Representation of non-rectangular boundaries in numerical simulations of natural convection flows in reservoir sidearms

This research investigates turbulent natural convection in a triangular cavity heated by solar radi- ation. This is a simplified model representing the sidearm of a lake or water reservoir. Lateral temperature gradients exist due to the varying depth of the cavity, resulting in lateral circulation. These flows are important in a reservoir as they can carry with them particles and various pollutants, transporting and mixing them with the central section. Therefore study in this area is important in water quality management. The solar radiation model consists of a heat flux from the sloped bottom boundary as well as an internal heating source term in the body of the water. The heat flux at the bottom boundary induces natural convection including convective plumes and a large scale circulation, while the internal heating acts to stabilise the flow through the generation of a stable density stratification. Numerical simulations up to a Rayleigh number of 10 9 have been run to investigate different approaches for representing the oblique boundary on a Cartesian grid using the finite volume method. In the initial case a Cartesian grid with a stepped boundary for the sloping bottom was used. This approach gave relatively poor results. The steps appear to provide local perturbations in the velocity field that can trigger thermal plumes. The thermal plumes are seen rising from the sloped boundary at intervals proportional to the step size, and the number and location of plumes was found to vary significantly as the grid resolution was changed. Refining the grid to a sufficient degree near the boundary is not practical for anything other than a basic 2D model, since this requires that the simple Cartesian grid be fine over the entire domain. Two alternative approaches are investigated; using a grid with cell aspect ratio equal to the slope of the bottom boundary, and sloping the grid so that it is aligned with the boundary. Representing the bottom boundary using an Immersed Boundary method is also currently being implemented. The Immersed Boundary method involves using forcing terms in the flow equations to represent an interface or the surface of an object. The surface may split a computational cell so that the grid does not need to be aligned with the surface. Other approaches commonly used include cut cells for Cartesian grids, or body fitted coordinates with an unstructured mesh. The methods investigated here have the advantage of greatly simplifying grid generation and boundary condition implementation, while still being less computationally expensive than the alternatives. The methods investigated aim to remove the local fluctuations that induce the early appearance of thermal plumes. Changing the aspect ratio of the cells allows the Cartesian grid to remain aligned with the vertical direction, however it is not possible to refine the grid close to the boundary. Aligning the grid with the sloped bottom surface enables the grid to be refined close to this boundary, however the vertical plumes and density stratification are now skewed with respect to the grid. This increases the magnitude of the numerical errors associated with flux terms in the internal regions of the flow.