Mechanical Engineering - Research Publications
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ItemSecondary motion in turbulent pipe flow with three-dimensional roughness(Cambridge University Press (CUP), 2018-08-31)The occurrence of secondary flows is investigated for three-dimensional sinusoidal roughness where the wavelength and height of the roughness elements are systematically altered. The flow spanned from the transitionally rough regime up to the fully rough regime and the solidity of the roughness ranged from a wavy, sparse roughness to a dense roughness. Analysing the time-averaged velocity, secondary flows are observed in all of the cases, reflected in the coherent stress profile which is dominant in the vicinity of the roughness elements. The roughness sublayer, defined as the region where the coherent stress is non-zero, scales with the roughness wavelength when the roughness is geometrically scaled (proportional increase in both roughness height and wavelength) and when the wavelength increases at fixed roughness height. Premultiplied energy spectra of the streamwise velocity turbulent fluctuations show that energy is reorganised from the largest streamwise wavelengths to the shorter streamwise wavelengths. The peaks in the premultiplied spectra at the streamwise and spanwise wavelengths are correlated with the roughness wavelength in the fully rough regime. Current simulations show that the spanwise scale of roughness determines the occurrence of large-scale secondary flows.
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ItemThe minimal-span channel for rough-wall turbulent flows(Cambridge University Press (CUP), 2017-04-10)Roughness predominantly alters the near-wall region of turbulent flow while the outer layer remains similar with respect to the wall shear stress. This makes it a prime candidate for the minimal-span channel, which only captures the near-wall flow by restricting the spanwise channel width to be of the order of a few hundred viscous units. Recently, Chung et al. (J. Fluid Mech., vol. 773, 2015, pp. 418–431) showed that a minimal-span channel can accurately characterise the hydraulic behaviour of roughness. Following this, we aim to investigate the fundamental dynamics of the minimal-span channel framework with an eye towards further improving performance. The streamwise domain length of the channel is investigated with the minimum length found to be three times the spanwise width or 1000 viscous units, whichever is longer. The outer layer of the minimal channel is inherently unphysical and as such alterations to it can be performed so long as the near-wall flow, which is the same as in a full-span channel, remains unchanged. Firstly, a half-height (open) channel with slip wall is shown to reproduce the near-wall behaviour seen in a standard channel, but with half the number of grid points. Next, a forcing model is introduced into the outer layer of a half-height channel. This reduces the high streamwise velocity associated with the minimal channel and allows for a larger computational time step. Finally, an investigation is conducted to see if varying the roughness Reynolds number with time is a feasible method for obtaining the full hydraulic behaviour of a rough surface. Currently, multiple steady simulations at fixed roughness Reynolds numbers are needed to obtain this behaviour. The results indicate that the non-dimensional pressure gradient parameter must be kept below 0.03–0.07 to ensure that pressure gradient effects do not lead to an inaccurate roughness function. An empirical costing argument is developed to determine the cost in terms of CPU hours of minimal-span channel simulations a priori. This argument involves counting the number of eddy lifespans in the channel, which is then related to the statistical uncertainty of the streamwise velocity. For a given statistical uncertainty in the roughness function, this can then be used to determine the simulation run time. Following this, a finite-volume code with a body-fitted grid is used to determine the roughness function for square-based pyramids using the above insights. Comparisons to experimental studies for the same roughness geometry are made and good agreement is observed.
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ItemA systematic investigation of roughness height and wavelength in turbulent pipe flow in the transitionally rough regime(CAMBRIDGE UNIV PRESS, 2015-05)Direct numerical simulations (DNS) are conducted for turbulent flow through pipes with three-dimensional sinusoidal roughnesses explicitly represented by body-conforming grids. The same viscous-scaled roughness geometry is first simulated at a range of different Reynolds numbers to investigate the effects of low Reynolds numbers and low$R_{0}/h$, where$R_{0}$is the pipe radius and$h$is the roughness height. Results for the present class of surfaces show that the Hama roughness function${\rm\Delta}U^{+}$is only marginally affected by low Reynolds numbers (or low$R_{0}/h$), and observations of outer-layer similarity (or lack thereof) show no signs of sensitivity to Reynolds number. Then, building on this, a systematic approach is taken to isolate the effects of roughness height$h^{+}$and wavelength${\it\lambda}^{+}$in a turbulent wall-bounded flow in both transitionally rough and fully rough regimes. Current findings show that while the effective slope$\mathit{ES}$(which for the present sinusoidal surfaces is proportional to$h^{+}/{\it\lambda}^{+}$) is an important roughness parameter, the roughness function${\rm\Delta}U^{+}$must also depend on some measure of the viscous roughness height. A simplistic linear–log fit clearly illustrates the strong correlation between${\rm\Delta}U^{+}$and both the roughness average height$k_{a}^{+}$(which is related to$h^{+}$) and$\mathit{ES}$for the surfaces simulated here, consistent with published literature. Various definitions of the virtual origin for rough-wall turbulent pipe flow are investigated and, for the surfaces simulated here, the hydraulic radius of the pipe appears to be the most suitable parameter, and indeed is the only virtual origin that can ever lead to collapse in the total stress. First- and second-order statistics are also analysed and collapses in the outer layer are observed for all cases, including those where the largest roughness height is a substantial proportion of the reference radius (low$R_{0}/h$). These results provide evidence that turbulent pipe flow over the present sinusoidal surfaces adheres to Townsend’s notion of outer-layer similarity, which pertains to statistics of relative motion.