Hinkelmann, R.

Jourieh, Ayman

English

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Conference Paper, Published VersionJourieh, Ayman; Hinkelmann, R.Multi-dimensional Numerical Simulation of Wind-inducedFlow and Transport Processes in an Urban Water SystemZur Verfügung gestellt in Kooperation mit/Provided in Cooperation with:Kuratorium für Forschung im Küsteningenieurwesen (KFKI)Verfügbar unter/Available at: https://hdl.handle.net/20.500.11970/99516Vorgeschlagene Zitierweise/Suggested citation:Jourieh, Ayman; Hinkelmann, R. (2014): Multi-dimensional Numerical Simulation of Wind-induced Flow and Transport Processes in an Urban Water System. In: Lehfeldt, Rainer;Kopmann, Rebekka (Hg.): ICHE 2014. Proceedings of the 11th International Conference onHydroscience & Engineering. Karlsruhe: Bundesanstalt für Wasserbau. S. 897-904.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding. 1 INTRODUCTION Urban water systems are generally stressed by various contaminations coming from, for example, treated waste water, industry, households, runoff from streets. They consist of natural (e.g. rivers, lakes, ground-water) and technical compartments (e.g. wastewater treatment plants, sewer systems) which are often in strong interactions. The major advantage of using multi-dimensional numerical models is their capability of giving details about the flow and transport processes in two or three directions. These models also help to understand the physical, chemical and biological processes in rivers, estuaries, lakes, and coastal waters. A three-dimensional model should be chosen for example in the case of density and wind-induced flow (e.g. in this study). If only the horizontal variability of the flow is important (e.g. flood modelling), a two-dimensional approach is generally sufficient. In this contribution, the Unterhavel river in Berlin, Germany has been chosen. This system consists of a shallow lake (Wannsee) and some channels (see Fig. 2), and it has, of course, limnic character being characterized by slow flow velocities and temporarily inflow of treated waste water. For the numerical simulation of flow and transport processes, the modeling system TELEMAC has been applied to solve the 2D and 3D flow and transport equations using unstructured grids. Taking into account various conditions (e.g. low, mean and high discharge, tracer injection), a 2D and 3D model was set-up and hydrodynamic as well as transport studies were computed, in order to investigate the impact of the mean and strong wind on the flow and transport processes (Jourieh 2014). 2 MODELING SYSTEM The TELEMAC modelling system was used to set up a 2D and 3D model. It has been developed by the National Hydraulics and Environment Laboratory (Laboratoire National d´Hydraulique et Environnement - LNHE) of the Research and Development Directorate of the French Electricity Board (EDF-DRD) and is now managed and further developed by a consortium of core organizations: Artelia (formerly Sogreah, France), Bundesanstalt für Wasserbau (Germany), Centre d’Etudes Techniques Maritimes et Fluviales (France), Elec tricité de France R&D (France) and HR Wallingford (United Kingdom). TELEMAC is mainly based on the FEM and it offers various stabilisation techniques and fast solvers. The FEM using Multi-dimensional Numerical Simulation of Wind-induced Flow and Transport Processes in an Urban Water System A. Jourieh & R. Hinkelmann Technische Universität Berlin, Chair of Water Resources Management and Modeling of Hydrosystems, Germany  ABSTRACT: The Unterhavel water system in Berlin has been chosen to numerically investigate wind-induced two- and three-dimensional flow and transport processes. Mean wind and a storm have been con-sidered. The results show that the wind has a considerable influence on the flow field as well as on the tracer distribution. Wind generates complex horizontal and vertical circulations with different flow direc-tions at the surface and the bottom in parts of the water systems. Keywords: Wind-induced flow, Numerical simulation, 2D and 3D flow and transport, TELEMAC model-ing system ICHE 2014, Hamburg - Lehfeldt & Kopmann (eds) - © 2014 Bundesanstalt für Wasserbau ISBN 978-3-939230-32-8897triangular elements in 2D enables a good approximation of complex boundaries, islands etc. The grid can be refined in areas of special interest such as around narrow channels. 2.1 2D simulation of flow and transport For the 2D simulation, TELEMAC-2D has been chosen to solve the shallow water equations together with the corresponding transport equation for a conservative tracer (Hervouet 2007, Hinkelmann 2005). TELEMAC-2D solves the following equations: 2D shallow water equations: ∂ + + =∂ hh u grad h h divu St  (1) 1 ( )∂ ∂+ = − +∂ ∂t xu zu grad u div hv grad u g St h x (2) 1 ( )∂ ∂+ = − +∂ ∂t yh zu grad v div h v grad v g St h y (3) 2D tracer conservation equation: 1 ( )∂ + = +∂T TT u grad T div hv grad T St h (4) where h = water depth (m), u= velocity vector (m/s), u, v = velocity components (m/s), T = tracer con-centration (g/l), hS = source or sink of fluid (m/s), tυ = turbulent viscosity (m²/s), g = gravitational accel-eration (m/s²), z = free surface elevation (m), ,x yS S = source or sink terms of momentum (e.g. bottom friction, wind, see 2.3), Tυ = turbulent diffusivity (m²/s), TS = source or sink of tracer (g/(ls)), x, y = hori-zontal space coordinates (m), t = time (s).  The same discretisation methods, solvers and numerical parameters have been chosen for the 2D simu-lation of hydrodynamics and transport. The Methods of Characteristics (with fractional step) and the con-servative scheme with SUPG method have been chosen to solve the advection step for the velocity com-ponents and the water depth respectively. The BiCGSTAB (Biconjugate Gradient Stabilized Method) was chosen as the solver.  The main results at each node of the computational mesh are the depth of the water, the depth-averaged velocity components and tracer concentrations.  2.2 3D simulation of flow and transport TELEMAC-3D solves the three-dimensional shallow water equations together with a corresponding transport equation for a conservative tracer. 3D hydrodynamic equations: =divu q  (5) 01υ ρ∂ ∂ + = + − ∂ ∂ t xu Pu grad u div grad u ft x (6) 01υ ρ ∂ ∂+ = + − ∂ ∂ t yv Pu grad v div grad v ft y (7) 0 00 01 0 ( )sZatm szP g P P g z z g dzzρρ ρρ ρ∂ ∆+ = ⇔ = + − +∂ ∫  (8) 3D tracer transport equation: ( )TT u grad T div grad T Qtυ∂ + = +∂ (9) 898     ;  where u  = velocity vector (m/s), u, v, w = velocity components (m/s), x, y, z = space coordinates (m), t = time (s), sz = vertical component of the water surface (m), 0ρ = reference density (kg/m³), ρ∆  = density difference (kg/m³), P = pressure (Pa), Patm = atmospheric pressure (Pa), yxf , f = momentum source terms (kg/(s²m²)), Q = source or sink of tracer (kg/m³s), vt = turbulent viscosity tensor (m²/s), tυ = horizontal turbulent viscosity (m²/s), vυ = vertical turbulent viscosity (m²/s), vT= turbulent diffusivity tensor (m²/s), T hυ = horizontal turbulent diffusivity (m²/s), T vυ = vertical turbulent diffusivity (m²/s). TELEMAC-3D basic algorithm is spilt into three computational steps called fractional step method (Hervouet 2007, Hinkelmann 2005). In the first step, the advection is computed with the Method of Char-acteristics. In the second step, the diffusion and some right-hand side terms are determined with the FEM, the transport simulation is then finished. The third step computes the free surface, continuity and pressure terms using TELEMAC-2D. The BiCGSTAB (Biconjugate Gradient Stabilized Method) was used as the solver. The main results at each point in the mesh are the velocity in all three directions, the water level and the tracer concentration. 2.3 Accounting for wind  In this section it is explained how the wind is accounted for in 2D and 3D. Wind causes flow in the hori-zontal as well as the vertical direction such as circulations and thus also may have a considerable impact on the transport processes. 2D In the two-dimensional model, the wind resistance is as part of the momentum source terms Sx and Sy. The resistance of the wind has the following form, neglecting the slope of the free surface:  2 2,1x wind air D ax ax ayS c v v vhρ= − + ; 2 2, 1y wind air D ay ax ayS c v v vh ρ= − +  (10) where vax, vay = components of the wind velocity, [ / ³]air kg mρ  = air density, [ ]Dc − = wind-resistance coef-ficient. In the TELEMAC modeling system the following approach is available: 3| | 5 / 0,565 10a Dv m s c−< ⇒ = ⋅  35 | | 19, 22 / ( 0,12 0,137 | |) 10−< < ⇒ = − + ⋅ a D av m s c v  (11) 3| | 19,22 / 2,513 10a Dv m s c−< ⇒ = ⋅  where [ / ]av m s = vector of wind velocity The coefficient Dc  hides complex phenomena. In fact, the influence of the wind depends on many ef-fects such as the smoothness of the free surface, the distance over which it acts, the location of the meas-urement station, etc. Generally, the wind is measured 10 m above the water depth. The wind can be con-stant in space and time. Often a time series of wind velocity and direction with for example hourly values is used. If data of more than one measurement stations are available, a spatial interpolation is necessary. 3D In the three-dimensional model, the wind resistance is taken into account through a boundary condition similar as in 2D. The profile illustrated in Figure 1 shows the effect of a wind-induced circulation. The wind aligns with the flow at the surface imposing return flow areas along the bottom (Lui and Perez 1971, Shanahan et al. 1981). A similar velocity profile was expected in the Wannsee.  0 00 00 0hhvυυ υυ=0 00 00 0ThThTTvυυ υυ=899close to the bottom and the water surface as done here. The 3D mesh consisted of 17 planes, 1212100 nodes and 1540870 prisms. The 2D and 3D simulations started with a prescribed initial water level of 29.5 m (SenGUV 2008) equal in all points of the computational mesh and initial flow velocities were zero. The following bounda-ry conditions have been selected for the hydrodynamic simulations (Fig 2, right): i) Neumann-boundary conditions: At two inflow boundaries, discharges were imposed. They were set as constant values representing mean discharge conditions (SenGUV 2008). A value of 30.7 m³/s was imposed as inflow boundary condition at Pichelssee and 8.3 m³/s as inflow boundary condition at Teltow channel.  ii) Dirichlet-boundary conditions: Water levels were prescribed at outflow boundaries at Jungfernsee and Glienicker See. The prescribed constant water level is equal to 29.5 m. As the water level varia-tions are small, choosing a constant value is justified. The horizontal turbulent viscosity was set to 0.0001 m²/s and the friction coefficient of Manning-Stickler was set to 30 m1/3/s. For the 2D and 3D simulations of hydrodynamics and transport a time step of 3 seconds was chosen corresponding to a Courant number of about 6.  The computations for the hydrodynamics were carried out with constant boundary conditions until steady state was reached and then the simulation of transport has been carried out. In these simulations, the spreading of a passive tracer was investigated. The COD (chemical oxygen demand) which is a repre-sentative component of treated waste water, has been considered as passive and conservative tracer.  As initial conditions, the tracer concentration was assumed to be 0 mg/l and the tracer’s turbulent dif-fusivity was set to 0.0001m²/s (as the turbulent viscosity). The mean COD concentration record of seven years (2000-2007) was determined and set to 12 mg/l at the upper open boundary (Pichelsee) and to 10 mg/l at the lower open boundary (Teltow channel) (SenGUV, 2008). It was expected that the duration of the inflow of the tracers is 10 hours. Strong storms in the Unterhavel generally occurred during the winter months coming from southwest and west. The climatological winds from 10 years collected data of hourly values at the station Wannsee have been considered. Two scenarios are computed in the following: i) South wind with a velocity of 5.7 m/s representing mean conditions.  ii) West wind with a velocity of 15.5 m/s, representing the maximum conditions. The transport simulations have been carried out for 120 days, and then west and south wind were im-posed for 5 hours. 4.2 2D results The 2D flow field and tracer concentration distribution are presented in the Wannsee as well as its bathing beach for the cases without wind and with south wind (mean conditions, Fig. 3). As the flows are in op-posite direction for the case with and without wind, this has a considerable influence on the tracer concen-tration.   Figure 3. Wind field (left), 2D flow field and tracer concentration at Wannsee with south wind (top) and without wind (bot-tom), after 5 hours 901to move northwards (Fig. 7). Moreover, the velocities decrease with increasing water depth, and in the deeper layers horizontal circulations occur. Further, it can be observed that the velocity at the free surface is smaller for the south wind compared to the west wind. The reason is that the west wind is about 3 times higher than the south wind.   Figure 6. Flow field for west wind at three horizontal levels at Wannsee: A) free surface, B) mid-depth, C) bottom, after 5 hours   Figure 7. Flow field for south wind at three horizontal levels at Wannsee: A) free surface, B) mid-depth, C) bottom, after 5 hours 5 CONCLUSIONS In this paper, two- and three-dimensional numerical simulations of wind-induced flow and transport pro-cesses in the Unterhavel river in Berlin, Germany are presented. Mean wind and a storm have been con-sidered. The 2D and 3D results show that the wind has a considerable influence on the flow fields as well as the tracer distributions. Complex horizontal and vertical circulations occur. In same cases the velocity follows the direction of the wind at the surface, while the velocity is in the opposite direction at the bot-tom. REFERENCES Hervouet, J. M. (2007): Hydrodynamics of Free Surface Flows - Modelling with the Finite Element Method. John Wiley and Sons Ltd Hinkelmann, R. (2005): Efficient Numerical Methods and Information-Processing Techniques for Modeling Hydro- and Environmental Systems, Vol. 21, Springer-Verlag, Berlin, Heidelberg, Germany Jourieh, A. (2014): Multi-dimensional Numerical Simulation of Hydrodynamics and Transport Processes in Surface Water Systems in Berlin. Dissertation, School VI - Planning Building Environment, Technische Universität Berlin Lui, H., Perez, H. (1971): Wind-induced Circulation in shallow water. Journal of the Hydraulics Division, Vol. 97, No. 7, pp. 923-935 Shanahan, P., Harleman, D., Somlyody, L. (1981): Modeling Wind driven Circulation in Lake Balaton. Collaborative paper/International Institute for Applied Systems Analysis, Working Paper WP-81-7 SenGUV (2008): Senatsverwaltung für Stadtentwicklung und Umweltschutz: Umweltatlas. Besondere Mitteilung zum Gewässerkundlichen Jahresbericht für Berlin und Umland: Berlin  Smile consult GmbH (2009): www.smileconsult.de  903

Multi-dimensional Numerical Simulation of Wind-induced Flow and Transport Processes in an Urban Water System

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Multi-dimensional Numerical Simulation of Wind-induced Flow and Transport Processes in an Urban Water System

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