 Mechanical Engineering  Research Publications
Mechanical Engineering  Research Publications
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ItemNo Preview AvailableDefining an equivalent homogeneous roughness length for turbulent boundary layers developing over patchy or heterogeneous surfacesHutchins, N ; Ganapathisubramani, B ; Schultz, MP ; Pullin, DI (Elsevier BV, 20230301)A new approach based on the power mean is suggested for defining an equivalent homogeneous roughness length kehr which takes into account patchiness or heterogeneous distribution of roughness on ship hulls and can be readily incorporated into existing fullscale drag prediction methods. In the limit where patch sizes are much greater than the boundary layer thickness, it is readily shown that the relationship between drag coefficient and roughness length is nonlinear, highlighting an obvious source of error with current approaches that attempt to define an equivalent homogeneous roughness through an areaweighed arithmetic mean. The degree of error is dependent on the roughness distribution, but is estimated to exceed 16% for highly skewed beta heterogeneous distributions. For fullyrough models, the powermean approach returns errors of <1% for the distributions tested here. The efficacy of the powermean approach is also evaluated in the transitional regime and with different transitional roughness models (Nikuradse and Colebrook) and retains accuracy for most realistic operating scenarios.

ItemNo Preview AvailableModelling the downstream development of a turbulent boundary layer following a step change of roughnessLi, M ; de Silva, CM ; Chung, D ; Pullin, D ; Marusic, I ; Hutchins, N (CAMBRIDGE UNIV PRESS, 20220923)In this study, we develop an analytical model to predict the turbulent boundary layer downstream of a stepchange in the surface roughness where upstream flow conditions are given. We first revisit the classical model of Elliott (Trans. Am. Geophys. Union, vol. 39, 1958, pp. 1048–1054), who modelled the velocity distribution within and above the internal layer with a simple piecewise logarithmic profile, and evolved the velocity profile using the streamwise momentum equation. Elliott's model was originally developed for an atmospheric surface layer, and to make the model applicable to a spatially developing turbulent boundary layer with finite thickness, we propose a number of more physical refinements, including adding a wake function to the velocity profile, considering the growth of the entire boundary layer in the streamwise direction, and using a more realistic shear stress profile in the momentum equation. In particular, we implement the blending model (Li et al., J. Fluid Mech., vol. 923, 2021, p. A18) to account for the deviation of the mean flow within the internal layer from a canonical velocity profile based on the local wall condition. These refinements lead to improved agreement between the prediction and the measurement, especially in the vicinity of the roughtosmooth change.

ItemNo Preview AvailableInvestigation of unsteady secondary flows and largescale turbulence in heterogeneous turbulent boundary layersWangsawijaya, DD ; Hutchins, N (CAMBRIDGE UNIV PRESS, 20220119)Following the findings by Wangsawijaya et al. (J. Fluid Mech., vol. 894, 2020, A7), we reexamine the turbulent boundary layers developing over surfaces with spanwise heterogeneous roughness of various roughness halfwavelengths $0.32 \leq S/\bar {\delta } \leq 3.63$, where $S$ is the width of the roughness strips and $\bar {\delta }$ is the spanwiseaveraged boundarylayer thickness. The heterogeneous cases induce counterrotating secondary flows, and these are compared with the largescale turbulent structures that occur naturally over the smooth wall. Both appear as meandering elongated high and lowmomentum streaks in the instantaneous flow field. Results based on the triple decomposed velocity fluctuations suggest that the secondary flows are spanwiselocked turbulent structures, with $S/\bar {\delta }$ governing the strength of the turbulent structures and the efficacy of the surface in locking the structures in place (most effective when $S/\bar {\delta } \approx 1$). In terms of unsteadiness, we find additional evidence from conditional averages of the fluctuating velocity fields showing that the secondary flows exhibit maximum unsteadiness (or meandering) when $S/\bar {\delta } \approx 1$. The conditional averages of both spanwise heterogeneous and smoothwall cases result in structures that are reminiscent of those proposed for the streakvortex instability model for the inner cycle of wallbounded turbulence. However, in this case these structures are larger and do not necessarily share the same formation mechanism with the inner cycle. Secondary flows and largescale structures coexist in the limits where either $S/\bar {\delta } \gg 1$ or $S/\bar {\delta } \ll 1$, where the secondary flows scale on $\delta$ or $S$, respectively. When $S/\bar {\delta } \gg 1$, the secondary flows are locked about the roughness transition, while relatively unaltered largescale structures occur further from the transition. In the case where $S/\bar {\delta } \ll 1$, $S$scaled secondary flows are confined close to the surface, coexisting with unaltered largerscale turbulent structures that penetrate much deeper into the layer.

ItemNo Preview AvailableInvestigation of coldwire spatial and temporal resolution issues in thermal turbulent boundary layersXia, Y ; Rowin, WA ; Jelly, T ; Marusic, I ; Hutchins, N (ELSEVIER SCIENCE INC, 20220125)

ItemHeattransfer scaling at moderate Prandtl numbers in the fully rough regimeZhong, K ; Hutchins, N ; Chung, D (Cambridge University Press, 20230325)In the fully rough regime, proposed models predict a scaling for a roughness heattransfer coefficient, e.g. the roughness Stanton number Stk ∼ (k+)−pPr−m where the exponent values p and m are model dependent, giving diverse predictions. Here, k+ is the roughness Reynolds number and Pr is the Prandtl number. To clarify this ambiguity, we conduct direct numerical simulations of forced convection over a threedimensional sinusoidal surface spanning k+ = 5.5–111 for Prandtl numbers Pr = 0.5, 1.0 and 2.0. These unprecedented parameter ranges are reached by employing minimal channels, which resolve the roughness sublayer at an affordable cost. We focus on the fully rough phenomenologies, which fall into two groups: p = 1/2 (Owen & Thomson, J. Fluid Mech., vol. 15, issue 3, 1963, pp. 321–334; Yaglom & Kader, J. Fluid Mech., vol. 62, issue 3, 1974, pp. 601–623) and p = 1/4 (Brutsaert, Water Resour. Res., vol. 11, issue 4, 1975b, pp. 543–550). Although we find the mean heat transfer favours the p = 1/4 scaling, the Prandtl–Blasius boundarylayer ideas associated with the Reynolds–Chilton–Colburn analogy that underpin the p = 1/2 can remain an apt description of the flow locally in regions exposed to high shear. Sheltered regions, meanwhile, violate this behaviour and are instead dominated by reversed flow, where no clear correlation between heat and momentum transfer is evident. The overall picture of fully rough heat transfer is then not encapsulated by one singular mechanism or phenomenology, but rather an ensemble of different behaviours locally. The implications of the approach to a Reynoldsanalogylike behaviour locally on bulk measures of the Nusselt and Stanton numbers are also examined, with evidence pointing to the onset of a regime transition at evenhigher Reynolds numbers.

ItemReorganisation of turbulence by large and spanwisevarying ribletsEndrikat, S ; Newton, R ; Modesti, D ; GarcíaMayoral, R ; Hutchins, N ; Chung, D (Cambridge University Press, 20221210)We study the flow above nonoptimal riblets, specifically large dragincreasing and twoscale trapezoidal riblets. In order to reach large Reynolds numbers and large scale separation while retaining access to flow details, we employ a combination of boundarylayer hotwire measurements and direct numerical simulation (DNS) in minimalspan channels. Although the outer Reynolds numbers differ, we observe fair agreement between experiments and DNS at matched viscousfrictionscaled riblet spacings in the overlapping physical and spectral regions, providing confidence that both data sets are valid. We find that hotwire velocity spectra above very large riblets with are depleted of nearwall energy at scales that are (much) greater than. Largescale energy likely bypasses the turbulence cascade and is transferred directly to secondary flows of size, which we observe to grow in strength with increasing riblet size. Furthermore, the present very large riblets reduce the von Kármán constant of the spanwise uniform mean velocity in a logarithmic layer and, thus, reduce the accuracy of the roughnessfunction concept, which we link to the nearwall damping of large flow structures. Halfheight riblets in the groove, which we use as a model of imperfectly repeated (spanwisevarying) riblets, impede ingroove turbulence. We show how to scale the drag optimum of imperfectly repeated riblets based on representative measurements of the true geometry by solving inexpensive Poisson equations.

ItemRibletgenerated flow mechanisms that lead to local breaking of Reynolds analogyRouhi, A ; Endrikat, S ; Modesti, D ; Sandberg, RD ; Oda, T ; Tanimoto, K ; Hutchins, N ; Chung, D (CAMBRIDGE UNIV PRESS, 20221114)We investigate the Reynolds analogy over riblets, namely the analogy between the fractional increase in Stanton number Ch and the fractional increase in the skinfriction coefficient Cf, relative to a smooth surface. We investigate the direct numerical simulation data of Endrikat et al. (Flow Turbul. Combust., vol. 107, 2021, pp. 1–29). The riblet groove shapes are isosceles triangles with tip angles α = 30◦, 60◦, 90◦, a trapezoid, a rectangle and a right triangle. The viscousscaled riblet spacing varies between s+ ≈ 10 to 60. The global Reynolds analogy is primarily influenced by Kelvin–Helmholtz rollers and secondary flows. Kelvin–Helmholtz rollers locally break the Reynolds analogy favourably, i.e., cause a locally larger fractional increase in Ch than in Cf. These rollers induce negative wall shear stress patches which have no analogue in wall heat fluxes. Secondary flows at the riblets’ crests are associated with local unfavourable breaking of the Reynolds analogy, i.e., locally larger fractional increase in Cf than in Ch. Only the triangular riblets with α = 30◦ trigger strong Kelvin–Helmholtz rollers without appreciable secondary flows. This riblet shape globally preserves the Reynolds analogy from s+ = 21 to 33. However, the other riblet shapes have weak or nonexistent Kelvin–Helmholtz rollers, yet persistent secondary flows. These riblet shapes behave similarly to rough surfaces. They unfavourably break the global Reynolds analogy and do so to a greater extent as s+ increases.

ItemNo Preview AvailableThe effect of cleaning and repainting on the ship drag penaltyUtama, IKAP ; Nugroho, B ; Yusuf, M ; Prasetyo, FA ; Hakim, ML ; Suastika, IK ; Ganapathisubramani, B ; Hutchins, N ; Monty, JP (TAYLOR & FRANCIS LTD, 20210701)Although the hull of a recently drydocked large ship is expected to be relatively smooth, surface scanning and experimentation reveal that it can exhibit an "orangepeel" roughness pattern with an equivalent sandgrain roughness height ks = 0. 101 mm. Using the known ks value and integral boundary layer evolution, a recently cleaned and coated fullscale ship was predicted to experience a significant increase in the average coefficient of friction %ΔC¯f and total hydrodynamic resistance %ΔR¯T during operation. Here the report also discusses two recently reported empirical estimations that can estimate ks directly from measured surface topographical parameters, bypassing the need for experiments on replicated surfaces. The empirical estimations are found to have an accuracy of 4.5  5 percentage points in %ΔC¯f.

ItemNo Preview AvailableNonktype behaviour of roughness when inplane wavelength approaches the boundary layer thicknessNugroho, B ; Monty, JP ; Utama, IKAP ; Ganapathisubramani, B ; Hutchins, N (CAMBRIDGE UNIV PRESS, 20210122)Abstract

ItemHeat Transfer Coefficient Estimation for Turbulent Boundary LayersWang, S ; Xia, Y ; Abu Rowin, W ; Marusic, I ; Sandberg, R ; Chung, D ; Hutchins, N ; Tanimoto, K ; Oda, T (The University of Queensland, 20201211)Convective heat transfer in rough wallbounded turbulent flows is prevalent in many engineering applications, such as in gas turbines and heat exchangers. At present, engineers lack the design tools to accurately predict the convective heat transfer in the presence of nonsmooth boundaries. Accordingly, a new turbulent boundary layer facility has been commissioned, where the temperature of an interchangeable test surface can be precisely controlled, and conductive heat losses are minimized. Using this facility, we can estimate the heat transfer coefficient (Stanton number, St), through measurement of the power supplied to the electrical heaters and also from measurements of the thermal and momentum boundary layers evolving over this surface. These methods have been initially investigated over a shorter smooth prototype heated surface and compared with existing St prediction models. Preliminary results suggest that we can accurately estimate St in this facility.