This thesis investigates turbulent wall-bounded flows using the Smoothed Particle Hydrodynamics (SPH) method. The first part focuses on the SPH method itself in the context of the Navier-Stokes equations with a special emphasis on wall boundary conditions. After discussing classical wall boundary conditions a detailed introduction to unified semi-analytical wall boundary conditions is given where the key parameter is a renormalization factor that accounts for the truncated kernel support in wall-bounded flows. In the following chapter it is shown that these boundary conditions fulfill energy conservation only approximately. This leads to numerical noise which, interpreted as form of Brownian motion, is treated using an additional volume diffusion term in the continuity equation where it is shown to be equivalent to an approximate Riemann solver. Two extensions to the boundary conditions are presented dealing with variable driving forces and a generalization to Robin type and arbitrary-order interpolation. Two modifications for freesurface flows are then presented, one for the volume diffusion term and the other for the algorithm that imposes Robin boundary conditions. The variable driving force is validated using a Poiseuille flow and the results indicate an error which is five orders of magnitude smaller than with the previous formulation. Discretising the wave equation with Robin boundary conditions proves that these are correctly imposed and that increasing the order of the interpolation decreases the error. The two modifications for flows under the influence of external forces significantly reduce the error at the free-surface. Finally, a dam break over a wedge demonstrates the capabilities of all the proposed modifications. With the aim of simulating turbulent flows in channels, the thesis moves on to extending the unified semi-analytical wall-boundary conditions to three dimensions. The thesis first presents the consistent computation of the vertex particle mass. Then, the computation of the kernel renormalization factor is considered, which in 3-D consists of solving an integral over a two dimensional manifold where the smoothing kernel intersects the boundary. Using a domain decomposition algorithm special integration areas are obtained for which this integral can be solved for the 5 th -order Wendland kernel. This algorithm is successfully applied to several validation cases including a dam break with an obstacle which show a significant improvement compared to other approximative methods and boundary conditions. The second part of this thesis investigates turbulent flows, in particular turbulent channel flow. This test case is introduced in detail showing both the physical properties as well as established numerical methods such as direct numerical simulation (DNS) and large eddy simulation (LES). In the penultimate chapter several SPH simulations of the turbulent channel flow are shown. The first section deals with a quasi DNS of the minimal-flow unit, a channel flow with a minimal domain size to sustain turbulent flow structures. The Eulerian statistics are compared to literature and show good agreement except for some wall-normal quantities. Furthermore, preliminary Lagrangian statistics are shown and compared to results obtained from a mesh-based DNS. The final simulation shows a LES of a full-sized channel at Reynolds number Re τ = 1000. The Eulerian statistics are compared to literature and the discrepancies found are explained using simulations of the Taylor-Green vortex, indicating that the momentum is not transferred appropriately due to an unresolved velocity-pressure-gradient tensor.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:603229 |
| Date | January 2014 |
| Creators | Mayrhofer, Arno |
| Contributors | Laurence, Dominique; Rogers, Benedict |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/an-investigation-into-wall-boundary-conditions-and-threedimensional-turbulent-flows-using-smoothed-particle-hydrodynamics(fb79ec9f-ca72-4ca6-a5ca-27e25e1357db).html |
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