Transitions between smooth and rough surfaces in turbulent channel flows for d- and k-type rough elements
Gabriel Maltese Meletti de Oliveira, Erick de Moraes Franklin
备注：
This is a pre-print of an article published in Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40:187, 2018. The final authenticated version is available online at: http://dx.doi.org/10.1007/s40430-018-1113-9
发表信息：
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40:187, 2018
This paper presents an experimental study on the transition from smooth to rough walls, and back to the smooth one, in turbulent closed-conduit flows. These transitions cause a shift on flow velocity profiles that changes their parameters when compared to the flow over a smooth wall. Different water flow rates were imposed in a closed conduit of rectangular cross section, where rough elements consisting of cavities of d- and k-type were positioned covering a part of the bottom wall of the test section. Reynolds numbers based on the channel half-height were moderate, varying between 7800 and 9600, and the regime upstream of the rough elements was hydraulically smooth. Experimental data for this specific case remain scarce and the involved physics rests to be understood. The flow field was measured by low frequency PIV (particle image velocimetry) and by flow visualization, the latter using a continuous 0.1 W laser, a high-speed camera, and scripts written by the authors. From the instantaneous fields measured with PIV, the mean velocities, fluctuations, shear stresses and turbulence production were computed. The results show the presence of oscillations in Reynolds stress and turbulence production, that are higher for the k-type roughness and were not shown in previous experimental works. From the high-speed movies, the angular velocities and frequencies of vortices in the cavities were computed, and the occurrence of fluid ejection from the cavities to upper layers of the flow was observed. A relation between the angular velocities of inner-cavities vortices and the oscillations in Reynolds stress and turbulence production is proposed.
This paper gives a new unified formula for the Newtonian fluids valid for all pipe flow regimes from laminar to the fully rough turbulent. It includes laminar, unstable sharp jump from laminar to turbulent, and all types of the turbulent regimes: smooth turbulent regime, partial non-fully developed turbulent and fully developed rough turbulent regime. The formula follows the inflectional form of curves as suggested in Nikuradse's experiment rather than monotonic shape proposed by Colebrook and White. The composition of the proposed unified formula consists of switching functions and of the int…
Turbulent characteristics within shear layer have been studied, recently, within vegetative canopy, buildings, dunes. Kevin-Helmholtz instability triggered hairpin vortex shedding has been widely concluded as the "signature" of mixing layer analogy. However, convoluted roughness types complicate the observing practice of turbulent evolving progress. To simplify that, spanwise homogeneous roughness has been adopted in this work to capture the streamwise flow alternations under different streamwise roughness element distances. Streamwise successive object distance $λ_x$ is used to show the rough…
We investigate rough-wall turbulent flows through direct numerical simulations of flow over three-dimensional transitionally rough sinusoidal surfaces. The roughness Reynolds number is fixed at $k^+=10$, where $k$ is the sinusoidal semi-amplitude, and the sinusoidal wavelength is varied, resulting in the roughness solidity, $Λ$ (frontal area divided by plan area) ranging from 0.05 to 0.54. The high cost of resolving both the flow around the dense roughness elements and the bulk flow is circumvented by the use of the minimal-span channel technique, recently demonstrated by Chung et al. (J. Flui…
Wall-roughness induces extra drag in wall-bounded turbulent flows. Mapping any given roughness geometry to its fluid dynamic behaviour has been hampered by the lack of accurate and direct measurements of skin-friction drag. Here the Taylor-Couette (TC) system provides an opportunity as it is a closed system and allows to directly and reliably measure the skin-friction. However, the wall-curvature potentially complicates the connection between the wall friction and the wall roughness characteristics. Here we investigate the effects of a hydrodynamically fully rough surface on highly turbulent, …
The friction f is the property of wall-bounded flows that sets the pumping cost of a pipeline, the draining capacity of a river, and other variables of practical relevance. For highly turbulent rough-walled pipe flows, f depends solely on the roughness length scale r, and the f -- r relation may be expressed by the Strickler empirical scaling f $\propto$ r$^{\frac{1}{3}}$. Here, we show experimentally that for soap film flows that are the two-dimensional (2D) equivalent of highly turbulent rough-walled pipe flows, f $\propto$ r and the f -- r relation is not the same in 2D as in 3D. Our findin…
Direct numerical simulations were performed to characterize fully developed supersonic turbulent channel flows over isothermal rough walls. The effect of roughness was incorporated using a level-set/volume-of-fluid immersed boundary method. Turbulence statistics of five channel flows are compared, including one reference case with both walls smooth and four cases with smooth top walls and bottom walls with two-dimensional (2D) and three-dimensional (3D) sinusoidal roughnesses. Results reveal a strong dependence of the turbulence on the roughness topography and the associated shock patterns. Sp…
Direct Numerical Simulations are used to solve turbulent flow and heat transfer over a variety of rough walls in a channel. The wall geometries are exactly resolved in the simulations. The aim is to understand the effect of roughness morphology and its scaling on the augmentation of heat transfer relative to that of skin friction. A number of realistic rough surface maps obtained from the scanning of gas turbine blades and internal combustion engines as well as several artificially generated rough surfaces are examined. In the first part of the paper, effects of statistical surface properties,…
Drawing on an analogy to critical phenomena, it was shown that the Nikuradse turbulent friction factor ($f_t$) measurements in pipes of radius $R$ and wall roughness $r$ can be collapsed onto a one-dimensional curve expressed as a conveyance law $f_t Re^{1/4}=g_o(χ)$, where $Re$ is a bulk Reynolds number, $χ=Re^{3/4}\left({r}/{R}\right)$. The implicit function $g_o(.)$ was conjectured based on matching two asymptotic limits of $f_t$. However, the connection between $g_o(.)$ and the phenomenon it proclaims to represent - turbulent eddies - remains lacking. Using models for the wall-normal veloc…
We present a physical model for turbulent friction on rough surfaces with regularly distributed roughness elements. Wall shear stresses are expressed as functions of physical quantities. Surfaces with varying roughness densities and roughness elements with different aspect ratios are considered. We propose a straight forward method based on the conservation of momentum to deduce the drag on elements by expressing it as functions of the maximum drag and drag reductions ratios, as the drag on individual elements decreases as packing density increases. A drag reduction effect of momentum redistri…
The probability density function of single-point velocity fluctuations in turbulence is studied systematically using Fourier coefficients in the energy-containing range. In ideal turbulence where energy-containing motions are random and independent, the Fourier coefficients tend to Gaussian and independent of each other. Velocity fluctuations accordingly tend to Gaussian. However, if energy-containing motions are intermittent or contaminated with bounded-amplitude motions such as wavy wakes, the Fourier coefficients tend to non-Gaussian and dependent of each other. Velocity fluctuations accord…
Heat and momentum transfer in wall-bounded turbulent flow, coupled with the effects of wall-roughness, is one of the outstanding questions in turbulence research. In the standard Rayleigh-Bénard problem for natural thermal convection, it is notoriously difficult to reach the so-called ultimate regime in which the near-wall boundary layers are turbulent. Following the analyses proposed by Kraichnan [Phys. Fluids vol 5., pp. 1374-1389 (1962)] and Grossmann & Lohse [Phys. Fluids vol. 23, pp. 045108 (2011)], we instead utilize recent direct numerical simulations of forced convection over a rough w…
Large-eddy simulations are conducted to contrast momentum and passive scalar transport over large, three-dimensional roughness elements in a turbulent channel flow. Special attention is given to the dispersive fluxes, which are shown to be a significant fraction of the total fluxes within the roughness sublayers. Based on point-wise quadrant analysis, the turbulent components of the transport of momentum and scalars are found to be similar in general, albeit with increasing dissimilarity for roughnesses with low frontal blockage. However, strong dissimilarity is noted between the dispersive mo…
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 $Pr=0.7$, to study heat transfer by forced convection over this rough surface. The minimal 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 channel agrees well with that of the conventional full-span channel, indicating it can be readily used for heat-transfer…
Liquid-infused surfaces (LIS) are a promising technique for reducing friction, fouling and icing in both laminar and turbulent flows. Previous work has demonstrated that these surfaces are susceptible to shear-driven drainage. Here, we report a different failure mode using direct numerical simulations of a turbulent channel flow with liquid-infused longitudinal grooves. When the liquid-liquid surface tension is small and/or grooves are wide, we observe traveling-wave perturbations on the interface with amplitudes larger than the viscous sublayer of the turbulent flow. These capillary waves ind…
We present a systematic investigation of the effects of roughness geometry on turbulent Rayleigh-Bénard convection (RBC) over rough plates with pyramid-shaped and periodically distributed roughness elements. Using a parameter $λ$ defined as the height of a roughness element over its base width, the heat transport, the flow dynamics and local temperatures are measured for the Rayleigh number range $7.50\times 10^{7} \leq Ra\leq 1.31\times 10^{11}$, and the Prandtl number $Pr$ from 3.57 to 23.34 at four values of $λ$. It is found that the heat transport scaling, i.e. $Nu\sim Ra^α$ where $Nu$ is …
Direct numerical simulation (DNS) of flow in a turbulent channel with a random rough wall is performed at $Re_τ=400$ and $600$. The roughness geometry corresponds to the experiments of Flack and Schultz (personal communication). The rough surface is used on the bottom wall of the channel. DNS of a smooth channel flow and a rod-roughened channel flow are also performed at $Re_τ=400$ for validation and comparison. The skin friction coefficient of the random-rough channel shows good agreement with the experimental results of Flack and Schultz. Due to the roughness, the slip velocity on the rough …
We present highly resolved measurements of the near-wall temperature field in thermally driven convection at a rough surface. Our measurements have been undertaken in a very large experimental facility called the "Barrel of Ilmenau". They provide a unique insight into the local transport process at the interface between a hot solid surface and a surrounding fluid. In order to probe the near-wall temperature field, we used a tiny micro-thermistor of 130 $μ$m in diameter and 330 $μ$m in length with a response time $τ_{70}$ of less than 150 ms. This sensor is forty times smaller than the thicknes…
The focus of this paper is to systematically study the influence of solid obstacle surface roughness in porous media on the microscale flow physics and report its effect on macroscale drag and Nusselt number. The Reynolds averaged flow field is numerically simulated for a flow through a periodic porous medium consisting of an in-line arrangement of square cylinders with square roughness particles on the cylinder surface. Two flow regimes are identified with respect to the surface roughness particle height: fine and coarse roughness regimes. The effect of the roughness particles in the fine rou…
A source-term interpretation of turbulent rough wall-pressure spectra
Center for Turbulence Research, Stanford University（斯坦福大学湍流研究中心）；Department of Mechanical and Aerospace Engineering, Princeton University（普林斯顿大学机械与航空航天工程系）
A stochastic modeling framework to generate 2-D rough-wall high-Reynolds-number turbulent boundary layers
Saint Anthony Falls Laboratory, University of Minnesota（明尼苏达大学圣安东尼瀑布实验室）；Department of Civil, Environmental, and Geo-Engineering, University of Minnesota（明尼苏达大学土木、环境与地球工程系）
In this study, we combine experiments and direct numerical simulations to investigate the effects of the height of transverse ribs at the walls on both global and local flow properties in turbulent Taylor-Couette flow. We create rib roughness by attaching up to 6 axial obstacles to the surfaces of the cylinders over an extensive range of rib heights, up to blockages of 25% of the gap width. In the asymptotic ultimate regime, where the transport is independent of viscosity, we emperically find that the prefactor of the $Nu_ω \propto Ta^{1/2}$ scaling (corresponding to the drag coefficient $C_f(…
We present convincing evidence of a direct connection between the pressure drop, viscous dissipation, and the turbulent energy spectrum. We use this finding to explain Nikuradse's experimental results of pressure drop for turbulent flows in rough pipes, in terms of a modified Kolmogorov length scale that varies with the surface roughness. Furthermore, we use Laufer's measurements of turbulent energy spectra in pipe flow to calculate -- to a good approximation -- the turbulent component of the pressure drop directly from an averaged turbulent energy spectrum. We also show that the incompressibi…
We show that the main results of the analysis of the friction factor for turbulent pipe flow reported in G. Gioia and P. Chakraborty (GC), Phys. Rev. Lett. 96, 044502 (1996) can be recovered by assuming the Heisenberg closure hypothesis for the turbulent spectrum. This highlights the structural features of the turbulent spectrum underlying GC's analysis.
Data available in literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (2015), Bernardini et al. (2014), Yamamoto and Tsuji (2018) and Orlandi et al. (2015) in a large range of Reynolds number have been used to find that shear parameter the ratio between the eddy turnover time and the time scale of the mean deformation (1/S), scales very well with the Reynolds number in the near-wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near t…
Roughness predominantly alters the near-wall region of turbulent flow while the outer layer remains similar. This makes it a prime candidate for the minimal-span channel, which only captures the near-wall flow by restricting the spanwise channel width to be of the order of a few hundred viscous units. Recently, Chung et al. (J. Fluid Mech., vol. 773, 2015, pp. 418-431) showed that a minimal-span channel can accurately characterise the hydraulic behaviour of roughness. Following this, we aim to investigate the fundamental dynamics of the minimal-span channel framework with an eye towards furthe…
Following the findings in \cite{wangsawijaya2020}, we re-examine the turbulent boundary layers developing over surfaces with spanwise heterogeneous roughness of various roughness wavelengths $0.32 \leq S/\overlineδ \leq 3.63$, where $S$ is the width of the roughness strips and $\overlineδ$ is the spanwise-averaged boundary-layer thickness. The heterogeneous cases induce counter-rotating secondary flows, and these are compared to the large-scale turbulent structures that occur naturally over the smooth wall. Both appear as meandering elongated high- and low-momentum streaks in the instantaneous…
The classical experiments on turbulent friction in rough pipes were performed by J. Nikuradse in the 1930's. Seventy years later, they continue to defy theory. Here we model Nikuradse's experiments using the phenomenological theory of Kolmogórov, a theory that is widely thought to be applicable only to highly idealized flows. Our results include both the empirical scalings of Blasius and Strickler, and are otherwise in minute qualitative agreement with the experiments; they suggest that the phenomenological theory may be relevant to other flows of practical interest; and they unveil the existe…
Pore-resolved direct numerical simulations of turbulent open channel flow are performed comparing the structure and dynamics of turbulence over impermeable rough and smooth walls to a porous sediment bed at permeability Reynolds number ($Re_K$) of 2.6, representative of aquatic beds. Four configurations are investigated; namely, (i) permeable bed with randomly packed sediment grains, (ii) an impermeable-wall with full layer of roughness elements matching the top layer of the sediment bed, (iii) an impermeable-wall with half layer of roughness elements , and (iv) a smooth wall. A double-averagi…
We theoretically investigate the pattern formation observed when a fluid flows over a solid substrate that can dissolve or melt. We use a turbulent mixing description that includes the effect of the bed roughness. We show that the dissolution instability at the origin of the pattern is associated with an anomaly at the transition from a laminar to a turbulent hydrodynamic response with respect to the bed elevation. This anomaly, and therefore the instability, disappears when the bed becomes hydrodynamically rough, above a threshold roughness-based Reynolds number. This suggests a possible mech…
We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto\textrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $\textrm{Re}^{-1/4}$. For large Re, $f \sim r$ in the enstrophy-dominated case. We use …
Turbulence intensity profiles are compared for smooth- and rough-wall pipe flow measurements made in the Princeton Superpipe. The profile development in the transition from hydraulically smooth to fully rough flow displays a propagating sequence from the pipe wall towards the pipe axis. The scaling of turbulence intensity with Reynolds number shows that the smooth- and rough wall level deviates with increasing Reynolds number. We quantify the correspondence between turbulence intensity and the friction factor.
Highly turbulent Taylor-Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations (DNS) with an immersed boundary method (IBM)) to determine the effects of the spacing and axial width $s$ of the spanwise varying roughness on the total drag and {on} the flow structures. We apply sandgrain roughness, in the form of alternating {rough and smooth} bands to the inner cylinder. Numerically, the Taylor number is $\mathcal{O}(10^9)$ and the roughness width is varied between $0.47\leq \tilde{s}=s/d \leq 1.23$, where $d$ is the gap width. E…
The aim of this study is to improve the prediction of near-wall mean streamwise velocity profile $U^+$ by using a simple method. The $U^+$ profile is obtained by solving the momentum equation which is written as an ordinary differential equation. An eddy viscosity formulation based on a near-wall turbulent kinetic energy $k^+$ function (R. Absi, Analytical solutions for the modeled $k$-equation, ASME J. Appl. Mech. \textbf{75}, 044501, 2008) and the van Driest mixing length equation (E.R. van Driest, On turbulent flow near a wall, J. Aero. Sci. \textbf{23}, 1007, 1956) is used. The parameters …
Direct numerical simulations (DNS) are 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 laminar Couette flow is studied with varying interface heights $h$ to understand the effect on slip and drag reduc…
