In this paper, the lid driven cavity flow inside a semi-ellipse shallow cavity was simulated using the stream function vorticity approach emphasising the non-uniform grid method. Three aspect ratios of 1:4, 1:3 and 3:8 were simulated using laminar flow conditions (range of Reynolds numbers of 100-2000). Primary and secondary vortexes were monitored extensively through centre vortex location, streamlines pattern and peak stream function values. Secondary vortexes developed at Re 1500 for the aspect ratio of 1:4, whereas secondary vortexes formed at an earlier Reynolds number of 1000 for the aspect ratios of 1:3 and 3:8. The size of secondary vortexes increases as the Reynolds number increases. Similar trends can be observed in the differences between primary vortex separation angle and reattachment angle. For the entire streamline pattern, many primary vortex centre locations were situated at the right side of the cavity.
Problem statement: Investigation of fluid flow behavior through porous media in a liddriven square cavity. Approach: The Brinkman-Forcheimer equation is coupled with the lattice Boltzmann formulation to predict the velocity field in the system. Three numerical experiments were preformed with different values of Darcy number to investigate the effect of porosity on the fluid flow.Results: In the current study, we found that the magnitude of velocity, strength of vortex and velocity boundary layer is significantly affected porosity of the media. Conclusion: The lattice Boltzmann simulation scheme is capable in prediction of fluid flow behavior through porous media.
Model verification is necessary before numerical models can be applied to produce meaningful results. For solid-liquid phase change modelling involving convection, pure gallium and tin melting have been widely used as reference for verification. It was later found that contrasting observations have been reported on the flow structure of both metals in the liquid region during the phase change process. Some researchers have reported monocellular while others reported multicellular structures in past works. In this work, tin melting problem was revisited by extending the results to flow structure visualization with Line Integral Convolution (LIC) plots to confirm the flow structure for tin melting thus pure metals in general. Enthalpy-porosity formulation coupled with Finite-Volume Method (FVM) was used to solve the set of governing equations which represented the problem at Prandtl Number = 0.02, Stefan Number = 0.01 and Rayleigh Number = 2.5 x 105. The location of solid-liquid interface and LIC plots at different times were presented. At initial state, the solid-liquid interface was closely similar for all grid sizes but as time progresses, finer grids provided improved solutions as expected. Reasonable fine grid size must be selected for solid-liquid phase change models to ensure complete physics of the problems are captured and eventually yield acceptable numerical results. The LIC plots confirmed that the flow structure is multicellular. Future phase change models referring to pure metal melting problem for verification should obtain similar flow structure to be considered acceptable.
A review on numerical simulations performed for solidification and melting process of Nano-Enhanced Phase Change Materials (NEPCM) is reported. The studies were conducted to understand the factors influencing the outcome such as nanoparticle fraction in the mixture, nanoparticle size, boundary conditions imposed and container geometry. It was found that while most studies investigated particle fraction effect, very few was conducted on the effect of nanoparticle size and shape. The numerical models applied to simulate the numerical works were compared. Most researchers applied enthalpy-porosity formulation coupled with finite volume method to perform the simulations. Most models solved a single macroscale domain at each iteration by assuming NEPCM as a single-phase substance which resulted in no attempt to model it as a two-phase substance which requires multidomain approach. Such dilemma is avoided when mesoscale method (Lattice Boltzmann Method - LBM) is applied.
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