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Aim of modelling and consequences on the choice of models
Modelling floods in urban areas is compulsory for any sound flood risk management planning, yet the required accuracy strongly depends on the type of risk estimation that is carried out afterwards. Simulation results from a depth averaged two-dimensional model (2D) solving the full shallow water equations can provide global flood extents and spatial distributions of maximum water levels, but also detailed time series of local flow depths and velocities. However this method is not always well-fitted for applications such as real time forecasting, uncertainty analysis or modelling at large scale (Golding 2009). Therefore a significant number of simplified urban flood models have been presented in the literature, by solving simplified forms of the shallow water equations 2 (Aronica and Lanza 2005; Yu and Lane 2006), adding porosity while removing building representation (Guinot and Soares-Frazao 2006; Soares-Frazao et al. 2008; Cea and Vazquez-Cendon 2010) or specific sub grid treatments (Inoue et al. 2000; Chen et al. 2012) to increase computational efficiency. Obviously, these simplifications cannot achieve similar accuracy as explicit modelling based on full shallow water equations, as they tend to neglect some flows patterns or average them in space, or simplify flow dynamics.
This question on models accuracy has been directly discussed when the modelling aims at some economical flood damages modelling or cost-benefit assessment (Apel et al. 2009; Freni et al. 2010), usually carried out by applying depth damages curves on computed flow depth fields. One of the conclusions of these studies is that the uncertainty associated to the depth-damage curves is much greater than the uncertainties on the hazard assessment (that is, the flows characteristics). For such applications, the flood dynamics (e.g. arrival time or flow velocities) is not really considered and this pushes towards the use of simple flood models, reporting modelling efforts on economic aspects.
Now, other applications require a better description of the surface flows dynamics. Evaluating human losses or the capacity of pedestrians to walk in a flooded street requires empirical relationships based on both flow depths and velocities (Jonkman et al. 2008; Ishigaki et al. 2010; Gomez et al. 2011). Similarly, vehicles in the streets can be moved by flood waves, leading to increased damages and potentially flow blockages if a car dam is created in the street network (Cemagref 2009). Role of the flow velocity on cars motion has been proved to be of paramount importance (Xia et al. 2011). At a larger scale, for violent flows, collapse of buildings is obviously associated to high momentum flows. By coupling an adequate hydrodynamic model with different damage functions, (Gallegos et al. 2012) managed to predict buildings washout or structural failures during a real dam break. Similarly, (Xia et al. 2011) use detailed simulation results to assess detailed vulnerability maps for cars and people during flash floods. In the end, numerous urban flood models have been presented in the literature, including more or less physics and having different initial potential. Two recurrent questions remain for all modellers, namely how to adapt models to particularities of urban areas, and what accuracy can be expected.
Integration of urban areas impervious elements
Buildings are probably the features that distinguish most urban areas from natural areas when studying floods, as these impervious macro-elements represent a large part of the surface area. When studying dense urban areas or urban drainage systems, flows can be assumed to occur mainly in the street network so that surface flow models can be restrained to this network (e.g. Lhomme et al. 2006; Mignot et al. 2006; Leandro et al. 2009). In other cases (significant flooding in moderately urbanized areas), flows can occur outside the streets and reach built-up areas. A common approach consists in considering buildings as totally impervious and excluding them from the computational domain (Schubert et al. 2008; Tsubaki and Fujita 2010). A quite similar method consists in including directly buildings elevation in the digital elevation model (Yu and Lane 2006; Vojinovic and Tutulic 2009). Both methods explicitly account for the effects of buildings, with slight differences arising from the buildings footprint delineation and different sensitivity to the mesh resolution. An implicit modelling well fitted to structured grids consists in assigning occupying and conveyance ratios to each cell partly at least partly occupied by buildings (Inoue et al. 2000), to account for the decrease of surface storage capacity and flow conveyance. A complementary approach to the latter consists in analysing a priori the possible flow pathways (Chen et al. 2012), and integrating them to more precisely account for flow blockages. Finally, for large scale flooding, impact of buildings on surface flows can be computed in a statistical and macroscopic manner. The most precise method includes addition of porosity and specific head losses to account for the non-explicit consideration of the flow contractions and expansions through the urban areas (Guinot and Soares-Frazao 2006). A less detailed method consists in increasing friction in built-up areas (Gallegos et al. 2009), the main problem being that the adequate friction is difficult to define. Clearly, integration of buildings in urban flood models has been well studied and there are several approaches to represent their effects. Now, consider a typical urban area and its representation by a quite accurate model (Figure 1.1). It can be easily seen that buildings alone cannot depict all surface elements that can affect floods: cars, trees, urban furniture, walls, fences…etc. Somehow, effect of small size ob stacles is acknowledged but it is often considered as an uncertainty source, or included in friction parameterization, which is quite arbitrary. Effects of singular walls (when not part of a building) have been seldom investigated (Yu and Lane 2011), perhaps because of the difficulty to gather relevant data (Mason et al. 2007). In a detailed modelling perspective, effects of these elements remain to be assessed.
Preliminary description of the physical processes expected in the experiments
The problem of combing and dividing flows in channel junctions has been extensively studied, as it is linked to many engineering applications. Studies have covered a wide range of junction configurations and hydraulic conditions, to provide practical ways of determining flow distribution and energy losses (e.g. Taylor 1944; Law and Reynolds 1966; Hsu et al. 2002), or to accurately describe the flow patterns (e.g. Neary and Odgaard 1993; Mignot et al. 2008).
In order to reduce the number of flow parameters and junction geometrical parameters, one type of dividing flow is studied. It consists in a subcritical dividing flow through a 3 branch junction, the 3 branches being horizontal and having the same width, and joining with a 90° angle. The choice of subcritical flows is jus tified first by the general framework of this thesis, and also because the ability of 2D numerical models to simulate such flows has been demonstrated (Shettar and Murthy 1996), whereas supercritical (Mignot et al. 2008) or transcritical (El Kadi Abderrezzak et al. 2011) flows can lead to discrepancies when using 2D numerical models. As one aim of this study is to assess the ability of a 2D model to predict influence of obstacles and detailed topography on the dividing flows, a prior requirement is the ability of such model to accurately simulate dividing flows without obstacles. Then, the chosen junction configuration is the most studied configuration, for which flow patterns have been described and relationships linking global flow characteristics have been derived. Results of previous studies on such configuration are summed up in the following.
Dividing flow in a 3 branch junction
It should be noted that dividing flows that remain subcritical everywhere form only one fraction of what is usually considered as “subcriti cal dividing flows”. Indeed, as stated in Riviere et al. (2007), three regimes can be identified:
· Subcritical flow everywhere.
· Subcritical everywhere except in the contracted region of the branch channel (occurrence of a choked flow).
· Transition from sub to supercritical flow in the main channel.
Choked flow in the branch channel is reported to occur for a branch channel Froude number larger than 0.35 (Ramamurthy et al. 1990), despite this should be considered as a fuzzy transition (Riviere et al. 2007).
The flow pattern for a full subcritical dividing flow in a 3 branch junction has been studied with laboratory measurements and 3D simulations by Neary et al. (1999), and a scheme is shown on Figure 2.1. The flow in the main (upstream) branch is divided through a dividing stream surface, starting upstream of the junction and reaching the downstream corner of the junction. The location of the corresponding dividing streamlines varies over depth, because the velocities are larger near the surface than near the bed, and the capacity of the flow to rotate towards the branch is then higher near the bed than near the surface. This was observed experimentally by Neary and Odgaard (1993), with larger variations occurring for larger bed roughness or upstream to branch velocity ratios. The flow entering the branch channel separates at the upstream corner of the junction, leading to a separation zone along the upstream wall of the branch channel (zone A in Figure 2.1). This separation zone reduces the effective width and capacity of the branch channel, and corresponding contraction coefficient has been studied to develop flow distribution models (Law and Reynolds 1966; Hsu et al. 2002). A stagnation region is located at the downstream corner of the junction, where downflow occurs and secondary flows are generated in both downstream and branch channels. The secondary circulation interacts with the recirculating flow in the branch 14 channel, which leads to very complex 3D flow patterns (Neary et al. 1999). Finally, for large branch to main channel flow discharges ratios, another separation zone can form downstream of the junction, along the channel wall opposite to the branch (zone B in Figure 2.1).
Because of the flow expansion in the junction and its contraction in the branch channel, local Froude number can rise and exceed 1, leading to supercritical flows in the junction or in its vicinity. In such cases, besides the flow patterns described for subcritical flows, additional flow structure can form (e.g. hydraulic jumps, standing waves or bow waves). Law and Reynolds (1966) shows that occurrence of these flow structures can be related to both the main branch Froude number and the discharge ratio. The whole flow in the junction can become supercritical for high main branch Froude numbers and/or extreme values of the discharge distribution, but no threshold values are reported in the literature.
Distribution models and numerical modelling
Presence of waves and hydraulic jumps can affect the control of the flow distribution, therefore the proposed analytical distribution models are usually restrained to a range of flow conditions (e.g. Froude number in one branch) (Ramamurthy and Satish 1988; Hsu et al. 2002; Riviere et al. 2007). For urban flood modelling, integrating such models for 1D modelling of the flows through a street network is compulsory. However, attempts previously carried out (Lhomme et al. 2006; Kouyi et al. 2010; Ghostine et al. 2012) showed that these distribution models may not be appropriate, and in all cases lead to higher errors than when using an explicit modelling with two-dimensional models. Complexity of street cross sections and of urban flood flows in a street network do not actually allow for a generalization and extensive use of these analytical distribution models, the latter being more adapted for standard geometries (open channels, pipe networks…e tc.).
Flow around obstacles
Graf and Yulistiyanto (1998) reported laboratory measurements of a fully turbulent subcritical open-channel flow around a non-submerged cylinder. Extensive 3D velocity fields allowed them to describe the flow pattern in the vicinity of the cylinder (Figure 2.2). Presence of the obstacle forces the flow to pile up upstream, creating an adverse pressure gradient upstream and a separation of the incoming flow from the bottom. This results in a three-dimensional horseshoe-vortex system, with a vortex which starts in front of the cylinder bottom, and stretches downstream, remaining close to the cylinder. As the flow is deviated around the cylinder, local accelerations are observed on the sides of the cylinder. Moreover, a wake is observed downstream of the cylinder, with a reverse flow and high turbulent intensities.
Chen and Jirka (1995) studied the structure of the wake for turbulent shallow flows. At high Reynolds number, the structure of the wake downstream of the obstacle does not depend on the Reynolds number (in contrast with low Reynolds number flow) and is governed by a wake parameter S=fD/4H, with D the obstacle width, H the water depth upstream and f the channel Darcy-Weisbach friction factor. For a cylinder, for S<0.2, vortex shedding occurs and leads to a vortex street in the wake, differing from the low Reynolds Von Karman vortex street because of the two-dimensionality of the coherent structures in shallow flows. For 0.2<S<0.5, the wake consists in an unsteady bubble reaching a length between 1.5 and 2.5 times the obstacle width. For higher wake parameters (S>0.5), a steady bubble wake appears, with the same length as the unsteady ones.
Applications of flow around obstacles in hydraulics mainly concern evaluation of scour around bridge piers (e.g., Breusers et al. 1977) and flow resistance of vegetated channels (e.g., Wilkerson 2007; Aberle and Järvelä 2013), and corre sponding studies are carried out with uniform approaching flow. One example of study of emerged obstacles in the vicinity of a dividing flow is reported by Nougaro et al. (1975). The authors place an emerged cylinder at the entrance of a branch channel to stabilize the flow in this channel. The study does not report precise measurements of the effects of the obstacle, but visual observations indicate that the latter can stop oscillations in the branch channel. No other studies coupling dividing flows and obstacles could be found.
Experimental facility and measuring devices
Experiments were carried out at the LMFA (Laboratoire de Mécanique des Fluides et Acoustique), on the urban crossroad model (see Figure 2.3). The facility consists in 3 horizontal glass channels with the same width (b=0.3 m) joining perpendicularly. A flow is generated in the upstream channel (length Lu = 2.0 m) and divides into the branch and the downstream channel (of respective lengths Lb = 2.6 m and Ld = 2.6 m). The upstream flow discharge Qu is generated using a pump and a valve, and is stabilized through the use of a feeding tank and a honeycomb placed at the entrance of the channel. Branch and downstream channel flows are controlled at the outlets by sharp crested weirs of adjustable height (respectively Cb and Cd), and outflows are collected in tanks located downstream. The branch flow is redirected to the downstream channel collecting tank, and the whole collected flow returns into the pumping loop, so that the whole set-up operates in a closed loop.
Table of contents :
Chapter 1. Introduction
1.1 Flood risk and urban areas
1.2 Modelling floods in urban areas
1.2.1 Aim of modelling and consequences on the choice of models
1.2.2 General principles of urban flood modelling
1.2.3 Friction Parameterization
1.2.4 Coupling of several flow types
1.2.5 Model validation
1.3 Thesis objectives and manuscript outline
Part I. Influence of obstacles and sidewalks on 3 branch bifurcation flows
Chapter 2. Experimental study on the LMFA urban crossroad model
2.1 Preliminary description of the physical processes expected in the experiments
2.1.1 Dividing flow in a 3 branch junction
2.1.2 Flow around obstacles
2.2 Experimental facility and measuring devices
2.3 Choice of flows, obstacles and sidewalks configurations
2.3.1 Dimensional analysis
2.3.2 Obstacles and sidewalks configurations
2.3.3 Methodology and measurements
2.4 Results
2.4.1 Influence of single obstacles
2.4.2 Influence of double obstacles
2.4.3 Influence of sidewalks
Conclusion
Chapter 3. Numerical simulations of experimental crossroad flows
3.1 Review of numerical simulations on dividing flows and flows around obstacle
3.1.1 Dividing flows
3.1.2 Flows around obstacles
3.2 Numerical model
3.2.1 Equations
3.2.2 Numerical scheme
3.2.3 Parameters
3.3 Modelling of initial flows
3.3.1 Validation on branch flow discharge
3.3.2 Validation on water depths
3.3.3 Validation on velocity field
3.3.4 Prediction of the different flow structures
3.4 Modelling of flows with obstacles
3.4.1 Global validation on branch flow discharge and upstream water depth evolutions
3.4.2 Detailed analysis of simulation results
3.5 Modelling of flows with sidewalks
3.5.1 Parameters of the different numerical simulations
3.5.2 Results
Conclusion
Part II. Interactions between street flows and underground pipe flows
Chapter 4. Experimental study on the DPRI urban drainage model
4.1 Introduction
4.2 Literature review of exchange flows studies
4.2.1 General considerations
4.2.2 Exchanges characterization
4.2.3 Implementation of the exchange discharge calculation in urban drainage models
4.3 Experimental measurements on the urban drainage model
4.3.1 Presentation of the experimental facility
4.3.2 Measurement devices
4.3.3 Flow measurements
4.3.4 Street topography measurements
4.3.5 Use of the experimental data
4.4 Description of experimental flows
4.4.1 Street flows
4.4.2 Pipe flows
4.4.3 Exchange flows
4.5 Exchanges analysis
4.5.1 Development of an exchange model
4.5.2 Validation of the exchange model
4.5.3 Analysis of the exchange model results
4.6 Extrapolation to real-scale urban drainage systems
4.6.1 Studied exchange structures
4.6.2 Exchange model
4.6.3 Reference results
4.6.4 Sensitivity analysis
Chapter 5. Numerical simulations of the urban drainage model experimental flows
5.1 Model set-up
5.1.1 Street flow model
5.1.2 Pipe flow model
5.1.3 Exchange model
5.2 Reference simulations
5.2.1 Steady flows
5.2.2 Unsteady flows
5.3 Influence of the surface topography
5.3.1 Definition of different surface model topographies
5.3.2 Steady flow simulations
5.3.3 Unsteady flow simulations
Conclusion
Part III. Modelling of floods in Oullins
Chapter 6. Surface flows modelling during floods in Oullins
6.1 Presentation of the study case and modelling objectives
6.1.1 The Yzeron River
6.1.2 Recent flood events
6.1.3 Analysis of recorded maximum water levels during past floods
6.1.4 Modelling objectives
6.2 Numerical model set-up
6.2.1 Topographical data processing and mesh generation
6.2.2 Structural elements
6.2.3 Friction
6.2.4 Boundary conditions
6.3 Study of the 2008 flood
6.3.1 Analysis of the reference simulation results
6.3.2 Comparison with the measured flood marks and river water levels
6.3.3 Comparison of simulations
6.3.4 Analysis of the flow in the central crossroad
6.4 Validation on other past floods
6.4.1 Simulation of the 2003 flood
6.4.2 Simulation of the 2005 flood
6.4.3 Simulation of the 2009 flood
Chapter 7. Interactions between surface flows and underground pipe flows in Oullins
7.1 Description of the sewer system
7.1.1 Pipe network
7.1.2 Exchange points with surface flows
7.2 Numerical model set-up
7.2.1 Underground drainage pipes and exchange points
7.2.2 Street/Sewer exchange modelling
7.2.3 Definition of flow hydrographs
7.3 Numerical simulations
7.3.1 Integration of street inlets in the surface flows simulations
7.3.2 Coupled modelling of interactions between surface and pipe flows
General conclusion and perspectives
General conclusion
Integration of structural elements in urban flood models
Exchange models between streets and drainage pipes
On the need of considering detailed streets topography into numerical models
A few lessons from the modelling of floods in Oullins
Perspectives
Additional physical processes
Data acquisition and pre-processing
Use of simplified numerical models
References
