JP2001160043A - Simulation apparatus for water pipe network - Google Patents
Simulation apparatus for water pipe networkInfo
- Publication number
- JP2001160043A JP2001160043A JP34268599A JP34268599A JP2001160043A JP 2001160043 A JP2001160043 A JP 2001160043A JP 34268599 A JP34268599 A JP 34268599A JP 34268599 A JP34268599 A JP 34268599A JP 2001160043 A JP2001160043 A JP 2001160043A
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- water
- pipe network
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- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 title claims abstract description 222
- 238000004088 simulation Methods 0.000 title claims abstract description 51
- 238000004364 calculation method Methods 0.000 claims abstract description 78
- 238000012545 processing Methods 0.000 claims abstract description 22
- 238000000034 method Methods 0.000 claims description 40
- 230000008859 change Effects 0.000 claims description 17
- 230000008569 process Effects 0.000 claims description 16
- 230000004044 response Effects 0.000 claims description 2
- 230000007423 decrease Effects 0.000 description 16
- 238000010586 diagram Methods 0.000 description 12
- 238000012937 correction Methods 0.000 description 10
- 230000014509 gene expression Effects 0.000 description 7
- 230000000694 effects Effects 0.000 description 6
- 238000012360 testing method Methods 0.000 description 6
- 238000007796 conventional method Methods 0.000 description 5
- 230000003247 decreasing effect Effects 0.000 description 2
- 208000003906 hydrocephalus Diseases 0.000 description 2
- 230000008439 repair process Effects 0.000 description 2
- 238000005406 washing Methods 0.000 description 2
- 101100052669 Schizosaccharomyces pombe (strain 972 / ATCC 24843) N118 gene Proteins 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000002347 injection Methods 0.000 description 1
- 239000007924 injection Substances 0.000 description 1
- 238000003012 network analysis Methods 0.000 description 1
- 239000000243 solution Substances 0.000 description 1
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Abstract
Description
【0001】[0001]
【発明の属する技術分野】本発明は、水圧が不足したと
きに水の出が悪くなるという現象を忠実に模擬できる配
水管網のシミュレーション装置の改良に関する。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】[0002]
【従来の技術】従来から、上水道の配水管網のシミュレ
ーション装置が知られている。この従来の配水管網のシ
ミュレーション装置では、配水管網の各需要節点(ノー
ド)に対して需要量を固定値として与え、管網の流量、
圧力を計算している。この従来の配水管網のシミュレー
ション装置では、ある需要節点の圧力が低下しても需要
量(引き抜き量ともいう)は変化せず、負圧になっても
水が引き抜かれて出るというシミュレーション結果とな
り、現実の配水管網とかけ離れた結論が得られることに
なる。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.
【0003】そこで、水圧の低下が水の出に影響を与え
る現象をシミュレーションする配水管網のシミュレーシ
ョン装置として、需要節点の水圧Pと需要量Dとに以下
の関係式を与えてシミュレーションする需要量を逐次修
正する需要量逐次修正法が提案されている。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.
【0004】 D=D0 (ただし、P≧Pth) …(3) D=D0(P/Pth)1/2 (ただし、0<P<Pth)…(4) D=0 (ただし、P≦0) …(5) ここで、符号Pthは閾値である。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.
【0005】その需要量Dと水圧Pとの関係をグラフ化
して図示すると、図1に示す如くとなる。FIG. 1 is a graph showing the relationship between the demand amount D and the water pressure P.
【0006】この需要量逐次修正法では、水圧Pが閾値
Pth以上のときに、需要量Dとして固定値D0が与えら
れ、水圧Pが0<P<Pthのとき、水圧Pの減少に伴っ
て水圧Pのルート関数に従って需要量Dが減少し、水圧
PがP≦0のとき、すなわち、負圧のとき、需要量Dと
して固定値0が与えられる。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.
【0007】この需要量の逐次修正法の管網シミュレー
ションを図2、図3を参照しつつ説明する。ここで、図
2は配水管網の模式図を示し、図3はこの逐次修正法の
管網シミュレーションの手順を説明するためのフローチ
ャートを示す。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.
【0008】その図2において、1は水源節点、2は需
要節点、3は管路を示す。水源節点1、需要節点2をノ
ードという意味で記号Nを用い、この記号Nに添え字i
を付してその節点1又は節点2の番号を示すこととす
る。例えば、節点N1は水源節点1(N0)に接続されて
いる「i=1」番目の需要節点2を示す。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 ).
【0009】また、管路3にはパイプという意味で記号
Pを用い、i番目のノードNiとj番目のノードNjとを
接続しているという意味で添え字ijを付して、その管
路3の番号を示すこととする。例えば、管路P01は水源
節点N0と需要節点N1を結ぶ管路3を示し、管路P12は
需要節点N1と需要節点N2とを結ぶ管路3を示す。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.
【0010】ここでは、節点N5を一般化してi番目の
節点という意味でNiで示し、節点N 6を一般化してj番
目の節点という意味でNjで示し、節点N5と節点N6と
を結ぶ管路P56を一般化してPijで示すこととする。Here, the node NFiveGeneralize to
N in the sense of a nodeiAnd the node N 6Generalized to j
N in the sense of an eye nodejAnd the node NFiveAnd node N6When
Pipeline P connecting56Generalize to PijIt will be shown by.
【0011】この従来の需要量逐次修正法では、図3に
示すように、各需要節点Niに需要量DiとしてDi=D
i0を与える(S.1)。ここで、Di0はその需要節点N
iに与えられた固有の固定値である。そして、公知の管
網シミュレーションを行って、各需要節点Niにおける
需要量Diと水圧Piとを演算する(S.2)。[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】次に、各需要節点Niについて、演算によ
り求められた需要量Diと水圧Piとの関係が(3)〜
(5)式のいずれに当てはまるか否かを判断する。各需
要節点Niについて、演算により求められた需要量Diと
水圧Piとの関係が(3)〜(5)式のいずれかに当て
はまれば、全ての需要節点Niが条件を満足していると
して、管網シミュレーションの演算を終了する(S.
3)。[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).
【0013】演算により求められた需要量Diと水圧Pi
との関係が(3)〜(5)式のいずれにも当てはまらな
い需要節点Nがあるときには、その(3)〜(5)式の
関係を満たさない需要節点Nについて、その演算により
求められた水圧Piと(3)〜(5)式とに基づいて、
修正需要量Di’を演算する。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.
【0014】例えば、需要節点N1の需要量D1=D10で
あるのに、その需要節点N1について求められた水圧P
1がP1<Pthであるときには、(3)式の条件を満足し
ないので、需要節点N1について修正需要量D1’を演算
する。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 .
【0015】そして、修正需要量Di’と修正前の需要
量Diとに基づいて、その需要節点N iに固定値として新
たに与えるべき需要量Dinewを、下記の(6)式に
基づいて演算する。 Dinew=(Di+Di’)/2 …(6) この新たに求められた需要量Dinewを修正前の需要
量Diと置き換えて(S.4)、S.2に移行し、管網
計算を再び行う。Then, the corrected demand amount Di’And demand before correction
Quantity DiAnd the demand node N iNew as fixed value
Demand D to be giveninew into the following equation (6)
Calculate based on Dinew = (Di+ Di') / 2 (6) The newly calculated demand amount DiDemand before correcting new
Quantity Di(S.4), and Move to 2 and pipe network
Perform the calculation again.
【0016】ここで、修正需要量Di’をそのまま用い
ずに、修正需要量Di’と修正前の需要量Diとの平均値
Dinewを用いて、管網計算を行うことにしている理
由は、過剰修正によるハンチングを防止するためであ
る。[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.
【0017】つまり、修正需要量Di’は経験的に任意
に与える値であり、修正量が大きすぎると、修正前需要
量Diと修正需要量Di’との間での繰り返しが生じるの
を極力避けるためである。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.
【0018】このS.2〜S.4の処理を、演算により
求められた需要量Diと水圧Piとの関係が(3)〜
(5)式のいずれかに当てはまるまで繰り返し、全ての
需要節点Niが(3)〜(5)式のいずれかに当てはま
れば、管網計算処理が収束したとして管網シミュレーシ
ョンの演算を終了する。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】[0019]
【発明が解決しようとする課題】この従来の需要量逐次
修正法では、管路網の大きさが小規模である場合、水圧
Pの低下を起こす需要節点Nが少ない場合には、管網計
算処理が収束する。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.
【0020】しかしながら、管路網の大きさが大規模に
なり、かつ、水圧低下を起こす需要節点Nの個数が多く
なると、管網計算処理がいつまで経っても収束せず、管
網計算処理を効率よく行うことができない、管網計算が
煩雑化するという問題がある。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.
【0021】従って、この従来の需要量逐次修正法で
は、高台などで水圧不足のために水の出が悪いという現
象、管工事、管洗浄等の修理作業時に管路のバルブを閉
鎖したときの各需要節点の水の出に与える影響、管路の
バルブを絞って給水制限を行うときの給水量の減少度合
い、消火作業のために消火栓から大量の水を引き抜くこ
とに起因する水圧の低下が各需要節点の水の出に与える
影響、管路破損によっての水の大量流出に起因する水圧
の低下が各需要節点の水の出に与える影響等、現実の現
象に忠実に反映したシミュレーションを行うにはいまだ
に不十分である。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.
【0022】本発明は、上記の事情に鑑みて為されたも
ので、その目的とするところは、水圧が不足したときに
水の出が悪くなるという現象を忠実に模擬できかつ管網
計算処理の収束を迅速に図ることのできる配水管網のシ
ミュレーション装置を提供することにある。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】[0023]
【課題を解決するための手段】請求項1に記載の配水管
網のシミュレーション装置は、配水管網の需要節点の水
圧Pの閾値をPthとして、P≧Pthのときには、前記需
要量DをD=D0とし、前記水圧PがP≦0のときには
前記需要量DをD=0とし、前記水圧Pが0<P<Pth
のときには、前記水圧Pの変化に対応して前記需要量D
が変化する水圧・需要量関数が与えられている配水管網
のシミュレーション装置において、前記需要節点を実在
節点と定義しかつ前記管路を実在管路と定義し、前記実
在節点に仮想管路を介して仮想節点を接続し、しかも、
前記仮想管路に流れる流量Qが前記需要量Dとして取り
扱われるように前記仮想管路が接続された前記実在節点
から引き抜かれる需要量Dを0とし、前記仮想節点に前
記実在節点の地盤標高Gを与えて、前記水圧・需要量関
数を変換して得られる損失水頭式であってかつ前記仮想
管路に流れる流量Qと損失水頭hとの関係を示す損失水
頭式を用いて管網計算することにより、各需要節点の水
圧Pと該需要節点における需要量Dとの関係をシミュレ
ーションすることを特徴とする。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.
【0024】請求項2に記載の配水管網のシミュレーシ
ョン装置は、前記水圧・需要量関数が下記の(7)式で
表され、前記損失水頭式が下記の(8)式で表されるこ
とを特徴とする。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.
【0025】 D=D0(P/Pth)1/2(ただし、0<P<Pth)…(7) h=(Pth/D0 2)・Q2 …(8) 請求項3に記載の配水管網のシミュレーション装置は、
前記配水管網に存在する各需要節点を、全需要節点のう
ち水圧PがP≧Pthに属する需要節点を流出量固定タイ
プ、前記配水管網に存在する全需要節点のうち、水圧P
が0<P<Pthに属する需要節点を流出量変化タイプ、
前記配水管網に存在する全需要節点のうち、水圧PがP
≦0に属する需要節点を流出量0タイプとの三タイプに
分類し、まず最初に、全需要節点が前記流出量固定タイ
プに属すると仮定して、各需要節点に前記仮想管路と前
記仮想節点とを接続することなく固定需要量値を与え
て、前記管網計算処理を行うことにより、前記配水管網
に存在する各需要節点が前記三タイプのいずれに属する
かを判断することを特徴とする。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
【0026】請求項4に記載の配水管網のシミュレーシ
ョン装置は、前記配水管網に存在する各需要節点のう
ち、前記流出量固定タイプに属する各需要節点には前記
仮想管路と前記仮想節点とを接続することなく固定需要
量値を与え、前記流出量変化タイプに属する各需要節点
と前記流出量0タイプに属する各需要節点とには需要量
Dを0として前記仮想管路と前記仮想節点とを接続し、
二度目の管網計算処理を行うことにより、前記配水管網
に存在する各需要節点が前記三タイプのいずれに属する
かを判断すると共に、前記各需要節点のタイプに変更が
あったか否かを判断することを特徴とする。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.
【0027】請求項5に記載の配水管網のシミュレーシ
ョン装置は、前記各需要節点のタイプに変更があったと
きには、前記配水管網に存在する各需要節点のうち、前
記流出量固定タイプに属する各需要節点には前記仮想管
路と前記仮想節点とを接続することなく固定需要量値を
与え、前記流出量変化タイプに属する各需要節点には需
要量Dを0として前記仮想管路と前記仮想節点とを接続
し、前記流出量0タイプに属する各需要節点には前記仮
想管路と前記仮想節点とを接続することなく需要量D=
0を与えて、三度目の管網計算処理を行うことにより前
記配水管網に存在する各需要節点が前記三タイプのいず
れに属するかを判断すると共に、前記各需要節点のタイ
プに変更があったか否かを判断して、各需要節点のタイ
プに変更がなくなるまで、前記管網計算処理を繰り返し
行って、各需要節点の水圧と該需要節点における需要量
との関係をシミュレーションすることを特徴とする。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】[0028]
【発明の実施の形態】図4は管網モデルの一例を示して
いる。この図4において、10は配水池等の水の注入点
としての水源節点、11は配水池等以外の節点、12は
各節点同士を結ぶ管路である。ここで、節点11には管
路12同士の合流・分岐点、蛇口等を含むことにし、こ
の節点11を需要節点ということにする。この図4に示
す配水管網は図2に示す配水管網と同一であり、この図
4に示す記号のうち図2に示す記号と同一記号は同一内
容を意味する。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】管網計算では、与えられた施設条件と境界
条件とに基づき、管路12に流れる水の流量Qijと節点
11の水圧Piとを演算する。二つの任意の節点Ni、N
j、この節点Niと節点Njとを結ぶ管路Pijに着目し、
節点Ni、Njの水頭をそれぞれHi、Hj、管路Pijに流
れる流量をQij、節点Niからの水の需要量をDiとす
る。ここで、水の需要量Diとは節点Niから引き抜かれ
る水の流出量を意味する。[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】管網解析では、与えられた施設条件と境界
条件とに基づき管路12の流量Qij、節点Ni、Njの水
圧Pi、Pjが計算され、管路12の流量Qij、節点11
の水圧Piには以下の関係式が成り立つ。[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 .
【0031】 Hi−Hj=Rij・Qij 1.85 …(9) ΣQij(jについて和をとる)=Di …(10) ここで、Rijは管路Pijの抵抗係数であり、Hi−Hjは
管路12の損失水頭hを意味する。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.
【0032】節点Niの水頭Hiはその節点Niの地盤標
高Giと水圧Piとを加算した値であり、管路Pijの抵抗
係数Rijは管路Pijの口径、その長さ、流速係数等によ
り決まる値である。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】その(9)式は、管路Pijの両端に存在す
る節点Niと節点Njとの間の損失水頭(Hi−Hj)が管
路Pijに流れる水の流量Qijの1.85乗に比例するこ
とを意味し、いわゆるハーゼン−ウイリアムスと呼ばれ
る公知の実験式である。[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.
【0034】管路Pijの代わりに、バルブ、ポンプ等の
制御機器が接続されている場合には、(9)式とは異な
る関数形のものが使用されるが、この発明の本質には関
係しないのでその説明は省略する。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.
【0035】その(10)式は、節点Niにおける流量
の収支条件を意味し、流量Qijは水が管路Pijを節点N
iから節点Njに向かって流れるときを正、その逆方向に
水が流れているときを負とする。節点Niに流れ込んだ
水の量と節点Niから流れ出た水の量とは等しいはずで
あり、その差は節点Niから配水管網外へ引き抜かれた
水の量、すなわち、節点Niの需要量Diに等しい。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 .
【0036】管網計算では、施設条件として管路12の
接続構造、管路12の口径、その長さ、流速係数を与
え、かつ、境界条件としてその管路12の長さ、水源節
点10の水頭、需要節点11からの流出量を与えて、各
管路12に流れる水の流量、各需要節点11の水頭、水
源節点10から管網への水の流入量を計算する。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.
【0037】ここで、管網計算では、各節点11に対し
て水頭か流出量かのいずれかを与えることが、一意的な
解を得るための条件であり、節点11の水頭が求まれ
ば、下記の式に基づき水圧Piが求められる。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】 Pi=Hi−Gi …(11) ここで、Giは節点Niの地盤標高である。[0038] In P i = H i -G i ... (11) Here, G i is a ground elevation of the node N i.
【0039】なお、節点Niの流出量、すなわち、水の
需要量は、水道検針データ、各需要節点でカバーすべき
区域(エリア)の給水人口データ等を解析して作成す
る。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.
【0040】管網計算の代表的手法としては、節点水頭
法とメッシュ流量法とが知られている。その節点水頭法
は、(9)式と(10)式とから管路12に流れる流量
Qijを消去して得られる節点Niの水頭Hiのみを変数と
する非線形代数方程式をニュートン法を用いて解き、そ
の結果、求まった節点水頭と(9)式とを用いて、管路
Pijの流量Qijを計算する方法である。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).
【0041】メッシュ流量法は、管網モデルをグラフ理
論的に解析してメッシュを検出し、メッシュ流量のみを
変数とする方程式を組み立て、これをニュートン法で解
き、次に、メッシュ流量と節点Niの流出量Diとから各
管路Pijに流れる流量Qijを計算し、この結果と(9)
式とに基づいて節点Niの水頭Hiを計算する方法であ
る。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.
【0042】この公知の管網計算では、需要量Diが流
出量Diとして固定して与えられるので、従来技術で述
べたように、水圧低下に伴う水の出が悪くなるというシ
ミュレーションを忠実に模擬することができない。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.
【0043】そこで、本発明では、管路Pijとこの管路
Pijの端部に接続された需要節点N iとを含む配水管網
の需要節点Niからの水圧Piの低下に伴う需要量Diを
シミュレーションするために、水圧Piの閾値Pthを定
義して、Pi≧Pthのときには、需要量DiをD=D0と
し、水圧PiがPi≦0のときには需要量DをD=0と
し、水圧Piが0<Pi<Pthのときには、水圧Piの変
化に対応して需要量Diが変化する水圧・需要量関数を
定義する。Therefore, in the present invention, the pipe PijAnd this pipeline
PijNode N connected to the end of iWater distribution network including
Demand node NiWater pressure P fromiDemand D due to declineiTo
To simulate, the water pressure PiThreshold PthSet
Justify, Pi≧ Pth, The demand DiIs D = D0When
And water pressure PiIs PiWhen ≦ 0, the demand D is set to D = 0.
And water pressure PiIs 0 <Pi<PthAt the time of water pressure PiStrange
Demand D in response toiChanges the water pressure / demand function
Define.
【0044】その水圧・需要量関数は下記の(12)式
〜(14)式で表される。The water pressure / demand function is represented by the following equations (12) to (14).
【0045】 D=D0 (ただし、Pi≧Pth) …(12) D=D0(Pi/Pth)1/2 (ただし、0<Pi<Pth)…(13) D=0 (ただし、Pi≦0) …(14) この(12)式〜(14)式を用いれば、従来技術で説
明したように、水圧P iの低下に伴って水の出が悪くな
るという現象を忠実にシミュレーションすることができ
るが、管路網の大きさが大規模となり、水圧低下を起こ
す需要節点の個数が多くなると、この従来の逐次修正法
では、管網計算処理がいつまで経っても収束しないとい
う傾向がある。D = D0 (However, Pi≧ Pth) (12) D = D0(Pi/ Pth)1/2 (However, 0 <Pi<Pth) ... (13) D = 0 (however, Pi.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.
【0046】そこで、図5に示すように、配水管網の各
需要節点11を実在節点NRiと定義し、配水管網の管
路12を実在管路PRijと定義する。添え字i、jは図
4に示す配水管網と同じ意味で用いている。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】そして、実在節点NRiに仮想管路PViを
介して仮想節点NViを接続する。また、仮想節点NVi
を水頭既知節点であると仮定して仮想節点NViに実在
節点NRiの地盤標高Giを与える。ここで、NViはi
番目の実在節点NRiに接続された仮想節点を意味し、
PViはi番目の実在節点NRiと仮想節点NViとを結
ぶ仮想管路を意味する。[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 .
【0048】図5では、実在節点NR5に仮想管路PVi
(PV5)が接続され、その仮想管路PVi(PV5)に
仮想節点NVi(NV5)が接続されており、仮想節点N
V5には実在節点NR5の地盤標高Gi(G5)が与えられ
ている。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】そして、仮想管路PViの損失水頭hiを演
算して需要節点NRiの水圧Piを求めると共に、仮想管
路PViに流れる流量Qiiを需要量Diとして取り扱うた
めに、仮想管路PViが接続された実在節点NRiから引
き抜かれる需要量Diを0として、仮想管路PViの損失
水頭hiと流量Qiiとの関係を損失水頭式で求める。[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.
【0050】と同時に、損失水頭式の損失水頭hiを水
圧Piで置換して、流量Qiiを水圧P iの関数として求め
て変形し、各需要節点NRiの水圧Piとこの需要節点N
Riにおける需要量Diとの関係を管網計算処理によりシ
ミュレーションする。At the same time, the head loss h of the head loss typeiThe water
Pressure PiAnd the flow rate QiiIs the water pressure P iAs a function of
And deform, each demand node NRiWater pressure PiAnd this demand node N
RiDemand D iniIs calculated by pipe network calculation processing.
To simulate.
【0051】その損失水頭式は以下の(15)式で表さ
れ、これを変形すると以下の(16)式が得られる。The head loss equation is represented by the following equation (15). By modifying this equation, the following equation (16) is obtained.
【0052】 hii=(Pth/D0 2)・Qii 2 …(15) また、実在節点NRiの水頭Hiは地盤標高Giにその実
在節点NRiの水圧Piを加えたものであり、仮想節点N
Viの地盤標高としてその仮想節点NViが接続されてい
る需要節点NRiの地盤標高Giを与えているから、仮想
管路PViの損失水頭hiiは、 hii=(Gi+Pi)−Gi=Pi …(16) となる。[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)
【0053】ここで、(16)式を用いて、(15)式
を解くと、下記の(17)式が得られる。Here, by solving equation (15) using equation (16), the following equation (17) is obtained.
【0054】 Qii=D0(Pi/Pth)1/2 …(17) この(17)式を(13)式と比較することにより、仮
想管路PViに流れる流量Qiiが需要量Diに対応してい
ることがわかる。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.
【0055】従って、この仮想管路PViを付加した配
水管網モデルでは、管網計算処理において需要量Diは
固定値として扱われず、仮想管路PViに流れる水の流
量Qiiとして取り扱われる。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.
【0056】本発明の方法は、仮想管路PViと仮想節
点NViとを接続して、管路網の規模を仮想的に拡大し
て演算を行う方法である。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.
【0057】本発明では、現実の配水管網に存在する各
需要節点について、全需要節点のうち水圧PiがPi≧P
thに属する需要節点を流出量固定タイプ、配水管網に存
在する全需要節点のうち、水圧Piが0<Pi<Pthに属
する需要節点を流出量変化タイプ、配水管網に存在する
全需要節点のうち、水圧PiがPi≦0に属する需要節点
を流出量0タイプとの三タイプに分類する。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.
【0058】そして、まず最初に、図6に示すように、
全需要節点が流出量固定タイプに属すると仮定して、各
需要節点NRiに仮想管路PViと仮想節点NViとを接
続することなく固定需要量値Di=Di0を与える(S.
1)。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).
【0059】最初から全ての需要節点NRiに仮想節点
NViを接続することとすると、管路規模が大きくなり
すぎて、計算処理が煩雑化するので、第1回目の計算処
理では、需要節点NRiに仮想節点NViを接続すること
なく管網計算を行うことにしたのである。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.
【0060】次に、既存の管網計算処理プログラムを用
いて管網計算処理を行う(S.2)。この既存の管網計
算処理によって、各需要節点NRiの水圧Piが求められ
る。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.
【0061】次に、第1回目の管網計算処理か否かを判
断する(S.3)。第1回目の管網計算処理のときに
は、その水圧Piに基づき配水管網に存在する各需要節
点NRiが三タイプのいずれに属するかを判断する。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.
【0062】そして、配水管網に存在する各需要節点N
Riのうち、流出量固定タイプに属する各需要節点には
仮想管路と仮想節点とを接続することなく前回と同じ固
定需要量値Di=Di0を与え、流出量変化タイプに属す
る各需要節点NRiと流出量0タイプに属する各需要節
点NRiとには仮想管路PViと仮想節点NViとを接続
して需要量Di=0を与える(S.4)。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).
【0063】流出量0タイプに属する需要節点NRiに
仮想管路PViと仮想節点NViとを接続して管網計算処
理を行うことにしたのは、ハンチングを避けるためであ
る。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】そして、需要節点NRiについてタイプの
変更があったか否かを判断し、いずれの需要節点NRi
についてにタイプの変更がなかったときは、管網計算処
理が収束したとして処理を終了する(S.5)管網計算
処理が収束していないときには、S.2に移行して、二
回目以降の管網計算を行う。[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.
【0065】そして、二回目以降の管網計算のときに
は、S.6に移行して、配水管網に存在する各需要節点
NRiが三タイプのいずれに属するか否かを判断する。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.
【0066】S.6では、配水管網に存在する各需要節
点NRiのうち、流出量固定タイプに属する各需要節点
NRiには仮想管路と仮想節点とを接続することなく固
定需要量値Di=Di0を与え、流出量変化タイプに属す
る各需要節点NRiには仮想管路PViと仮想節点NVi
とを接続して需要量Di=0を与え、流出量0タイプに
属する各需要節点NRiには仮想管路と仮想節点とを接
続することなく需要量Di=0を与える。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.
【0067】そして、S.5に移行して、各需要節点N
Riのタイプに変更があったか否かを判断し、各需要節
点NRiのタイプに変更がなくなるまで、管網計算を繰
り返し、各需要節点NRiの水圧Piと需要節点NRiに
おける需要量Diとの関係をシミュレーションする。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.
【0068】この管網計算を繰り返すことにより、各需
要節点NRiに第1回目に与えられた(初期に与えられ
た)需要量Di0が水圧Piに応じて修正され、最終的に
各需要節点NRiにおける需要量Diト水圧Piとの関係が
求められることになる。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.
【0069】以下に、シミュレーションテストを説明す
る。 (格子状テスト配水管網のシミュレーションによる収束
性テスト)このテストでは、図5に示す格子状の一辺の
需要節点NRiの個数を10とし、需要節点NRiの総個
数を10×10の100個と水源節点1個との101個
とし、管路PRijの個数を181個としてしミューレー
ションテストを行った。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.
【0070】需要量Di0は各需要節点NRiで同一であ
るとし、境界水圧(閾値)Pthは20m、水頭Hi、水
圧Piの単位はm、流量Qiiの単位はm3/sを用いて行
った。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.
【0071】各需要量(流出量)Di0を0.0025m
3/sから0.0050m3/sまで、0.0005m3
/s間隔で変化させたときの管網計算の繰り返し回数を
表1に示した。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】[0072]
【表1】 [Table 1]
【0073】この表1において、第1回目の管網計算の
結果の水圧Piが20m以下の節点NRiの個数を示した
のは、この水圧Piが20m以下の節点NRiの個数が大
きくなると、管網計算の繰り返し回数が大きくなると予
想されるからである。[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.
【0074】表1に示すように、初期設定流出量(初期
設定需要量Di0)の値を増加させると、各管路PRijで
の圧力損失が増加するので、最初の管網計算の結果、水
圧P iが20m以下の節点NRiの個数は増加する。As shown in Table 1, the initially set outflow amount (initial
Set demand Di0) 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 miIncrease.
【0075】従来の需要量の逐次修正による方法では、
初期設定流出量の増加に伴って管網計算処理の繰り返し
回数が増加し、初期設定流出量0.0045m3/sあ
たりから繰り返し回数が急激に増加し、初期設定流出量
を0.0050m3/sに設定すると、繰り返し回数が
100回を越えても収束せず、100回を越えた時点で
管網計算処理を打ち切った。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.
【0076】これに対して、本発明の仮想管路による管
網シミュレーション方法では、各節点NRiに仮想管路
PViと仮想節点NViとを接続するので、管路網の規模
は大きくなるが、初期流出量の設定に拘わらず、いずれ
も管網計算を3回又は4回繰り返すのみで、管網計算処
理が収束している。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.
【0077】従来の需要量の逐次修正による方法(式
(3)ないし式(5)に基づく方法)でも、この発明の
仮想管路による管網シミュレーション方法でも、管網計
算処理が収束する場合には同一の結果が得られる。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.
【0078】しかし、従来の管網計算による方法と、本
発明の仮想管路による管網シミュレーション方法とで
は、その結果について差異が生じる。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.
【0079】すなわち、図7に示すように、初期流出量
を0.0035m3/sに設定したとき、従来の管網計
算方法と本発明による管網計算処理では、例えば、節点
N20〜N34のうち、節点N21を除いて、各節点の
水圧Piが閾値Pth=20を下回る結果が得られる。そ
れにもかかわらず、従来の管網計算処理では、需要量D
i0が初期流出量として固定して与えられているので、図
8に示すように水圧P iの低下によらず一定(0.00
35m3/s)であり、これは、管網シミュレーション
が水圧Piの低下に忠実に反映していないことを意味す
る。That is, as shown in FIG.
0.0035mThree/ 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 PiIs the threshold Pth= 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)
35mThree/ S), which is the pipe network simulation
Is water pressure PiDoes not faithfully reflect the decline in
You.
【0080】これに対して、本発明による管網計算処理
では、図7に示すように、節点N24〜N34の水圧P
iが閾値Pth=20を下回る結果が得られるが、図8に
示すように、最終流出量は節点N24〜N34で示すよ
うに水圧Piの減少変化に対応しており、管網シミュレ
ーションが水圧Piの低下に忠実に反映している。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.
【0081】ここで、節点N20〜N34は101個の
節点に連続して付した番号のうちの20番目から34番
目までを意味している。Here, the nodes N20 to N34 mean the 20th to 34th of the numbers consecutively assigned to the 101 nodes.
【0082】(実際の配水管網のシミュレーションによ
る収束性テスト)図9は実際の配水管網の一例を示す図
である。この配水管網では、節点NRiの個数は390
個である。そのうちわけは、水源の節点個数が6個、需
要節点の個数が384個である。また、管路PRijの総
個数は452個である。なお、この図9では、水の全体
的な流れの状況を示すため、節点流出量の合計値(全節
点の需要量の総和)が0.1844m3/sのとき(す
なわちケース1のとき)の管路PRijの流量Qijを矢印
で示し、矢印の幅が流量の大きさに比例している。(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.
【0083】この管路の流量は、従来の管網計算処理に
より得られた結果である。The flow rate in the pipe is a result obtained by the conventional pipe network calculation processing.
【0084】[0084]
【表2】 [Table 2]
【0085】まず、最初に、初期設定流出量を、表2に
示すように、0.1844m3/s、0.2458m3/
s、0.3073m3/s、0.3687m3/sと増加
させて、本発明による管網計算を行った。[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.
【0086】その結果、初期設定流量を上記のいずれに
設定しても3〜4回で管網計算処理は収束した。次に、
高台としてエリアC1を設定した。図9に示すエリアC
1の14個の需要節点NRiの地盤標高Giを元の値から
一律10m増やした。そして、初期設定流出量を0.1
844m3/sとして、本発明による管網計算を行い、
水圧Pi及び水の出の状況をシミュレーションした。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.
【0087】図10は高台C1の水圧のグラフであり、
図11は高台C1の各節点の水の流出量である。従来の
管網計算法では、図10に示すように、高台C1の14
個の節点NRiのうち3個の節点N107、N108、
N109で負圧が発生しているにもかかわらず、図11
に示すように、この3個の節点N107、N108、N
109については、初期流出量が存在していることにな
り、水圧と流出量との関係に矛盾が存在している。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.
【0088】しかしながら、本発明の仮想管路による管
網シミュレーションによる管網計算が収束した場合に
は、この3個の節点N107、N108、N109につ
いては、水圧が3m前後あることになり、水圧と最終流
出量との関係に矛盾は生じない。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】また、本発明の仮想管路による管網計算方
法の収束の結果、水圧PiはN107、N108、N1
09を除いて10m前後にまで回復している。[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】なお、水圧Piが3m前後であるのは、も
ともとこの節点N107、N108、N109の地盤標
高Giが高台C1の残余の節点の地盤標高Giよりも3m
前後高いからであり、これらの節点N107、N10
8、N109の最終流出量Diは初期設定値の30%程
度まで落ちている。[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.
【0091】このように、本発明の仮想管路による管網
シミュレーションによれば、高台C1で水の出が悪くな
るという現象をシミュレーションできる。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.
【0092】次に、6個の配水池の水が流出する側にバ
ルブを設置し、このバルブを絞ることによる給水制限の
シミュレーションを行った。バルブの開度は6箇所共一
律に変更することにした。そのバルブの開度の変更は、
通水断面積比で、1/2、1/4、1/8、1/16、
1/32、1/64の6段階とした。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.
【0093】その結果を図12、図13に示す。図12
はバルブの開度の変更に伴う水圧P iの変化を示し、こ
の水圧Piは全節点の平均値であり、図13は全節点か
らの流出量Diの合計値である。The results are shown in FIGS. FIG.
Is the hydraulic pressure P due to the change in the valve opening. iChange
Water pressure PiIs the average value of all nodes.
Outflow DiIs the sum of
【0094】従来の管網計算方法では、図13に示すよ
うに、初期流出量は固定値であるので変化せず、水圧P
iのみが大きく低下し、バルブの開度1/32、1/6
4で負圧が発生している。それにも拘わらず、一定の水
が引き抜かれるという矛盾したシミュレーション結果と
なる。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.
【0095】これに対して、本発明の仮想管路による管
網シミュレーションによれば、バルブを絞って行くと、
バルブの絞りに伴って流出量が減少し、水圧は低下する
もののその低下は緩やかとなるシミュレーション結果が
得られる。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.
【0096】通常の管網計算方法によって負圧となった
バルブ開度1/32においては、12.6mの水圧が得
られ、バルブ開度1/64においては、7.4mの水圧
が得られ、負圧が発生するのが解消されており、水圧と
流出量との関係に矛盾のないシミュレーション結果が得
られている。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.
【0097】ここで、節点N106からN118は39
0個の節点のうち高台C1に存在する節点の番号が10
6番目から118番目であることを意味する。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】[0098]
【発明の効果】本発明によれば、水圧が不足したときに
水の出が悪くなるという現象を忠実に模擬できかつ管網
計算処理の収束を迅速に図ることができる。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】本発明は、高台などで水圧不足のために、
水の出が悪いという現象、管工事、管洗浄等の修理作業
時に管路のバルブを閉鎖したときの各需要節点の水の出
に与える影響、管路のバルブを絞って給水制限を行うと
きの給水量の減少度合い、消火作業のために消火栓から
大量の水を引き抜くことに起因する水圧の低下が各需要
節点の水の出に与える影響、管路破損によっての水の大
量流出に起因する水圧の低下が各需要節点の水の出に与
える影響等の現実の現象に忠実に反映したシミュレーシ
ョンを行うことに好適である。[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.
【図1】 水圧・需要量関数を示すグラフである。FIG. 1 is a graph showing a water pressure / demand amount function.
【図2】 図1に示す水圧・需要量関数を用いての需要
量の逐次修正による方法を説明するための配水管網の模
式図である。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;
【図3】 従来の需要量の逐次修正による方法の処理手
順を説明するためのフローチャートである。FIG. 3 is a flowchart for explaining a processing procedure of a conventional method based on sequential correction of a demand amount.
【図4】 本発明に係わる配水管網のシミュレーション
装置の説明に使用する配水管網の模式図である。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.
【図5】 図4に示す配水管網に仮想管路と仮想節点と
を接続した状態を示す図である。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;
【図6】 本発明に係わる仮想管路により管網計算シミ
ュレーションの手順を説明するためのフローチャートで
ある。FIG. 6 is a flowchart for explaining a procedure of a pipe network calculation simulation using a virtual pipe according to the present invention.
【図7】 配水管網を模式的に作成して本発明の管網計
算シミュレーションを適用した結果の一例を示す図であ
って、その配水管網について各需要節点の初期水圧と最
終水圧とを示す図である。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.
【図8】 配水管網を模式的に作成して本発明の仮想管
路による管網計算シミュレーションを適用した結果の一
例を示す図であって、図7に示す各需要節点の初期流出
量と最終流出量とを示す図である。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.
【図9】 本発明の仮想管路による管網計算シミュレー
ションを適用する実在の配水管網の一例を示す図であ
る。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.
【図10】 図9に示す配水管網に本発明の仮想管路に
よる管網計算シミュレーションを適用した結果の一例を
示す図であって、その配水管網について各需要節点の初
期水圧と最終水圧とを示す図である。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.
【図11】 図9に示す配水管網に本発明の仮想管路に
よる管網計算シミュレーションを適用した結果の一例を
示す図であって、図9に示す各需要節点の初期流出量と
最終流出量とを示す図である。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.
【図12】 図9に示す配水管網に本発明の仮想管路に
よる管網計算シミュレーションを適用した結果の一例を
示す図であって、バルブの開度を変化させた場合の水圧
の変化を示す図である。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.
【図13】 図9に示す配水管網に本発明の仮想管路に
よる管網計算シミュレーションを適用した結果の一例を
示す図であって、バルブの開度を変化させた場合の流出
量の変化を示す図である。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.
11 需要節点 12 管路 D 需要量 P 水圧 Pth 閾値 NR 実在節点 PR 実在管路 NV 仮想節点 PV 仮想管路 Q 流量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)
thとして、P≧Pthのときには、前記需要量DをD=D
0とし、前記水圧PがP≦0のときには前記需要量Dを
D=0とし、前記水圧Pが0<P<Pthのときには、前
記水圧Pの変化に対応して前記需要量Dが変化する水圧
・需要量関数が与えられている配水管網のシミュレーシ
ョン装置において、 前記需要節点を実在節点と定義しかつ前記管路を実在管
路と定義し、前記実在節点に仮想管路を介して仮想節点
を接続し、しかも、前記仮想管路に流れる流量Qが前記
需要量Dとして取り扱われるように前記仮想管路が接続
された前記実在節点から引き抜かれる需要量Dを0と
し、前記仮想節点に前記実在節点の地盤標高Gを与え
て、前記水圧・需要量関数を変換して得られる損失水頭
式であってかつ前記仮想管路に流れる流量Qと損失水頭
hとの関係を示す損失水頭式を用いて管網計算すること
により、各需要節点の水圧Pと該需要節点における需要
量Dとの関係をシミュレーションすることを特徴とする
配水管網のシミュレーション装置。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.
で表され、前記損失水頭式が下記の(2)式で表される
ことを特徴とする請求項1に記載の配水管網のシミュレ
ーション装置。 D=D0(P/Pth)1/2(ただし、0<P<Pth)…(1) h=(Pth/D0 2)・Q2 …(2)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)
全需要節点のうち水圧PがP≧Pthに属する需要節点を
流出量固定タイプ、前記配水管網に存在する全需要節点
のうち、水圧Pが0<P<Pthに属する需要節点を流出
量変化タイプ、前記配水管網に存在する全需要節点のう
ち、水圧PがP≦0に属する需要節点を流出量0タイプ
との三タイプに分類し、まず最初に、全需要節点が前記
流出量固定タイプに属すると仮定して、各需要節点に前
記仮想管路と前記仮想節点とを接続することなく固定需
要量値を与えて、前記管網計算処理を行うことにより、
前記配水管網に存在する各需要節点が前記三タイプのい
ずれに属するかを判断することを特徴とする請求項2に
記載の配水管網のシミュレーション装置。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.
ち、前記流出量固定タイプに属する各需要節点には前記
仮想管路と前記仮想節点とを接続することなく固定需要
量値を与え、前記流出量変化タイプに属する各需要節点
と前記流出量0タイプに属する各需要節点とには需要量
Dを0として前記仮想管路と前記仮想節点とを接続し、
二度目の管網計算処理を行うことにより、前記配水管網
に存在する各需要節点が前記三タイプのいずれに属する
かを判断すると共に、前記各需要節点のタイプに変更が
あったか否かを判断することを特徴とする請求項3に記
載の配水管網のシミュレーション装置。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:
ときには、前記配水管網に存在する各需要節点のうち、
前記流出量固定タイプに属する各需要節点には前記仮想
管路と前記仮想節点とを接続することなく固定需要量値
を与え、前記流出量変化タイプに属する各需要節点には
需要量Dを0として前記仮想管路と前記仮想節点とを接
続し、前記流出量0タイプに属する各需要節点には前記
仮想管路と前記仮想節点とを接続することなく需要量D
=0を与えて、三度目の管網計算処理を行うことにより
前記配水管網に存在する各需要節点が前記三タイプのい
ずれに属するかを判断すると共に、前記各需要節点のタ
イプに変更があったか否かを判断して、各需要節点のタ
イプに変更がなくなるまで、前記管網計算処理を繰り返
し行って、各需要節点の水圧と該需要節点における需要
量との関係をシミュレーションすることを特徴とする請
求項4に記載の配水管網のシミュレーション装置。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.
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