Mechanical Engineering - Research Publications
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ItemModelling the effect of roughness density on turbulent forced convection(Cambridge University Press, 2024-01-11)By examining a systematic set of direct numerical simulations, we develop a model which captures the effect of roughness density on global and local heat transfer in forced convection. The surfaces considered are zero-skewed three-dimensional sinusoidal rough walls with solidities, Λ (defined as the frontal area divided by the total plan area), ranging from low Λ=0.09, medium Λ=0.18 to high Λ=0.36. For each solidity, we vary the roughness height characterised by the roughness Reynolds number, k+, from transitionally rough to fully rough conditions. The findings indicate that, as the fully rough regime is approached, there is a pronounced breakdown in the analogy between heat and momentum transfer, whereby the velocity roughness function ΔU+ continues to increase and the temperature roughness function ΔΘ+ attains a peak with increasing k+. This breakdown occurs at higher sand-grain roughness Reynolds numbers (k+s) with increasing solidity. Locally, we find that the heat transfer can be meaningfully partitioned into two categories: exposed, high-shear regions experiencing higher heat transfer obeying a local Reynolds analogy and sheltered, reversed-flow regions experiencing lower and spatially uniform heat transfer. The relative contribution of these distinct mechanisms to the global heat transfer depends on the fraction of the total surface area covered by these regions, which ultimately depends on Λ. These insights enable us to develop a model for the rough-wall heat-transfer coefficient, Ch,k(k+,Λ,Pr), where Pr is the molecular Prandtl number, that assumes different heat-transfer laws in exposed and sheltered regions. We show that the exposed–sheltered surface-area fractions can be modelled through simple ray tracing that is solely dependent on the surface topography and a prescribed sheltering angle. Model predictions compare well when applied to heat-transfer data of traverse ribs from the literature.
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ItemA viscous vortex model for predicting the drag reduction of riblet surfaces(Cambridge University Press, 2024-01-10)This paper introduces a viscous vortex model for predicting the optimal drag reduction of riblet surfaces, eliminating the need for expensive direct numerical simulations (DNSs) or experiments. The footprint of a typical quasi-streamwise vortex, in terms of the spanwise and wall-normal velocities, is extracted from smooth-wall DNS flow fields in close proximity to the surface. The extracted velocities are then averaged and used as boundary conditions in a Stokes-flow problem, wherein riblets with various cross-sectional shapes are embedded. Here, the same smooth-wall-based boundary conditions can be used for riblets, as we observe from the DNSs that the quasi-streamwise vortices remain unmodified apart from an offset. In particular, the position of these vortices remain unpinned above small riblets. The present approach is compared with the protrusion-height model of Luchini et al. (J. Fluid Mech., vol. 228, 1991, pp. 87–109), which is also based on a Stokes calculation, but represents the vortex with only a uniform spanwise velocity boundary condition. The key novelty of the present model is the introduction of a wall-normal velocity component into the boundary condition, thus inducing transpiration at the riblet crests, which becomes relevant as the riblet size increases. Consequently, the present model allows for the drag-reduction prediction of riblets up to the optimal size. The present approach does not rely on the scale separation formally required by homogenisation techniques, which are only applicable for vanishingly small riblets.
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ItemNo Preview AvailableHigh-Fidelity Computational Assessment of Aero-Thermal Performance and the Reynolds' Analogy for Additively Manufactured Anisotropic Surface Roughness(ASME, 2023-11-01)Abstract Direct numerical simulations of incompressible turbulent forced convection over irregular, anisotropic surface roughness in a pressure-driven plane channel flow have been performed. Heat transfer was simulated by solving the passive scalar transport equation with Prandtl number Pr = 0.7. The roughness topographies under investigation here are based on an X-ray computed tomography scan of an additively manufactured internal cooling passage, which had an irregular, multiscale and mildly non-Gaussian height distribution. Three different roughness topographies and three different friction Reynolds numbers (Reτ = 395, 590, 720) were considered, along with reference smooth-wall simulations at matched Reτ. By systematically varying the roughness topography and flow conditions, a direct computational assessment of aero-thermal performance (pressure losses and heat transfer) and the Reynolds analogy factor, i.e., 2Ch/Cf, where Ch is the heat-transfer coefficient (Stanton number) and Cf is the skin-friction coefficient, was conducted. The results highlight the profound impact that the roughness orientation (relative to the flow direction) has upon the aero-thermal performance of additively manufactured internal passages, with transverse-aligned roughness augmenting heat transfer by as much as 33%, relative to its streamwise-aligned counterpart. An interrogation of velocity and temperature statistics in the near-wall region was also performed, which underlined the growing dissimilarity between heat transfer and drag as fully rough conditions are approached.
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ItemNo Preview AvailableModelling the downstream development of a turbulent boundary layer following a step change of roughness(CAMBRIDGE UNIV PRESS, 2022-09-23)In this study, we develop an analytical model to predict the turbulent boundary layer downstream of a step-change 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 rough-to-smooth change.
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ItemHeat-transfer scaling at moderate Prandtl numbers in the fully rough regime(Cambridge University Press, 2023-03-25)In the fully rough regime, proposed models predict a scaling for a roughness heat-transfer 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 three-dimensional 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 boundary-layer 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 Reynolds-analogy-like 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 even-higher Reynolds numbers.
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ItemReorganisation of turbulence by large and spanwise-varying riblets(Cambridge University Press, 2022-12-10)We study the flow above non-optimal riblets, specifically large drag-increasing and two-scale trapezoidal riblets. In order to reach large Reynolds numbers and large scale separation while retaining access to flow details, we employ a combination of boundary-layer hot-wire measurements and direct numerical simulation (DNS) in minimal-span channels. Although the outer Reynolds numbers differ, we observe fair agreement between experiments and DNS at matched viscous-friction-scaled riblet spacings in the overlapping physical and spectral regions, providing confidence that both data sets are valid. We find that hot-wire velocity spectra above very large riblets with are depleted of near-wall energy at scales that are (much) greater than. Large-scale 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 roughness-function concept, which we link to the near-wall damping of large flow structures. Half-height riblets in the groove, which we use as a model of imperfectly repeated (spanwise-varying) riblets, impede in-groove 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.
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ItemRiblet-generated flow mechanisms that lead to local breaking of Reynolds analogy(CAMBRIDGE UNIV PRESS, 2022-11-14)We investigate the Reynolds analogy over riblets, namely the analogy between the fractional increase in Stanton number Ch and the fractional increase in the skin-friction 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 viscous-scaled 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 non-existent 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.
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ItemDispersive stresses in turbulent flow over riblets(Cambridge University Press, 2021-06-25)We carry out direct numerical simulations of turbulent flow over riblets, streamwise- aligned grooves that are designed to reduce drag by modifying the near-wall flow. Twenty riblet geometries and sizes are considered, namely symmetric triangular with tip angle, and, asymmetric triangular, blade and trapezoidal. To save on computational cost, simulations are performed using the minimal-channel flow configuration. With this unprecedented breadth of high-fidelity flow data near the wall, we are able to obtain more general insights into the flow physics of riblets. As observed by García-Mayoral & Jiménez (J. Fluid Mech., vol. 678, 2011, pp. 317-347), we confirm that the drag-change curves of all the present groove geometries better collapse when reported with the viscous-scaled square root of the groove area, rather than the riblet spacing. Using a two-dimensional generalization of the Fukagata-Iwamoto-Kasagi identity in difference form we isolate the different drag-change contributions. We show that the drag increase associated with dispersive stresses carried by secondary flows can be as important as the one associated with the turbulent stresses and the pre-eminence of dispersive stresses can be estimated by the groove width at the riblet mean height.
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ItemInfluence of riblet shapes on the occurrence of Kelvin-Helmholtz rollers(CAMBRIDGE UNIV PRESS, 2021-03-02)We investigate turbulent flow over streamwise-aligned riblets (grooves) of various shapes and sizes. Small riblets with spacings of typically less than 20 viscous units are known to reduce skin-friction drag compared to a smooth wall, but larger riblets allow inertial-flow mechanisms to appear and cause drag reduction to break down. One of these mechanisms is a Kelvin–Helmholtz instability that García-Mayoral & Jiménez (J. Fluid Mech., vol. 678, 2011, pp. 317–347) identified in turbulent flow over blade riblets. In order to evaluate its dependence on riblet shape and thus gain a broader understanding of the underlying physics, we generate an extensive data set comprising 21 cases using direct numerical simulations of fully developed minimal-span channel flow. The data set contains six riblet shapes of varying sizes between maximum drag reduction and significant drag increase. Comparing the flow fields over riblets to that over a smooth wall, we find that in this data set only large sharp-triangular and blade riblets have a drag penalty associated with the Kelvin–Helmholtz instability and that the mechanism appears to be absent for blunt-triangular and trapezoidal riblets of any size. We therefore investigate two indicators for the occurrence of Kelvin–Helmholtz rollers in turbulent flow over riblets. First, we confirm for all six riblet shapes that the groove cross-sectional area in viscous units serves as a proxy for the wall-normal permeability that is necessary for the development of Kelvin–Helmholtz rollers. Additionally, we find that the occurrence of the instability correlates with a high momentum absorption at the riblet tips. The momentum absorption can be qualitatively predicted using Stokes flow.
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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.