Bos, B.S. (1998) Numerical simulation of channel flow with separated flow regions. Master's Thesis / Essay, Mathematics.
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Abstract
We all know that in applied science models are being used. These models are usually mathematically formulated. This is also the case with models used in the area of fluid mechanics. In the first half of the 19th century two men, Navier and Stokes, presented a couple of equations which describe the evolution in time of a fluid flow. These equations have normally no analytic solution, except in a few simple cases. Nowadays we can solve these equations with numerical methods and with the help of powerful computers. We have to remember that when we use numerical methods, we will not get an analytic solution but just an estimate of the solution. This point has to be made because there are fluid flows which cannot be "solved" by any computer. In those cases the computer would take such a long time calculating that it would not be worth waiting for. Sometimes it is even impossible. When there is no analytic solution of the Navier-Stokes equations we have to use numerical methods, requiring a computational grid. If this grid has not got enough grid points then the solution calculated by the computer will not be an estimate of the "real" solution, for example with turbulent flows. Unfortunately, in reality flows are turbulent. A company as the "Gasunie" is dealing with such flows in gas carriers. There are a few points that have to be made clear about flows we encounter in reality. First, in reality flows are three-dimensional. However we try to model them two-dimensional because these problems are easier to solve by the computer. Second, to simulate turbulent flows we need very fine grids. Calculation on fine grids takes a lot of time and computing power. We have now explained a few problems of the flows we encounter in reality. These turbulent flows and their study, however are of great importance, therefore there are models that only describe these turbulent flows. These models use less computing power then the full Navier-Stokes equations. A problem with these models is that they contain parameters which have to be tuned for each separate problem. In this thesis we will use a Direct Numerical Simulation (DNS)-solver ComFlo by Gerrits [4]. This DNS-solver uses a Cartesian grid approach. One of the ingredients of this DNS-solver is the boundary handling. In the thesis by Dijkstra [3] a more accurate boundary handling has been developed. This thesis gives also a small report of an industrial problem put forward by the "Gasunie". Our goal is to investigate the influence of the rough innersurface of gas pipes on pressure drops. The first simulations have been done by Dijkstra and the results are discussed at the end of his thesis. These results where not satisfying. So Dijkstra came to the conclusion that there has to be done some further investigation for this project. One of the areas that needed some improvement was the numerical stability of ComFlo. To improve the numerical stability of ComFlo we have changed the program in three areas, namely: • the in- and outflow conditions • the buffer zone • the time integration In Chapter 3 we will explain the changes made in ComFlo in more detail. In Chapter 4 we will evaluate the current potential of ComFlo as a simulation method for turbulent flows. It describes in the first two sections the results of a laminar flow over a backward facing step. We start with the 2D problems at Re = 150. In the next section we simulate the flow at Re = 800 as a 2D and 3D problem. We will show in that section that Re = 800 cannot be modelled as a 2D flow. The final section contains a simulation of a turbulent flow in a gas pipe. In Chapter 5 conclusions will be made regarding our results and that also ends our thesis.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 15 Feb 2018 07:29 |
| Last Modified: | 15 Feb 2018 07:29 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/8755 |
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