JP2001160043A - Simulation apparatus for water pipe network - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a simulation apparatus for water pipe network for faithfully simulating a phenomenon in which water does not smoothly run, when water pressure is insufficient and for quickly converging distributing pipe network calculation processing. SOLUTION: Threeshold of a water pressure P of a demand node 11 of a distributing pipe network is set to Pth. When P>=Pth, demanded quantity D=D0, and when P<=0, D=0, and when 0<P< Pth, water pressure and demand quantity function is applied. The demand node 11 is defined as a real node NR, a pipeline 12 is defined as a real pipeline PR, a virtual node NV is connected through a virtual pipeline PV with the NR, a demand quantity extracted from the NR with which the PV is connected is set to be 0 so that a flow rate Q of the PV can be treated as a demand quantity D, and a ground altitude G of the NR is applied to the NV. Then, pipeline calculation is performed by using a loss of head formula obtained, by converting the water pressure and demand quantity function for indicating the relation between the flow rate Q running through the PV and a loss of head h. Thus, a relation between water pressure P at each demand node and a demand quantity D at a demand node is simulated.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an improvement in a water distribution network simulation apparatus capable of faithfully simulating a phenomenon that water flow becomes poor when water pressure is insufficient.

[0002]

2. Description of the Related Art Conventionally, a simulation device for a water distribution network of a water supply system is known. In this conventional water distribution network simulation apparatus, the demand is given as a fixed value to each demand node (node) of the water distribution network, and the flow rate of the network,
Calculate pressure. With this conventional water distribution network simulation device, even if the pressure at a certain demand node is reduced, the demand amount (also called the withdrawal amount) does not change, and the simulation results show that water is drawn out even when the pressure becomes negative. However, conclusions far from the actual distribution network can be obtained.

Therefore, as a simulation device for a water distribution pipe network that simulates a phenomenon in which a decrease in water pressure affects the outflow of water, a demand amount simulated by giving the following relational expression to the water pressure P and the demand amount D at the demand node: Has been proposed.

D = D ₀ (where P ≧ P _th ) (3) D = D ₀ (P / P _th ) ^1/2 (where 0 <P <P _th ) (4) D = 0 ( (P ≦ 0) (5) Here, the symbol _Pth is a threshold value.

FIG. 1 is a graph showing the relationship between the demand amount D and the water pressure P.

In this demand amount sequential correction method, when the water pressure P is equal to or higher than the threshold value _Pth , a fixed value D ₀ is given as the demand amount D, and when the water pressure P is 0 <P < _Pth , the water pressure P decreases. Accordingly, the demand D decreases in accordance with the route function of the water pressure P, and when the water pressure P is P ≦ 0, that is, when the pressure is a negative pressure, a fixed value 0 is given as the demand D.

A pipe network simulation of the method for successively correcting the demand will be described with reference to FIGS. Here, FIG. 2 shows a schematic diagram of a water distribution network, and FIG. 3 shows a flow chart for explaining a procedure of the network simulation of the sequential correction method.

In FIG. 2, 1 indicates a water source node, 2 indicates a demand node, and 3 indicates a pipeline. The water source node 1 and the demand node 2 are represented by a symbol N which means a node, and a subscript i is added to the symbol N.
Is added to indicate the number of the node 1 or the node 2. For example, the node N ₁ indicates the “i = 1” -th demand node 2 connected to the water source node 1 (N ₀ ).

Further, using the symbol P in the sense that the pipe to conduit 3, denoted by the letter ij subscript in the sense that connects the i-th node N _i and the j-th node N _j, the The number of the pipeline 3 is indicated. For example, the conduit P ₀₁ represents a conduit 3 connecting the water source nodes N ₀ and demand node N _1, the conduit P ₁₂ represents a conduit 3 connecting the demand node N ₁ and the demand node N _2.

Here, the node N_FiveGeneralize to
N in the sense of a node_iAnd the node N ₆Generalized to j
N in the sense of an eye node_jAnd the node N_FiveAnd node N₆When
Pipeline P connecting₅₆Generalize to P_ijIt will be shown by.

[0011] In the conventional demand successive correction method, as shown in FIG. 3, D _i = D a demand D _i to each customer node N _i
i0 is given (S.1). Here, D _i0 is the demand node N
It is a unique fixed value given to _i . Then, by performing a known pipe network simulation, it calculates the demand D _i hydraulically P _i at each demand node N _i (S.2).

[0012] Next, for each demand node N _i, the relationship between the demand D _i hydraulically P _i obtained by the calculation (3) -
It is determined whether any of the expressions (5) applies. For each customer node N _i, the relationship between the demand D _i hydraulically P _i obtained by the calculation (3) total wager on any one of the - (5), all the demand node N _i satisfies the conditions Is completed, the calculation of the pipe network simulation is terminated (S.
3).

The demand amount D _i and the water pressure P _i obtained by the calculation
When there is a demand node N whose relationship with does not apply to any of the expressions (3) to (5), the demand node N that does not satisfy the relationship of the expressions (3) to (5) is obtained by the calculation. Based on the water pressure _Pi and the equations (3) to (5),
The corrected demand amount D _i 'is calculated.

For example, although the demand amount D ₁ = D ₁₀ of the demand node N ₁ , the water pressure P obtained for the demand node N _{1
When 1} satisfies P ₁ <P _th , the condition of the equation (3) is not satisfied, so the corrected demand amount D ₁ ′ is calculated for the demand node N ₁ .

Then, the corrected demand amount D_i’And demand before correction
Quantity D_iAnd the demand node N _iNew as fixed value
Demand D to be given_inew into the following equation (6)
Calculate based on D_inew = (D_i+ D_i') / 2 (6) The newly calculated demand amount D_iDemand before correcting new
Quantity D_i(S.4), and Move to 2 and pipe network
Perform the calculation again.

[0016] Here, 'without intact, modified demand D _i' modified demand D _i by using the average value D _i new new the demand D _i before correction and, to be carried out the pipe network calculation The reason for this is to prevent hunting due to overcorrection.

In other words, the corrected demand D _i ′ is a value arbitrarily determined empirically, and if the correction is too large, repetition between the pre-correction demand D _i and the corrected demand D _i ′ occurs. This is to avoid as much as possible.

This S. 2-S. 4 processing of the relationship between the demand D _i hydraulically P _i obtained by the calculation (3) -
(5) repeatedly until true either type, total wager on any of all the demand node N _i (3) - (5), and terminates the operation of the tube network simulation as a tube network computation has converged .

[0019]

According to the conventional method of successively correcting the demand amount, when the size of the pipeline network is small, and when the number of demand nodes N causing a decrease in the water pressure P is small, the pipeline network calculation is performed. Processing converges.

However, if the size of the pipeline network becomes large and the number of demand nodes N causing a decrease in water pressure increases, the pipeline network calculation process will not converge forever, and the pipeline network calculation process will not be completed. There is a problem that the calculation cannot be performed efficiently and the pipe network calculation becomes complicated.

Therefore, according to the conventional method of successively correcting the demand, the water is not well discharged due to insufficient water pressure on a hill or the like, and the valve of the pipeline is closed at the time of repair work such as pipe work and pipe washing. The effect of each demand node on water output, the degree of decrease in water supply when restricting water supply by restricting pipe valves, and the decrease in water pressure due to withdrawing a large amount of water from a fire hydrant for fire fighting work. Perform simulations that faithfully reflect actual phenomena, such as the effect on water output at each demand node and the effect on water output at each demand node due to a decrease in water pressure caused by the large outflow of water due to pipe breakage. Is still inadequate.

The present invention has been made in view of the above circumstances, and an object thereof is to faithfully simulate a phenomenon that water is poorly discharged when water pressure is insufficient, and to perform pipe network calculation processing. It is an object of the present invention to provide a water distribution network simulation device capable of rapidly achieving convergence.

[0023]

Means for Solving the Problems] simulation system water distribution network according to claim 1, the threshold value of the pressure P demand nodes water distribution network as P _th, when P ≧ P _th, the demand D Is set to D = D _0, and when the hydraulic pressure P is P ≦ 0, the demand amount D is set to D = 0, and the hydraulic pressure P is 0 <P <P _th
, The demand amount D corresponds to the change of the water pressure P.
In the simulation device of the water distribution network in which a water pressure / demand amount function that changes is defined, the demand node is defined as a real node and the pipeline is defined as a real pipeline, and a virtual pipeline is defined at the real node. Connect the virtual nodes via
The demand amount D drawn from the real node to which the virtual pipeline is connected is set to 0 so that the flow rate Q flowing through the virtual pipeline is treated as the demand amount D, and the virtual node has a ground elevation G of the real node. Pipe network calculation using a loss head equation obtained by converting the water pressure / demand amount function and a relation between the flow rate Q flowing through the virtual pipeline and the loss head h. In this manner, the relationship between the water pressure P at each demand node and the demand D at the demand node is simulated.

According to a second aspect of the present invention, the water distribution / demand function is represented by the following equation (7), and the head loss equation is represented by the following equation (8). It is characterized by.

D = D ₀ (P / P _th ) ^1/2 (where 0 <P <P _th ) (7) h = (P _th / D ₀ ² ) · Q ² (8) The water distribution network simulation device described in
Each demand node existing in the water distribution network is defined as a demand node whose water pressure P belongs to P ≧ _Pth among all demand nodes is of a fixed outflow type, and a water pressure P among all demand nodes existing in the water distribution network is
Is a demand node belonging to 0 <P < _Pth ,
Of all demand nodes existing in the distribution network, water pressure P is P
Demand nodes belonging to ≦ 0 are classified into three types, that is, an outflow amount of 0 type. First, assuming that all demand nodes belong to the outflow amount fixed type, the virtual pipeline and the virtual line are assigned to each demand node. By providing a fixed demand value without connecting nodes and performing the pipe network calculation processing, it is characterized by determining which of the three types each demand node present in the water distribution pipe network belongs to. And

In a fourth aspect of the present invention, the virtual pipeline and the virtual node are provided for each of the demand nodes belonging to the outflow fixed type among the demand nodes existing in the water distribution network. And a fixed demand value is given without connecting the demand line and the demand node belonging to the outflow amount change type and the demand node belonging to the outflow amount 0 type with the demand amount D set to 0. Connect the nodes and
By performing the pipe network calculation process for the second time, it is determined whether each of the demand nodes existing in the water distribution pipe network belongs to any of the three types, and it is determined whether or not the type of each of the demand nodes has been changed. It is characterized by doing.

According to a fifth aspect of the present invention, when the type of each demand node is changed, among the demand nodes existing in the water distribution network, the simulation device for the water distribution network belongs to the outflow fixed type. A fixed demand value is given to each demand node without connecting the virtual pipeline and the virtual node, and a demand D is set to 0 for each demand node belonging to the outflow variation type, and the virtual pipeline and the virtual pipeline are connected to each other. A virtual node is connected to each of the demand nodes belonging to the outflow amount 0 type without connecting the virtual pipeline and the virtual node.
By giving 0 and performing a third pipe network calculation process, it is determined which of the three types each demand node present in the water distribution pipe network belongs to, and whether the type of each demand node has been changed. Judging whether or not there is no change in the type of each demand node, the pipe network calculation process is repeatedly performed to simulate the relationship between the water pressure of each demand node and the demand amount at the demand node. I do.

[0028]

FIG. 4 shows an example of a pipe network model. In FIG. 4, reference numeral 10 denotes a water source node as a water injection point of a distribution reservoir or the like, reference numeral 11 denotes a node other than the distribution reservoir or the like, and reference numeral 12 denotes a pipe connecting the nodes. Here, the node 11 includes a junction / branch point, a faucet, and the like of the pipelines 12, and the node 11 is referred to as a demand node. The water distribution network shown in FIG. 4 is the same as the water distribution network shown in FIG. 2, and among the symbols shown in FIG. 4, the same symbols as those shown in FIG. 2 mean the same contents.

[0029] In the tube network computing, based on the given facility conditions and the boundary conditions, calculating the pressure P _i of the flow rate Q _ij and the node 11 of the water flowing through the conduit 12. Two arbitrary nodes N _i , N
_j , paying attention to a pipeline P _ij connecting this node N _i and node N _j ,
Node N _i, respectively head of water N _j H _i, H _j, flow rate Q _ij flowing through the pipe P _ij, the demand for water from the node N _i and D _i. Here, the demand D _i of water means the outflow of water is withdrawn from the node N _i.

[0030] In the tube network analysis, the flow rate Q _ij given facility conditions and on the basis of conduit 12 to the boundary condition, the node N _i, the water pressure P _i of N _j, P _j is computed, the flow rate Q of the conduit 12 _ij , node 11
The following relational expression holds for the water pressure P _i .

H _i −H _j = R _ij · Q _ij ^1.85 (9) ΣQ _ij (sum of j) = D _i (10) where R _ij is a resistance coefficient of the pipeline P _ij . , H _i -H _j mean the head loss h of the pipeline 12.

The node N hydrocephalus H _i of _i is a value obtained by adding the ground elevation G _i hydraulically P _i of the node N _i, resistance coefficient R _ij is the diameter of the pipe P _ij in line P _ij, its The value is determined by the length, flow velocity coefficient, and the like.

[0033] The formula (9), the water head loss between the node N _i and the node N _j present in both ends of the pipe P _ij (H _i -H _j) flows through the pipe P _ij flow Q It means that it is proportional to _{ij to} the 1.85th power, and is a known empirical formula called Hazen-Williams.

When a control device such as a valve or a pump is connected instead of the pipe P _ij, a function type different from the equation (9) is used. The description is omitted because it is not relevant.

Equation (10) means the condition of balance of the flow rate at the node N _i , and the flow rate Q _ij is determined by the water flowing through the pipe P _ij
Positive when the water flows from _i toward the node _Nj , and negative when the water flows in the opposite direction. Node N and should be equal to the amount the amount of flowing water from the node N _i of water flowing into the _i, the amount of the difference has been withdrawn from the node N _i to distribution network outside water, i.e., the node N _i Of demand D _i .

In the pipe network calculation, the connection structure of the pipe 12, the diameter of the pipe 12, its length and the flow velocity coefficient are given as facility conditions, and the length of the pipe 12 and the water source node 10 as boundary conditions. Given the head and the outflow from the demand node 11, the flow rate of water flowing through each pipeline 12, the head of each demand node 11, and the inflow of water from the water source node 10 into the pipe network are calculated.

Here, in the pipe network calculation, it is a condition for obtaining a unique solution that either the head or the outflow amount is given to each node 11, and if the head of the node 11 is obtained, , The water pressure _Pi is calculated based on the following equation.

[0038] In _{P i = H i -G i ...} (11) Here, G _i is a ground elevation of the node N _i.

It should be noted, outflow node N _i, namely, the demand for water, water meter reading data is created by analyzing the population served data of zone (area) to be covered by each customer node.

As typical methods of pipe network calculation, a nodal head method and a mesh flow rate method are known. Its nodal hydrocephalus method Newton's method the nonlinear algebraic equations as variables only water head H _i of the node N _i which is obtained by erasing the flow Q _ij flowing through the conduit 12 from the equation (9) and (10) This is a method of calculating the flow rate Q _ij of the pipeline P _ij using the nodal head obtained as a result and the equation (9).

In the mesh flow method, a pipe network model is analyzed by graph theory to detect a mesh, an equation using only the mesh flow as a variable is solved, and this is solved by the Newton method. the _i flow Q _ij flowing through the pipe P _ij from the outflow D _i of calculated, the result (9)
This is a method of calculating the head H _i of the node N _i based on the following equation.

In this known pipe network calculation, since the demand amount D _i is fixedly given as the outflow amount D _i, as described in the prior art, the simulation that the outflow of water due to a decrease in water pressure becomes worse is faithfully performed. Cannot be simulated.

Therefore, in the present invention, the pipe P_ijAnd this pipeline
P_ijNode N connected to the end of _iWater distribution network including
Demand node N_iWater pressure P from_iDemand D due to decline_iTo
To simulate, the water pressure P_iThreshold P_thSet
Justify, P_i≧ P_th, The demand D_iIs D = D₀When
And water pressure P_iIs P_iWhen ≦ 0, the demand D is set to D = 0.
And water pressure P_iIs 0 <P_i<P_thAt the time of water pressure P_iStrange
Demand D in response to_iChanges the water pressure / demand function
Define.

The water pressure / demand function is represented by the following equations (12) to (14).

D = D₀ (However, P_i≧ P_th) (12) D = D₀(P_i/ P_th)^1/2 (However, 0 <P_i<P_th) ... (13) D = 0 (however, P_i.Ltoreq.0) (14) By using the equations (12) to (14), it is possible to explain in the prior art.
As mentioned, water pressure P _iThe water flow is worse
Can be simulated faithfully.
However, the size of the pipeline network is large and water pressure drops.
When the number of demand nodes increases, the conventional sequential correction method
Says that the pipe network calculation process will not converge
Tend to.

Therefore, as shown in FIG. 5, each demand node 11 of the water distribution network is defined as a real node NR _i, and the pipeline 12 of the water distribution network is defined as a real network PR _ij . The suffixes i and j are used in the same meaning as the water distribution network shown in FIG.

[0047] Then, connect the virtual node NV _i via a virtual pipeline PV _i to a real node NR _i. Also, the virtual node NV _i
Assuming the a hydrohead known node to provide a ground elevation G _i of the virtual node NV _i to a real node NR _i. Where NV _i is i
Means a virtual node connected to the th real node NR _i ,
PV _i means a virtual conduit connecting the i-th real node NR _i and the virtual node NV _i .

In FIG. 5, the virtual conduit PV _i is connected to the real node NR _5.
(PV ₅ ) is connected, the virtual node NV _i (NV ₅ ) is connected to the virtual conduit PV _i (PV ₅ ), and the virtual node N
The V ₅ Ground Elevation G _i real node NR ₅ (G ₅₎ is given.

[0049] Then, the determined water pressure P _i demand node NR _i by computing the headloss h _i of virtual pipeline PV _i, to handle the flow Q _ii flowing through the virtual pipeline PV _i as demand D _i Assuming that the demand amount D _i extracted from the real node NR _i to which the virtual pipeline PV _i is connected is 0, the relationship between the loss head h _i and the flow rate Q _ii of the virtual pipeline PV _i is determined by a loss head equation.

At the same time, the head loss h of the head loss type_iThe water
Pressure P_iAnd the flow rate Q_iiIs the water pressure P _iAs a function of
And deform, each demand node NR_iWater pressure P_iAnd this demand node N
R_iDemand D in_iIs calculated by pipe network calculation processing.
To simulate.

The head loss equation is represented by the following equation (15). By modifying this equation, the following equation (16) is obtained.

[0052] _{h ii = (P th / D} 0 2) · Q ii 2 ... (15) Further, the water head H _i real node NR _i has added pressure P _i of the actual node NR _i to ground altitude G _i Virtual node N
Since the virtual node NV _i has given ground elevation G _i demand node NR _i connected as ground elevation V _i, head losses h _ii of virtual pipeline PV _{i is, h ii = (G i +} P _i ) -G _i = P _i (16)

Here, by solving equation (15) using equation (16), the following equation (17) is obtained.

Q _ii = D ₀ (P _i / P _th ) ^1/2 (17) By comparing the expression (17) with the expression (13), the flow rate Q _ii flowing through the virtual conduit PV _i becomes the demand. it can be seen that correspond to the amount D _i.

Therefore, in the water distribution pipe network model to which the virtual pipe PV _i is added, the demand D _i is not treated as a fixed value in the pipe network calculation processing, but is treated as a flow rate Q _ii of water flowing through the virtual pipe PV _i. It is.

The method of the present invention is a method of connecting the virtual pipeline PV _i and the virtual node NV _i to virtually enlarge the scale of the pipeline network to perform the calculation.

In the present invention, for each demand node existing in the actual water distribution network, the water pressure P _i of all the demand nodes is P _i ≧ P
outflow fixed type demand nodes belonging to _th, of the total demand nodes present in water distribution network, there demand nodes pressure P _i belongs to 0 <P _i <P _th runoff variation type, the water distribution network Among all the demand nodes, the demand nodes whose water pressure P _i belongs to P _i ≦ 0 are classified into three types, that is, an outflow amount 0 type.

Then, first, as shown in FIG.
Assuming that all demand nodes belong to the fixed outflow type, a fixed demand value D _i = D _i0 is given to each demand node NR _i without connecting the virtual pipeline PV _i and the virtual node NV _i (S .
1).

If the virtual nodes NV _i are connected to all the demand nodes NR _i from the beginning, the pipeline scale becomes too large and the calculation process becomes complicated. it was decided to perform no pipe network calculation to connect the NR _i to a virtual node NV _i.

Next, pipe network calculation processing is performed using an existing pipe network calculation processing program (S.2). This existing pipe network calculation process, the water pressure P _i of each customer node NR _i is determined.

Next, it is determined whether or not it is the first pipe network calculation processing (S.3). At the time of the first pipe network calculation processing, it is determined based on the water pressure P _i to which of the three types the demand nodes NR _i present in the water distribution pipe network belong.

Then, each demand node N existing in the distribution pipe network
Among the R _i, the same fixed demand value D _i = D _i0 as in the previous time is given to each demand node belonging to the outflow fixed type without connecting the virtual pipeline and the virtual node to each demand node belonging to the outflow fixed type. the and demand node NR _i and each customer node belonging to runoff 0 type NR _i give demand D _i = 0 by connecting the virtual pipeline PV _i and virtual node NV _i (S.4).

The reason why the virtual pipeline PV _i and the virtual node NV _i are connected to the demand node NR _i belonging to the outflow amount 0 type to perform the pipe network calculation processing is to avoid hunting.

[0064] Then, it is determined whether or not there is a type of change for the demand node NR _i, one of the demand node NR _i
If the type has not been changed, the processing is terminated assuming that the pipe network calculation processing has converged (S.5). The process proceeds to step 2 to perform the second and subsequent pipe network calculations.

Then, at the time of the second and subsequent pipe network calculations, S.P. The process proceeds to 6 to determine whether each of the demand nodes NR _i existing in the water distribution network belongs to any of the three types.

S. In 6, of the demand node NR _i present in water distribution network, a fixed demand value without connecting the virtual nodes and virtual pipeline to each customer node NR _i belonging to runoff fixed type D _i = D given _i0, and each demand node NR _i belonging to runoff variation type and virtual pipeline PV _i virtual node NV _i
Given demand D _i = 0 by connecting the door, each demand node NR _i belonging to runoff 0 type give demand D _i = 0, without connecting the virtual nodes and virtual pipeline.

Then, S. 5 and each demand node N
Determines whether there is a change in the type of R _i, until there is no change in the type of each customer node NR _i, repeated tube network calculation, demand in the pressure P _i and the demand node NR _i of each customer node NR _i to simulate the relationship between the D _i.

By repeating this pipe network calculation, the demand amount D _i0 (first given) given to each demand node NR _i for the first time is corrected according to the water pressure P _i , and finally each demand node NR _i is corrected. The relationship between the demand amount D _i and the water pressure P _i at the demand node NR _i is obtained.

The simulation test will be described below. (Convergence Test by Simulation of Grid Test Water Distribution Network) In this test, the number of demand nodes NR _{i on} one side of the grid shown in FIG. 5 is 10, and the total number of demand nodes NR _i is 10 × 10 ₌ 100. A muting test was performed with the number of pipes and one water source node being 101, and the number of pipelines PR _ij being 181.

It is assumed that the demand amount D _i0 is the same at each demand node NR _i , the boundary water pressure (threshold) P _th is 20 m, the head H _i , the water pressure P _i is m, and the flow rate Q _ii is m ³ / m. s.

Each demand (outflow) D _i0 is 0.0025 m
From ³ / s to 0.0050m ³ / s, 0.0005m ³
Table 1 shows the number of repetitions of the pipe network calculation when changing at the / s interval.

[0072]

[Table 1]

[0073] In Table 1, the results of the water pressure P _i of the first pipe network calculation showed the number of the following node NR _i 20m, it the number of the pressure P _i is 20m or less nodes NR _i This is because when it becomes large, it is expected that the number of repetitions of the pipe network calculation will become large.

As shown in Table 1, the initially set outflow amount (initial
Set demand D_i0) Increases the value of each pipeline PR._ijso
Pressure loss increases, the result of the first pipe network calculation indicates that water
Pressure P _iIs no more than 20 m_iIncrease.

In the conventional method of successively correcting the demand,
The number of repetitions of the pipe network calculation process increases with an increase in the initial set flow rate, and the number of repetitions rapidly increases from around the initial set flow rate of 0.0045 m3 / s to reduce the initial set flow rate to 0.0050 m3 / s. With this setting, the convergence did not converge even when the number of repetitions exceeded 100, and the pipe network calculation processing was terminated when the number of repetitions exceeded 100.

On the other hand, in the pipe network simulation method using virtual pipes of the present invention, since the virtual pipes PV _i and the virtual nodes NV _i are connected to the nodes NR _i , the scale of the pipe network becomes large. However, irrespective of the setting of the initial outflow amount, the pipe network calculation process converges only by repeating the pipe network calculation three or four times.

In the conventional method based on the sequential correction of the demand (the method based on the equations (3) to (5)) and the pipe network simulation method using the virtual pipeline according to the present invention, when the pipe network calculation processing converges, Gives the same result.

However, there is a difference in the result between the conventional pipe network calculation method and the pipe network simulation method using the virtual pipe according to the present invention.

That is, as shown in FIG.
0.0035m^Three/ S, the conventional pipe network meter
In the calculation method and the pipe network calculation processing according to the present invention, for example,
Of the nodes N20 to N34, except for the node N21,
Water pressure P_iIs the threshold P_th= 20. So
Nevertheless, in the conventional pipe network calculation processing, the demand D
_i0Is given as a fixed amount of initial runoff.
As shown in FIG. _i(0.000)
35m^Three/ S), which is the pipe network simulation
Is water pressure P_iDoes not faithfully reflect the decline in
You.

On the other hand, in the pipe network calculation processing according to the present invention, as shown in FIG.
_{Although the} result that _i is less than the threshold value P _th = 20 is obtained, as shown in FIG. 8, the final outflow corresponds to the decreasing change of the water pressure P _i as shown by nodes N24 to N34, and the pipe network simulation It is faithfully reflected in decreased water pressure P _i.

Here, the nodes N20 to N34 mean the 20th to 34th of the numbers consecutively assigned to the 101 nodes.

(Convergence Test by Simulation of Actual Water Distribution Network) FIG. 9 is a diagram showing an example of an actual water distribution network. In this water distribution network, the number of nodes NR _i is 390
Individual. For that reason, the number of water source nodes is 6, and the number of demand nodes is 384. The total number of pipelines PR _ij is 452. In FIG. 9, in order to show the state of the overall flow of water, when the total value of the outflow amount of the nodes (the sum of the demand amounts of all the nodes) is 0.1844 m ³ / s (that is, in the case 1). The flow rate Q _ij of the pipeline PR _ij is indicated by an arrow, and the width of the arrow is proportional to the magnitude of the flow rate.

The flow rate in the pipe is a result obtained by the conventional pipe network calculation processing.

[0084]

[Table 2]

[0085] First, the first, the initial setting runoff, as shown in Table 2, 0.1844m ³ /s,0.2458m ³ /
s, it is increased and 0.3073m ³ /s,0.3687m ³ / s, was pipe network calculation according to the present invention.

As a result, the pipe network calculation process converged three to four times regardless of the initial set flow rate set to any of the above. next,
Area C1 was set as a hill. Area C shown in FIG.
It increased uniformly 10m the ground elevation G _i of 1 of the 14 demand nodes NR _i from the original value. Then, the initial set flow rate is 0.1
Assuming 844 m ³ / s, the pipe network calculation according to the present invention is performed,
The simulation of the water pressure Pi and the _outflow of water was performed.

FIG. 10 is a graph of the water pressure of the hill C1.
FIG. 11 shows the outflow amount of water at each node of the hill C1. In the conventional pipe network calculation method, as shown in FIG.
Three nodes of the number of nodes NR _i N107, N108,
Although a negative pressure is generated at N109, FIG.
As shown in the figure, these three nodes N107, N108, N
For 109, the initial outflow amount exists, and there is a contradiction in the relationship between the water pressure and the outflow amount.

However, when the pipe network calculation by the pipe network simulation using the virtual pipe of the present invention converges, the water pressure of these three nodes N107, N108 and N109 is about 3 m, and the water pressure is about 3 m. There is no contradiction in relation to the final runoff.

[0089] As a result of the convergence of the tube network calculation method by the virtual line of the present invention, the water pressure P _i is N107, N108, N1
Except for 09, it has recovered to around 10m.

[0090] In addition, the water pressure P _i in the range of around 3m was originally the node N107, N108, N109 ground elevation G _i is 3m than the ground elevation G _i of the nodes of the remainder of the hill C1 of
This is because these nodes N107, N10
8, the final outflow D _i of N109 is dropped to about 30% of the initial value.

As described above, according to the pipe network simulation using the virtual pipe according to the present invention, it is possible to simulate the phenomenon that the outflow of water becomes worse on the hill C1.

Next, a valve was installed on the side of the six distribution reservoirs on which water flows out, and a simulation of water supply restriction by narrowing the valve was performed. The opening degree of the valve was changed uniformly at all six locations. Changing the opening of the valve
1/2, 1/4, 1/8, 1/16,
There were six stages, 1/32 and 1/64.

The results are shown in FIGS. FIG.
Is the hydraulic pressure P due to the change in the valve opening. _iChange
Water pressure P_iIs the average value of all nodes.
Outflow D_iIs the sum of

In the conventional pipe network calculation method, as shown in FIG. 13, the initial discharge amount is a fixed value and does not change.
Only i greatly decreases and the valve opening 1/32, 1/6
At 4, a negative pressure is generated. Nevertheless, inconsistent simulation results indicate that certain water is withdrawn.

On the other hand, according to the pipe network simulation using the virtual pipe of the present invention, when the valve is narrowed down,
A simulation result is obtained in which the amount of outflow decreases with the throttle of the valve, and the water pressure decreases, but the decrease is gradual.

At a valve opening of 1/32, which is a negative pressure by the ordinary pipe network calculation method, a water pressure of 12.6 m is obtained, and at a valve opening of 1/64, a water pressure of 7.4 m is obtained. The generation of negative pressure has been eliminated, and a simulation result consistent with the relationship between the water pressure and the outflow amount has been obtained.

Here, nodes N106 to N118 are 39
The number of the node existing on the hill C1 out of the 0 nodes is 10
It means from the 6th to the 118th.

[0098]

According to the present invention, it is possible to faithfully simulate the phenomenon that the water flow becomes poor when the water pressure is insufficient, and it is possible to quickly converge the pipe network calculation processing.

[0099] The present invention is based on
Poor water flow, effects on water flow at each demand node when closing a pipe valve during repair work such as pipe work, pipe washing, etc., when restricting water supply by narrowing the pipe valve Of water supply at each demand node due to the decrease in water supply volume, the effect of water pressure drop due to withdrawing a large amount of water from a fire hydrant for fire fighting work, and the large amount of water flowing out due to pipeline breakage This is suitable for performing a simulation that faithfully reflects an actual phenomenon such as the effect of a decrease in water pressure on water output at each demand node.

[Brief description of the drawings]

FIG. 1 is a graph showing a water pressure / demand amount function.

FIG. 2 is a schematic diagram of a water distribution pipe network for explaining a method of sequentially correcting a demand amount using the water pressure / demand amount function shown in FIG. 1;

FIG. 3 is a flowchart for explaining a processing procedure of a conventional method based on sequential correction of a demand amount.

FIG. 4 is a schematic diagram of a water distribution network used for explaining a water distribution network simulation apparatus according to the present invention.

FIG. 5 is a diagram showing a state where a virtual pipeline and a virtual node are connected to the water distribution network shown in FIG. 4;

FIG. 6 is a flowchart for explaining a procedure of a pipe network calculation simulation using a virtual pipe according to the present invention.

FIG. 7 is a diagram showing an example of a result of applying a pipe network calculation simulation of the present invention by schematically creating a water distribution pipe network, in which an initial water pressure and a final water pressure at each demand node for the water distribution pipe network; FIG.

8 is a diagram showing an example of a result of applying a pipe network calculation simulation based on a virtual pipe according to the present invention by schematically creating a water distribution pipe network, showing an initial outflow amount of each demand node shown in FIG. It is a figure which shows a final outflow amount.

FIG. 9 is a diagram illustrating an example of a real distribution pipe network to which a pipe network calculation simulation using a virtual pipeline according to the present invention is applied.

10 is a diagram showing an example of a result obtained by applying a pipe network calculation simulation using a virtual pipe according to the present invention to the water distribution pipe network shown in FIG. 9, wherein the initial water pressure and the final water pressure at each demand node for the water distribution pipe network; FIG.

11 is a diagram showing an example of a result obtained by applying a pipe network calculation simulation using a virtual pipeline according to the present invention to the water distribution pipe network shown in FIG. 9, wherein an initial outflow amount and a final outflow at each demand node shown in FIG. 9; It is a figure which shows an amount.

12 is a diagram showing an example of a result obtained by applying a pipe network calculation simulation using a virtual pipe according to the present invention to the water distribution pipe network shown in FIG. 9, and illustrating a change in water pressure when the valve opening is changed. FIG.

13 is a diagram showing an example of a result obtained by applying a pipe network calculation simulation using a virtual pipe according to the present invention to the water distribution pipe network shown in FIG. 9, showing a change in an outflow amount when the opening degree of a valve is changed; FIG.

[Explanation of symbols]

11 Demand Node 12 Pipe D Demand P Water Pressure P _th Threshold NR Real Node PR Real Pipe NV Virtual Node PV Virtual Pipe Q Flow

Claims (5)

[Claims] 1. A threshold value of a water pressure P at a demand node of a water distribution network is P
As _th, when P ≧ P _th is the demand D D = D
₀ , the demand D is set to D = 0 when the water pressure P is P ≦ 0, and the demand D changes in response to the change of the water pressure P when the water pressure P is 0 <P < _Pth. In a water distribution / pipe network simulation apparatus provided with a water pressure / demand amount function, the demand node is defined as a real node and the pipeline is defined as a real pipeline, and the real node is defined via a virtual pipeline. Virtual nodes are connected, and the demand amount D drawn from the real node to which the virtual pipeline is connected is set to 0 so that the flow rate Q flowing through the virtual pipeline is treated as the demand amount D. Is the head loss obtained by converting the water pressure / demand function by giving the ground elevation G of the real node to the head, and indicating the relationship between the flow rate Q flowing through the virtual pipe and the head loss h. To calculate the pipe network using the formula Ri, simulation system water distribution network, characterized in that to simulate the relationship between the demand D in pressure P and 該需 main nodes of each customer node. 2. The distribution pipe according to claim 1, wherein the water pressure / demand amount function is represented by the following equation (1), and the head loss equation is represented by the following equation (2). Net simulation device. D = D ₀ (P / P _th ) ^1/2 (where 0 <P <P _th ) (1) h = (P _th / D ₀ ² ) · Q ² (2) 3. Demand nodes existing in the water distribution network are:
Runoff fixed type water pressure P is a demand nodes belonging to P ≧ P _th of the total demand nodes, of the total demand nodes existing in the water distribution network, the water pressure P is 0 <P <outflow demand nodes belonging to P _th Demand nodes whose water pressure P satisfies P ≦ 0 are classified into three types, that is, an outflow amount 0 type, out of all the demand nodes existing in the water distribution pipe network. Assuming that it belongs to the fixed quantity type, by giving a fixed demand value to each demand node without connecting the virtual pipeline and the virtual node, and performing the pipe network calculation processing,
The apparatus according to claim 2, wherein each of the demand nodes existing in the water distribution network belongs to one of the three types. 4. A fixed demand value is given to each of the demand nodes belonging to the fixed runoff type among the demand nodes existing in the water distribution network without connecting the virtual pipeline and the virtual nodes. Connecting the virtual pipeline and the virtual node to each demand node belonging to the outflow amount change type and each demand node belonging to the outflow amount 0 type by setting the demand amount D to 0;
By performing the pipe network calculation process for the second time, it is determined whether each of the demand nodes existing in the water distribution pipe network belongs to any of the three types, and it is determined whether or not the type of each of the demand nodes has been changed. The simulation apparatus for a water distribution network according to claim 3, wherein: 5. When there is a change in the type of each demand node, of the demand nodes existing in the water distribution network,
A fixed demand value is given to each demand node belonging to the fixed runoff type without connecting the virtual pipeline and the virtual node, and a demand D is set to 0 for each demand node belonging to the runoff change type. The virtual pipeline and the virtual node are connected to each other, and the demand amount D without connecting the virtual pipeline and the virtual node is connected to each demand node belonging to the outflow amount 0 type.
= 0, and by performing a third pipe network calculation process, it is determined which of the three types each demand node present in the water distribution pipe network belongs to, and the type of each demand node is changed. It is determined whether or not there is, and the pipe network calculation process is repeated until there is no change in the type of each demand node, thereby simulating the relationship between the water pressure at each demand node and the demand amount at the demand node. The simulation device for a water distribution pipe network according to claim 4.