The hydraulic efficiency to secure optimization of the flood detention pool system will be treated through mathematical simulation. The mathematical model is approximated by the point-sink virtually located at the center of the deversoir section. Numerical computations show that the optimization of the system in hydraulic efficiency will be given through a combination of the deversoir length and the initial diversion discharge. Furthermore, it is seen the whole pool volume will be nearly constant for any possible combination

INOUE, Kazuya

IWASA, Yoshiaki

TSUNEMATSU, Yoshiaki

English

Kyoto University Research Information Repository

RIGHT:URL:CITATION:AUTHOR(S):ISSUE DATE:TITLE:Hydraulic Efficiency of FloodDetention Pools Evaluated byMeans of Mathematical SimulationIWASA, Yoshiaki; INOUE, Kazuya; TSUNEMATSU,YoshiakiIWASA, Yoshiaki ...[et al]. Hydraulic Efficiency of Flood Detention Pools Evaluated byMeans of Mathematical Simulation. Memoirs of the Faculty of Engineering, KyotoUniversity 1970, 32(3): 297-3061970-09-30http://hdl.handle.net/2433/280825Hydraulic Efficiency of Flood Detention Pools Evaluated by Means of Mathematical Simulation By Yoshiaki IWASA, Kazuya INOUE and Yoshiaki TsuNEMATsu* (Received March 28, 1970) The hydraulic efficiency to secure optimization of the flood detention pool system will be treated through mathematical simulation. The mathematical model is approxi-mated by the point-sink virtually located at the center of the deversoir section. Numerical computations show that the optimization of the system in hydraulic efficiency will be given through a combination of the deversoir length and the initial diversion discharge. Furthermore, it is seen the whole pool volume will be nearly constant for any possible combination. Recognition of Underlying Problem 297 A system of flood detention pool is a physical device, which bridges, in technical aspect, the surface water during flood as water resources, and the flood control as a need of socio-economic life. Excess water in capacity of the downstream channel is charged temporarily in the pool and it will be discharged later when the flood has passed and regional security will be obtained. The physical structure of the system consists of pool, inlet, outlet and other appurtenant structures along the main channel course and frequently near the confluence of two rivers. The main characteristic of the system in physical be-haviour will be exhibited in the inlet structure, through which the main channel and the pool are connected. The lateral deversoir (weir) will be mostly used as the inlet. The inflow-outflow relationship between the main flow and the pool water through the inlet will be then a function of the weir length (L), the weir height (D) and the capacity of pool ( V) as structural elements. However, the weir height will be related to the main flow discharge at the initial diversion. This type of inflow-outflow relationship will be established at the uncontrolled lateral deversoir, which can show no man-made regulation against the diverted flow. The flood * Department of Civil Engineering 298 Yoshiaki IwASA, Kazuya INOUE and Yoshiaki TSUNEMATSU control project by means of the detention pool system will be designed under ex-tremely rare hydrologic conditions, in order to warrant the socio-economic life in human-ecological, regional and national levels. This is one of the reasons why the inlet structure is uncontrolled. More effective use of the flood flow as water re-sources by changing the physics from natural to man-made with the system matrix of the detention pool will be expected. Mathematical Simulation of Physical Models A simplified model of the original system will be seen in Fig. 1-a, where a design flood hydrograph as input will be divided into the main downstream channel -Ou main channel I ~;~x~ . pool l l Z Z Z deversoir (b) Fig. I. Flood Detention Pool System flow and the charge in the detention pool through the lateral deversoir as the inlet. A mathematical abstraction in the one-dimensional theoretical hydraulics from the physical model gives a set of partial differential equations with two independent variables of the time (t) and the distance travelled (x) and two dependent variables of the flow depth (H) and the mean velocity (v) or the discharge (Q), which is the so-called system of unsteady flow equations with variable discharge. The solution will be obtained through the method of characteristics or by the use of the Lax-Wendroff scheme. 1> However, the nun1erical procedure is so complicated that an approximation is the most that can be expected. The dynamic programming for the non-serial system will not be applied because of the physical structure in diversion. The quasi-steady flow assumption will be then introduced without making any verification. The problem becomes simplified and the following set of ordinary Hydraulic Efficiency of Flood Detention Pools 299 differential equations gives the mathematical simulation2 > at every moment: dS = i- n2Q: + apqQ, de R3l'A2 ~2gA2 ( I ) dx _ l aQ: 8A de - -gA3 as ( 2) dQ, = _ (i - aQ,2 8-'!_) de q gA3 as ( 3) where, adding to the previous notations, R: the hydraulic radius, A: the flow area in the main channel, q: the diverted discharge per unit length of the lateral dever-·soir, n: the Manning roughness, i: the channel slope, a: the Coriolis coefficient, p: the coefficient due to the energy diversion, g: the acceleration of gravity, and e: the parameter with length dimension. The constraints for the system are Qg~Q,d = Qu-i q dx v~H qdxdt ( 4) ( 5) where Q,8: the design discharge in the downstream main channel, Q,d: the actual downstream discharge, Q,": the upstream discharge, and V: the volumetric capacity of pool. The integral with respect to the time must be made throughout the flood duration. As described in the above, the main characteristic of the physical system will be reproduced in the expression of q. The deversoir will be 102m or more in length and thus q will be variable from location to location along the deversoir. This description enables us to approximate the original distributed system in a lumped system schematically shown in Fig. l-b. The set of Eqs. (I )-(3) is used for each component of the lumped system and usually is replaced by the set of finite difference equations. Most hydraulic practices require no such detailed behaviour in each system component. In reality, the Japanese standard for river improvement works gives technical information concerning channel and hydraulic geometries at every 200 m. The lumped system may be then replaced by a single component, through which the relationship among inflow, outflow and diversion will be established. The hydraulic performance of the lateral deversoir will be simply simulated by a point sink. The present procedure of analysis will be based on this simulation. General geometric patterns of the flood detention pool system are I) a single pool system, 2) a serial system of pools, 3) a non-serial system of pools and so on. 300 Yoshiaki IwAsA, Kazuya INOUE and Yoshiaki TsuNEMATSU (a) (b) ( C) Fig. 2. Typical Geometric Patterns of System The system is a physical device for flood control, so that it will locate near the con-fluence of two rivers. Trpical geometric patterns of the system will be shown in schematic figure 2. The mathematical simulation will be then made, in order to warrant two constratints of (4) and (5). Because of underlying characteristics of the inflow-outflow relationship, the downstream discharge Qd will be ( 6) where Q0 : the main flow discharge at initial diversion stage. In Eq. (6), L, V and Q0 will be considered to be system parameters. However, as described in the foregoing, the flood control project aims the security of downstream basin, and therefore the capacity of the pool must be so lrge that the maximum value of the downstream discharge after control (Qd)max is less than the design flood discharge Qg- In technical aspect, it means that V will be assumed to be constant. Then, the hydraulic efficiency of the detention pool system may be evaluated by aQd = 0 and 8L (7) Actual mathematical procedures, for example, in the case ofa single pool system near the confluence will be in the following: l) Determine design hydrographs of both rivers after hydrologic analysis, and the stage-discharge relationship at the confluence. 2) Assume Qd1 and add it to Q2 at a given instant, to obtain the discharge at the confluence. Estimate the stage at the confluence for Qd1 + Q2 through the given relationship. 3) Trace the surface profiles of water with the use of Eqs. (I )-(3) under the initial value estimated at the confluence. 4) Obtain the stage at the center of lateral deversoir where a point sink will be virtually assumed to exist. 5) Estimate the diverted discharge (Qw) at the stage obtained through the experience or the use of a proper hydraulic formula. Hydraulic Effici4ncy of Flood Detention Pools 301 6) Obtain the upstream discharge Q,.1 by summing Qd1 and Qw1, and compare with the given design hydrograph. 7) If the initial assumption for Qd1 is not correct, repeat the same procedure until the correct answer is obtained. 8) At the next instant after passing Jt, the same computation will be made, until the complete calculation is finished. The flow chart in mathematical computation will be seen in Fig. 3. In the case of a non-serial system shown in Fig. 2-c, a little modification must be made. Qd1 and Qd2 will be initially assumed and the same procedure will be used. Check must be made through Qd1+Qw1=Q,.1 and Qd2+Qw2=Q"2. The hydraulic per-formance of the pool system to the main flow pattern will then be evaluated after establishing the modification in flow patterns. NO YES give Q (t) and Q2(t) ul calculate the stage at the eon fl uence trace the surface profiles oi' w&.ter Fig. 3. Flow Chart of Mathematical Computations Fig. 4. Design Hydrographs 302 Yoshiaki lwASA, Kazuya lNolJE and Yoshiaki TsuNEMATSU Numerical Evaluation of Hydraulic Efficiency Through Mathematical Simulation Some numerical calculations for a simplified channel system, of which the hydraulic and geometric characteristics have been extracted from a real compli-cated system, will next be shown. The channel geometry of all three rivers is of rectangular shape with 100 min width, 0.035 in Manning roughness and 1/1000 in slope. The design hydrographs used in the numerical analysis will be shown in Fig. 4. The bottom elevation of the pool is assumed to be the same as the channel. The capacity of pool per unit depth C is 4.00 x 105 m 3 • Furthermore, the point sink will be assumed to be 0.6 km upstream from the confluence. Numerical computations have been proceeded with the time increment of 15 min. ( =900 sec). Fig. 5-7 are graphical representations for the maximum control-led downstream discharge Q/ against Q0 after dividing by Qp as parametric values in deversoir length. Fig. 5 corresponds to the pattern (a) in Fig. 2 and Figs. 6 and 7 to those of (b) and (c), respectively. When the length of deversoir L will be given, the optimized discharge Q/ will be determined for a particular discharge at an initial diversion Q0 • This is the graphical indication ofEq. (7). The three-dimen-sional representation among L, Q0 and Q/ shown in Fig. 8 will give a better 1.01--------------------. 0. 0.8 0.7 0.6 ,/y 0.5L----------"---------_.__ 0.0 0.5 1.0 Q'?f: Op Fig. 5. Ql versus ~ for Pattern (a) Hydraulic Efficiency of Flood Detention Pools 1.0r----------------------. 0.9 0.8 0.7 0.6 0.5'----------~---------0.0 0.5 1.0 Q96p Fig. 6. Ql versus QD for Pattern (b) 1.0-----------------~ 0.9 0.8 0.7 0.6 C1=300X103m3 C2=100X1Q3m3 0.5---------~--------'--o.o 0.5 1.0 Q96p Fig. 7. Ql versus QD for Pattern (c) 303 304 Yoshiaki IWASA, Kazuya INOUE and Yoshiaki TsuNEMATSU a: tp L,ii:::Const.plane Fig. 8. Three-dimensional Representation for Hydraulic Efficiency understanding for the optimization in the hydraulic efficiency of the pool system to the design hydrograph. A suitable combination of the deversoir length and the initial diversion discharge to warrant the optimization of the system or the minimum downstream discharge (Qi)min will be thus obtained, if Qg~Q/. On the contrary, if Qi>Qg, the pool capacity must be increased. Fig. 9 is a graphical indication for the necessary pool volume V max numerically calculated under the condition of C = 4.00 x 105 m 3• In the same figure, a relationship among (Q/)min• L, and Q0 is also shown. It will be understood that various combinations among (Q/)min• L, and Q0 give a nearly constant Vmax· This figure will be a practical contribution to the design problem. Much calculation also give the information that the confluence effect to the hydraulic efficiency will be substantial. Fig. 10 shows the relationship between Q/ and Q0 as parametric expressions of Land C. For a particular value of L, all the increasing limbs correspond to each other. This is an indication that the maximum efficiency of the system will be war-ranted by making a suitable combination of C and Q0 . 1.0 0.8 Hydraulic Efficiency of Flood Detention Pools l/8 {°10p)min 5 4 f 3 . 2 0.6 0.4 0.2 0 2. 4 6 8 ¾ ¼ia'}C Fig. 9. Necessary Pool Volume Vmax 1,01---------------------, 0.9 0.8 0.6 C=200x1d C=400x1dm C=600Xldm3 10 05'--------_J_~-------..l-M OE 1D 0D/Qp Fig. 10. Ql versus QD in Terms of L and C 305 12 306 Yoshiaki IWASA, Kazuya INOUE and Yoshiaki TSUNEMATSU Conclusive Description The present study has described the hydraulic efficiency of the detention pool system through mathematical simulation. A number of computations with the use of FACOM 230-60 at the Data Processing Center, Kyoto University give the following conclusive information: 1. For a given whole volume of the pool, the maximum hydraulic efficiency of the sys1 em, which warrants the minimum controlled downstream discharge (Q./)min• will be obtained as a combination of the deversoir length and the initial diversion discharge. 2. The optimum system designed for a particular hydrograph gives the same controlled discharge as the optimized discharge, when small hydrograph will be experienced. 3. If C is given, the optimized efficiency will be easily obtained, after several combinations of L and Q.0 are examined. References 1) Lax, P. and B. Wendroff, Comm. Pure Appl. Math., Vol. 13, pp. 217-237, 1960. 2) Iwasa, Y., Hydraulics, Asakura Civil Eng. Series No. 3, p. 124, 1967. 

Hydraulic Efficiency of Flood Detention Pools Evaluated by Means of Mathematical Simulation

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Hydraulic Efficiency of Flood Detention Pools Evaluated by Means of Mathematical Simulation

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