Reynolds-number dependence of the near-wall flow over irregular rough surfaces

Busse, Angela; Thakkar, Manan; Sandham, Neil D.

doi:10.1017/jfm.2016.680

Cited by 87 publications

(96 citation statements)

References 58 publications

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“…Above the highest roughness crest (x 3 > h max ), a very close collapse between the smooth-and rough-wall data is observed indicating similarity in the outer layer mean flow. These results provide evidence for Townsend's outer similarity hypothesis [38] and agree with the findings of past numerical [20] and experimental [39,40] studies.…”

Section: Mean Velocity Profilesupporting

confidence: 91%

“…For example, Yuan & Piomelli [19] used large-eddy simulations to investigate flow over artificial sand-paper roughness and rough surfaces replicated from turbine blades. Busse et al [20] investigated the Reynolds number dependence of turbulent flow over a grit-blasted and a graphite surface using direct numerical simulation. Forooghi et al [21] created systematically varied isotropic, irregular roughness using random arrangements of roughness elements to investigate the effect of topographical parameters on mean flow and turbulence statistics.…”

Section: Introductionmentioning

confidence: 99%

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Influence of Surface Anisotropy on Turbulent Flow Over Irregular Roughness

Busse

Jelly

2019

Flow Turbulence Combust

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The influence of surface anisotropy upon the near-wall region of a rough-wall turbulent channel flow is investigated using direct numerical simulation (DNS). A set of nine irregular rough surfaces with fixed mean peak-to-valley height, near-Gaussian height distributions and specified streamwise and spanwise correlation lengths were synthesised using a surface generation algorithm. By defining the surface anisotropy ratio (SAR) as the ratio of the streamwise and spanwise correlation lengths of the surface, we demonstrate that surfaces with a strong spanwise anisotropy (SAR <1) can induce an over 200% increase in the roughness function ΔU + , compared to their streamwise anisotropic (SAR >1) equivalent. Furthermore, we find that the relationship between the roughness function ΔU + and the SAR parameter approximately follows an exponentially decaying function. The statistical response of the near-wall flow is studied using a "double-averaging" methodology in order to distinguish form-induced "dispersive" stresses from their turbulent counterparts. Outer-layer similarity is recovered for the mean velocity defect profile as well as the Reynolds stresses. The dispersive stresses all attain their maxima within the roughness canopy. Only the streamwise dispersive stress reaches levels that are comparable to the equivalent Reynolds stress, with surfaces of high SAR attaining the highest levels of streamwise dispersive stress. The Reynolds stress anisotropy also shows distinct differences between cases with strong streamwise anisotropy that stay close to an axisymmetric, rodlike state for all wall-normal locations, compared to cases with spanwise anisotropy where an axisymmetric, disk-like state of the Reynolds stress anisotropy tensor is observed around the roughness mean plane. Overall, the results from this study underline that the drag penalty incurred by a rough surface is strongly influenced by the surface topography and highlight its impact upon the mean momentum deficit in the outer flow as well as the Reynolds and dispersive stresses within the roughness layer.

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Section: Mean Velocity Profilesupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Influence of Surface Anisotropy on Turbulent Flow Over Irregular Roughness

Busse

Jelly

2019

Flow Turbulence Combust

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“…The value of B decreases with increasing φ g going from B ≈ 5.5 to B ≈ 2 for Case T-RI2 and B ≈ −4 for Case T-RI3. Similar trends have been observed in the literature (Busse & Sandham 2012;Yuan & Piomelli 2014;Busse et al 2017). The decrease in B implies an increase in friction as discussed in the literature through surface manipulation (Luchini et al 1991;Jiménez 1994;Garcia-Mayoral & Jiménez 2011).…”

Section: Mean Velocity Profilessupporting

confidence: 87%

Wall-bounded flow over a realistically rough superhydrophobic surface

Alamé

Mahesh

2019

J. Fluid Mech.

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Direct numerical simulation (DNS) is performed for two wall-bounded flow configurations: laminar Couette flow at Re = 740 and turbulent channel flow at Re τ = 180, where τ is the shear stress at the wall. The top wall is smooth and the bottom wall is a realistically rough superhydrophobic surface (SHS), generated from a three-dimensional surface profile measurement. The air-water interface, which is assumed to be flat, is simulated using the volume-of-fluid (VOF) approach. The two flow cases are studied with varying interface heights h to understand its effect on slip and drag reduction (DR). For the laminar Couette flow case, the presence of the surface roughness is felt up to 40% of the channel height in the wall-normal direction. Nonlinear dependence of DR on h is observed with three distinct regions. A nonlinear curve fit is obtained for gas fraction φ g as a function of h, where φ g determines the amount of slip area exposed to the flow. A power law fit is obtained from the data for the effective slip length as a function of φ g and is compared to those derived for structured geometry. For the turbulent channel flow, statistics of the flow field are compared to that of a smooth wall to understand the effects of roughness and h. Four cases are simulated ranging from fully wetted to fully covered and two intermediate regions in between. Scaling laws for slip length, slip velocity, roughness function and DR are obtained for different penetration depths and are compared to past work for structured geometry. DR is shown to depend on a competing effect between slip velocity and turbulent losses due to the Reynolds shear stress contribution. Presence of trapped air in the cavities significantly alters near-wall flow physics where we examine near-wall structures and propose a physical mechanism for their behaviour. The fully wetted roughness increases the peak value of turbulent intensities, whereas the presence of the interface suppresses them. The pressure fluctuations have competing contributions between turbulent pressure fluctuations and stagnation due to asperities, the near-wall structure is altered and breaks down with increasing slip. Overall, there exists a competing effect between the interface and the asperities, the interface suppresses turbulence whereas the asperities enhance them. The present work demonstrates DNS over a realistic SHS for the first time, to the best of our knowledge.

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“…This corresponds to the centreline velocity of internal flows, which are related to the bulk quantities through U h ≡ U (z = h) = U b + 1/κ m and Θ h ≡ Θ(z = h) = Θ a + 1/κ h , where we have assumed logarithmic profiles across the entire channel, with no wake component. The fully rough regime of roughness is associated with the pressure (or form) drag becoming dominant over the viscous drag (Schultz & Flack 2009;Busse et al 2017). The pressure drag component is independent of molecular viscosity, which is why in this regime the skin-friction coefficient is independent of the bulk Reynolds number.…”

Section: Introductionmentioning

confidence: 99%

Roughness effects in turbulent forced convection

2018

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We conducted direct numerical simulations (DNSs) of turbulent flow over three-dimensional sinusoidal roughness in a channel. A passive scalar is present in the flow with Prandtl number P r = 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 it can be readily used for heattransfer studies at a much reduced cost compared to conventional DNS. As the roughness Reynolds number, k + , is increased, the Hama roughness function, ∆U + , increases in the transitionally rough regime before tending towards the fully rough asymptote of κ −1 m log(k + ) + C, where C is a constant that depends on the particular roughness geometry and κ m ≈ 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, ∆Θ + , appears to tend towards a constant value, ∆Θ + F R . 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 ∆Θ + F R 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 ∆Θ + F R . 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.

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Reynolds-number dependence of the near-wall flow over irregular rough surfaces

Cited by 87 publications

References 58 publications

Influence of Surface Anisotropy on Turbulent Flow Over Irregular Roughness

Influence of Surface Anisotropy on Turbulent Flow Over Irregular Roughness

Wall-bounded flow over a realistically rough superhydrophobic surface

Roughness effects in turbulent forced convection

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