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Erick de Moraes Franklin

Publications and source records attributed to Erick de Moraes Franklin.

At least 55 records · Page 3Linked to original sources
arXiv2020

Shape evolution of numerically obtained subaqueous barchan dunes

In the realm of granular bedforms, barchan dunes are strong attractors that can be found in rivers, terrestrial deserts and other planetary environments. These bedforms are characterized by a crescentic shape, which, although robust, presents different scales according to the environment they are in, their length scale varying from the decimeter under water to the kilometer on Mars. In addition to the scales of bedforms, the transport of grains presents significant differences according to the nature of the entraining fluid, so that the growth of barchans rests to be fully understood. Given the smaller length and time scales of the aquatic case, subaqueous barchans are the ideal object to study the growth of barchan dunes. In the present paper, we reproduce numerically the experiments of Alvarez and Franklin [Phys. Rev. E 96, 062906 (2017) and Phys. Rev. Lett. 121, 164503 (2018)] on the shape evolution of barchans from their initiation until they have reached a stable shape. We computed the bed evolution by using computational fluid dynamics - discrete element method (CFD-DEM), where we coupled DEM with large eddy simulation (LES) for the same initial and boundary conditions of experiments, performed in a closed-conduit channel where initially conical heaps evolved to single barchans under the action of a water flow in turbulent regime. Our simulations captured well the evolution of the initial pile toward a barchan dune in both the bedform and grain scales, with the same characteristic time and lengths observed in experiments. In addition, we obtained the local granular flux and the resultant force acting on each grain, the latter not yet previously measured nor computed. This shows that the present method is appropriate to numerical computations of bedforms, opening new possibilities for accessing data that are not available from current experiments.

physics.flu-dyn↗
arXiv2019

Horns of subaqueous barchan dunes: A study at the grain scale

Many complex aspects are involved in the morphodynamics of crescent-shaped dunes, known as barchans. One of them concerns the trajectories of individual grains over the dune, and how they affect its shape. In the case of subaqueous barchans, we proposed in Alvarez and Franklin [Phys. Rev. Lett. 121, 164503 (2018)] that their extremities, called horns, are formed mainly by grains migrating from upstream regions of the initial pile, and that they exhibit significant transverse displacements. Here, we extend our previous work to address the dynamics of grains migrating to horns after the dune has reached its crescentic shape, and present new aspects of the problem. In our experiments, single barchans evolve, under the action of a water turbulent flow, from heaps of conical shape formed from glass beads poured on the bottom wall of a rectangular channel. Both for evolving and developed barchans, the horns are fed up with grains coming from upstream regions of the bedform and traveling with significant transverse components, differently from the dynamics usually described for the aeolian case. For these grains, irrespective of their size and strength of water flow, the distributions of transverse and streamwise components of velocities are well described by exponential functions, with the probability density functions of their magnitudes being similar to results obtained from previous studies on flat beds. Focusing on moving grains whose initial positions were on the horns, we show that their residence time and traveled distance are related following a quasi-linear relation. Our results provide new insights into the physical mechanisms underlying the shape of barchan dunes.

physics.flu-dyn↗
arXiv2019

Velocity fields and particle trajectories for bed load over subaqueous barchan dunes

This paper presents an experimental investigation of moving grains over subaqueous barchan dunes that consisted of spherical glass beads of known granulometry. Prior to each test run, a pre-determined quantity of grains was poured inside a closed conduit, and the grains settled on its bottom wall forming one conical heap. As different turbulent water flows were imposed, each heap evolved to a barchan dune, which was filmed with a high-speed camera. An image processing code was written to identify some of the moving grains and compute their velocity fields and trajectories. Our results show that the velocity of grains varies along the barchan dune, with higher velocities occurring close to the dune centroid, and that grains trajectories are intermittent. Depending on the region over the dune, we found that the velocity fields present values within 1 and 10 % of the cross-sectional mean velocity of the fluid. Considering the average trajectories of grains moving over a given dune, their mean displacement varies within 30 and 60 grain diameters and their characteristic velocities within 10 and 20 % of the cross-sectional mean velocity of the fluid. The displacement time varies between 30 and 90 % of the settling time, and it seems to have two asymptotic behaviors: one close to bed load inception and other far from it. When compared with bed load over a plane bed, we observe that grains have the same mean velocity, but they travel distances up to 5 times larger, with higher densities of moving grains.

cond-mat.soft↗
arXiv2018

Birth of a subaqueous barchan dune

Barchan dunes are crescentic shape dunes with horns pointing downstream. The present paper reports the formation of subaqueous barchan dunes from initially conical heaps in a rectangular channel. Because the most unique feature of a barchan dune is its horns, we associate the timescale for the appearance of horns to the formation of a barchan dune. A granular heap initially conical was placed on the bottom wall of a closed conduit and it was entrained by a water flow in turbulent regime. After a certain time, horns appear and grow, until an equilibrium length is reached. Our results show the existence of the timescales $0.5t_c$ and $2.5t_c$ for the appearance and equilibrium of horns, respectively, where $t_c$ is a characteristic time that scales with the grains diameter, gravity acceleration, densities of the fluid and grains, and shear and threshold velocities.

physics.flu-dyn↗
arXiv2018

Numerical solution for Kapitza waves on a thin liquid film

The flow of a liquid film over an inclined plane is frequently found in nature and industry, and, under some conditions, instabilities in the free surface may appear. These instabilities are initially two-dimensional surface waves, known as Kapitza waves. Surface waves are important to many industrial applications. For example, liquid films with surface waves are employed to remove heat from solid surfaces. The initial phase of the instability is governed by the Orr-Sommerfeld equation and the appropriate boundary conditions; therefore, the fast and accurate solution of this equation is useful for industry. This paper presents a spectral method to solve the Orr-Sommerfeld equation with free surface boundary conditions. Our numerical approach is based on a Galerkin method with Chebyshev polynomials of the first kind, making it possible to express the Orr-Sommerfeld equation and their boundary conditions as a generalized eigenvalue problem. The main advantages of the present spectral method when compared to others such as, for instance, spectral collocation, are its stability and its readiness in including the boundary conditions in the discretized equations. We compare our numerical results with analytical solutions based on Perturbation Methods, which are valid only for long wave instabilities, and show that the results agree in the region of validity of the long-wave hypothesis. Far from this region, our results are still valid. In addition, we compare our results with published experimental results and the agreement is very good. The method is stable, fast, and capable to solve initial instabilities in free surface flows.

physics.flu-dyn↗
arXiv2018

Transitions between smooth and rough surfaces in turbulent channel flows for d- and k-type rough elements

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.

physics.flu-dyn↗
arXiv2018

Turbulent channel flow perturbed by triangular ripples

This paper presents an experimental investigation of the perturbation of a turbulent closed-conduit flow by two-dimensional triangular ripples. Two ripple configurations were employed: one single asymmetric triangular ripple, and two consecutive asymmetric triangular ripples, all of them with the same geometry. Different water flows were imposed over either one or two ripples fixed to the bottom wall of a closed conduit, and the flow field was measured by PIV (particle image velocimetry). Reynolds numbers based on the channel height were moderate, varying between 27500 and 34700. The regime was hydraulically smooth, and the blockage ratio was significant. Experimental data for this specific case remain scarce, and the physics involved has yet to be fully elucidated. Using the instantaneous flow fields, the mean velocities and fluctuations were computed, and the shear stresses over the ripples were determined. The velocities and stresses obtained in this way for the single ripple and for the pair of ripples are compared, and the surface shear stress is discussed in terms of bed stability. Our results show that for the single and upstream ripples the shear stress increases at the leading edge and decreases toward the crest, while for the downstream ripple it decreases monotonically between the reattachment point and the crest. The stress distribution over the downstream ripple, which is different from both the upstream and single ripples, is shown to sustain existing ripples over loose beds.

physics.flu-dyn↗
arXiv2018

Intermittent gravity-driven flow of grains through narrow pipes

Grain flows through pipes are frequently found in various settings, such as in pharmaceutical, chemical, petroleum, mining and food industries. In the case of size-constrained gravitational flows, density waves consisting of alternating high- and low-compactness regions may appear. This study investigates experimentally the dynamics of density waves that appear in gravitational flows of fine grains through vertical and slightly inclined pipes. The experimental device consisted of a transparent glass pipe through which different populations of glass spheres flowed driven by gravity. Our experiments were performed under controlled ambient temperature and relative humidity, and the granular flow was filmed with a high-speed camera. Experimental results concerning the length scales and celerities of density waves are presented, together with a one-dimensional model and a linear stability analysis. The analysis exhibits the presence of a long-wavelength instability, with the most unstable mode and a cut-off wavenumber whose values are in agreement with the experimental results.

cond-mat.soft↗
arXiv2017

The perturbation of a turbulent boundary layer by a two-dimensional hill

Turbulent boundary layers over flat walls in the presence of a hill are frequently found in nature and industry. Some examples are the air flows over hills and desert dunes, but also water flows over aquatic dunes inside closed conduits. The perturbation of a two-dimensional boundary layer by a hill introduces new scales in the problem, changing the way in which velocities and stresses are distributed along the flow. When in the presence of sediment transport, the stress distribution along the hill is strongly related to bed instabilities. This paper presents an experimental study on the perturbation of a fully-developed turbulent boundary layer by a two-dimensional hill. Water flows were imposed over a hill fixed on the bottom wall of a closed conduit and the flow field was measured by Particle Image Velocimetry. From the flow measurements, mean and fluctuation fields were computed. The general behaviors of velocities and stresses are compared to published asymptotic analyses and the surface shear stress is analyzed in terms of instabilities of a granular bed.

physics.flu-dyn↗
arXiv2016

The feedback effect caused by bed load on a turbulent liquid flow

Experiments on the effects due solely to a mobile granular layer on a liquid flow are presented (feedback effect). Nonintrusive measurements were performed in a closed conduit channel of rectangular cross section where grains were transported as bed load by a turbulent water flow. The water velocity profiles were measured over fixed and mobile granular beds of same granulometry by Particle Image Velocimetry. The spatial resolution of the measurements allowed the experimental quantification of the feedback effect. The present findings are of importance for predicting the bed-load transport rate and the pressure drop in activities related to the conveyance of grains.

physics.flu-dyn↗
arXiv2016

Length scale of density waves in the gravitational flow of fine grains in pipes

Gravitational flow of grains in pipes is frequently encountered in industry. When the grains and pipes are size-constrained, granular flow may result in density waves consisting of alternate high- and low-compactness regions. This paper discusses the length scale of density waves that appear when fine grains fall vertically in pipes. A one-dimensional model and a linear stability analysis of the model are presented. The analysis suggests the presence of long-wavelength instability for the most unstable mode, moreover, a cut-off wavenumber from which the length scale is estimated. Finally, the model results are compared to experimental data.

cond-mat.soft↗
arXiv2016

Morphology and displacement of dunes in a closed-conduit flow

The transport of solid particles entrained by a fluid flow is frequently found in industrial applications. A better knowledge of it, is of importance to improve particle related industrial processes. When shear stresses exerted by the fluid on the bed of particles are bounded to some limits, a mobile layer of particles known as bed-load takes place in which the particles stay in contact with the fixed bed. If it takes place over a non-erodible ground, and if the particle flow rate is small enough, an initial thin continuous layer of particles becomes discontinuous and composed of isolated dunes. We present here an experimental study to understand some features of the dynamics of isolated dunes under a fluid flow using a closed-conduit experimental loop made of transparent material. Acquired data concerns mainly dune morphology and displacement velocity under different conditions: different types of beads (diameters and densities) and different water flow conditions. We observed that an initial pile of beads placed in the conduit is rapidly deformed by the water flow, adopting a "croissant" shape, like barchan dunes found in deserts at a much larger scale. We observed also self-similarity in dunes dimensions and that dune displacement velocity scales with the inverse of their dimensions. The variation of the dune displacement velocity with the fluid shear velocity is discussed here.

physics.flu-dyn↗
arXiv2016

Linear and nonlinear instabilities of a granular bed: determination of the scales of ripples and dunes in rivers

Granular media are frequently found in nature and in industry and their transport by a fluid flow is of great importance to human activities. One case of particular interest is the transport of sand in open-channel and river flows. In many instances, the shear stresses exerted by the fluid flow are bounded to certain limits and some grains are entrained as bed-load: a mobile layer which stays in contact with the fixed part of the granular bed. Under these conditions, an initially flat granular bed may be unstable, generating ripples and dunes such as those observed on the bed of rivers. In free-surface water flows, dunes are bedforms that scale with the flow depth, while ripples do not scale with it. This article presents a model for the formation of ripples and dunes based on the proposition that ripples are primary linear instabilities and that dunes are secondary instabilities formed from the competition between the coalescence of ripples and free surface effects. Although simple, the model is able to explain the growth of ripples, their saturation (not explained in previous models) and the evolution from ripples to dunes, presenting a complete picture for the formation of dunes.

physics.flu-dyn↗
arXiv2016

Formation of sand ripples under a turbulent liquid flow

Sand ripples are commonly observed in both nature and industry. For example, they are found on riverbeds and in oil pipelines that transport sand. In both natural and industrial cases, ripples increase friction between the bed and fluid and are related to flooding, high pressure drops, and transients. Ripples appear when sediments are entrained as bed load (a mobile granular layer) and are usually considered to be the result of initial bedforms that eventually saturate. Given the small aspect ratio of the initial bedforms, linear analyses can be used to understand the formation of ripples. This paper presents a linear stability analysis of a granular bed under a turbulent flow of a liquid. This analysis takes into consideration all the main mechanisms and parameters involved in the turbulent liquid case, including some important parameters that have not yet been considered together such as the bed compactness and the bed-load threshold shear stress. The results of this analysis are compared with published experimental results and they show good agreement.

physics.flu-dyn↗
arXiv2016

The formation and migration of sand ripples in closed conduits: experiments with turbulent water flows

The transport of solid particles by a fluid flow is frequently found in nature and industry. Some examples are the transport of sand in rivers and hydrocarbon pipelines. When the shear stresses exerted by a fluid flow on a granular bed remain moderate, some grains are set in motion without fluidizing the bed; the moving grains form a layer, known as bed load, that moves while maintaining contact with the fixed part of the bed. Under bed load conditions, the granular bed may become unstable, generating ripples and dunes. Sand ripples are commonly observed in closed conduits and pipes such as in petroleum pipelines, sewer systems, and dredging lines. Although of importance for many scientific domains and industrial applications, the formation of ripples in closed conduits is not well understood, and the problem is still open. This paper presents an experimental study on the formation and migration of sand ripples under a turbulent closed-conduit flow and bed-load conditions. In our experiments, fully-developed turbulent water flows were imposed over a granular bed of known granulometry in a transparent channel, and bed load took place. For different water flow rates and grain diameters, the growth and migration of bedforms were filmed by a high-definition camera, and a numerical code was developed to determine the wavelength and celerity of the bedforms from the acquired images. The obtained results are compared with published stability analyses.

physics.flu-dyn↗
arXiv2016

Velocity fields of a bed-load layer under a turbulent liquid flow

The transport of sediments by a fluid flow is commonly found in nature and in industry. In nature, it is found in rivers, oceans, deserts, and other environments. In industry, it is found in petroleum pipelines conveying grains, in sewer systems, and in dredging lines, for example. This study investigates experimentally the transport of the grains of a granular bed sheared by a turbulent liquid flow. In our experiments, fully developed turbulent water flows were imposed over a flat granular bed of known granulometry. Under the tested conditions, the grains were transported as bed load, i.e., they became entrained by rolling and sliding over each other, forming a moving granular layer. The present experiments were performed close to incipient bed load, a case for which experimental data on grains velocities are scarce. Distinct from previous experiments, an entrance length assured that the water stream over the loose bed was fully developed. At different water flow rates, the moving layer was filmed using a high-speed camera, and the grains' displacements and velocities were determined by post-processing the images with a numerical code developed in the course of this study. The bed-load transport rate was estimated and correlated to the water flow conditions.

physics.flu-dyn↗
arXiv2016

Three-dimensional sand ripples as the product of vortex instability

Three-dimensional sand ripples can be observed under steady liquid flows in both nature and industry. Some examples are the ripples observed on the bed of rivers and in petroleum pipelines conveying sand. Although of importance, the formation of these patterns is not completely understood. There are theoretical and experimental evidence that aquatic ripples grow from two-dimensional bed instabilities, so that a straight vortex is formed just downstream of their crests. The proposition of Raudkivi (2006), that three-dimensionality has its origin in a vortex instability, is employed here. This paper presents a linear stability analysis of the downstream vortex in order to obtain the transverse scales of three-dimensional ripples. The obtained wavelength is compared with experimentally observed ripples.

physics.flu-dyn↗