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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 Δ U+ 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 (ks+ ) 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. [ABSTRACT FROM AUTHOR]

A surface roughness from a recently cleaned and painted ship's hull was scanned, scaled and replicated for laboratory testing to systematically investigate the influence of the ratio of in-plane roughness wavelength, $\lambda$ , with respect to the boundary layer thickness $\delta$. The experiments were performed by geometrically scaling the surface which maintains a constant effective slope $ES_x$ and solidity $\varLambda$ , while the ratio of $\lambda /\delta$ is varied. Here we scale the scanned roughness topography by a factor of 2.5 and 15, and measure the mean velocity profiles in the turbulent boundary layers developing over these surfaces at a range of free stream velocities and streamwise measurement locations. The results show that the $2.5\times$ scaled roughness, which has $\lambda /\delta \ll 1$ , behaves in the expected $k$ -type manner, with a roughness function ${\rm \Delta} U^+$ that is proportional to the viscous-scaled roughness height. The $15\times$ surface, however, which has $\lambda /\delta \approx 1$ , exhibits very different non- $k$ -type behaviour. This larger surface does not approach the fully rough asymptote and also exhibits a drag penalty that is comparable to the $2.5\times$ case despite the sixfold increase in the roughness height. Measurements on a spanwise–wall-normal plane reveal that the $15\times$ surface has introduced a large-scale spanwise variation in mean streamwise velocity (dispersive stresses) that extend far beyond the logarithmic region. Together this evidence suggests that a demarcation between $k$ -type and non- $k$ -type behaviour can occur in situations where the in-plane roughness wavelength approaches the boundary layer thickness. This finding has important implications to how we scale small-scale roughness from high Reynolds number (Re) large-scale applications for testing in low Re small-scale laboratory facilities or simulations. [ABSTRACT FROM AUTHOR]

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, $\unicode[STIX]{x0394}U^{+}$ , increases in the transitionally rough regime before tending towards the fully rough asymptote of $\unicode[STIX]{x1D705}_{m}^{-1}\log (k^{+})+C$ , where $C$ is a constant that depends on the particular roughness geometry and $\unicode[STIX]{x1D705}_{m}\approx 0.4$ is the von Kármán constant. In this fully rough regime, the skin-friction coefficient is constant with bulk Reynolds number, $Re_{b}$. Meanwhile, the temperature difference between smooth- and rough-wall flows, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}^{+}$ , appears to tend towards a constant value, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with $Re_{b}$ 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 $k_{s}/k$ and the temperature difference $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$ are known. In meteorology, this corresponds to the ratio of momentum and heat-transfer roughness lengths, $z_{0m}/z_{0h}$ , being linearly proportional to the inner-normalised momentum roughness length, $z_{0m}^{+}$ , where the constant of proportionality is related to $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. 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. [ABSTRACT FROM AUTHOR]

Fully resolved measurements of turbulent boundary layers are reported for the Reynolds number range Reτ = 6000-20 000. Despite several decades of research in wall-bounded turbulence there is still controversy over the behaviour of streamwise turbulence intensities near the wall, especially at high Reynolds numbers. Much of it stems from the uncertainty in measurement due to finite spatial resolution. Conventional hot-wire anemometry is limited for high Reynolds number measurements due to limited spatial resolution issues that cause attenuation in the streamwise turbulence intensity profile near the wall. To address this issue we use the nano-scale thermal anemometry probe (NSTAP), developed at Princeton University to conduct velocity measurements in the high Reynolds number boundary layer facility at the University of Melbourne. The NSTAP has a sensing length almost one order of magnitude smaller than conventional hot-wires. This enables us to acquire fully resolved velocity measurements of turbulent boundary layers up to Reτ = 20 000. Results show that in the near-wall region, the viscous-scaled streamwise turbulence intensity grows with Reτ in the Reynolds number range of the experiments. A second outer peak in the streamwise turbulence intensity is also shown to emerge at the highest Reynolds numbers. Moreover, the energy spectra in the near-wall region show excellent inner scaling over the small to moderate wavelength range, followed by a large-scale influence that increases with Reynolds number. Outer scaling in the outer region is found to collapse the energy spectra over high wavelengths across various Reynolds numbers. [ABSTRACT FROM AUTHOR]

The spatial structure of smooth- and rough-wall boundary layers is examined spectrally at approximately matched friction Reynolds number (δ+ ≈ 12000). For each wall condition, temporal and true spatial descriptions of the same flow are available from hot-wire anemometry and high-spatial-range particle image velocimetry, respectively. The results show that over the resolved flow domain, which is limited to a streamwise length of twice the boundary layer thickness, true spatial spectra of smooth-wall streamwise and wall-normal velocity fluctuations agree, to within experimental uncertainty, with those obtained from time series using Taylor’s frozen turbulence hypothesis (Proc. R. Soc. Lond. A, vol. 164, 1938, pp. 476–490). The same applies for the streamwise velocity spectra on rough walls. For the wall-normal velocity spectra, however, clear differences are observed between the true spatial and temporally convected spectra. For the rough-wall spectra, a correction is derived to enable accurate prediction of wall-normal velocity length scales from measurements of their time scales, and the implications of this correction are considered. Potential violations to Taylor’s hypothesis in flows above perturbed walls may help to explain conflicting conclusions in the literature regarding the effect of near-wall modifications on outer-region flow. In this regard, all true spatial and corrected spectra presented here indicate structural similarity in the outer region of smooth- and rough-wall flows, providing evidence for Townsend’s wall-similarity hypothesis (The Structure of Turbulent Shear Flow, vol. 1, 1956). [ABSTRACT FROM AUTHOR]