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.
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ItemNumerical study of internal wall-bounded turbulent flows( 2011)Direct numerical simulation (DNS) of turbulent pipe flow has been performed at Reynolds numbers ranging from Reτ ≈ 170 to 2000. A literature review highlights a need for higher Reynolds number pipe flow DNS data. There have been many numerical studies for internal geometry (pipe and channel) wall-bounded turbulent flows. Many of the numerical data for both pipe and channel flows, which are now readily accessible are at lower Reynolds numbers. At higher Reynolds numbers, there is a lack of pipe flow DNS data as compared to channel flow DNS data. As the highest Reynolds numbers in numerical simulations are starting to overlap the lower region of experiments, validation of both experimental and numerical results is now possible. Moreover, numerical simulations are extremely useful in complementing experimental results in the near-wall region where accurate experimental data are often difficult to obtain. However, available DNS data of internal wall-bounded turbulent flows are performed with different grid resolutions and computational domain sizes, making it difficult to directly compare between them. An undertaking of this thesis involves a systematic study (using constant grid resolutions) of the domain length effect on the convergence of turbulence statistics. Investigations carried out using numerical data from fully developed pipe flow simulations indicate a recommended computational length of 8π pipe radius or half channel height for turbulence statistics to converge. It is hoped that this will serve as a benchmark computational domain length for future numerical simulations performed. A study is also carried out to better understand the similarities and differences of the flow physics between turbulent channel and pipe flows. This is performed using the newly obtained pipe flow DNS data and channel flow DNS data of del ´ Alamo et al. (2004) at a comparable Reynolds number of Reτ ≈ 1000. Different turbulence statistics investigated including mean flow, turbulence intensities, correlations and energy spectra. Comparison of both wall-bounded channel and pipe flows shows little discrepancies in the near-wall region but differences are observed in the outer-region. Although there is abundant literature for both experimental and numerical wall bounded turbulent flows, further analysis reveals discrepancies in the open literature. One of the primary contributing factors that plagues reported results are spatial resolution issues. In this thesis, the numerical data is used to investigate the effects of insufficient spatial resolution in wall-bounded turbulence by averaging the streamwise velocity component in the spanwise direction. A correction scheme is proposed to correct experimental results suffering from insufficient spatial resolution. The correction scheme is applied to attenuated experimental results such as streamwise turbulence intensity and one-dimensional energy spectra and is shown to be effective. The method of using DNS data to analysis and correct experimental results can be extended to other experimental techniques such as particle image velocimetry and laser doppler velocimetry.