CN112052545A - Urban surface runoff and pipe network confluence coupling method based on cellular automaton - Google Patents
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Abstract
The invention discloses an urban surface runoff and pipe network confluence coupling method based on a cellular automaton. According to the method, firstly, surface production confluence calculation is carried out to obtain a change process of inflow flow of a rainwater wellhead along with time as a boundary condition of pipe network confluence calculation, then, pipe network confluence calculation is carried out to obtain current time step pipeline flow and a node water head, current time node net flow is determined according to three different flow processes of surface inflow, node overflow and backwater backflow in the rainfall process, and a pipeline flow basic equation and a drainage pipe network node control equation are substituted to obtain the next time pipeline flow and the node water head. The method disclosed by the invention couples the pipeline confluence with the surface runoff process based on the cellular automata, realizes the dynamic simulation of the water exchange between the surface and the pipe network, and is more consistent with the real urban rainfall runoff process.
Description
Technical Field
The invention relates to the field of urban hydrology and pipe network drainage, in particular to an urban surface runoff and pipe network confluence coupling method based on a cellular automaton.
Background
Along with the rapid development of urbanization, the impervious surface of a city is continuously enlarged, and in addition, the drainage capability of a previously built urban drainage system is insufficient, urban waterlogging is easily formed when a rainstorm event occurs, so that social life and economic production are influenced. The urban rainfall flood model can simulate the drainage condition of an urban pipe network under a rainfall event, and is one of important decision tools for planning and constructing the urban pipe network. The existing urban rainfall flood model is mainly a one-dimensional drainage pipe network model, is difficult to simulate the two-dimensional motion of overflow water on the ground surface under the condition of insufficient drainage capacity, and cannot determine the influence range of waterlogging.
The cellular automaton is a grid dynamic model with discrete time, space and state, has the capability of simulating the space-time evolution process of a complex system, and has certain advantages in the surface runoff process simulation under the urban complex terrain condition. The underground pipe network drainage model is coupled with the urban surface runoff model based on the cellular automata, so that the exchange of the ground underground water quantity is realized, the urban waterlogging process is simulated, and a reference can be provided for the planning and design of the urban underground drainage pipe network.
Therefore, the method takes the water flow ground-ground underground movement process under the rainfall event period into consideration, constructs a ground surface cellular geographical scene, generalizes an underground urban drainage pipe network, takes a rainwater wellhead as a ground surface underground water volume exchange node, realizes the coupling calculation of the convergence of the surface runoff and the underground pipe network based on the cellular automata, simulates the real urban rainfall runoff process under the rainstorm event, determines the urban inland inundation generation time and the surface ponding submergence range, and has important guiding significance for urban planning and pipe network design.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a cellular automaton-based urban surface runoff and pipe network confluence coupling method, which can better describe surface inflow, node overflow and backwater backflow processes in the urban rainfall process and better accord with the real rainfall runoff condition.
The technical scheme is as follows: the invention relates to an urban surface runoff and pipe network confluence coupling method based on a cellular automaton, which mainly comprises the following steps:
(1) constructing a surface cellular geographic scene, obtaining the type and the elevation of an underlying surface of each cell and the rainfall changing along with time according to the type of the underlying surface of a research area, the DEM elevation and the rainfall changing along with time, and defining the size, the neighborhood relationship and the model boundary of the cells of the model geographic scene;
(2) generalizing an urban underground drainage pipe network, obtaining drainage pipe network pipeline parameters, node parameters and drainage outlet positions according to the construction condition of a drainage pipe network in a research area, and taking a rainwater wellhead as an exchange node of surface and pipe network water flow;
(3) use the rainwater well head as coupling node, carry out surface runoff and pipe network and converge the coupling and calculate, include: performing surface production confluence calculation to obtain a change process of inflow flow of a rainwater wellhead along with time as a boundary condition of pipe network confluence calculation; performing pipe network confluence calculation to obtain the pipeline flow and the node water head at the current time step, and determining the node net flow at the current moment according to three different processes of surface inflow, node overflow and water return backflow in the rainfall process; substituting the current pipeline flow, the node water head and the node net flow into a pipeline flow basic equation and a drainage network node control equation to obtain the next pipeline flow and the node water head, determining the node net flow, repeating the calculation until the total simulation time is reached, and finishing the calculation.
Preferably, the step (3) of performing surface production confluence calculation to obtain a time-dependent change process of inflow flow of the rainwater wellhead as a boundary condition of pipe network confluence calculation includes:
carrying out runoff yield calculation by using an initial damage and post-damage method to obtain the water depth of each cellular;
comparing the water levels of the central cell and the neighbor cells, eliminating the neighbor cells higher than the average water level, and determining the neighbor cells capable of transferring water quantity;
on the basis of determining the current and the flow direction, calculating the water quantity which can be transferred by the central cell in a time step by adopting a Manning formula, obtaining the potential maximum water quantity which can be transferred by the central cell to the neighbor cell according to the water level difference between the cells, and comparing the potential maximum water quantity with the potential maximum water quantity to obtain the real water quantity transferred by the central cell in the time step;
and calculating the flow of each neighbor cell flowing into the rainwater wellhead node by adopting a side contraction weir flow calculation formula, and summing to obtain the total flow of the earth surface flowing into the rainwater wellhead node.
Preferably, in the step (3), the pipeline flow and the node water head are calculated through a pipeline flow basic equation and a drainage pipe network node control equation; the finite difference form of the pipeline flow basic equation and the node control equation is expressed as follows:
wherein,
is the flow rate of the pipeline at the time t,
for the net traffic at the node at time t,
is the node water head at the moment t, delta t is the model time step length,
average flow velocity of the pipe, A1、A2Respectively are the section areas of the pipeline at the upstream and downstream of the node, Delta A is the average section area change value in a time step length, L is the length of the pipeline,
is the cross-sectional area of the widest part of the pipeline, g is the gravitational acceleration, H1、H2The water heads of the upstream and downstream nodes of the pipeline respectively, k is a loss coefficient,
is the average hydraulic radius, AskIs the node area.
Preferably, in the step (3), when the water current flows into the pipe network from the earth surface in the early rainfall period, the node net flow calculation method is as follows:
wherein,
the flow rate of the node surface inflow at the time t is calculated by adopting a side contraction weir flow calculation formulaThe sum of the incoming traffic of each neighbor cell,
and
the flow rates of the upstream pipeline and the downstream pipeline of the t-time node are respectively.
Preferably, in the step (3), when the pipe network water flow overflows the ground surface after the rainfall intensity is increased, the node net flow calculation mode is as follows:
when node cells transfer out water volume Volt trans_outLess than the amount Vol of water transferred into its neighbor cellst trans _inWhen the temperature of the water is higher than the set temperature,
wherein,
and
respectively the upstream and downstream pipeline flow of the t-time node;
when node cells transfer out water volume Volt trans_outThe volume Vol of water which is larger than the volume of water transferred by the neighbor cellst trans _inWhen the temperature of the water is higher than the set temperature,
wherein
Preferably, in the step (3), when the water flow enters the pipeline again in the late rainfall period, the node flow calculation mode is as follows: in the process of water return and backflow, when the water head of the node is higher than the elevation of the earth surface, calculating the net flow of the node according to the overflow process of the node; and (4) when the surface water is removed and the node water head is lower than the surface elevation, calculating the node net flow according to the surface inflow process.
Has the advantages that: compared with the prior art, the urban surface runoff and pipe network confluence coupling method based on the cellular automata has the following beneficial effects: 1. the cellular automaton theory is applied to the research of the urban rainfall runoff model, and the complex equation is replaced by the bottom-up modeling mode, so that the method is more favorable for analyzing and researching the urban hydrological process mechanism compared with the traditional lumped hydrological model. 2. The invention constructs an urban rainfall runoff model capable of dynamically simulating an earth surface runoff process, an overflow waterlogging process and a water-return backflow process based on a cellular automaton model coupled with an urban earth surface runoff and pipe network confluence model.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
FIG. 2 is a schematic diagram of cell boundary conditions in an embodiment of the present invention.
Fig. 3 is a diagram of a coupling node of a surface runoff model and a drainage network model in an embodiment of the invention.
Fig. 4 is a schematic diagram of the flow exchange of surface runoff and pipe network confluence at a node in the embodiment of the invention.
Fig. 5 is a schematic diagram of a rainfall runoff process simulation in an embodiment of the invention.
Detailed Description
As shown in fig. 1, an embodiment of the present invention discloses a method for coupling urban surface runoff and pipe network confluence based on a cellular automaton, which includes the following steps:
(1) and constructing a geographical scene of the earth surface cells, obtaining the type and the elevation of the underlying surface of each cell and the rainfall changing along with time according to the type of the underlying surface of the research area, the DEM elevation and the rainfall changing along with time, and defining the size, the neighborhood relation and the model boundary of the geographical scene model cells. The method specifically comprises the following steps:
(1.1) obtaining the type of the underlying surface of a research area and digital elevation Data (DEM) to construct a basic geographic scene of cells, obtaining the type (such as a road surface, a roof, a grassland and the like) and the elevation of the underlying surface of each cell, setting a boundary condition of a model and an outlet of the model, and defining the size of the cells, a Manning roughness coefficient, coordinates, a neighborhood relation, a time step length of the model and simulation duration. The boundary of the cells is set as shown in fig. 2, the neighborhood relationship of the cells in the invention is Moore type eight neighborhoods, and the boundary cells are set as the maximum value so as to ensure that the water quantity cannot enter.
(1.2) acquiring rainfall of the research area changing along with time, which can be a rainfall process under a real condition or a rainfall process under different conditions assumed according to flood control standards, and further acquiring the rainfall of each cellular at different moments.
(2) The method is characterized in that a generalized urban underground drainage pipe network obtains the outlet position, the pipeline length, the pipe diameter, the pipeline quantity, the node quantity and the position of the drainage pipe network according to the construction condition of the drainage pipe network in a research area, the rainwater well mouth is used as an exchange node of the earth surface and the pipe network water flow, and earth surface cells corresponding to the rainwater well mouth are used as node cells. The method specifically comprises the following steps:
(2.1) acquiring the information of the drainage pipe network in the research area, and acquiring parameters of the drainage pipe network, such as the length of the pipeline, the inner diameter of the pipeline, the gradient of the pipeline, the roughness of the pipeline, the number and the positions of nodes, the position of a drainage outlet and the like.
And (2.2) taking the cells where the rainwater wellheads are located as node cells for exchanging water flow of the earth surface and the pipe network, and calculating the water exchange of the earth surface and the pipe network by coupling the rainwater wellheads with the surface runoff model and the pipe network confluence model. The coupling of the pipe network to the surface at a node is schematically illustrated in fig. 3.
(3) The method comprises the steps of calculating the confluence coupling of surface runoff and a pipe network, carrying out surface production confluence calculation to obtain the change process of inflow flow of a rainwater wellhead along with time as the boundary condition of the pipe network confluence calculation, carrying out the pipe network confluence calculation to obtain the pipeline flow and the node water head at the current time step, determining the node net flow at the current time according to three different processes of surface inflow, node overflow and water return in the rainfall process, solving the pipeline flow, the node water head and the node net flow at the next time by a simultaneous pipeline flow equation and a node control equation, and repeating the calculation until the rainfall runoff process is finished. The method specifically comprises the following steps:
(3.1) performing surface production confluence calculation to obtain a change process of inflow flow of a rainwater wellhead along with time as a boundary condition of pipe network confluence calculation, and specifically:
(3.1.1) carrying out runoff yield calculation by using an initial loss and post loss method to obtain the water depth of each cellular: the initial loss and post-loss method simplifies infiltration into two parts of initial loss and post-loss, and the water loss from the beginning of rainfall to the occurrence of runoff is initial loss I0(ii) a The water loss after the runoff is the after-loss which is expressed by the average after-loss infiltration rate f and is mm/min; the net rain depth and net rain amount of each unit cell are calculated according to the following formula:
h＝X-I0-ftc-Xn
Vol＝0.001×h×A
in the formula, X is the total rainfall, mm; h is the water depth of each cell formed by X, mm; t is tcThe time for the super-osmotic flow lasts for min; xnThe rainfall is mm when the back damage stage is not over-seeping; a is the area of each cell, m2(ii) a Vol is the amount of water per cell, m3。
(3.1.2) judging the flow direction of the water flow: and comparing the water levels of the central cellular and the neighbor cellular, excluding the neighbor cellular higher than the average water level, and determining the neighbor cellular capable of transferring water quantity.
(3.1.3) performing surface confluence calculation: on the basis of determining the current and the flow direction, calculating the water quantity which can be transferred by the central cell in a time step by adopting a Manning formula, obtaining the potential maximum water quantity which can be transferred by the central cell to the neighbor cell according to the water level difference between the cells, and comparing the potential maximum water quantity with the potential maximum water quantity to obtain the real water quantity transferred by the central cell in the time step; the calculation formula is as follows:
in the formula, TiThe time required for transferring the water depth of the central cellular cell to the ith neighbor cellular cell is min; h is the depth of the central cell in water, mm; siThe water surface gradient between the central cell and the ith neighbor cell; n is the coefficient of Mannich roughness, s/m1/3(ii) a Δ t is the model time step, s; d is the distance between the central cell and the neighbor cell, m;
represents the amount of water transferred from the central cell to the i-th neighbor cell, m3；hi' denotes the water depth, mm, of the i-th neighbor cell after transfer.
(3.1.4) calculating the flow rate of the earth surface flowing into the rainwater well head: in the drainage system of the urban road, the flow of the side ditch is generally not more than 0.4m3The longitudinal slope is not more than 0.08, so the flow state of the water flow of the side ditch flowing into the rainwater inlet is weir flow, the side ditch corresponds to each neighbor cell of the rainwater wellhead, the water flow flows into the node cell neighbor cells, and the cell water flow with the water depth h' flows into the flow (q, m) of the rainwater inlet3And/s) adopting a side contraction weir flow calculation formula:
in the formula, the contraction coefficient is calculated by adopting an empirical formula, m is a weir flow coefficient, m is 0.375 according to weir flow calculation in drainage specifications, and B' is the width of a weir top water passing section; g is the acceleration of gravity, m2/s；H0As the total head height of the water flow, H0＝0.001×h′+v22g, m; v is the water flow velocity of the neighbor cells, m/s.
Obtaining the ith neighbor cellular water depth h 'of the node cellular at the time t according to surface confluence calculation'iThe ith neighbor cell at time tThe flow of the inflow rainwater wellhead node is calculated by adopting a side contraction weir flow formula to obtain qiThe total flow rate of the earth surface flowing into the rainwater well mouth is the sum q of the flow rates of all the neighbor cells flowing into the rainwater well mouthsum＝∑qi。
(3.2) calculating the convergence of the pipe network to obtain the change process of the pipeline flow and the node water head along with time, which specifically comprises the following steps:
(3.2.1) obtaining a basic equation of the pipeline flow and a control equation of the drainage pipe network node, and simultaneously solving the pipeline water flow and the node water head at each moment:
basic equation of flow in the pipeline:
the control equation of the drainage pipe network nodes is as follows:
wherein Q ispipeIs the flow rate of the pipeline, m3S; a is the water passing section area of the pipeline, m2；HpipeIs a pipeline static pressure water head m; t is time, s; x is the distance, m; k is a loss coefficient, and k is gn2(ii) a R is hydraulic radius, m; v is the flow velocity of water flow in the pipeline, m/s, and the use of an absolute value can ensure that the friction resistance is opposite to the direction of the water flow; hnodeIs the node head, m; qnodeIs the node net flow, m3/s；AskIs the node area, m2。
The basic equation of the pipeline flow and the node control equation are expressed in a finite difference form:
wherein H1、H2Is the water head of the upstream and downstream nodes of the pipeline, m; a. the1、A2Is the cross-sectional area, m, of the pipe upstream and downstream of the node2(ii) a Delta A is the average change value of the section area in a time step; l is the length of the pipeline, m;
is the average area of the water cross section of the pipeline, m2(ii) a When the pipeline is full of water flow, taking
The cross section area of the widest position of the pipeline;
is the average hydraulic radius, m;
is the average flow velocity of the pipe, m3/s；
Is the node net flow at time t, m3/s；
Is the node head at time t, m;
is the pipe flow at time t, m3/s。
(3.2.2) solving the equation set: according to a known initial nodal head
Net flow at node
Flow rate of pipeline
And (c) aInitial pipeline water head
In general, when t is 0, the pipeline flow and the water head, and the node flow and the water head are both 0, or the initial node water head and the pipeline flow are given according to the actual situation, but are known quantities, the initial conditions are substituted into the pipeline flow basic equation and the node control equation in the step (3.2.1), and each pipeline flow at the beginning of the next time step is solved
And individual nodal heads
And (4) calculating the net flow of the node by combining the flow processes of the nodes in different rainfall periods in the step (3.3)
Repeating the steps, and obtaining the node water head at the t moment through t/delta t time steps
And pipe flow Qt pipeThe calculation is repeated until the simulation is finished.
(3.3) calculating the net flow of the node: according to the three processes of the surface inflow process that the water flow of the pipe network flows into the pipe network from the surface in the early rainfall period, the node overflow process that the water flow of the pipe network overflows the surface after the rainfall intensity is increased and the water return reflux of the pipe network that the water flow of the late rainfall period reenters the pipeline, the net flow calculation modes of the nodes are different when the water flow is in different processes, and the method specifically comprises the following steps:
surface inflow process: in the early stage of rainfall, the drainage capacity of the drainage pipe network is greater than the drainage quantity, the node does not overflow and is in a surface inflow state, water flows into the rainwater well mouth from the surface and enters the underground pipe network, the node water head is lower than the node surface elevation (shown as (a) in figure 4), and then the node surface inflow quantity is obtained at the moment t according to the step (3.1)
Determining the flow of the upstream and downstream pipelines of the node according to the flow of each pipeline at the t moment obtained in the step (3.2)
And
and further acquiring node net flow:
and (3) node overflow process: when the rainfall is gradually increased, the node water head of the rainwater wellhead is gradually increased, the node overflows, when the node water head of the rainwater wellhead is higher than the surface elevation, the water quantity above the surface elevation of the node cellular is calculated according to the surface runoff calculation process based on the cellular automata in the steps (3.1.1) - (3.1.3), and when the water quantity Vol transferred out by the node cellular is increased graduallyt trans_outLess than the amount Vol of water transferred into its neighbor cellst trans_inTime appears as node inflow ((b) in fig. 4), and at time t, node earth surface inflow flow rate
Then, according to the step (3.2), the flow rates of the upstream pipeline and the downstream pipeline of the node are respectively obtained
And
and obtaining the node flow at the moment:
when node cells transfer out water volume Volt trans_outIs larger than the flow Vol transferred by the neighbor cellt trans _inTime, appear as node outgoing flow ((c) in FIG. 4), node outgoing flow
Then, according to the step (3.2), the flow rates of the upstream pipeline and the downstream pipeline of the node are respectively obtained
And
and acquiring the node net flow at the time:
obtaining the net flow of the node at the time t
Then, according to the node water head at the time t obtained in the step (3.2)
And pipe flow Qt pipeSubstituting the basic equation of the pipeline flow and the control equation of the drainage pipe network node to obtain the node water head and the pipeline flow at the next moment.
A water-removing reflux process: when rainfall is reduced gradually after the peak value, the water discharge is reduced gradually, surface accumulated water enters an underground pipe network gradually and enters a water return stage, when a node water head is still higher than the surface elevation in the water return stage, the node net flow is calculated according to the node overflow process, the surface accumulated water is returned, when the node water head is lower than the surface elevation, the node net flow is calculated according to the surface inflow process, and the node net flow and the node water head are substituted into a pipeline flow basic equation and a water discharge pipe network node control equation to obtain the node water head and the pipeline flow at the next moment until the rainfall runoff process is finished.
The obtained rainfall runoff process simulation situation according to the set ground surface and pipe network conditions of the research area and the rainfall process is shown in fig. 5.
Claims (6)
1. A method for coupling urban surface runoff and pipe network confluence based on a cellular automaton is characterized by comprising the following steps:
(1) constructing a surface cellular geographic scene, obtaining the type and the elevation of an underlying surface of each cell and the rainfall changing along with time according to the type of the underlying surface of a research area, the DEM elevation and the rainfall changing along with time, and defining the size, the neighborhood relationship and the model boundary of the cells of the model geographic scene;
(2) generalizing an urban underground drainage pipe network, obtaining drainage pipe network pipeline parameters, node parameters and drainage outlet positions according to the construction condition of a drainage pipe network in a research area, and taking a rainwater wellhead as an exchange node of surface and pipe network water flow;
(3) use the rainwater well head as coupling node, carry out surface runoff and pipe network and converge the coupling and calculate, include: performing surface production confluence calculation to obtain a change process of inflow flow of a rainwater wellhead along with time as a boundary condition of pipe network confluence calculation; performing pipe network confluence calculation to obtain the pipeline flow and the node water head at the current time step, and determining the node net flow at the current moment according to three different processes of surface inflow, node overflow and water return backflow in the rainfall process; substituting the current pipeline flow, the node water head and the node net flow into a pipeline flow basic equation and a drainage network node control equation to obtain the next pipeline flow and the node water head, determining the node net flow, repeating the calculation until the total simulation time is reached, and finishing the calculation.
2. The method for coupling urban surface runoff and pipe network confluence based on the cellular automata as claimed in claim 1, wherein the step (3) of performing surface runoff and pipe network confluence calculation to obtain the time-dependent change process of rainwater wellhead inflow flow as the boundary condition of pipe network confluence calculation comprises the following steps:
carrying out runoff yield calculation by using an initial damage and post-damage method to obtain the water depth of each cellular;
comparing the water levels of the central cell and the neighbor cells, eliminating the neighbor cells higher than the average water level, and determining the neighbor cells capable of transferring water quantity;
on the basis of determining the current and the flow direction, calculating the water quantity which can be transferred by the central cell in a time step by adopting a Manning formula, obtaining the potential maximum water quantity which can be transferred by the central cell to the neighbor cell according to the water level difference between the cells, and comparing the potential maximum water quantity with the potential maximum water quantity to obtain the real water quantity transferred by the central cell in the time step;
and calculating the flow of each neighbor cell flowing into the rainwater wellhead node by adopting a side contraction weir flow calculation formula, and summing to obtain the total flow of the earth surface flowing into the rainwater wellhead node.
3. The method for coupling urban surface runoff and pipe network confluence based on the cellular automata as claimed in claim 1, wherein in the step (3), the pipe flow and the node water head are calculated through a pipe flow basic equation and a drainage pipe network node control equation; the finite difference form of the pipeline flow basic equation and the node control equation is expressed as follows:
wherein,
is the flow rate of the pipeline at the time t,
for the net traffic at the node at time t,
is the node head at time t, Δ t is the modelThe length of the intermediate step,
average flow velocity of the pipe, A1、A2Respectively are the section areas of the pipeline at the upstream and downstream of the node, Delta A is the average section area change value in a time step length, L is the length of the pipeline,
is the cross-sectional area of the widest part of the pipeline, g is the gravitational acceleration, H1、H2The water heads of the upstream and downstream nodes of the pipeline respectively, k is a loss coefficient,
is the average hydraulic radius, AskIs the node area.
4. The method for coupling urban surface runoff and pipe network confluence based on the cellular automata as claimed in claim 1, wherein in the step (3), when water flows from the surface to the pipe network in the early stage of rainfall, the node net flow calculation mode is as follows:
wherein,
the flow is the total of the inflow flow of each neighbor cell of the node cell calculated by adopting a side contraction weir flow calculation formula at the time t,
and
the flow rates of the upstream pipeline and the downstream pipeline of the t-time node are respectively.
5. The method for coupling urban surface runoff and pipe network confluence based on the cellular automata according to claim 1, wherein in the step (3), when the pipe network water flow overflows the surface of the earth after the rainfall intensity is increased, a node net flow calculation mode is as follows:
when node cells transfer out water volume Volt trans_outLess than the amount Vol of water transferred into its neighbor cellst trans_inWhen the temperature of the water is higher than the set temperature,
wherein,
and
respectively the upstream and downstream pipeline flow of a t-time node, and delta t is the model time step length;
when node cells transfer out water volume Volt trans_outThe volume Vol of water which is larger than the volume of water transferred by the neighbor cellst trans_inWhen the temperature of the water is higher than the set temperature,
wherein
6. The method for coupling urban surface runoff and pipe network confluence based on the cellular automata according to claim 1, wherein in the step (3), when the water flow enters the pipeline again in the late stage of rainfall, the node flow calculation mode is as follows: in the process of water return and backflow, when the water head of the node is higher than the elevation of the earth surface, calculating the net flow of the node according to the overflow process of the node; and (4) when the surface water is removed and the node water head is lower than the surface elevation, calculating the node net flow according to the surface inflow process.
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