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Delft University of Technology

1. Dijkstra, Y.M. Turbulence modelling in environmental flows: Improving the numerical accuracy of the k-epsilon model by a mathematical transformation:.

Degree: 2014, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:251b4a5a-2823-4a2b-aa4a-1a2f52bc9272

Numerical modelling for environmental flow applications, such as for rivers, lakes, estuaries and coastal flows, faces a trade-off between the numerical accuracy and the required computation time. This trade-off results in grids which typically contain 10 to 100 layers in the vertical direction. Such a grid resolution poses severe limitations to the numerical accuracy of the model. The turbulence model determines a significant part of this accuracy. This research therefore investigates an unexplored method of using transformations to improve the numerical accuracy of two-equation turbulence models at a low resolution.
The k-epsilon model is used as starting point for this method. The equation for epsilon is transformed to equations for omega and tau. This results in three turbulence models, the k-epsilon, k-omega and k-tau models, which are physically equivalent, but possess different numerical properties. This research identifies these different numerical properties in order to explain when and why a certain transformation is beneficial to the numerical accuracy. The three turbulence models are tested in six cases of homogeneous and stratified flows in a one-dimensional vertical (1DV) numerical model, which is representative for the implementation in the 3D simulation system Delft 3D-FLOW.
It is shown that the k-tau model yields more accurate results than the k-epsilon and k-omega models in boundary friction dominated flows, such as those found in rivers, partially stratified estuaries and along the coast. This improved performance is explained from the profile of tau, which is linear near the frictional boundary and therefore accurately approximated on a low resolution grid. The profiles of epsilon and omega are hyperbolic near the frictional boundary and therefore not accurately represented on such a grid.
The boundary condition for tau is well-posed, while no natural boundary conditions for epsilon and omega exist. Dirichlet boundary conditions for epsilon and omega are therefore inaccurate. The Neumann boundary condition is found to be the most accurate alternative boundary condition for epsilon and omega. An adjusted Dirichlet conditions used in Delft 3D-FLOW improves on the result of the ordinary Dirchlet condition, but shows bad convergence behaviour, with results being significantly worse at 100 vertical layers than at 10 vertical layers. A new adjusted Dirichlet condition is developed, which has better convergence behaviour, but is still somewhat worse than the Neumann condition.
The k-tau and k-omega models contain a number of diffusive terms, the implementation of which may introduce numerical diffusion in the model. Some of these diffusive terms are essential to the stability of the model. Others are optional. It is argued that the choice whether or not to include such optional diffusive terms should be based on both physical and numerical arguments, because the numerical diffusion associated with the implementation of the terms may have a significant desired or undesired effects on the model…
*Advisors/Committee Members: Pietrzak, J.D., Schuttelaars, H.M., Uittenbogaard, R.E., Van Kester, J.A.T.M..*

Subjects/Keywords: turbulence modelling; numerical accuracy; stratification; k-epsilon model; k-tau model; convergence

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Dijkstra, Y. M. (2014). Turbulence modelling in environmental flows: Improving the numerical accuracy of the k-epsilon model by a mathematical transformation:. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:251b4a5a-2823-4a2b-aa4a-1a2f52bc9272

Chicago Manual of Style (16^{th} Edition):

Dijkstra, Y M. “Turbulence modelling in environmental flows: Improving the numerical accuracy of the k-epsilon model by a mathematical transformation:.” 2014. Masters Thesis, Delft University of Technology. Accessed October 19, 2019. http://resolver.tudelft.nl/uuid:251b4a5a-2823-4a2b-aa4a-1a2f52bc9272.

MLA Handbook (7^{th} Edition):

Dijkstra, Y M. “Turbulence modelling in environmental flows: Improving the numerical accuracy of the k-epsilon model by a mathematical transformation:.” 2014. Web. 19 Oct 2019.

Vancouver:

Dijkstra YM. Turbulence modelling in environmental flows: Improving the numerical accuracy of the k-epsilon model by a mathematical transformation:. [Internet] [Masters thesis]. Delft University of Technology; 2014. [cited 2019 Oct 19]. Available from: http://resolver.tudelft.nl/uuid:251b4a5a-2823-4a2b-aa4a-1a2f52bc9272.

Council of Science Editors:

Dijkstra YM. Turbulence modelling in environmental flows: Improving the numerical accuracy of the k-epsilon model by a mathematical transformation:. [Masters Thesis]. Delft University of Technology; 2014. Available from: http://resolver.tudelft.nl/uuid:251b4a5a-2823-4a2b-aa4a-1a2f52bc9272

Delft University of Technology

2. Schonewille, H.H. 3D numerical simulation of a harbour flow applied to Waalhaven, Port of Rotterdam:.

Degree: Faculty of Civil Engineering and Geosciences, Hydraulic Engineering, 2006, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:6e3bf66f-ce44-4317-9e87-139c738f0bfa

The Port of Rotterdam has requested to investigate siltation problems and the silt trap
in the Waalhaven. Before the computational modelling can be started it needs to be investigated
whether the computational model, DELFT3D, is suitable to the problem. The
Waalhaven is a relatively small area, compared to other DELFT3D problems. The final
future goal of the model would be to analyse the working of a silt trap. There has been
started with the simulation of the flow in a small scale model harbour to investigate the
flow features and the way they can be modelled. Measurement data for this model scale
harbour have been used for calibration. The value of the chosen horizontal eddy viscosity
is of major influence on the resulting flow pattern. The application of two vertical
grid-models, the -model and the Z-model, has been looked at. Harbours with entrance
angles of 90 and 45 degrees have been modelled. For the âslantingâ harbour two methods
for the calculation of the flow along staircase boundaries have been compared. With the
âCut Cellsâ method the area of the cell is adjusted and the velocity is only calculated for the
two non-boundary sides of the grid cells. For the â45 degrees closed boundaryâ method the
advection terms are corrected as well. This method can only be applied to to 45 degrees
boundaries with Z-model grids. This method shows the largest improvement of the flow
along the boundary. The Cut Cells method only shows a small improvement compared
to not applying any method. Both methods are also applied at a 1:1 scale model for the
same harbour geometries and for a 71 degrees slanting boundary. The application of the
âCut Cellsâ method shows a larger improvement than at scale 1:200. Especially for the 71
degrees slanting harbour improvement shows. With this knowledge a model has been made
for the Waalhaven. Due to the lack of necessary data the model has also been calibrated
with help of the scale models. This qualitative Waalhaven model shows that tidal filling
and the mixing layer are both important exchange mechanisms. They can cause siltation in
the Waalhaven. Sediment and density flows need to be investigated, they can be of major
influence on these conclusions.
It is possible to model the flow at the surface of the Waalhaven with DELFT3D. It is questionable
if the flow along the bottom, which is important for modelling sediment flows, can
be modelled representatively, because the boundary conditions are dominant. In a sequence
to this investigation the major issues will be the gathering of data for the calibration of the
model and to find out the dominant exchange mechanism.
*Advisors/Committee Members: Stelling, G.S., Winterwerp, J.C., Vellinga, T., van Kester, J.A.T.M., de Nijs, M.A.J..*

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Schonewille, H. H. (2006). 3D numerical simulation of a harbour flow applied to Waalhaven, Port of Rotterdam:. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:6e3bf66f-ce44-4317-9e87-139c738f0bfa

Chicago Manual of Style (16^{th} Edition):

Schonewille, H H. “3D numerical simulation of a harbour flow applied to Waalhaven, Port of Rotterdam:.” 2006. Masters Thesis, Delft University of Technology. Accessed October 19, 2019. http://resolver.tudelft.nl/uuid:6e3bf66f-ce44-4317-9e87-139c738f0bfa.

MLA Handbook (7^{th} Edition):

Schonewille, H H. “3D numerical simulation of a harbour flow applied to Waalhaven, Port of Rotterdam:.” 2006. Web. 19 Oct 2019.

Vancouver:

Schonewille HH. 3D numerical simulation of a harbour flow applied to Waalhaven, Port of Rotterdam:. [Internet] [Masters thesis]. Delft University of Technology; 2006. [cited 2019 Oct 19]. Available from: http://resolver.tudelft.nl/uuid:6e3bf66f-ce44-4317-9e87-139c738f0bfa.

Council of Science Editors:

Schonewille HH. 3D numerical simulation of a harbour flow applied to Waalhaven, Port of Rotterdam:. [Masters Thesis]. Delft University of Technology; 2006. Available from: http://resolver.tudelft.nl/uuid:6e3bf66f-ce44-4317-9e87-139c738f0bfa