Browsing by Subject "Sphere"

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Flow Past a Sphere and a Prolate Spheroid at Low Reynolds Numbers
(2013-12-04) Zhang, Youfeng
The present work carries out numerical simulations of viscous incompressible flow past a sphere or a spheroid at low Reynolds numbers. When the flow passes a sphere or a spheroid, the flow will have its motion changed because of the shear stress from the surface of the object. This change of motion also differs at different Reynolds numbers based on the geometry of the sphere or spheroid. Many fluids researchers have conducted experiments to investigate the variations of the flow past a sphere at low Reynolds numbers. But the research on flow past a spheroid mainly focuses on cases at high Reynolds numbers (Re>105). Up to date, numerical study on flow past a spheroid at low and intermediate Reynolds numbers (<1000) has not been done thoroughly. The first part of this work is to investigate variations of the flow past a sphere occurring with increasing Reynolds number up to 400. The code used in this thesis is OpenFOAM which is an open source package providing a solver based on the Finite Volume Method. To verify the accuracy of the simulations by the code, results for velocity, vorticity and drag coefficient at very low Reynolds number (Re<0.1) are compared with exact solutions by Stokes Law. Then variations of the flow pattern are displayed up to Reynolds number 400. Some characteristics such as the drag coefficient, wake length and wake angle are recorded for contrast with data in publications. The wake length and separation angle both show logarithmic relationship with the Reynolds number. Flow patterns such as streamline around the sphere and periodic shedding are also discussed on the ground of previous knowledge. The second part will investigate the flow past a prolate spheroid. Discussion on this topic is developed in the regime of low Reynolds number (Re<1000). The present work investigates cases at very low Reynolds numbers (Re<0.1) and compares the results with exact solutions predicted by previous researchers. For higher Reynolds numbers, present work mainly focuses on studying variations of the drag coefficient with the Reynolds number and aspect ratio. The simulation shows that a spheroid has larger drag coefficient than a sphere at lower Reynolds numbers and then tends to be the smaller one for higher Reynolds numbers.
Richardson extrapolation of a positive method for numerically solving the transport equation in spherical geometry
(Texas Tech University, 1989-05) Abbott, William Ervin
This thesis presents a positive method for numerically solving the neutron transport equation in spherical geometry. The method is shown to have an asymptotic error expansion allowing the use of Richardson extrapolation to improve the numerical results. Numerical results for the method are presented for several spherical models. These results are compared to exact solutions where possible and to numerical results from standard nonpositive difference methods. In addition, a convergence analysis is presented for the method.
Surface Signature of Flow Past a Sphere at Moderate Reynolds Numbers
(2014-04-29) Shao, Qi
The incompressible viscous flow past a sphere is investigated numerically at moderate Reynolds numbers. Periodic vortex shedding happens at these Reynolds numbers. The primary objective is to identify the surface signature when the wake reaches the surface. The numerical method is a direct numerical simulation based on finite volume method using open-sourced code OpenFOAM. This work can contribute to the detection of underwater obstacles. The unsteady flow is calculated at Reynolds number of 300. The flow shows a planar symmetric pattern with vortex shedding. When Reynolds number increases to 500, the flow becomes more chaotic and loses its planar symmetry. At Reynolds number of 500, highly organized periodic surface signatures appear on the shear-free surface when the sphere is near the surface. The signatures are identified as the cold regions with hot edges when constant heat flux is performed on the surface. There is a pair of vortices with opposite rotating directions inside the signature, which can be visualized by passive Lagrangian particles. The incompressible flow acts like compressible flow on the surface because the surface divergence and convergence happen. At Reynolds number of 500, the cylindrical vortex sheet is reorganized into vortex rings due to complex instabilities effects. The periodic vortex rings attach the surface to form the periodic thermal surface signatures.