11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008
1D modelling of the interactions between heavy rainfall-runoff in urban area and flooding flows from sewer network and river G. Lipeme Kouyi1*, D. Fraisse1, N. Rivière2, V. Guinot3 and B. Chocat1 1
Université de Lyon, F-69000, Lyon, France ; INSA-Lyon, F- 69621 Villeurbanne, France ; Laboratory of Civil & Environmental Engineering. 2 Université de Lyon, LMFA, INSA-Lyon, Bat Jacquard, 20 avenue A. Einstein, F-69621 Villeurbanne Cedex, France. 3 HydroSciences Montpellier UMR 5569, Université Montpellier 2, CC MSE, 34095 Montpellier cedex 5, France. *Corresponding author, e-mail
[email protected]
ABSTRACT Many investigations have been carried out in order to find models which allow the linking of complex physical processes involved in urban flooding. The modelling of interactions between overland flows on the street and flooding flows from rivers and sewer networks becomes a main objective of recent and current research programs in Hydraulics and Urban Hydrology. In the RIVES project framework (Estimation of Scenario and Risks of Urban Floods), this paper shows the original one-dimensional linking of heavy rainfall-runoff in urban area and flooding flows from river and sewer network. The first part of the paper highlights good capacity of Canoe software to simulate the street flows. In the second part, we show the original device of connection which enables to model interactions between processes in urban flooding. Comparisons between simulated and Despotovic et al. (2004) or Gomez and Mur (2004) results show a good agreement of the calibrated one-dimensional connection model. Orifice/Weir coefficients were used as calibration parameters. So, the structure of connection operates like a manhole. The influence of flooding flows from river was taken into account as variable water depth boundary condition.
KEYWORDS Urban flooding; 1D modelling of interactions; manhole operation; Canoe software.
INTRODUCTION Urban flooding may be due to various causes: overland flows on the street, flooding flows from rivers and sewer networks. In some cases, one of those phenomena causes more damages than the two others. In others situations, urban flooding is due to complex interactions between those three phenomena. Hydraulic models used to understand various processes during urban flooding are all different (1D or 2D model) and take into account a lot of data for the description of the river, streets network or sewer systems. Many investigations are carried out to find models which allow the linking of complex physical processes involved in urban flooding. The modelling of interactions between phenomena listed above becomes a main objective of recent and current research programs in
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11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008 Hydraulics and Urban Hydrology (Djordjevic et al., 1999; Chen et al., 2007). The understanding of these complex processes represents a major concern for many urban designers or managers in order to reduce the impacts of urban flooding. In the RIVES project framework (Estimation of Scenario and Risks of Urban Floods; Abderrezzak et al., 2007), this paper shows the original one-dimensional linking of heavy rainfall-runoff in urban area and flooding flows from river and sewer network. The 1D linking has two main advantages, among others: i) the simplification of the streets and the sewer networks schematization and ii) the significant decrease of the computation time. In the first part of paper, we check capacity of the one-dimensional Canoe software to simulate the street flows. In the second part, we show the original device of connection which allows modelling interactions between processes in urban flooding.
METHODS Simulation of the street flows Presentation of the street network. In order to check the capacity of the Canoe software to simulate street flows, we used the virtual street network developed in Hy2ville project (hydraulics and hydrology in urban areas, France). The virtual street network layout is shown in Figure 1.
North
1000 m
1000 m
Figure 1. Street network layout (proposed by partners of national Hy2ville project) This street network is chosen to represent dense urban area in cities like Paris, Lyon or Montpellier in France. It is a virtual physical model with size of 1000 m x 1000 m. There are two kinds of street: small and big streets with respectively 10 and 25 m width. Its well defined geometry facilitates its use as a benchmark for different numerical models. Besides, it allows focusing on local elements well documented elsewhere, for instance four branch crossroads (Mignot, et al., 2008). Simulation of the street flow. Canoe 1D and SW2D softwares were used to simulate the distribution of flow rates through virtual overland network from north (with Hnorth as upstream hydraulic head) to south (with Hsouth as downstream hydraulic head) in order to check the capacity of 1D model to represent surface flows. Figure 2 highlights boundary conditions for 1D simulations. The north-south flow is only due to the difference between upstream and downstream hydraulic heads. 2
1D modelling of the interactions between street flows and flooding flows from sewer network and river
11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008
Hnorth
Wall
QNS
Wall
Hsouth Figure 2. Boundary conditions for the 1D simulation of the north-south flow through virtual street network. The circle indicates the crossroad through which we check the distribution of flow rates. Canoe software is based on Barré de Saint Venant equations according to x-direction (Eq 1 and Eq 2): •
•
Continuity equation: ∂S + ∂Q = q ∂t
Momentum equation:
∂x
U ∂U ∂h ∂U = g ( I − J ) + (ε − 1) ⋅ q ⋅ +U +g ∂x ∂x S ∂t
Eq 1
Eq 2
where S is the cross-sectional area, Q is the discharge, q the lateral flow rate per unit of length, U is the mean velocity according to x-direction, g is the gravitational acceleration, h is the water depth, I is the bottom slope, J is the energy loss and ε represents the lateral momentum transfer coefficient. In our study the lateral effect due to the lateral flow was neglected. The SW2D model solves the two-dimensional shallow water equations with porosity (Guinot and Soares-Frazão, 2006; Lhomme, 2006) that allow the macroscopic properties of the flow in urban areas to be represented at a large scale. The classical shallow water equations, which are used as the governing equations in the present simulations, arise as a particular case of such equations with porosity uniformly equal to unity. The two-dimensional equations can be written in conservation form as: ⎫ ∂h ∂q ∂r + + =0 ⎪ ∂t ∂x ∂y ⎪ ⎪⎪ 2 g ⎞ ∂ ⎛ qr ⎞ ∂q ∂ ⎛ q Eq 3 + ⎜⎜ + h 2 ⎟⎟ + ⎜ ⎟ = gh( S0, x − S f ,x )⎬ ∂t ∂x ⎝ h 2 ⎠ ∂y ⎝ h ⎠ ⎪ ⎪ ∂r ∂ ⎛ qr ⎞ ∂ ⎛ r 2 g 2 ⎞ + ⎜ ⎟ + ⎜ + h ⎟ = gh( S0, y − S f , y ) ⎪ ∂t ∂x ⎝ h ⎠ ∂y ⎜⎝ h 2 ⎟⎠ ⎪⎭ where h is the water depth, q and r are the unit discharge in the x- and y-direction respectively, S0,x and S0,y are the bottom slopes in the x- and y-direction respectively, and Sf,x Lipeme Kouyi et al.
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11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008 and Sf,y denote the friction slope in the x- and y-direction respectively. When the classical shallow water equations are solved, the friction slope is computed using a standard ManningStrickler formulation. The equations Eq 3 are discretized on grids with arbitrary-shaped cells (triangular, quadrangular or polygonal) using the Godunov (1959) approach, a finite volume formalism that allows to calculate the discontinuous flows such as hydraulic jumps, moving bores, etc. The mass and momentum fluxes between the computational cells are computed using approximate Riemann solvers (Guinot and Soares-Frazão, 2006; Lhomme and Guinot, 2007) that allow to improve the treatment of the source terms arising from the variations in the porosity and/or the ground level. Three Riemann solvers named HLL, HLLC and AS are tested. A specific higher-order reconstruction technique of the flow variables allows doing a robust treatment of wetting/drying fronts on arbitrary topographies (Soares-Frazão and Guinot, 2007). Figure 3 shows the computational mesh for the 2D simulations. Specific attention was focused on the mesh of crossroads.
Figure 3. Computational mesh for 2D simulation with SW2D software 1D Modelling of interactions between sewer and street flows Test network layout. A simplified network was used to represent interactions between surface flows and flooding from river and sewer network. Figure 4 shows this test network layout. Longitudinal slope = 0.4% Street network
Inlet point Outlet towards river
Connection
Original structure
Sewer network
100m
Figure 4. Test network layout 4
1D modelling of the interactions between street flows and flooding flows from sewer network and river
11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008 The shape of the street channel is shown in Figure 5. Sewer network channels are circular pipes with diameter of 1.5 m. The Strickler roughness coefficient was 70 m1/3/s for all tests.
10 m
1m
10 cm
Figure 5. Cross-section of the street channels Presentation of the structure of connection. The interactions between street and sewer flows are done through a channel of connection without slope to avoid numerical perturbations. The channel of connexion has low length (1 m length) and is very high in order to support important hydraulic head. Exchanges between sewer and street networks are done through orifice/weir devices as shown in Figure 6.
Channel of connection
Street flow
Exchange through Orifice/Weir
Sewer flow
Figure 6. Simplified scheme of the original device of connection between street and sewer networks Tests of the numerical stability. This step aims to check the numerical stability related to the way that the interactions are simulated. Brutal and gradual injections are set at the sewer and street networks inlet points. Simultaneous injections of different or same kind of hydrograph were tested with various downstream water depths to represent the influence of the river. Discharges which allow exchanges between the two networks were chosen. Figure 7 shows kinds of injected hydrograph.
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11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008
Q
brutal injection
Q 15 m3/s
gradual injection
0.01 m3/s time
time Figure 7. Kinds of injected hydrograph at sewer and street networks inlet points
RESULTS AND DISCUSSIONS Simulations of the street flows with Canoe software Comparison between 1D and 2D distribution of discharges through virtual network. Table 1 shows results of comparison represented in Figure 8. Table 1. Comparison between 1D and 2D north-south simulated discharges through virtual network Hnorth (m)
Hsouth (m)
1.64 1.60 1.57 1.56 1.17 1.16
1.54 1.32 1.09 0.86 1.02 0.80
Q2D (m3/s) HLL Solver
HLLC Solver
AS Solver
Q1D (m3/s)
30 (Q2D/Q1D =17 %) 70 (28 %) 99 (35 %) 117 (38 %) 33 (29 %) 59 (41 %)
116 (67%) 169 (68 %) 190 (67 %) 198 (65 %) 84 (75 %) 108 (74 %)
116 (67 %) 169 (68 %) 190 (67 %) 198 (65 %) 84 (75 %) 108 (74 %)
172 248 285 304 112 145
1D simulated discharges are always greater than 2D simulated discharges. Indeed, 2D modelling takes into account all lateral transfers of flow as well as the energy losses due to crossroads in the network according to the main direction of the flow. Nevertheless, 1D and 2D simulated distribution of discharges through virtual network have same order of magnitude. The mean ratio between 2D and 1D discharges is near of 0.70 for all simulations carried out. Good agreements are obtained with 2D HLL and AS solvers.
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1D modelling of the interactions between street flows and flooding flows from sewer network and river
11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008
Q 2D (m3/s)
400
HLL
300
HLLC AS
200
y =x
100 Q 1D (m3/s) 0 0
100
200
300
400
Figure 8. Comparison between 1D and 2D simulated north-south discharges through virtual overland network Differences between 1D and 2D discharges increase when the flow rates are high (more than 200 m3/s). So results become far from the y=x line where x and y represent the values of 1D and 2D discharges respectively. We can explain that by the increasing of the losses of energy according to the growth of the flow rate. Confrontation to the experimental data. Some simulations were also carried out with Canoe software in order to check its capacity to represent the share of discharges through crossroad. We used Mignot (2005) experimental data as reference. Mignot (2005) did the experimental study of the distribution of flow rates through crossroad small-scale physical test bench according to several slopes along x- and y- directions. Slopes along x- and y- direction are named sx and sy respectively. The distribution of the flow rates was checked for each couple of slopes sx-sy. Figure 9 shows the directions of flows during experimental tests. The main experimental results are presented on Figure 10.
Figure 9. Directions of flows during experimental operations (Qex and Qey are inlet discharges according to x and y direction respectively; Qsx and Qsy are outlet discharges according to the same directions)
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11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008 1.2
sx=5%-sy=5%
Qsy/Qex
Canoe Results - 0%-0% 1
1%-1% 1%-5% 5%-1%
0.8
3%-3% 0%-0% 0.6
0.4
0.2
Qey/Qex
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 10. Comparison between experimental results (Mignot, 2005) and simulated distribution of discharge through crossroad The results of simulation arose from Canoe are related to the virtual network crossroad indicated on Figure 2 by a circle. We can see in figure 10 that the contour of results provided by Canoe and experimental data obtained with sx=sy=1% are equivalent. Indeed, this slope is related to the hydraulic head line (near of 1%) and not to the bottom slope of channel which is 0%. Those first results of comparison show the capacity of Canoe software to represent the distribution of discharges through regular crossroad. More tests should be carried out in various conditions in order to improve the capacity of the Canoe software to simulate overland flow by adding terms related to the energy losses through crossroads. Modelling of exchanges between sewer and overland networks Numerical stability. The evolution of the intercepted or flooding flow rates is done according to the kind of injection. Steady state behaviour is reached after 1000 minutes (Figure 11). No divergences are observed during simulations. Simulated results gave satisfactory accordance regarding hydraulic law. So, the original device of connection can be used without numerical perturbations or divergences. Q (m3/s)
Q (m3/s)
time (minutes)
time (minutes)
a)
b)
Figure 11. Exchange between sewer and street networks after brutal and gradual injection: a) intercepted flow after injection at street inlet point; b) flooding flow after injection at sewer inlet point Agreement with manhole operation. We compared the hydraulic behaviour of the original device of connection to the results found in literature like Despotovic et al. (2004) or Gomez 8
1D modelling of the interactions between street flows and flooding flows from sewer network and river
11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008 and Mur (2004). Orifice/Weir coefficients were used as parameters for the calibration of the model. The influence of flooding flows from river has been taken into account as variable water depth boundary condition.
Transitional operation
a) Simulated behaviour of the original device
b) Manhole operating (Despotovic et al.,2004)
Figure 12. Similarity between structure of connection behaviour and Manhole operating There is a transitional operation of the device until the intercepted Qi and the approached (upstream discharge) Qa flow rates reach the values of 0.35 m3/s and 1.5 m3/s respectively (Figure 12 a). For the street flow rates lower than 1.5 m3/s the intercepted flow rates increase quickly until the beginning of the real operation of a manhole. It may be due to the perturbations related to the weir/orifice combined operation for the low street flow rates. 0,30
Transitional operation
0,25
0,20 y = 0,6344x-0,6863 R2 = 0,9694
E
y = 2,2401x-1,2885 R2 = 0,9964
0,15 -1,1326
y = 1,5232x 2 R = 0,9673
0,10
0,05 2
4
6
8
10
12
14
16
Q/y
a) Simulated efficiency of the original device
b) Manhole efficiency (Gomez and Mur, 2004)
Figure 13. Similarity between the original device and Manhole efficiencies Figure 13 shows the evolution of the efficiency (the ration between the street and intercepted flow rates) according to the ration between the street upstream flow rate and the water depth in the street near of the manhole. For the same reason as previously, we note a transitional zone on Figure 13 a. So, Results on Figures 11, 12 and 13 show that the single calibrated 1D model like Canoe seems relevant to take into account interactions between street and sewer flows. Mark et al. (2004) used as well the 1D approach to simulate urban flooding. In our case, the influence of the river flooding is integrated as water depths boundary conditions.
CONCLUSIONS The purpose of this paper was to simulate interactions between heavy rainfall-runoff in urban area and flooding flows from river and sewer network by means of the original onedimensional linking with specific device.
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11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008 Canoe 1D software was used to simulate in the one hand the street flow and in the other hand exchanges between overland and sewer networks. The Canoe 1D software shows good capacity to simulate the street flows. We used the simulated distribution of discharges through the virtual street network (developed in the french project Hy2ville) provided by SW2D software and Mignot (2005) experimental data as references. Numerical model of linking has consistent response according to various kinds of inlet waves. Some tests carried out in this study highlight similarities between the original device and manhole operation regarding Despotovic et al. (2004) and Gomez and Mur (2004) results. The influence of flooding flows from river has been taken into account as variable water depth boundary condition. So, developed model with better calibration can help designers to manage urban area in order to reduce disorders due to urban flooding. Authors will use the original device of connection to simulate flooding processes took place in Oullins in 2003 (France). There is data base with details on phenomena.
ACKNOWLEDGEMENTS The authors thank ANR for funding this work through the RIVES (grant ANR05-PRGCU004) and Hy2Ville (grant ANR-05-ECCO-016) projects so as Hervé NEGRO (Alison company) for his work on the adaptation of Canoe software to the case study.
REFERENCES Abderrezzak K. E. K., Paquier A., Rivière N., Leblois E., Guinot V. (2007). Towards a better knowledge and management of flood risks in urban area: the RIVES project. Novatech 2007, Lyon, France. Chen A., Djordjevic S., Leandro J., Savic D. (2007). The urban inundation model with bidirectional flow interaction between 2D overland surface and 1D sewer networks. Novatech 2007, Lyon, France. Despotovic J., stefanovic N., Pavlovic D., Plavsic J. (2004). Inefficiency of urban pavement inlets as source of urban floodings. Novatech 2004, Lyon, France. Djordjevic S., Prodanovic D. and Maksimovic C. (1999). An approach to simulation of dual drainage. Water Science and Technology, 39 (9): 95-103. Godunov S.K. (1959). A difference method for the calculation of discontinuous solutions of hydrodynamics. Matematicheski Sbornik. Gomez M., Mur M. J. (2004). Optimization of inlet dimensions with laboratory tests. Novatech 2004, Lyon, France. Guinot V., Soares-Frazão S. (2006). Flux and source term discretization in two-dimensional shallow water models with porosity on unstructured grids. International Journal for Numerical Methods in Fluids, 50, 309-345. Lhomme J. (2006). Modélisation des inondations en milieu urbain: approches unidimensionnelle, bidimensionnelle et macroscopique. PhD thesis, University Montpellier 2, 298 p. Lhomme J., Guinot V. (2007). A general, approximate-state Riemann solvers for hyperbolic systems of conservation laws with source terms. International Journal for Numerical Methods in Fluids, 53, 15091540. Mark O., Weesakul S., Apirumanekul C., Aroonet S. B., Djordjevic S. (2004). Potential and limitations of 1D modelling of urban flooding. Journal of Hydrology, 299 (3-4), 284-299. Mignot E. (2005). Etude expérimentale et numérique de l'inondation d'une zone urbanisée : cas des écoulements dans les carrefours en croix. PhD thesis, Ecole Centrale de Lyon, France, 333 p. Mignot E., Riviere N., Perkins R.J., Paquier A. (2008)Flow Patterns in a Four-Branch Junction with Supercritical Flow. Journal of Hydraulic Engineering, to be published (june 2008) Soares-Frazão S., Guinot V. (2007). An eigenvector-based linear reconstruction scheme for the shallow-water equations on two-dimensional unstructured meshes. International Journal for Numerical Methods in Fluids, 53, 23-55.
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1D modelling of the interactions between street flows and flooding flows from sewer network and river
