Dispersive stresses in turbulent flow over riblets

Modesti, Davide; Endrikat, Sebastian; Hutchins, Nicholas; Chung, Daniel

doi:10.1017/jfm.2021.310

Cited by 47 publications

(70 citation statements)

References 57 publications

(207 reference statements)

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“…In fact, only sharp-triangular and blade riblets show a significant friction contribution of KH rollers , whereas the breakdown of the viscous regime occurs inevitably for all riblets. Furthermore, Modesti et al (2021) showed that secondary flows contribute significantly to ΔU + for various riblet shapes by analysing the dispersive stresses as a footprint of secondary flows.…”

Section: Introductionmentioning

confidence: 99%

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From drag-reducing riblets to drag-increasing ridges

Deyn

Gatti

2022

J. Fluid Mech.

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Small drag-reducing riblets and larger drag-increasing ridges are longitudinally invariant and laterally periodic surface structures that differ only in the details of their lateral periodicity and their size in viscous units. Due to their different drag behaviour, typically riblets and ridges have been analysed separately. By studying experimentally trapezoidal-grooved surfaces of different sizes, we address systematically the transition from riblet-like to ridge-like behaviour in a unified framework. The structure height and lateral wavelength are varied both physically, by considering eight different surfaces, and in their viscous-scaled form, by spanning a wide range of bulk Reynolds number $Re_b$ . The effective skin-friction coefficient $C_f$ is determined via pressure-drop measurement in a turbulent channel flow facility designed for accurate drag measurements. An unexpectedly rich drag behaviour is unveiled, in which different drag regimes are distinguished depending on the value of $l_g^+$ , the viscous-scaled square root of the groove area. The well-known drag-reducing regime of riblets that spans up to $l_g^+=17$ is followed by a regime in which the roughness function ${\rm \Delta} U^+$ increases logarithmically with $l_g^+$ , indicating an apparent fully rough behaviour up to $l_g^+\approx 40$ . Further increase of $l_g^+$ leads to a clear departure from the fully rough regime, and an unexpected non-monotonic behaviour of the roughness function ${\rm \Delta} U^+$ for $50< l_g^+<200$ is reported for the first time. For sufficiently large $Re_b$ and $l_g$ , it is shown that a single parameter, similar to the classical hydraulic diameter, is sufficient to describe the drag behaviour of ridges. We find that an appropriate definition of the effective channel height is crucial for interpreting the drag behaviour. When the longitudinal protrusion height of the structured surface is accounted for in the channel height definition, a laminar flow exhibits the same $C_f(Re_b)$ relation known for flat surfaces. This approach thus allows us to discern the modification of $C_f$ induced by turbulence. We provide predictive correlations for the fully rough regime and the high Reynolds number range of trapezoidal-grooved surfaces that become possible thanks to the chosen channel height definition.

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Section: Introductionmentioning

confidence: 99%

“…Furthermore, Modesti et al. (2021) showed that secondary flows contribute significantly to for various riblet shapes by analysing the dispersive stresses as a footprint of secondary flows.…”

Section: Introductionmentioning

confidence: 99%

From drag-reducing riblets to drag-increasing ridges

Deyn

Gatti

2022

J. Fluid Mech.

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“…(2021 a , b ) and Modesti et al. (2021). Here, we extend this investigation by focusing on heat transport and its (Reynolds) analogy with momentum transport.…”

Section: Introductionmentioning

confidence: 97%

Riblet-generated flow mechanisms that lead to local breaking of Reynolds analogy

et al. 2022

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We investigate the Reynolds analogy over riblets, namely the analogy between the fractional increase in Stanton number $C_h$ and the fractional increase in the skin-friction coefficient $C_f$ , 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 $\alpha = {30}^{\circ }, {60}^{\circ }, {90}^{\circ }$ , a trapezoid, a rectangle and a right triangle. The viscous-scaled riblet spacing varies between $s^+ \approx 10$ 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 $C_h$ than in $C_f$ . 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 $C_f$ than in $C_h$ . Only the triangular riblets with $\alpha = {30}^{\circ }$ 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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“…2020; Modesti et al. 2021), spanwise-aligned bars (Volino, Schultz & Flack 2009; Krogstad & Efros 2012) and spanwise-alternating rough-to-smooth surfaces (Bakhuis et al. 2020; Wangsawijaya et al.…”

Section: Introductionmentioning

confidence: 99%

“…Whilst the drag behaviours of highly directional two-dimensional surfaces have been studied extensively, e.g. streamwise-aligned riblets (Gatti et al 2020;Modesti et al 2021), spanwise-aligned bars (Volino, Schultz & Flack 2009;Krogstad & Efros 2012) and spanwise-alternating rough-to-smooth surfaces (Bakhuis et al 2020;Wangsawijaya et al 2020), systematic studies of surface anisotropy in the context of irregular, three-dimensional roughness remain scarce. One exception to this trend is the work by Busse & Jelly (2020), which demonstrated that irregular roughness with spanwise-elongated features induces an over 200 % increase in U + , relative to roughness with streamwise-elongated features in fully developed turbulent channel flow.…”

Section: Introductionmentioning

confidence: 99%

Impact of spanwise effective slope upon rough-wall turbulent channel flow

et al. 2022

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Whereas streamwise effective slope ( $ES_{x}$ ) is accepted as a key topographical parameter in the context of rough-wall turbulent flows, the significance of its spanwise counterpart ( $ES_{y}$ ) remains largely unexplored. Here, the response of turbulent channel flow over irregular, three-dimensional rough walls with systematically varied values of $ES_{y}$ is studied using direct numerical simulation. All simulations were performed at a fixed friction Reynolds number 395, corresponding to a viscous-scaled roughness height $k^{+}\approx 65.8$ (where $k$ is the mean peak-to-valley height). A surface generation algorithm is used to synthesise a set of ten irregular surfaces with specified $ES_{y}$ for three different values of $ES_{x}$ . All surfaces share a common mean peak-to-valley height and are near-Gaussian, which allows this study to focus on the impact of varying $ES_{y}$ , since roughness amplitude, skewness and $ES_{x}$ can be eliminated simultaneously as parameters. Based on an analysis of first- and second-order velocity statistics, as well as turbulence co-spectra and the fractional contribution of pressure and viscous drag, the study shows that $ES_{y}$ can strongly affect the roughness drag penalty – particularly for low- $ES_{x}$ surfaces. A secondary observation is that particular low- $ES_{y}$ surfaces in this study can lead to diminished levels of outer-layer similarity in both mean flow and turbulence statistics, which is attributed to insufficient scale separation between the outer length scale and the in-plane spanwise roughness wavelength.

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Dispersive stresses in turbulent flow over riblets

Abstract: Abstract

Cited by 47 publications

References 57 publications

From drag-reducing riblets to drag-increasing ridges

From drag-reducing riblets to drag-increasing ridges

Riblet-generated flow mechanisms that lead to local breaking of Reynolds analogy

Impact of spanwise effective slope upon rough-wall turbulent channel flow

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