The minimal channel: a fast and direct method for characterising roughness

MacDonald, Michael; Chung, Daniel; Hutchins, Nicholas; Chan, Leon; Ooi, Andrew; García-Mayoral, Ricardo

doi:10.1088/1742-6596/708/1/012010

Cited by 9 publications

(6 citation statements)

References 32 publications

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“…According to Lozano-Durán & Jiménez (2014), our computational domain is sufficiently large. It is worth noting that domains that are much smaller were used to study rough-wall boundary layer flows at moderate surface coverage densities (Chung et al 2015;MacDonald et al 2016MacDonald et al , 2017. Table 1 summarizes all the LES cases.…”

Section: Large-eddy Simulationsmentioning

confidence: 99%

Drag forces on sparsely packed cube arrays

Yang

Huang

et al. 2019

J. Fluid Mech.

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Flow over aligned and staggered cube arrays is a classic model problem for rough-wall turbulent boundary layers. Earlier studies of this model problem mainly looked at rough surfaces with a moderate coverage density, i.e. $\unicode[STIX]{x1D706}_{p}>O(3\,\%)$, where $\unicode[STIX]{x1D706}_{p}$ is the surface coverage density and is defined to be the ratio between the area occupied by the roughness and the total ground area. At lower surface coverage densities, i.e. $\unicode[STIX]{x1D706}_{p}<O(3\,\%)$, it is conventionally thought that cubical roughness acts like isolated roughness elements; and that the single-cube drag coefficient, i.e. $C_{d}\equiv f/(\unicode[STIX]{x1D70C}U_{h}^{2}h^{2})$, equals $C_{R}$. Here, $f$ is the drag force on one cubical roughness element, $\unicode[STIX]{x1D70C}=\text{const.}$ is the fluid density, $h$ is the height of the cube, $U_{h}$ is the spatially and temporally averaged wind speed at the cube height, and $C_{R}$ is the drag coefficient of an isolated cube. In this work, we conduct large-eddy simulations and direct numerical simulations of flow over wall-mounted cubes with very low surface coverage densities, i.e. $0.08\,\%<\unicode[STIX]{x1D706}_{p}<4.4\,\%$. The large-eddy simulations are at nominally infinite Reynolds numbers. The results challenge the conventional thinking, and we show that, at very low surface coverage densities, the single-cube drag coefficient may increase as a function of $\unicode[STIX]{x1D706}_{p}$. Our analysis suggests that this behaviour may be attributed to secondary turbulent flows. Secondary turbulent flows are often found above spanwise-heterogeneous roughness. Although the roughness considered in this work is nominally homogeneous, the secondary flows in our simulations are very similar to those observed above spanwise-heterogeneous surface roughness. These secondary vortices redistribute the fluid momentum in the outer layer, leading to high-momentum pathways above the wall-mounted cubes and low-momentum pathways at the two sides of the wall-mounted cubes. As a result, the spatially and temporally averaged wind speed at the cube height, i.e. $U_{h}$, is an underestimate of the incoming flow to the cubes, which in turn leads to a large drag coefficient $C_{d}$.

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Section: Large-eddy Simulationsmentioning

confidence: 99%

Drag forces on sparsely packed cube arrays

Yang

Huang

et al. 2019

J. Fluid Mech.

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“…(2015) and MacDonald et al. (2016) employed the idea of DNS in minimal span channels (Jiménez & Moin 1991; Flores & Jiménez 2010) for prediction of roughness-induced drag over a regular sinusoidal roughness in a channel. The central idea followed by these authors is that the amount of downward shift in the inner-scaled velocity profile is the determining factor in the prediction of drag.…”

Section: Introductionmentioning

confidence: 99%

“…Standard DNS, however, involves resolving the entire spectrum of turbulent length scales ranging from large geometrical scales to the small viscous scale, which is computationally costly. To tackle this problem, Chung et al (2015) and MacDonald et al (2016) employed the idea of DNS in minimal span channels (Jiménez & Moin 1991;Flores & Jiménez 2010) for prediction of roughness-induced drag over a regular sinusoidal roughness in a channel. The central idea followed by these authors is that the amount of downward shift in the inner-scaled velocity profile ΔU + is the determining factor in the prediction of drag.…”

Section: Introductionmentioning

confidence: 99%

Direct numerical simulation-based characterization of pseudo-random roughness in minimal channels

et al. 2022

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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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“…In the present work, all simulations are performed at Re τ = 800. Due to the high computational demand of many DNS, the concept of DNS in minimal channels (Chung et al 2015;MacDonald et al 2016) is adopted for the considered simulations. Recently, Yang et al (2022) showed the applicability of this concept for flow over irregular roughness subject to certain criteria.…”

Section: Direct Numerical Simulationsmentioning

confidence: 99%

Prediction of equivalent sand-grain size and identification of drag-relevant scales of roughness – a data-driven approach

Yang,

Stroh,

Lee

et al. 2023

J. Fluid Mech.

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Despite decades of research, a universal method for prediction of roughness-induced skin friction in a turbulent flow over an arbitrary rough surface is still elusive. The purpose of the present work is to examine two possibilities; first, predicting equivalent sand-grain roughness size $k_s$ based on the roughness height probability density function and power spectrum (PS) leveraging machine learning as a regression tool; and second, extracting information about relevance of different roughness scales to skin-friction drag by interpreting the output of the trained data-driven model. The model is an ensemble neural network (ENN) consisting of 50 deep neural networks. The data for the training of the model are obtained from direct numerical simulations (DNS) of turbulent flow in plane channels over 85 irregular multi-scale roughness samples at friction Reynolds number $Re_\tau =800$ . The 85 roughness samples are selected from a repository of 4200 samples, covering a wide parameter space, through an active learning (AL) framework. The selection is made in several iterations, based on the informativeness of samples in the repository, quantified by the variance of ENN predictions. This AL framework aims to maximize the generalizability of the predictions with a certain amount of data. This is examined using three different testing data sets with different types of roughness, including 21 surfaces from the literature. The model yields overall mean error 5 %–10 % on different testing data sets. Subsequently, a data interpretation technique, known as layer-wise relevance propagation, is applied to measure the contributions of different roughness wavelengths to the predicted $k_s$ . High-pass filtering is then applied to the roughness PS to exclude the wavenumbers identified as drag-irrelevant. The filtered rough surfaces are investigated using DNS, and it is demonstrated that despite significant impact of filtering on the roughness topographical appearance and statistics, the skin-friction coefficient of the original roughness is preserved successfully.

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The minimal channel: a fast and direct method for characterising roughness

Cited by 9 publications

References 32 publications

Drag forces on sparsely packed cube arrays

Drag forces on sparsely packed cube arrays

Direct numerical simulation-based characterization of pseudo-random roughness in minimal channels

Prediction of equivalent sand-grain size and identification of drag-relevant scales of roughness – a data-driven approach

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