m+aInMΔQInM,m+esΔys＝0 (12.M)
in the formula:
Figure FDA0003485430900000044
Figure FDA0003485430900000045
Figure FDA0003485430900000046
Figure FDA0003485430900000047
thus, M values of Δ y are obtaineds、ΔQIn1,m、ΔyIn1,m、……、ΔQInM,m、ΔyInM,mThe equation of (c);
for the water outlet channel 1, the following formula (8.1) is obtained:
Figure FDA0003485430900000048
using the Newton-Simpson method, formula (13) is converted to:
FOut10+eOut1ΔyOut1,0+aOut1ΔQOut1,0+esΔys＝0 (14.1)
in the formula:
Figure FDA0003485430900000049
Figure FDA00034854309000000410
for the water outlet channels 2-N, obtaining
FOut20+eOut2ΔyOut2,n+aOut2ΔQOut2,n+esΔys＝0 (14.1)
……
FOutN0+eOutNΔyOutN,n+aOutNΔQOutN,n+esΔys＝0 (14.N)
In the formula:
Figure FDA0003485430900000051
Figure FDA0003485430900000052
Figure FDA0003485430900000053
Figure FDA0003485430900000054
for the mass conservation equation of the distribution pool, the mass conservation equation is obtained by integrating and taking second-order approximation by the formula (9):
Figure FDA0003485430900000055
Figure FDA0003485430900000056
in the formula: Δ t is the time step; suffix 0 represents the value of the physical quantity at the previous time step;
formula (15) can be converted to using the newton-simpson method:
Figure FDA0003485430900000057
in the formula:
Figure FDA0003485430900000058
Figure FDA0003485430900000059
Figure FDA00034854309000000510
thus, 1 for Δ y can be obtaineds、ΔQIn1,m、ΔyIn1,m、……、ΔQInM,m、ΔyInM,m、ΔQOut1,0、ΔyOut1,0、ΔQOut2,n、ΔyOut2,n、……、ΔQOutN,n、ΔyOutN,nThe equation of (c);
and 3, deducing the correlation between the flow increment and the water level increment of the inlet node of the water channel 1: for the current iteration step, the unknowns include: flow increment and water level increment, delta Q, of the water inlet channel 1, the water inlet channel 2, … …, the water inlet channel M, the water outlet channel 1, the water outlet channel 2, … … and the water outlet channel NIn1,m、ΔyIn1,m、……、ΔQInM,m、ΔyInM,m、ΔQOut1,0、ΔyOut1,0、ΔQOut2,n、ΔyOut2,n、……、ΔQOutN,n、ΔyOutN,nWater level increment of distribution reservoir, Δ ysIn total, 2(M + N) + 1; the quantity of the equation is 2(M + N), and the flow increment delta Q of the inlet node of the water channel 1 can be obtained through derivationOut1,0Increment of water level by delta yOut1,0The correlation of (2);
and 4, solving the flow increment and the water level increment of all the nodes of the water outlet channel 1 by back substitution: solving the flow increment and the water level increment of all the nodes of the water outlet channel 1 by utilizing a back substitution process, wherein the calculation formula is as follows:
Figure FDA0003485430900000061
step 5, solving the flow increment and the water level increment of the outlet node of the water inlet channel and the inlet node of the water outlet channel and the water level increment of the distribution pool: solving the outlet nodes of the water inlet channel 1, the water inlet channel 2, … … and the water inlet channel M, the flow increment and the water level increment of the inlet nodes of the water outlet channel 2, … … and the water outlet channel N and the water level increment of the distribution pool; utilizing the flow increment delta Q of the inlet node of the water outlet channel 1 obtained in the step 4Out1,0Increment of water level by delta yOut1,0Substituting the above-established equation to determine the flow increment and water level increment, delta Q, of the inlet nodes of the inlet water 1, the inlet water 2, … … and the inlet water M, and the inlet nodes of the outlet water 2, … … and the outlet water NIn1,m、ΔyIn1,m、……、ΔQInM,m、ΔyInM,m、ΔQOut2,n、ΔyOut2,n、……、ΔQOutN,n、ΔyOutN,nWater level increment of distribution reservoir, Δ ys；
And 6, solving the flow increment and the water level increment of other nodes of each channel in a back substitution way: respectively solving the flow increment and the water level increment of all nodes of the water inlet channel 1, the water inlet channel 2, the water inlet channel … …, the water inlet channel M, the water outlet channel 2, the water outlet channel … … and the water outlet channel N in a back-substitution mode, wherein the calculation formula is as follows:
Figure FDA0003485430900000062
and 7, calculating the flow and the water level of each node: calculating the flow and the water level of all nodes of the water inlet channel 1, the water inlet channel 2, … …, the water inlet channel M, the water outlet channel 1, the water outlet channel 2, … … and the water outlet channel N in the current iteration step and the water level of the distribution pool in the current iteration step; the flow rate is equal to the value of the previous iteration step plus the flow increment, and the water level is equal to the value of the previous iteration step plus the water level increment.
2. The method of claim 1, wherein if the water inlet channel or the water outlet channel is pressurized to flow, the solution is performed by using a narrow slit method, and the width of the slit is:
B＝gA/a2 (19)
in the formula: b is the gap width; a is the cross section of pressure flow; and a is the water shock wave speed.
CN202210079779.5A 2022-01-24 2022-01-24 Numerical simulation method for hydraulic control of water distribution hub Pending CN114460981A (en)

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