5.6 Multi-dimensional simulation of wind-driven flow and trans-
5.6.3 Results of 3D simulations
These simulations have been carried out following the 3D transport simula-tion of 30 days shown in secsimula-tion 5.5.2, and then west and south wind were imposed for 5 hours
A)
B)
P P
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S bottom (m)
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Figure 5.48: Velocity field: (A: horizontal circulation at section T-T, B: ver-tical section at section P-P), induced by west wind after 5 hours
The influence of the wind on the tracer transport is illustrated by comparing simulations with and without wind at different sections.
Figure 5.49 presents the vertical distribution of the tracer as well as the ve-locity field without wind (top) and with the effect of west wind (bottom).
The vertical profile at section C-C, which is located close to the bathing area of Wannsee, shows a little variability in the vertical direction (fig. 5.49, middle-top), while this variability is higher in the case with wind (fig. 5.49, middle-bottom). This indicates that the tracer spreads at the free surface in the wind direction. This figure (right) illustrates also the spatial variation of the tracer concentration and the velocity at 0.5 m depth under the free surface without and with west wind. The wind produces a circular distribu-tion of the concentradistribu-tion at the free surface, and the tracer spreads towards the wind direction (see fig. 5.49, left-bottom). Furthermore, the velocity when considering the wind effect (see fig. 5.49, right-bottom) is much higher and has another direction compared to the case without wind (see fig. 5.49, right-top).
Similar tracer distributions and velocity fields are presented in figure 5.50 after 5 hours of transport simulation at section S-S (see fig. 5.48). The three-dimensional profile of the velocity and the tracer is more distinct in the case of the wind. Furthermore, the influence of the wind is significant in the upper part of the water depth, where the velocities have the same direction as the wind.
Figure 5.51, 5.52 and 5.53 show the results at three section A-A, B-B and C-C. These sections are placed normal to the shore beach of the Wannsee, representing different water depths (see fig. 5.3). The middle part of the Wannsee-bathing beach (section B-B) is characterized by smaller water depth than the northern part (section A-A) as well as the northern part of the Wannsee (section C-C). In all these sections, there are considerable differ-ences in the velocities and the tracer concentrations when the cases with and without wind are compared. The flow velocity on the surface is in the direc-tion of the wind in all cases, and the velocity close to the bottom is in the opposite direction, as principally also shown in figures 5.51, 5.52 and 5.53,
transporting the tracer.
The flow fields taking into account west and south wind are shown in figure 5.54 and 5.55, respectively. The velocity field is presented here in three horizontal sections (at the free surface, at mid-depth and at the bottom).
Overall, distinct three-dimensional velocity fields occur. From these figures we can demonstrate, that the velocities at the free surface are strongly wind-dependent and have the direction of the wind. The west wind forces the surface water to move eastwards (fig. 5.54), while the south wind induces it to move northwards (fig. 5.55). 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.
Finally, we can demonstrate that the velocities at the free surface are strongly wind-dependent and point the direction of the wind, which in turn affects the (vertical) distribution of the tracer concentrations.
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[m]sectoin C-Csection A-A (from section C-C) Figure5.49:Left:Verticaldistributionoftracerandvelocity(top:withoutwind,bottom:withwestwind),right: Spatialdistributionoftracerconcentrationandvelocityat0.5munderfreesurface,atsectionC-C (top:withoutwind,bottom:withwestwind)after5hourswestwind
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Figure5.50:Verticaldistributionoftracerandvelocity(m/s)fordifferenttimestepsatthesectionS-S(seefig.5.48);left:withoutwind,right:withwestwind,after5hourswestwind
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[m] [m] Figure5.51:Left:Verticaldistributionoftracerandvelocity(top:withoutwind,bottom:withwestwind),right: Spatialdistributionoftracerconcentrationandvelocityat0.5munderfreesurfaceatsectionA-A [showninfigure5.51,middle]:(top:withoutwind,bottom:withwestwind)after5hourwestwind
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Figure5.52:Left:Verticaldistributionoftracerandvelocity(top:withoutwind,bottom:withwestwind),right:Spatialdistributionoftracerconcentrationandvelocityat0.5munderfreesurface,atsectionB-B
(top:withoutwind,bottom:withwestwind)after5hourwestwind
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[m] [m] [m] [m][m][m] [m] Figure5.53:Left:Verticaldistributionoftracerandvelocity(top:withoutwind,bottom:withwestwind,right: Spatialdistributionoftracerconcentrationandvelocityat0.5munderfreesurfaceatsectionC-C (top:withoutwind,bottom:withwestwind)after5hourwestwind
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[m] Figure5.55:SouthwindconditionandtheflowfieldatthreehorizontallevelsatWannsee:A)freesurface,B) mid-depth,C)bottom,after5hours
In this chapter, the content of the work is summarized, conclusions are drawn and an outlook on future research is given.
6.1 Conclusions
This doctoral thesis deals with two- and three-dimensional numerical simu-lations of flow and conservative transport processes in two free surface urban water systems of Berlin, a section of riverSpreeand theUnterhavel, both slow flowing water systems.
These two water systems are investigated including various effects of forcing, such as low, mean and high discharge conditions, various contaminations as well as wind with different intensities. The purpose of this thesis is to under-stand the processes, identifying important and less important effects, consid-ering the linkage between flow and transport, showing impacts of technical water systems to natural ones and providing a basis to estimate the impacts of possible future measures.
Chapter 1 introduces the topic and the motivation of this work and puts it into the framework of urban waters with its magnified loadings and inter-actions of natural and technical systems.
Chapter 2 provides a brief general introduction to numerical modeling in-cluding grid generation as well as space and time discretization methods.
Inchapter 3, the TELEMAC modeling system which has been applied for
this work is briefly explained covering the model concepts of the 2D and 3D model, the numerics as well as the pre- and postprocessors used here.
Chapter 4 focuses on a certain section of river Spree. This systems has a very simple geometry and is stressed by combined sewer overflows. The project SPREE-2011 is briefly introduced aiming to develop new off-shore storage capacities with integrated clean-up techniques in order to reduce combined sewer overflows which may enter the Spree in case of extreme events or possible leakages of a tank. Two computational domains have been considered, both using rectangular cross-sectional profiles being a reasonable simplification. The domain A is located at the Schillingsbrücke (length: 260 m and width: 90 m) only with one tank, and B located between Oberbaum-brücke and ElsenOberbaum-brücke (length: 1330 m and width is variable) with three tanks.
2D as well as 3D simulations have been carried out considering various con-ditions (low, mean and high discharge, turbulent diffusivity) in order to show the influence of the tanks on the hydraulics and water quality.
As a general result, the 2D hydrodynamical computations show, that the impact of the tank on the water level changes was small with 1 mm directly in front of the tank for steady state conditions and with up to 3 mm temporally.
The flow velocities are slightly increased up to several mm/s and recirculation zones occur behind the tank, when the simulations are compared to a system without tank.
For the 2D transport simulations, the COD (chemical oxygen demand) has been considered as conservative tracer in a first approach. The inflow of the tracer was imposed as a point source representing a possible damage.
For mean and high discharge conditions the transport is strongly advection dominated. The influence of turbulent diffusion may be strong, especially for low flow conditions. As no field measurements have been available, a value from experiences was chosen in all cases. The tracer did not reach the outflow at the Landwehr channel.
3D flow and transport effects were investigated in such a way that the tracer
is released 1.5 m below the free surface. After a small distance (∼100 m) the results become constant in the vertical direction due to advection and vertical turbulent diffusion, justifying a 2D approach.
In chapter 5 the Unterhavel water system is investigated. This system consists of shallow lakes (e.g. Wannsee, Glieniker See and Jungfernsee), small islands and channel-like rivers. The area considered is∼30km2 with a mean water depth of 5.5 m characterizing a very shallow lake which is very sensitive to corresponding winds. The bathymetry and geometry is highly complex being a challenge, for example for stable 3D simulations. This system is stressed by treated wastewater, and especially in summer, water quality problems may occur.
2D as well as 3D numerical simulations of hydrodynamics and transport processes are investigated considering various conditions (mean and high discharge, mean and strong wind).
The purpose of this study was to understand two- and three-dimensional flow and transport processes in theUnterhaveland their driving forces and mechanisms.
For mean flow conditions, the 2D hydrodynamics are characterized by very small water level fluctuations (~1 mm) and small flow velocities being less than 1 cm/s in large parts of the domain and up to a few centimeters in narrow passages. The average velocity at the Wannsee was v 0.01m/s.
For high flow condition, the overall velocities were relatively higher due to the higher inflow rate (factor 4 at Pichelssee in the north and factor 2 at Teltow channel in the south), however they also can be considered as small in general.
For the 2D simulation of transport processes, various scenarios have been in-vestigated with different injection locations (at Pichelssee in the north and at Teltow channel in the south), whereby treated wastewater has been idealised as conservative tracer. The results clearly show that the Wannsee is strongly influenced by the injection at the Teltow channel and only a little bit by the injection at Pichelssee. However, the tracer concentration in the Wannsee is
strongly reduced (with a factor of 20) when compared to the injection con-centration. A tracer injected in the north at Pichelssee mainly flows from north to south through the system. The transport is mainly advection domi-nated, expect in areas with nearly stagnant water where (turbulent) diffusion becomes visible.
For the 3D simulations, the grid was generated by duplicating the 2D grid along the vertical and using theσ-method which allows grid refinement close to the surface and bottom. 3D flow and transport simulations have been carried out without and with wind showing 3D velocity and tracer profiles.
Without wind these profile are parabolic in large parts of the domain, except in special stagnation areas.
Wind effects have been analysed considering mean conditions and an extreme storm condition. In such cases, strong 3D flow and transport effects occur with different flow directions in a profile at the surface (following the wind direction) and opposite flow direction at the bottom together with complex horizontal and vertical circulations. 3D effects are important in the Unter-havel when the wind is taken into account, especially when storm occur.