Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Jos&#233; R. Agudo; Jiwon Han; Jinyoung Park; Sinyoung Kwon; Soebiakto Loekman; Giovanni Luzi; Christoph Linderberger; Antonio Delgado; Andreas Wierschem

doi:10.3791/57238

JoVE Journal > Engineering

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Engenharia

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published: February 22, 2018

doi:

10.3791/57238

José R. Agudo, Jiwon Han, Jinyoung Park, Sinyoung Kwon, Soebiakto Loekman, Giovanni Luzi, Christoph Linderberger, Antonio Delgado⁴, Andreas Wierschem

¹Institute of Fluid Mechanics, FAU Busan Campus,University of Erlangen-Nuremberg, ²Institute of Chemical Reaction Engineering, FAU Busan Campus,University of Erlangen-Nuremberg, ³Institute of Bioprocess Engineering, FAU Busan Campus,University of Erlangen-Nuremberg, ⁴Institute of Fluid Mechanics,Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)

Summary

Two different methods for characterizing the incipient particle motion of a single bead as a function of the sediment bed geometry from laminar to turbulent flow are presented.

Abstract

Two different experimental methods for determining the threshold of particle motion as a function of geometrical properties of the bed from laminar to turbulent flow conditions are presented. For that purpose, the incipient motion of a single bead is studied on regular substrates that consist of a monolayer of fixed spheres of uniform size that are regularly arranged in triangular and quadratic symmetries. The threshold is characterized by the critical Shields number. The criterion for the onset of motion is defined as the displacement from the original equilibrium position to the neighboring one. The displacement and the mode of motion are identified with an imaging system. The laminar flow is induced using a rotational rheometer with a parallel disk configuration. The shear Reynolds number remains below 1. The turbulent flow is induced in a low-speed wind tunnel with open jet test section. The air velocity is regulated with a frequency converter on the blower fan. The velocity profile is measured with a hot wire probe connected to a hot film anemometer. The shear Reynolds number ranges between 40 and 150. The logarithmic velocity law and the modified wall law presented by Rotta are used to infer the shear velocity from the experimental data. The latter is of special interest when the mobile bead is partially exposed to the turbulent flow in the so-called hydraulically transitional flow regime. The shear stress is estimated at onset of motion. Some illustrative results showing the strong impact of the angle of repose, and the exposure of the bead to shear flow are represented in both regimes.

Introduction

Incipient particle motion is encountered in a wide range of industrial and natural processes. Environmental examples include the initial process of sediment transport in river and oceans, bed erosion or dune formation among others ¹^,²^,³. Pneumatic conveying⁴, removal of pollutants or cleaning of surfaces⁵^,⁶ are typical industrial applications involving the onset of particle motion.

Due to the broad range of applications, the onset of particle motion has been extensively studied over a century, mostly under turbulent conditions⁷^,⁸^,⁹^,¹⁰^,¹¹^,¹²^,¹³^,¹⁴^,¹⁵. Many experimental approaches have been applied to determine the threshold for the onset of motion. The studies include parameters such as the particle Reynolds number¹³^,¹⁶^,¹⁷^,¹⁸^,¹⁹^,²⁰, the relative flow submergence²¹^,²²^,²³^,²⁴ or geometrical factors as the angle of repose¹⁶^,¹⁸^,²⁵, exposure to the flow²⁶^,²⁷^,²⁸^,²⁹, relative grain protrusion²⁹ or streamwise bed slope³⁰.

The current data for the threshold including turbulent conditions are broadly scattered¹²^,³¹ and the results often seem inconsistent²⁴. This is mostly due to the inherent complexity of controlling or determining flow parameters under turbulent conditions¹³^,¹⁴. Besides, the threshold for sediment motion strongly depends on the mode of motion, i.e. sliding, rolling or lifting¹⁷ and the criterion to characterize the incipient motion³¹. The latter may be ambiguous in an erodible sediment bed.

During the last decade, experimental researchers have studied incipient particle motion in laminar flows³²^,³³^,³⁴^,³⁵^,³⁶^,³⁷^,³⁸^,³⁹^,⁴⁰^,⁴¹^,⁴²^,⁴³^,⁴⁴, where the wide spectrum of length scales interacting with the bed is avoided⁴⁵. In many practical scenarios implying sedimentation, the particles are quite small and the particle Reynolds number remains lower than about 5⁴⁶. On the other hand, laminar flows are able to generate geometric patterns as ripples and dunes as turbulent flows do⁴²^,⁴⁷. Similitudes in both regimens have been shown to reflect analogies in the underlying physics⁴⁷ so important insight for the particle transport can be obtained from a better controlled experimental system⁴⁸.

In laminar flow, Charru et al. noticed that the local rearrangement of a granular bed of uniformly sized beads, so-called bed armouring, resulted in a progressive increase of the threshold for the onset of motion until saturated conditions were achieved³². Literature, however, reveals different thresholds for saturated conditions in irregularly arranged sediment beds depending on the experimental set-up³⁶^,⁴⁴. This scattering may be due to the difficulty of controlling particle parameters such as orientation, protrusion level and compactness of the sediments.

The main goal of this manuscript is to describe in detail how to characterize the incipient motion of single spheres as a function of geometrical properties of the horizontal sediment bed. For that purpose, we use regular geometries, consisting of monolayers of fixed beads regularly arranged according to triangular or quadratic configurations. Regular substrates similar to that we use are found in applications such as for the template-assembly of particles in microfluidic assays⁴⁹, self-assembly of microdevices in confined structured geometries⁵⁰ or intrinsic particle-induced transport in microchannels⁵¹. More importantly, using regular substrates allows us to highlight the impact of local geometry and orientation and to avoid any dubiety about the role of the neighborhood.

In laminar flow, we observed that the critical Shields number increased by 50% only depending on the spacing between the substrate spheres and thus on the exposure of the bead to the flow³⁸. Similarly, we found that the critical Shields number changed by up to a factor of two depending on the orientation of the substrate to the flow direction³⁸. We noticed that immobile neighbors only affect the onset of the mobile bead if they were closer than about three particle diameters⁴¹. Triggered by the experiment findings, we have recently presented a rigorous analytical model that predicts the critical Shields number in the creeping flow limit⁴⁰. The model covers the onset of motion from highly exposed to hidden beads.

The first part of this manuscript deals with the description of the experimental procedure used in previous studies at shear Reynolds number, Re*, lower than 1. The laminar flow is induced with a rotational rheometer with a parallel configuration. In this low Reynolds number limit, the particle is not supposed to experience any velocity fluctuation²⁰ and the system matches the so-called hydraulically smooth flow where the particle is submerged within the viscous sublayer.

Once incipient motion at laminar flow is established, the role of turbulence can become clearer. Motivated by this idea, we introduce a novel experimental procedure in the second part of the protocol. Using a Göttingen low-speed wind tunnel with open jet test section, the critical Shields number can be determined in a wide range of Re* including the hydraulically transitional flow and the turbulent regime. The experimental results can provide important insight about how forces and torques act on a particle due to the turbulent flow depending on the substrate geometry. Besides, these results can be used as a benchmark for more sophisticated models at high Re* in a similar way that past work in laminar flow has been used to feed semi probabilistic models⁵² or to validate recent numerical models⁵³. We present some representative examples of applications at Re* ranging from 40 to 150.

The incipient criterion is established as the motion of the single particle from its initial equilibrium position to the next one. Image processing is used to determine the mode of onset of motion, i.e. rolling, sliding, lifting³⁹^,⁴¹. For that purpose, the angle of rotation of mobile spheres that were manually marked is detected. The algorithm tracks the position of the marks and compares it with the center of the sphere. A preliminary set of experiments was conducted in both experimental set-ups to clarify that the critical Shields number remains independent of finite size effects of the set-up and relative flow submergence. The experimental methods are thus designed to exclude any other parameter dependent on the critical Shields number beyond Re* and geometrical properties of the sediment bed. The Re* is varied using different fluid-particle combinations. The critical Shields number is characterized as a function of the burial degree, , defined by Martino et al.³⁷ as where is the angle of repose, i.e. the critical angle at which motion occurs⁵⁴, and is the exposure degree, defined as the ratio between the cross-sectional area effectively exposed to the flow to the total cross-sectional area of the mobile bead.

Protocol

1. Incipient Particle Motion in the Creeping Flow Limit. NOTE: The measurements are conducted in a rotational rheometer that has been modified for this specific application. Preparing the Rheometer. Connect the air supply to the rheometer in order to avoid damaging the air bearings. Open the valve besides the air filters until a pressure of approximately 5 bars in the system is achieved. Connect the fluid circulator to the measuring plate. En…

Representative Results

Figure 1(a) represents a sketch of the experimental set-up used to characterize the critical Shields number in the creeping flow limit, Section 1 of the protocol. The measurements are conducted in a rotational rheometer that was modified for this specific application. A transparent Plexiglas plate of 70 mm in diameter was carefully fixed to a parallel plate of 25 mm in diameter. The inertia of the measuring system was therefore readjusted bef…

Discussion

We present two different experimental methods for characterizing the incipient particle motion as a function of the sediment bed geometry. For that purpose, we use a monolayer of spheres regularly arranged according to a triangular or quadratic symmetry in such a way that the geometrical parameter simplifies to a single geometry. In the creeping flow limit, we describe the experimental method using a rotational rotameter to induce the laminar shear flow as in previous studies³⁹^,<sup cla…

Declarações

The authors have nothing to disclose.

Acknowledgements

The authors are thankful to unknown referees for valuable advice and to Sukyung Choi, Byeongwoo Ko and Baekkyoung Shin for the collaboration in setting up the experiments. This work was supported by the Brain Busan 21 Project in 2017.

Materials

MCR 302 Rotational Rheometer	Antoon Par	Induction of shear laminar flow
Measuring Plate PP25	Antoon Par	Induction of shear laminar flow
Peltier System P-PTD 200	Antoon Par	Keep temperature of silicon oils constant in the system at laminar flow
Silicone oils with viscosities of approx. 10 and 100 mPas	Basildon Chemicals	Fluid used to induced the shear in the particles
Soda-lime glass beads of (405.9 ± 8.7) μm	The Technical Glass Company	Construction of the regular substrates for laminar flow conditions
Opto Zoom 70 Module 0.3x-2.2x	WEISS IMAGING AND SOLUTIONS GmbH	Imaging system for recording the bead motion in the rheometer
2 x TV-Tube 1.0x, D=35 mm, L=146.5 mm	WEISS IMAGING AND SOLUTIONS GmbH	Imaging system for recording the bead motion in the rheometer
UI-1220SE CMOS Camera	IDS Imaging Development Systems GmbH	Imaging system for recording the bead motion in the rheometer
UI-3590CP CMOS Camera	IDS Imaging Development Systems GmbH	Imaging system for recording the bead motion in the rheometer
Volpi IntraLED 3 – LED light source	Volpi USA	Imaging system for recording the bead motion in the rheometer
Active light guide diameter 5mm	Volpi USA	Imaging system for recording the bead motion in the rheometer
300 Watt Xenon Arc Lamp	Newport Corporation	Imaging system for recording the bead motion in the rheometer
Wind-tunnel with open jet test section, Göttingen type	Tintschl BioEnergie und Strömungstechnik AG	Induction of turbulent flow
Glass spheres of (2.00 ± 0.10) mm	Gloches South Korea	Construction of the regular substrates for turbulent flow conditions
Alumina spheres of (5.00 ± 0.25) mm	Gloches South Korea	Targeted bead for experiments
CTA Anemometer DISA 55M01	Disa Elektronik A/S	Measurement of flow velocity in the wind tunnel
Miniaure Wire Probe Type 55P15	Dantec Dynamics	Measurement of flow velocity in the wind tunnel
HMO2022 Digital Oscilloscope, 2 Analogue. Ch., 200MHz	Rohde & Schwarz	Measurement of flow velocity in the wind tunnel
Phantom Miro eX1 High-speed Camera	Vision Research IncVis	Imaging system for recording the bead motion in the wind-tunnel
Canon ef 180mm f/3.5 l usm macro lens	Canon	Imaging system for recording the bead motion in the wind-tunnel
Table LED Lamp	Gloches South Korea	Imaging system for recording the bead motion in the wind-tunnel

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Agudo, J. R., Han, J., Park, J., Kwon, S., Loekman, S., Luzi, G., Linderberger, C., Delgado, A., Wierschem, A. Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions. J. Vis. Exp. (132), e57238, doi:10.3791/57238 (2018).