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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ItemDirect numerical simulation of high aspect ratio spanwise-aligned bars(Cambridge University Press (CUP), 2018-03-19)We conduct minimal-channel direct numerical simulations of turbulent flow over two-dimensional rectangular bars aligned in the spanwise direction. This roughness has often been described as d -type, as the roughness function ΔU+ is thought to depend only on the outer-layer length scale (pipe diameter, channel half-height or boundary layer thickness). This is in contrast to conventional engineering rough surfaces, named k -type, for which ΔU+ depends on the roughness height, k. The minimal-span rough-wall channel is used to circumvent the high cost of simulating high Reynolds number flows, enabling a range of bars with varying aspect ratios to be investigated. The present results show that increasing the trough-to-crest height, k, of the roughness while keeping the width between roughness bars, W, fixed in viscous units, results in non- k -type behaviour although this does not necessarily indicate d -type behaviour. Instead, for deep surfaces with k/W≳3, the roughness function appears to depend only on W in viscous units. In these situations, the flow no longer has any information about how deep the roughness is and instead can only ‘see’ the width of the fluid gap between the bars.
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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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ItemRoughness effects in turbulent forced convection(Cambridge University Press (CUP), 2019-02-25)We conducted direct numerical simulations of turbulent flow over three-dimensional sinusoidal roughness in a channel. A passive scalar is present in the flow with Prandtl number Pr=0.7 , to study heat transfer by forced convection over this rough surface. The minimal-span channel is used to circumvent the high cost of simulating high-Reynolds-number flows, which enables a range of rough surfaces to be efficiently simulated. The near-wall temperature profile in the minimal-span channel agrees well with that of the conventional full-span channel, indicating that it can be readily used for heat-transfer studies at a much reduced cost compared to conventional direct numerical simulation. As the roughness Reynolds number, k+ , is increased, the Hama roughness function, ΔU+ , increases in the transitionally rough regime before tending towards the fully rough asymptote of κ−1mlog(k+)+C , where C is a constant that depends on the particular roughness geometry and κm≈0.4 is the von Kármán constant. In this fully rough regime, the skin-friction coefficient is constant with bulk Reynolds number, Reb . Meanwhile, the temperature difference between smooth- and rough-wall flows, ΔΘ+ , appears to tend towards a constant value, ΔΘ+FR . This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with Reb in the fully rough regime. Using shifted logarithmic velocity and temperature profiles, the heat-transfer law as described by the Stanton number in the fully rough regime can be derived once both the equivalent sand-grain roughness ks/k and the temperature difference ΔΘ+FR are known. In meteorology, this corresponds to the ratio of momentum and heat-transfer roughness lengths, z0m/z0h , being linearly proportional to the inner-normalised momentum roughness length, z+0m , where the constant of proportionality is related to ΔΘ+FR . While Reynolds analogy, or similarity between momentum and heat transfer, breaks down for the bulk skin-friction and heat-transfer coefficients, similar distribution patterns between the heat flux and viscous component of the wall shear stress are observed. Instantaneous visualisations of the temperature field show a thin thermal diffusive sublayer following the roughness geometry in the fully rough regime, resembling the viscous sublayer of a contorted smooth wall.
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ItemSimilarity and structure of wall turbulence with lateral wall shear stress variations(Cambridge University Press (CUP), 2018-07-25)Wall-bounded turbulence, where it occurs in engineering or nature, is commonly subjected to spatial variations in wall shear stress. A prime example is spatially varying roughness. Here, we investigate the configuration where the wall shear stress varies only in the lateral direction. The investigation is idealised in order to focus on one aspect, namely, the similarity and structure of turbulent inertial motion over an imposed scale of stress variation. To this end, we analyse data from direct numerical simulation (DNS) of pressure-driven turbulent flow through a channel bounded by walls of laterally alternating patches of high and low wall shear stress. The wall shear stress is imposed as a Neumann boundary condition such that the wall shear stress ratio is fixed at 3 while the lateral spacing s of the uniform-stress patches is varied from 0.39 to 6.28 of the half-channel height 𝛿 . We find that global outer-layer similarity is maintained when s is less than approximately 0.39𝛿 while local outer-layer similarity is recovered when s is greater than approximately 6.28𝛿 . However, the transition between the two regimes through s≈𝛿 is not monotonic owing to the presence of secondary roll motions that extend across the whole cross-section of the flow. Importantly, these secondary roll motions are associated with an amplified skin-friction coefficient relative to both the small- and large- s/𝛿 limits. It is found that the relationship between the secondary roll motions and the mean isovels is reversed through this transition from low longitudinal velocity over low stress at small s/𝛿 to high longitudinal velocity over low stress at large s/𝛿 .
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ItemHeat transfer in rough-wall turbulent thermal convection in the ultimate regime(American Physical Society, 2019-07-22)Heat and momentum transfer in wall-bounded turbulent flow, coupled with the effects of wall roughness, is one of the outstanding questions in turbulence research. In the standard Rayleigh-Bénard problem for natural thermal convection, it is notoriously difficult to reach the so-called ultimate regime in which the near-wall boundary layers are turbulent. Following the analyses proposed by Kraichnan [Phys. Fluids 5, 1374 (1962)] and Grossmann and Lohse [Phys. Fluids 23, 045108 (2011)], we instead utilize recent direct numerical simulations of forced convection over a rough wall in a minimal channel [MacDonald et al., J. Fluid Mech. 861, 138 (2019)] to directly study these turbulent boundary layers. We focus on the heat transport (in dimensionless form, the Nusselt number Nu) or equivalently the heat transfer coefficient (the Stanton number Ch). Extending the analyses of Kraichnan and Grossmann and Lohse, we assume logarithmic temperature profiles with a roughness-induced shift to predict an effective scaling of Nu∼Ra0.42, where Ra is the dimensionless temperature difference, corresponding to Ch∼Re−0.16, where Re is the centerline Reynolds number. This is pronouncedly different from the skin-friction coefficient Cf, which in the fully rough turbulent regime is independent of Re, due to the dominant pressure drag. In rough-wall turbulence, the absence of the analog to pressure drag in the temperature advection equation is the origin for the very different scaling properties of the heat transfer as compared to the momentum transfer. This analysis suggests that, unlike momentum transfer, the asymptotic ultimate regime, where Nu∼Ra1/2, will never be reached for heat transfer at finite Rayleigh number.
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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.