Mechanical Engineering - Theses
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ItemDirect numerical simulations of flow past a rotating sphere and droplet( 2011)The transport of a spherical particle or droplet has been subjected to intensive research for centuries as the hydrodynamic forces acting on the spherical particle or droplet are known to affect its flight path. Typical engineering applications of the transport of a particle or droplet can be found in areas such as internal engine combustion, inkjet printing, drug and chemical delivery where the particle or droplet's trajectory is usually predicted using the standard drag coefficient correlation for a stationary sphere. The objective of this study is focused on the flow past a solid rotating sphere at small to moderate Reynolds numbers at different rotation axis angles. The deformation of the droplet on the total hydrodynamic forces is also investigated. At moderate Reynolds numbers, $\Rey = 100$, $250$ and $300$, a parametric study on the effect of rotation axis angles was performed. The goal was to identify the change in behaviour for the flow past a rotating sphere over a range of rotation axis angles, $\alpha = 0$, $\pi/6$, $\pi/3$ and $\pi/2$. The sphere was rotated at dimensionless rotation rates, $\varOmega^* = 0.05$, $0.20$, $0.50$ and $1.00$. For $\Rey = 100$, the flow is steady and the effect of rotation axis angles on both near wake flow fields and forces are insignificant at $\varOmega^* = 0.05$. The effect of rotation axis angles becomes more pronounced with increasing $\varOmega^*$. For $\Rey = 250$ and $300$, the dynamic behaviours of both wake structures and forces are highly correlated to the rotation axis angle, $\alpha$, and rotation rate, $\varOmega^*$. The flow was classified into five different regimes for all parameters considered at $\Rey = 250$ and $300$, the hydrodynamic forces acting on the sphere are closely related to the corresponding flow regime. The changes to the time-averaged flow fields as a result of increasing Reynolds numbers are less pronounced. The flow past a rotating sphere was also numerically simulated at a higher Reynolds number, $\Rey = 500$ and $1,\!000$ for streamwise and transverse rotation only. The non-dimensional rotation rates, $\varOmega^*$, were considered over the range of $0.00$ and $1.20$. For streamwise rotation at $\Rey = 500$, a dimensionless parameter was defined to differentiate the transition of the flow structures from rotating vortex shedding to spiral structures. For $\Rey = 1,\!000$, a reverse rotation is observed due to small-scale eddies release mechanism. The phase diagram $\left( C_{Ly}, C_{Lx} \right)$ no longer forms a closed curve for the reverse rotation flow regime. For transverse rotation, a newly observed flow regime is calculated for $\Rey = 500$ and $\varOmega^* = 1.00$; and $\Rey = 1,\!000$ and $\varOmega^* \geq 0.80$. At this flow regime, stable foci are formed in the near wake increasing the hydrodynamic forces oscillation amplitude. The deformation and dynamic behaviours of a droplet rotating in streamwise and transverse directions, released into a free stream were studied at initial Reynolds number, $\Rey_i = 40$, for different initial Weber numbers, $We_i$, viscosity ratios, density ratios and dimensionless rotation rates $\left( \varOmega^* \leq 1.00 \right)$. The upper limit of $\varOmega^*$ is chosen to be unity to avoid droplet breakup. For large $We_i$, the droplet shape pancakes along the free stream as a result of streamwise rotation. Hence, its frontal area increases and leads to an increase in the total drag coefficients. But a decrease in $We_i$ shows a negative total drag coefficient. For a transversely rotating sphere, the deformation is divided into along the free stream direction and along the rotating axis. The different deformation leads to two distinctively different droplet dynamic behaviours.