Mechanical Engineering - Research Publications

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    Modelling the effect of roughness density on turbulent forced convection
    Abu Rowin, W ; Zhong, K ; Saurav, T ; Jelly, T ; Hutchins, N ; Chung, D (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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    A viscous vortex model for predicting the drag reduction of riblet surfaces
    Wong, J ; Camobreco, CJ ; García-Mayoral, R ; Hutchins, N ; Chung, D (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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    High-Fidelity Computational Assessment of Aero-Thermal Performance and the Reynolds' Analogy for Additively Manufactured Anisotropic Surface Roughness
    Jelly, TO ; Abu Rowin, W ; Hutchins, N ; Chung, D ; Tanimoto, K ; Oda, T ; Sandberg, RD (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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    Modelling the downstream development of a turbulent boundary layer following a step change of roughness
    Li, M ; de Silva, CM ; Chung, D ; Pullin, D ; Marusic, I ; Hutchins, N (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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    Heat-transfer scaling at moderate Prandtl numbers in the fully rough regime
    Zhong, K ; Hutchins, N ; Chung, D (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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    Reorganisation of turbulence by large and spanwise-varying riblets
    Endrikat, S ; Newton, R ; Modesti, D ; García-Mayoral, R ; Hutchins, N ; Chung, D (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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    Riblet-generated flow mechanisms that lead to local breaking of Reynolds analogy
    Rouhi, A ; Endrikat, S ; Modesti, D ; Sandberg, RD ; Oda, T ; Tanimoto, K ; Hutchins, N ; Chung, D (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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    Important Parameters for a Predictive Model of ks for Zero-Pressure-Gradient Flows
    Flack, KA ; Chung, D (American Institute of Aeronautics and Astronautics (AIAA), 2022-10)
    To predict drag on a rough surface under turbulent flow conditions, practitioners rely on roughness correlations that map topographical features of the surface to the equivalent sand-grain roughness Ks However, details of the data that underpin these empirical correlations are not always immediately evident for comparison and discussion. Therefore, here we compile a table of roughness correlations with unified notation, in chronological order, listing the parameter ranges and the roughness types used in their development, noting idiosyncrasies. Overall, the table shows that tested roughness types have increased in generality from regular roughness elements to random surface elevations, and that the independent parameters of primary importance measure size (e.g. height), frontal area (e.g. slope) and coverage (e.g. skewness). In addition to the need for more data to populate the parameter space, outstanding questions facing practitioners are filtering and sampling of multiscale surfaces, and the treatment of heterogeneous surfaces, with answers appearing on the horizon.
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    Direct numerical simulation-based characterization of pseudo-random roughness in minimal channels
    Yang, J ; Stroh, A ; Chung, D ; Forooghi, P (CAMBRIDGE UNIV PRESS, 2022-05-04)
    Direct numerical simulations (DNS) are used to systematically investigate the applicability of the minimal-channel approach (Chung et al., J. Fluid Mech., vol. 773, 2015, pp. 418–431) for the characterization of roughness-induced drag on irregular rough surfaces. Roughness is generated mathematically using a random algorithm, in which the power spectrum (PS) and probability density function (p.d.f.) of the surface height can be prescribed. Twelve different combinations of PS and p.d.f. are examined, and both transitionally and fully rough regimes are investigated (roughness height varies in the range $k^+ = 25$ –100). It is demonstrated that both the roughness function ( ${\rm \Delta} U^+$ ) and the zero-plane displacement can be predicted with ${\pm }5\,\%$ accuracy using DNS in properly sized minimal channels. Notably, when reducing the domain size, the predictions remain accurate as long as 90 % of the roughness height variance is retained. Additionally, examining the results obtained from different random realizations of roughness shows that a fixed combination of p.d.f. and PS leads to a nearly unique ${\rm \Delta} U^+$ for deterministically different surface topographies. In addition to the global flow properties, the distribution of time-averaged surface force exerted by the roughness onto the fluid is calculated. It is shown that patterns of surface force distribution over irregular roughness can be well captured when the sheltering effect is taken into account. This is made possible by applying the sheltering model of Yang et al. (J. Fluid Mech., vol. 789, 2016, pp. 127–165) to each specific roughness topography. Furthermore, an analysis of the coherence function between the roughness height and the surface force distributions reveals that the coherence drops at larger streamwise wavelengths, which can be an indication that very large horizontal scales contribute less to the skin-friction drag.
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    Navier-Stokes-based linear model for unstably stratified turbulent channel flows
    Madhusudanan, A ; Illingworth, SJ ; Marusic, I ; Chung, D (AMER PHYSICAL SOC, 2022-04-06)