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NUMERAL SIMULATION OF FLOW AND SALINITY

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NUMERAL SIMULATION OF FLOW AND SALINITY

    NUMERICAL SIMULATIONS OF FLOW AND SALINITY

    DISTRIBUTIONS IN ÖRESUND

    Urban Svensson*, Jonny Svensson** and Sture Lindahl**

    *Computer-aided Fluid Engineering, Norrköping, Sweden

    **Swedish Meteorological and Hydrological Institute,

    Västra Frölunda, Sweden

    Date: 2000-03-31

    Computer: SGI, Challenge

    PHOENICS version: 2.1

ABSTRACT

Numeral simulations of the flow and salinity distributions in Öresund, which is the sound

    between Sweden and Denmark, are presented. The purpose of the simulations is to assess the

    impact of a bridge, that is under construction, over Öresund. The numerical model is fully

    three-dimensional, employs an advanced turbulence model and uses a body-fitted coordinate

    system. Simulations, covering several months, have been carried out and results have been

    compared with field measurements; good agreement is generally obtained. In this paper the

    calibration of the model will be in focus.

1. INTRODUCTION

A fixed link is currently being built between Sweden and Denmark. This is one of the major

    civil engineering projects in Scandinavia presently and the environmental impacts of the bridge

    have been carefully evaluated. One of these impacts concerns the salt water, originating from

    the North Sea, that passes through Öresund and eventually forms the bottom water of the

    Baltic. It was decided that advanced numerical simulation studies were needed to assess if the

    salt water inflow would be reduced or modified, due to the bridge piers and two artificial

    islands. The purpose of the present paper is to give a brief description of these simulations.

The main features of Öresund, see Figure 1, can be summarised as follows. Brackish water

    from the Baltic meets salt water from the North Sea and an estuarine circulation is set up.

    Variations of this basic pattern, for example a homogeneous density field, are frequent

    depending on the pressure difference between the north and south boundary of Öresund. The

    pressure difference is caused by the difference in free surface elevation and it is this pressure

    gradient that mainly governs the flow; direct windstress is of secondary importance.The length

    of Öresund is about 80 km, the width 20 km and the depth typically 20 metres.

     XFlinten SW

Figure 1. Schematic outline of Öresund

A mathematical model that can describe the transient flow and salinity distributions in Öresund

    needs to possess the following characteristics. It should solve the basic momentum equations,

    employ an advanced turbulence model (like the k-ε model with buoyancy damping) and solve

    the salt and mass balance equations. Advanced grid techniques, like multiblock and fine grid

    embedding in a three-dimensional body-fitted coordinate system, are needed in order to resolve

    local features (for example dredging). Such a model has been set up and simulations, based on

    measured pressures at boundaries and meteorological data, covering several months have been

    carried out.

In the following section the details of the mathematical model will be given and after that

    simulation results, including comparisons with field measurements, are discussed. Finally some

    conclusions are formulated.

2. MATHEMATICAL MODEL

It will be assumed that the flow can be regarded as incompressible and that density variations

    can be handled by the Boussinesq approximation, i.e. density variations are only significant in

    the gravitational term. It will further be assumed that molecular friction can be neglected and

    that turbulent friction can be parameterized with the eddy viscosity concept. Within these

    assumptions we may formulate the conservation equations for mass and momentum as follows:

    ??DU?U1?P?ii???????F Momentum: (1) Ti??????dtXXX??ijj

    ?Uj Mass: (2) ?0?Xj

    ??UUVW?,,?where is velocity, P pressure, density, kinematic turbulent viscosity and ?iT

    F forces due to gravity and Coriolis effect. i

    The salinity, S, is determined from the following conservation equation:

    ??DSS???T?? (3) ???dtXX?????jTj

where is a turbulent Prandtl/Schmidt number (put to 2.5). ?T

The kinematic eddy viscosity was calculated from the standard model, see Rodi (1986), k??

    including terms for production/destruction due to buoyancy effects. All coefficients in the turbulence model were set according to the recommendations by Rodi (1986). Due to space limitations the reader is referred to Rodi (1986) for the set of equations giving the model. k??

Finally an equation of state is needed to relate salinity to density:

    ?? ?????1S (4) 0

    3?4?where ? is a reference density (=1000 kg/m) and an expansion coefficient . ??810??0

    The general equation solver PHOENICS (Spalding 1981) was used to solve the set of equations formulated.

3. RESULTS

    The computational domain is specified using a body-fitted coordinate system, see Figure 2. The basic grid (55 cells north-south, 29 cells east-west and 15 cells in the vertical) has in total 23 925 cells. Boundary conditions were given as measured water levels and salinity profiles north and south of Öresund and windstress from meteorological data sets. Bottom stress was calculated from a log-law with a calibrated bottom roughness coefficient.

    Time series of velocity and salinity are available from several measuring points in Öresund. Part of these were used to calibrate the model; mainly tuning the bottom roughness length and the turbulent Prandtl/Schmidt number. The remaining part of the time-series were used for predictions, i.e. no tuning of the model was allowed in these comparisons. Examples of results from the calibration of the model are given in Figures 3 and 4. The position of the measuring station chosen, Flinten SW, is shown in Figure 1. Comparisons of the timeseries of velocity are shown in Figure 3; a time period of 20 days in 1997 is used in this case. The agreement is very close indeed. The corresponding comparisons for salinity are shown in Figure 4. Also this comparison is regarded as most satisfying. It should be pointed out that the salinity at a certain point reflects all upstream events; hence if the model predicts complete vertical mixing at a certain upstream position this will affect the comparison in the point in question. It is thus much more difficult to get good agreement for salinity, as compared to velocity.

    Figure 2. Computational grid. A vertical (top) and horizontal (bottom) section.

2.5

    CALIBRATION

    2

    1.5

    1

    0.5

    0

    -0.5current velocity (m/s)

    -1

    -1.5

    Mean deviation=-0.035076-2Std. deviation=0.19805

    Corr.coeff.=0.972-2.5970907970909970911970913970915970917970919970921970923970925970927

    2.5 CALIBRATION 2

     1.5

    1

     0.5

     0

    -0.5 current velocity (m/s)

     -1

     -1.5

    Mean deviation=-0.023317

    -2Std. deviation=0.13489 Corr.coeff.=0.9813 -2.5970907970909970911970913970915970917970919970921970923970925970927

Figure 3. Comparison of velocity time series (measured red) at Flinten SW for a period of 20

    days in 1997. Upper figure shows velocities at the surface while the lower one is for a depth of

    5 metres.

    35CALIBRATION

    mean deviation=0.3860130std. deviation=1.916

    corr.coeff.=0.9475925

    20

    salinity (psu)15

    10

    5

    0970907970909970911970913970915970917970919970921970923970925970927

     35

    CALIBRATIONmean deviation=-0.036028 30 std. deviation=2.9513 corr.coeff.=0.90549 25

     20

     salinity (psu)15

     10

     5

    0 970907970909970911970913970915970917970919970921970923970925970927

    Figure 4. Comparison of salinity time series (measured red) at Flinten SW for a period of 20 days in 1997. Upper figure shows conditions at a depth of 3 metres, while the lower one is for

    a depth of 9 metres.

Figure 5. Standard grid for Öresund and two embedded grids.

Figure 6. Flow-vectors at a mid-depth position for north-going flow in Öresund.

    The Öresund Link will start as an immersed tunnel at the Danish side and end as a bridge at the Swedish side. Two artificial islands will connect the tunnel to the bridge. It is of interest to study the blocking effect of the islands and, eventually, also optimise the shape of the islands. Such simulations call for a grid-refinement technique. The PHOENICS code offers a powerful technique for multi-block and fine-grid embedding. This technique is used to get a succession of fine grids around the artificial islands. In Figure 5 the grid and the two embedded grids are shown. In the finest grid the two islands are shown as blocked out cells. The finer grids were generated by splitting a cell in the coarse net into four cells, thus doubling the horizontal resolution by each finer grid. In the finest grid the gridspacing is of the order of 100 metres.

Predicted flow fields for the two embedded grids are shown in Figure 6. As can be seen a

    recirculation is predicted behind one of the islands.

These are some sample results of the simulations carried out to assess the environmental

    impact of the Öresund Link. A complete account of the simulations can be found in Svensson

    et al (1994) and Svensson (1999). In these reports it is concluded that the Öresund Link can be

    built without negative impact on the salt water transport into the Baltic.

4. CONCLUDING REMARKS

The flow and salinity distributions in Öresund are not easily predicted as a number of complex

    processes (stratification, Coriolis effects, transient boundary conditions, etc.) are significant.

    The simulation model presented has however been shown to provide a realistic description of

    most of the dynamical effects that need to be considered in the Öresund Link project. More

    specifically, our experiences from the project can be summarised as:

? A numerical model is the only tool (due to the Coriolis effect and complex boundary

    conditions) that can be used to assess the impact of the bridge.

? State of the art techniques (bodyfitted grid with local refinements, advanced turbulence

    model, higher order numerical schemes, etc) are needed to get acceptable results.

? Field measurements are essential in order to calibrate and validate the model. By careful

    calibration of the bottom roughness coefficient, very close agreement with field

    measurements can be obtained.

REFERENCES

    Rodi, W. (1976). Examples of calculation methods for flow and mixing in stratified fluids. J.Geophys. Res., 92 (C5), 5305-5328.

Spalding D.B. (1981). ”A general purpose computer program for multi-dimensional one- and

    two-phase flow”. Math. Comp. Sim., 8, 267-276.

Svensson J., Lindahl S., Liungman O., and Svensson U. (1994). Calibration, validation and

    3-D modelling using PHOENICS. Project report for Öresundskonsortiet.

    Svensson J. (1999). ). Calibration and validation of the 3-dimensional model PHOENICS with data from Öresund recorded at a time when the fixed link was partly constructed. SMHI

    Report no. 6.

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