Journal articles: 'Low Reynolds number hydrodynamics'

1

Peterson, Mark A. "Membrane hydrodynamics at low Reynolds number." Physical Review E 53, no. 1 (January 1, 1996): 731–38. http://dx.doi.org/10.1103/physreve.53.731.

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Winkler, Roland G. "Low Reynolds number hydrodynamics and mesoscale simulations." European Physical Journal Special Topics 225, no. 11-12 (November 2016): 2079–97. http://dx.doi.org/10.1140/epjst/e2016-60087-9.

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Putz, Victor B., and Jörn Dunkel. "Low Reynolds number hydrodynamics of asymmetric, oscillating dumbbell pairs." European Physical Journal Special Topics 187, no. 1 (September 2010): 135–44. http://dx.doi.org/10.1140/epjst/e2010-01278-y.

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Felderhof, B. U. "Sedimentation of a dilute suspension in low Reynolds number hydrodynamics." Physica A: Statistical Mechanics and its Applications 348 (March 2005): 16–36. http://dx.doi.org/10.1016/j.physa.2004.08.077.

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Golestanian, Ramin, Julia M. Yeomans, and Nariya Uchida. "Hydrodynamic synchronization at low Reynolds number." Soft Matter 7, no. 7 (2011): 3074. http://dx.doi.org/10.1039/c0sm01121e.

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Alexander, G. P., and J. M. Yeomans. "Hydrodynamic Interactions at Low Reynolds Number." Experimental Mechanics 50, no. 9 (August 3, 2010): 1283–92. http://dx.doi.org/10.1007/s11340-010-9387-6.

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Tseluiko, D., S. Saprykin, C. Duprat, F. Giorgiutti-Dauphiné, and S. Kalliadasis. "Pulse dynamics in low-Reynolds-number interfacial hydrodynamics: Experiments and theory." Physica D: Nonlinear Phenomena 239, no. 20-22 (October 2010): 2000–2010. http://dx.doi.org/10.1016/j.physd.2010.07.011.

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Ichiki, Kengo, and John F. Brady. "Many-body effects and matrix inversion in low-Reynolds-number hydrodynamics." Physics of Fluids 13, no. 1 (January 2001): 350–53. http://dx.doi.org/10.1063/1.1331320.

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Holmes, David W., John R. Williams, and Peter Tilke. "Smooth particle hydrodynamics simulations of low Reynolds number flows through porous media." International Journal for Numerical and Analytical Methods in Geomechanics 35, no. 4 (February 22, 2011): 419–37. http://dx.doi.org/10.1002/nag.898.

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Ripoll, M., K. Mussawisade, R. G. Winkler, and G. Gompper. "Low-Reynolds-number hydrodynamics of complex fluids by multi-particle-collision dynamics." Europhysics Letters (EPL) 68, no. 1 (October 2004): 106–12. http://dx.doi.org/10.1209/epl/i2003-10310-1.

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Manga, Michael, and H. A. Stone. "Collective hydrodynamics of deformable drops and bubbles in dilute low Reynolds number suspensions." Journal of Fluid Mechanics 300 (October 10, 1995): 231–63. http://dx.doi.org/10.1017/s0022112095003673.

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Deformation due to hydrodynamic interactions between two deformable buoyant drops may result in the alignment and coalescence of horizontally offset drops. Three-dimensional boundary integral calculations are presented for systems containing two, three or four drops and it is argued that the interactions which occur between three drops or four drops may be characterized qualitatively by the two-drop interactions. In a dilute monodisperse suspension, the rate of coalescence of deformable drops is calculated using far-field analytical results and is found to be proportional to the Bond number. The rate of coalescence in a dilute polydisperse suspension of bubbles in corn syrup is determined by performing a large number of laboratory experiments for Bond numbers based on the larger bubble radius 15 < [Bscr ] < 120. The rate of coalescence is enhanced (by a factor of 10 for [Bscr ] = 10), owing to the effects of deformation, compared to the predictions of models which include hydrodynamic interactions and van der Waals forces among spherical bubbles. The rate of coalescence is greater than the rate predicted by the Smoluchowski model which ignores all hydrodynamic interactions. The experimental results are used to calculate the evolution of the bubble size distribution in suspensions using a standard one-dimensional population dynamics model; deformation affects the size distribution in suspensions, resulting in a wider range of bubble sizes.

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STONE, H. A. "Philip Saffman and viscous flow theory." Journal of Fluid Mechanics 409 (April 25, 2000): 165–83. http://dx.doi.org/10.1017/s0022112099007697.

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Philip Saffman made valuable theoretical contributions to different areas of low-Reynolds-number hydrodynamics. Three themes are selected for discussion here: (i) the lift force on a sphere in a shear flow at small, but finite Reynolds number, (ii) Brownian motion in thin liquid films, and (iii) particle motion in rapidly rotating flows. In addition, brief descriptions are given of some of Saffman's other contributions including dispersion in porous media, the average velocity of sedimenting suspensions, and compressible low-Reynolds-number flows.

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Zhu, L., E. Lauga, and L. Brandt. "Low-Reynolds-number swimming in a capillary tube." Journal of Fluid Mechanics 726 (May 31, 2013): 285–311. http://dx.doi.org/10.1017/jfm.2013.225.

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AbstractWe use the boundary element method to study the low-Reynolds-number locomotion of a spherical model microorganism in a circular tube. The swimmer propels itself by tangential or normal surface motion in a tube whose radius is of the order of the swimmer size. Hydrodynamic interactions with the tube walls significantly affect the average swimming speed and power consumption of the model microorganism. In the case of swimming parallel to the tube axis, the locomotion speed is always reduced (respectively, increased) for swimmers with tangential (respectively, normal) deformation. In all cases, the rate of work necessary for swimming is increased by confinement. Swimmers with no force dipoles in the far field generally follow helical trajectories, solely induced by hydrodynamic interactions with the tube walls, and in qualitative agreement with recent experimental observations for Paramecium. Swimmers of the puller type always display stable locomotion at a location which depends on the strength of their force dipoles: swimmers with weak dipoles (small $\alpha $) swim in the centre of the tube while those with strong dipoles (large $\alpha $) swim near the walls. In contrast, pusher swimmers and those employing normal deformation are unstable and end up crashing into the walls of the tube. Similar dynamics is observed for swimming into a curved tube. These results could be relevant for the future design of artificial microswimmers in confined geometries.

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Zhu, Lailai, and Howard A. Stone. "Rotation of a low-Reynolds-number watermill: theory and simulations." Journal of Fluid Mechanics 849 (June 15, 2018): 57–75. http://dx.doi.org/10.1017/jfm.2018.416.

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Recent experiments have demonstrated that small-scale rotary devices installed in a microfluidic channel can be driven passively by the underlying flow alone without resorting to conventionally applied magnetic or electric fields. In this work, we conduct a theoretical and numerical study on such a flow-driven ‘watermill’ at low Reynolds number, focusing on its hydrodynamic features. We model the watermill by a collection of equally spaced rigid rods. Based on the classical resistive force (RF) theory and direct numerical simulations, we compute the watermill’s instantaneous rotational velocity as a function of its rod number $N$, position and orientation. When $N\geqslant 4$, the RF theory predicts that the watermill’s rotational velocity is independent of $N$ and its orientation, implying the full rotational symmetry (of infinite order), even though the geometrical configuration exhibits a lower-fold rotational symmetry; the numerical solutions including hydrodynamic interactions show a weak dependence on $N$ and the orientation. In addition, we adopt a dynamical system approach to identify the equilibrium positions of the watermill and analyse their stability. We further compare the theoretically and numerically derived rotational velocities, which agree with each other in general, while considerable discrepancy arises in certain configurations owing to the hydrodynamic interactions neglected by the RF theory. We confirm this conclusion by employing the RF-based asymptotic framework incorporating hydrodynamic interactions for a simpler watermill consisting of two or three rods and we show that accounting for hydrodynamic interactions can significantly enhance the accuracy of the theoretical predictions.

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Jabbarzadeh, Mehdi, and Henry Chien Fu. "Viscous constraints on microorganism approach and interaction." Journal of Fluid Mechanics 851 (July 31, 2018): 715–38. http://dx.doi.org/10.1017/jfm.2018.509.

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Microorganisms must approach other suspended organisms or particles in order to interact with them during a host of life processes including feeding and mating. Microorganisms live at low Reynolds number where viscosity dominates and strongly affects the hydrodynamics of swimmer and nearby cells and objects. Viscous hydrodynamics makes it difficult for two surfaces to approach closely at low Reynolds numbers. Nonetheless, it is observed that microorganisms in fluid are still able to approach closely enough to interact with each other or suspended particles. Here, we study how the physical constraints provided by viscous hydrodynamics affects the feasibility of direct approach of flagellated and ciliated microorganisms to targets of different sizes. We find that it is feasible for singly flagellated swimmers to approach targets that are the same size or bigger. On the other hand, for squirmers, the feasibility of approach depends on near-field flows that can be controlled by the details of their swimming strokes.

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WATANBE, Masao, and Tohru FUKANO. "Hydrodynamic Force between Slightly Deformable Bubbles at Low Reynolds Number." JSME International Journal Series B 41, no. 2 (1998): 480–85. http://dx.doi.org/10.1299/jsmeb.41.480.

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Li, Shao-bai, Jun-geng Fan, Run-dong Li, Lei Wang, and Jing-de Luan. "Effect of surfactants on hydrodynamics characteristics of bubble in shear thinning fluids at low Reynolds number." Journal of Central South University 25, no. 4 (April 2018): 805–11. http://dx.doi.org/10.1007/s11771-018-3785-9.

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18

Denner, Fabian, Alexandros Charogiannis, Marc Pradas, Christos N. Markides, Berend G. M. van Wachem, and Serafim Kalliadasis. "Solitary waves on falling liquid films in the inertia-dominated regime." Journal of Fluid Mechanics 837 (January 4, 2018): 491–519. http://dx.doi.org/10.1017/jfm.2017.867.

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We offer new insights and results on the hydrodynamics of solitary waves on inertia-dominated falling liquid films using a combination of experimental measurements, direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with experimental measurements in terms of the main wave characteristics and velocity profiles over the entire range of investigated Reynolds numbers. And, surprisingly, the LD model is found to predict accurately the film height even for inertia-dominated films with high Reynolds numbers. Based on a detailed analysis of the flow field within the liquid film, the hydrodynamic mechanism responsible for a constant, or even reducing, maximum film height when the Reynolds number increases above a critical value is identified, and reasons why no flow reversal is observed underneath the wave trough above a critical Reynolds number are proposed. The saturation of the maximum film height is shown to be linked to a reduced effective inertia acting on the solitary waves as a result of flow recirculation in the main wave hump and in the moving frame of reference. Nevertheless, the velocity profile at the crest of the solitary waves remains parabolic and self-similar even after the onset of flow recirculation. The upper limit of the Reynolds number with respect to flow reversal is primarily the result of steeper solitary waves at high Reynolds numbers, which leads to larger streamwise pressure gradients that counter flow reversal. Our results should be of interest in the optimisation of the heat and mass transport characteristics of falling liquid films and can also serve as a benchmark for future model development.

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Basu, S., and B. M. Cetegen. "Analysis of Hydrodynamics and Heat Transfer in a Thin Liquid Film Flowing Over a Rotating Disk by the Integral Method." Journal of Heat Transfer 128, no. 3 (September 12, 2005): 217–25. http://dx.doi.org/10.1115/1.2150836.

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An integral analysis of hydrodynamics and heat transfer in a thin liquid film flowing over a rotating disk surface is presented for both constant temperature and constant heat flux boundary conditions. The model is found to capture the correct trends of the liquid film thickness variation over the disk surface and compare reasonably well with experimental results over the range of Reynolds and Rossby numbers covering both inertia and rotation dominated regimes. Nusselt number variation over the disk surface shows two types of behavior. At low rotation rates, the Nusselt number exhibits a radial decay with Nusselt number magnitudes increasing with higher inlet Reynolds number for both constant wall temperature and heat flux cases. At high rotation rates, the Nusselt number profiles exhibit a peak whose location advances radially outward with increasing film Reynolds number or inertia. The results also compare favorably with the full numerical simulation results from an earlier study as well as with the reported experimental results.

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20

HINCH, JOHN. "A perspective of Batchelor's research in micro-hydrodynamics." Journal of Fluid Mechanics 663 (November 4, 2010): 8–17. http://dx.doi.org/10.1017/s0022112010003964.

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Batchelor made his name with research in turbulence in the 1940s and 1950s. He became disillusioned with turbulence at the Marseille meeting in 1961. At the end of the 1960s, he started his second wave of research on low-Reynolds-number suspensions of particles. Ten years after he died, I will describe his key results, what was before and what followed. Eight of his 10 most cited papers are in micro-hydrodynamics.

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Swan, James W., and John F. Brady. "The hydrodynamics of confined dispersions." Journal of Fluid Mechanics 687 (October 17, 2011): 254–99. http://dx.doi.org/10.1017/jfm.2011.351.

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AbstractA method is proposed for computing the low-Reynolds-number hydrodynamic forces on particles comprising a suspension confined by two parallel, no-slip walls. This is constructed via the two-dimensional analogue of Hasimoto’s solution (J. Fluid Mech., vol. 5, 1959, pp. 317–328) for a periodic array of point forces in a viscous, incompressible fluid, and, like Hasimoto, the summation of interactions is accelerated by substitution and superposition of ‘Ewald-like’ forcing. This method is akin to the accelerated Stokesian dynamics technique (J. Fluid Mech., vol. 448, 2001, pp. 115–146) and models the suspension dynamics with log–linear computational scaling. The effectiveness of this approach is demonstrated with a calculation of the high-frequency dynamic viscosity of a colloidal dispersion as function of volume fraction and channel width. Similarly, the short-time self-diffusivity for and the sedimentation rate of spherical particles in a confined suspension are determined. The results demonstrate the influence of confining geometry on the transport of small particles, which is becoming increasingly important for micro- and biofluidics.

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Arkharov, Ivan A., A. M. Arkharov, Ekaterina S. Navasardyan, and V. A. Chekhovich. "MODELING OF HYDRODYNAMICS IN A POROUS STRUCTURE OF LOW TEMPERATURE REGENERATOR. FRICTION FACTOR AT LOW REYNOLDS NUMBERS." Journal of Enhanced Heat Transfer 25, no. 2 (2018): 169–80. http://dx.doi.org/10.1615/jenhheattransf.2018027017.

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23

Avital, E. J., M. Alonso, and V. Supontisky. "Computational aeroacoustics: The low speed jet." Aeronautical Journal 112, no. 1133 (July 2008): 405–14. http://dx.doi.org/10.1017/s0001924000002360.

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AbstractLow speed circular, elliptic and planar jets are investigated computationally for basic sound generation and hydrodynamics. The jets are assumed to be incompressible and are simulated using the large eddy simulation (LES) approach. The emitted sound is calculated using Lighthill’s acoustic analogy. Two formulations are used, Lighthill’s stress tensor formulation and Powell’s vortex sound formulation. A new boundary correction for Powell’s formulation is developed in order to account for the finite size of the computational domain. Low to moderate Reynolds number jets are simulated. Good agreement with known hydrodynamic results is achieved. This includes the nature of the transition process, e.g. enhanced mixing and axis switching in the elliptic jet and in some statistical results. The new boundary correction for Powell’s formulation proves to be vital in order to achieve good agreement with Lighthill’s formulation. Some success in high frequency prediction at least for the circular and elliptic jets is achieved in terms of getting the expected asymptotic behaviour. Both formulations show that the elliptic jet noise level is mildly lower than the circular jet noise level. Good to very good agreement is achieved in terms of directivities and frequency spectra with known results for the various jets.

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Schuchardt, Karen, Jared Chase, Jeff Daily, Todd Elsethagen, Bruce Palmer, and Tim Scheibe. "Application of the SALSSA framework to the validation of smoothed particle hydrodynamics simulations of low Reynolds number flows." Journal of Physics: Conference Series 180 (July 1, 2009): 012065. http://dx.doi.org/10.1088/1742-6596/180/1/012065.

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Botte, Vincenzo, Maurizio Ribera D'Alcalà, and Marina Montresor. "Hydrodynamic interactions at low Reynolds number: an overlooked mechanism favouring diatom encounters." Journal of Plankton Research 35, no. 4 (April 19, 2013): 914–18. http://dx.doi.org/10.1093/plankt/fbt033.

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Greiner, Miles, Paul F. Fischer, and Henry Tufo. "Numerical Simulations of Resonant Heat Transfer Augmentation at Low Reynolds Numbers." Journal of Heat Transfer 124, no. 6 (December 1, 2002): 1169–75. http://dx.doi.org/10.1115/1.1517273.

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The effect of flow rate modulation on low Reynolds number heat transfer enhancement in a transversely grooved passage was numerically simulated using a two-dimensional spectral element technique. Simulations were performed at subcritical Reynolds numbers of Rem=133 and 267, with 20 percent and 40 percent flow rate oscillations. The net pumping power required to modulate the flow was minimized as the forcing frequency approached the predicted natural frequency. However, mixing and heat transfer levels both increased as the natural frequency was approached. Oscillatory forcing in a grooved passage requires two orders of magnitude less pumping power than flat passage systems for the same heat transfer level. Hydrodynamic resonance appears to be an effective method of increasing heat transfer in low Reynolds number systems, especially when pumping power is at a premium.

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Yarin, A. L. "Surface-tension-driven flows at low Reynolds number arising in optoelectronic technology." Journal of Fluid Mechanics 286 (March 10, 1995): 173–200. http://dx.doi.org/10.1017/s0022112095000693.

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Some methods of formation of preforms for drawing of polarization-maintaining optical fibres are based on utilization of the surface tension of glass in the liquid state. Under the action of surface tension non-circular glass articles begin to flow, which results in formation of an anisotropic internal structure of the preforms. The hydrodynamic analysis of two such methods is given in the paper. Analytical solutions of the Stokes equations with linearized boundary conditions for the corresponding creeping surface-tension-driven flows of liquid glass are obtained. By means of these solutions a processing strategy may be predetermined with a view to a specific internal structure of the fibre, as well as to the required value of birefringence. The theoretical results are compared with experimental data and agreement is fairly good.

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Nienow, A. W. "Hydrodynamics of Stirred Bioreactors." Applied Mechanics Reviews 51, no. 1 (January 1, 1998): 3–32. http://dx.doi.org/10.1115/1.3098990.

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This review of the hydrodynamics of stirred bioreactors begins with an introduction to the agitation problems of particular concern in such systems. This is followed by a brief review of some basic concepts in turbulence and rheology of relevance to bioreactors. Important aspects of single phase mixing in low viscosity, high viscosity and Theologically complex broths are then covered in some detail including flow patterns, power number versus Reynolds number plots (including the modification of the latter to allow for shear thinning broths), flow numbers, energy dissipation rates and flow close to impellers and between multiple impeller systems. From these basic principles, the problem of homogenization is then covered in depth because of its significance for bioreactor performance. Aeration concepts are then introduced and the behavior of traditional Rushton turbine impellers is then treated in detail, covering the flow patterns, aerated power characteristics, mixing time and scale-up considerations. The weaknesses of the Rushton turbine are then discussed which leads into a section describing how more modern impellers are able to improve on many of these, especially emphasising their ability to introduce more energy dissipation into the broth and handle more air before flooding, both of which enhance oxygen transfer. The improvement in bulk blending found with multiple axial flow agitators is brought out too. Finally, the retrofitting of fermenters originally containing Rushton turbines with these more modern impellers is discussed. In conclusion, it is clear that there have been substantial increases in the understanding of stirred bioreactor hydrodynamics. However, whilst further understanding will occur within the framework discussed here, the expectation must be that computational fluid dynamics will increase in importance in spite of the difficulty of handling complex rheology, multiphase systems and biological responses. This review article has 135 references.

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Ascoli, E. P., D. S. Dandy, and L. G. Leal. "Low Reynolds number hydrodynamic interaction of a solid particle with a planar wall." International Journal for Numerical Methods in Fluids 9, no. 6 (June 1989): 651–88. http://dx.doi.org/10.1002/fld.1650090603.

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Pawar, Suraj, and Stefano Brizzolara. "Relevance of transition turbulent model for hydrodynamic characteristics of low Reynolds number propeller." Applied Ocean Research 87 (June 2019): 165–78. http://dx.doi.org/10.1016/j.apor.2019.02.018.

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Bai, Hua, and Jia Wu Li. "Numerical Simulation of Flow over a Circular Cylinder at Low Reynolds Number." Advanced Materials Research 255-260 (May 2011): 942–46. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.942.

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The hydrodynamic characteristics of a circular cylinder in two-dimensional unsteady uniform cross flow was simulated numerically by the laminar model with the reasonable mesh used the method of fluent. The focus of this numerical simulation was to research the characteristics of pressure distribution, drag coefficient and lift coefficient, and the Strouhal number was calculated at Reynolds-numbers value of 200. The results agree well with experimental data and other numerical results according to the reference. In order to study the control measures of the flow over a circular cylinder, the different baffles inserted at various locations downstream of the cylinder have been compared. The results shows that the vortex shedding of flow over a circular cylinder could be well controlled by place the baffle at a right position of the downstream medial axis of the cylinder, which could reduce drag and resist vibration.

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Khosronejad, Ali, and C. D. Rennie. "Three-dimensional numerical modeling of unconfined and confined wall-jet flow with two different turbulence models." Canadian Journal of Civil Engineering 37, no. 4 (April 2010): 576–87. http://dx.doi.org/10.1139/l09-172.

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Wall-jet flow is an important flow field in hydraulic engineering, and its applications include flow from the bottom outlet of dams and sluice gates. An in-house three-dimensional (3-D) finite-volume Reynolds-averaged-Navier-Stokes (RANS) numerical model predicts the hydrodynamic characteristics of wall jets with square and rectangular source geometry. Either the low-turbulence Reynolds number k–ω or the standard k–ε turbulence closure models are applied. The calculated results for velocity profile and bed shear stress in both longitudinal and vertical directions compare favourably with both the published experimental results and the FLUENT® finite volume model. The two closure models are compared with the k–ω model, displaying 4% greater average accuracy than the k–ε model. Finally, the influence of lateral confinement of the receiving channel on wall-jet hydrodynamics is investigated, with decreased longitudinal deceleration and decreased bed shear stress observed in a confined jet. This has important implications for sediment transport in the receiving channels downstream of sluice gates.

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BOZKURTTAS, M., R. MITTAL, H. DONG, G. V. LAUDER, and P. MADDEN. "Low-dimensional models and performance scaling of a highly deformable fish pectoral fin." Journal of Fluid Mechanics 631 (July 17, 2009): 311–42. http://dx.doi.org/10.1017/s0022112009007046.

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The hydrodynamics of a highly deformable fish pectoral fin used by a bluegill sunfish (Lepomis macrochirus) during steady forward swimming are examined in detail. Low-dimensional models of the fin gait based on proper orthogonal decomposition (POD) are developed, and these are subjected to analysis using an incompressible Navier–Stokes flow solver. The approach adopted here is primarily motivated by the quest to develop insights into the fin function and associated hydrodynamics, which are specifically useful for the design of a biomimetic, pectoral fin propulsor. The POD analysis shows that the complex kinematics of the pectoral fin can be described by a few (<5) POD modes and that the first three POD modes are highly distinct. The significance of these modes for thrust production is examined by synthesizing a sequence of fin gaits from these modes and simulating the flow associated with these gaits. We also conduct a scale study of the pectoral fin in order to understand the effect of the two key non-dimensional parameters, Reynolds number and Strouhal number, on the propulsive performance. The implications of the POD analysis and performance scaling on the design of a robotic pectoral fin are discussed.

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CROWDY, DARREN, SUNGYON LEE, OPHIR SAMSON, ERIC LAUGA, and A. E. HOSOI. "A two-dimensional model of low-Reynolds number swimming beneath a free surface." Journal of Fluid Mechanics 681 (June 29, 2011): 24–47. http://dx.doi.org/10.1017/jfm.2011.223.

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Biological organisms swimming at low-Reynolds number are often influenced by the presence of rigid boundaries and soft interfaces. In this paper, we present an analysis of locomotion near a free surface with surface tension. Using a simplified two-dimensional singularity model and combining a complex variable approach with conformal mapping techniques, we demonstrate that the deformation of a free surface can be harnessed to produce steady locomotion parallel to the interface. The crucial physical ingredient lies in the nonlinear hydrodynamic coupling between the disturbance flow created by the swimmer and the free boundary problem at the fluid surface.

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Chen, Sheng, Wenwei Liu, and Shuiqing Li. "Scaling laws for migrating cloud of low-Reynolds-number particles with Coulomb repulsion." Journal of Fluid Mechanics 835 (November 28, 2017): 880–97. http://dx.doi.org/10.1017/jfm.2017.772.

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We investigate the evolution of spherical clouds of charged particles that migrate under the action of a uniform external electrostatic field. Hydrodynamic interactions are modelled by Oseen equations and the Coulomb repulsion is calculated through pairwise summation. It is shown that strong long-range Coulomb repulsion can prevent the breakup of the clouds covering a wide range of particle Reynolds number $Re_{p}$ and cloud-to-particle size ratio $R_{0}/r_{p}$. A dimensionless charge parameter $\unicode[STIX]{x1D705}_{q}$ is constructed to quantify the effect of the repulsion, and a critical value $\unicode[STIX]{x1D705}_{q,t}$ is deduced, which successfully captures the transition of a cloud from hydrodynamically controlled regime to repulsion-controlled regime. Our results also reveal that, with sufficiently strong repulsion, the cloud undergoes a universal self-similar expansion. Scaling laws of cloud radius $R_{cl}$ and particle number density $n$ are obtained by solving a continuum convection equation.

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Noor, Dedy Zulhidayat, Eddy Widiyono, Suhariyanto, Lisa Rusdiyana, and Joko Sarsetiyanto. "Laminar Flow Past a Circular Cylinder: Reduction of Drag and Fluctuating Lift Using Upstream and Downstream Rods." Applied Mechanics and Materials 493 (January 2014): 9–14. http://dx.doi.org/10.4028/www.scientific.net/amm.493.9.

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Laminar flow past a circular cylinder has been studied numerically at low Reynolds number. The upstream and downstream rods have been used as passive control in order to reduce hydrodynamics forces acting on the cylinder. Both the upstream and downstream rods significantly contribute in reduction of drag and fluctuating lift compared to single cylinder without the rods. More detail, the upstream installation rod is more dominant in drag reduction than the downstream one. On the contrary, the downstream rod has suppressed the magnitude of the fluctuating lift almost twice that of the upstream configuration. Placing the two rods together as the upstream and downstream passive control in tandem arrangement has given more hydrodynamics forces reduction than the single rod configurations.Keywords:circular cylinder, passive control, tandem, drag, lift.

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Keh, Huan J., and Shih H. Chen. "Low-Reynolds-number hydrodynamic interactions in a suspension of spherical particles with slip surfaces." Chemical Engineering Science 52, no. 11 (June 1997): 1789–805. http://dx.doi.org/10.1016/s0009-2509(96)00514-3.

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38

Lecoq, N., F. Feuillebois, N. Anthore, R. Anthore, F. Bostel, and C. Petipas. "Precise measurement of particle–wall hydrodynamic interactions at low Reynolds number using laser interferometry." Physics of Fluids A: Fluid Dynamics 5, no. 1 (January 1993): 3–12. http://dx.doi.org/10.1063/1.858787.

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Yeung, R. W., and C. F. Wu. "Viscosity Effects on the Radiation Hydrodynamics of Horizontal Cylinders." Journal of Offshore Mechanics and Arctic Engineering 113, no. 4 (November 1, 1991): 334–43. http://dx.doi.org/10.1115/1.2919939.

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The problem of a body oscillating in a viscous fluid with a free surface is examined. The Navier-Stokes equations and boundary conditions are linearized using the assumption of small body-motion to wavelength ratio. Generation and diffusion of vorticity, but not its convection, are accounted for. Rotational and irrotational Green functions for a divergent and a vorticity source are presented, with the effects of viscosity represented by a frequency Reynolds number Rσ = g2/νσ3. Numerical solutions for a pair of coupled integral equations are obtained for flows about a submerged cylinder, circular or square. Viscosity-modified added-mass and damping coefficients are developed as functions of frequency. It is found that as Rσ approaches infinity, inviscid-fluid results can be recovered. However, viscous effects are important in the low-frequency range, particularly when Rσ is smaller than O(104).

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Bogey, Christophe. "On noise generation in low Reynolds number temporal round jets at a Mach number of 0.9." Journal of Fluid Mechanics 859 (November 27, 2018): 1022–56. http://dx.doi.org/10.1017/jfm.2018.864.

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Two temporally developing isothermal round jets at a Mach number of 0.9 and Reynolds numbers of 3125 and 12 500 are simulated in order to investigate noise generation in high-subsonic jet flows. Snapshots and statistical properties of the flow and sound fields, including mean, root-mean-square and skewness values, spectra and auto- and cross-correlations of velocity and pressure, are presented. The jet at a Reynolds number of 12 500 develops more rapidly, exhibits more fine turbulent scales and generates more high-frequency acoustic waves than the other. In both cases, however, when the jet potential core closes, mixing-layer turbulent structures intermittently intrude on the jet axis and strong low-frequency acoustic waves are emitted in the downstream direction. These waves are dominated by the axisymmetric mode and are significantly correlated with centreline flow fluctuations. These results are similar to those obtained at the end of the potential core of spatially developing jets. They suggest that the mechanism responsible for the downstream noise component of these jets also occurs in temporal jets, regardless of the Reynolds number. This mechanism is revealed by averaging the flow and pressure fields of the present jets using a sample synchronization with the minimum values of centreline velocity at potential-core closing. A spot characterized by a lower velocity and a higher level of vorticity relative to the background flow field is found to develop in the interfacial region between the mixing layer and the potential core, to strengthen rapidly and reach a peak intensity when arriving on the jet axis, and then to break down. This is accompanied by the growth and decay of a hydrodynamic pressure wave, propagating at a velocity which, initially, is close to 65 per cent of the jet velocity and slightly increases, but quickly decreases after the collapse of the high-vorticity spot in the flow. During that process, sound waves are radiated in the downstream direction.

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BORZENKO, Evgeniy I., and Dmitriy N. GARBUZOV. "INVESTIGATION OF A HYDRODYNAMIC ENTRANCE REGION FOR A POWER-LAW FLUID FLOW IN A ROUND PIPE." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 67 (2020): 78–88. http://dx.doi.org/10.17223/19988621/67/8.

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The paper presents a study of the Ostwald – de Waele fluid flow in a round pipe with a uniform velocity profile specified at the inlet section. Mathematical formulation of the problem is presented using dimensionless variables. A numerical algorithm is developed on the basis of the finite volume method and SIMPLE procedure. Parametric studies of the flow are carried out for the Reynolds number varying from 0.1 to 80 and the power-law index varying from 0.2 to 1.5. It is shown that the flow can be distinguished into a developing flow zone in the inlet boundary vicinity and a fully developed flow zone in the rest part of the flow region. Dependency diagrams are plotted for the development length depending on the power-law index and Reynolds number. The first diagram is found to be non-monotonic. The development length is shown to be almost linearly dependent on the Reynolds number in the range from 1 to 80. In the region of low Reynolds numbers, the length remains almost uniform. The agreement of the obtained numerical results with data from other studies is shown.

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Mao, Wenbin, and Alexander Alexeev. "Motion of spheroid particles in shear flow with inertia." Journal of Fluid Mechanics 749 (May 14, 2014): 145–66. http://dx.doi.org/10.1017/jfm.2014.224.

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AbstractIn this article, we investigate the motion of a solid spheroid particle in a simple shear flow. Using a lattice Boltzmann method, we examine individual effects of fluid inertia and particle rotary inertia as well as their combination on the dynamics and trajectory of spheroid particles at low and moderate Reynolds numbers. The motion of a single spheroid is shown to be dependent on the particle Reynolds number, particle aspect ratio, particle initial orientation and the Stokes number. Spheroids with random initial orientations are found to drift to stable orbits influenced by fluid inertia and/or particle inertia. Specifically, prolate spheroids drift towards the tumbling mode of motion, whereas oblate spheroids drift to the rolling mode. The rotation period and the variation of angular velocity of tumbling spheroids decrease as Stokes number increases. With increasing Reynolds number, both the maximum and minimum values of angular velocity decrease, whereas the particle rotation period increases. We show that particle inertia does not affect the hydrodynamic torque on the particle. We also demonstrate that superposition can be used to estimate the combined effect of fluid inertia and particle inertia on the dynamics of spheroid particles at sufficiently low Reynolds numbers.

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Moon, Young J., and J. H. Seo. "A Splitting Method for Aeroacoustic Noise Prediction of Low Mach Number Viscous Flows." International Journal of Aeroacoustics 4, no. 1-2 (January 2005): 21–36. http://dx.doi.org/10.1260/1475472053730057.

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A set of perturbed compressible equations(PCE), based on a hydrodynamic/acoustic splitting method, is proposed for aeroacoustic noise prediction of low Mach number viscous flows. The present formulation corrects the deficiency of previous splitting methods that have no control over the coupling effects between the incompressible vorticity and the perturbed velocities. The validation test shows that the present PCE solution is in excellent agreement with those of direct acoustic numerical simulation(DaNS) and Curle's acoustic analogy for a laminar dipole tone from a 2D circular cylinder at Reynolds number based on the cylinder diameter, ReD=200 and free stream Mach number, M∞ = 0.3. Computational efficiency and accuracy requirements for PCE are also investigated for a vortex scattering noise from the trailing-edge of a thin plate at Reynolds number based on the plate thickness, Reh= 2000 and M∞ = 0.3. The test results indicate that the computational efficiency can be achieved with an acoustic grid at lower resolution, as long as the projection quality of the total derivative of the incompressible pressure, DP/Dt field is retained.

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SWAN, JAMES W., and ADITYA S. KHAIR. "On the hydrodynamics of ‘slip–stick’ spheres." Journal of Fluid Mechanics 606 (July 10, 2008): 115–32. http://dx.doi.org/10.1017/s0022112008001614.

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The breakdown of the no-slip condition at fluid–solid interfaces generates a host of interesting fluid-dynamical phenomena. In this paper, we consider such a scenario by investigating the low-Reynolds-number hydrodynamics of a novel ‘slip–stick’ spherical particle whose surface is partitioned into slip and no-slip regions. In the limit where the slip length is small compared to the size of the particle, we first compute the translational velocity of such a particle due to the force density on its surface. Subsequently, we compute the rotational velocity and the response to an ambient straining field of a slip–stick particle. These three Faxén-type formulae are rich in detail about the dynamics of the particles: chiefly, we find that the translational velocity of a slip–stick sphere is coupled to all of the moments of the force density on its surface; furthermore, such a particle can migrate parallel to the velocity gradient in a shear flow. Perhaps most important is the coupling we predict between torque and translation (and force and rotation), which is uncharacteristic of spherical particles in unbounded Stokes flow and originates purely from the slip–stick asymmetry.

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Dabros, T. "A singularity method for calculating hydrodynamic forces and particle velocities in low-Reynolds-number flows." Journal of Fluid Mechanics 156, no. -1 (July 1985): 1. http://dx.doi.org/10.1017/s0022112085001951.

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CROWDY, DARREN, and OPHIR SAMSON. "Hydrodynamic bound states of a low-Reynolds-number swimmer near a gap in a wall." Journal of Fluid Mechanics 667 (November 16, 2010): 309–35. http://dx.doi.org/10.1017/s0022112010004465.

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The motion of an organism swimming at low Reynolds number near an infinite straight wall with a finite-length gap is studied theoretically within the framework of a two-dimensional model. The swimmer is modelled as a point singularity of the Stokes equations dependent on a single real parameter. A dynamical system governing the position and orientation of the model swimmer is derived in analytical form. The dynamical system is studied in detail and a bifurcation analysis performed. The analysis reveals,inter alia, the presence of stable equilibrium points in the gap region as well as Hopf bifurcations to periodic bound states. The reduced-model system also exhibits a global gluing bifurcation in which two symmetric periodic orbits merge at a saddle point into symmetric ‘figure-of-eight’ bound states having more complex spatiotemporal structure. The additional effect of a background shear is also studied and is found to introduce new types of bound state. The analysis allows us to make theoretical predictions as to the possible behaviour of a low-Reynolds-number swimmer near a gap in a wall. It offers insights into the use of gaps or orifices as possible control devices for such swimmers in confined environments.

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Felderhof, B. U. "Speed and efficiency of two swimming planar sheets in hydrodynamic interaction at low Reynolds number." European Journal of Mechanics - B/Fluids 31 (January 2012): 168–70. http://dx.doi.org/10.1016/j.euromechflu.2011.08.006.

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Gonçalves de Matos, Gyell, Takeshi Kodama, and Tomoi Koide. "Uncertainty Relations in Hydrodynamics." Water 12, no. 11 (November 21, 2020): 3263. http://dx.doi.org/10.3390/w12113263.

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The qualitative behaviors of uncertainty relations in hydrodynamics are numerically studied for fluids with low Reynolds numbers in 1+1 dimensional system. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the work by two of the present authors [Phys. Lett. A 382, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schrödinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in the Navier-Stokes-Fourier equation or the Navier-Stokes-Korteweg equation. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.

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Bhattacharya, Sukalyan, Dil K. Gurung, and Shahin Navardi. "Radial lift on a suspended finite-sized sphere due to fluid inertia for low-Reynolds-number flow through a cylinder." Journal of Fluid Mechanics 722 (March 28, 2013): 159–86. http://dx.doi.org/10.1017/jfm.2012.636.

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AbstractThis article describes the radial drift of a suspended sphere in a cylinder-bound Poiseuille flow where the Reynolds number is small but finite. Unlike past studies, it considers a circular narrow conduit whose cross-sectional diameter is only $1. 5$–$6$ times the particle diameter. Thus, the analysis quantifies the effect of fluid inertia on the radial motion of the particle in the channel when the flow field is significantly influenced by the presence of the suspended body. To this end, the hydrodynamic fields are expanded as a series in Reynolds number, and a set of hierarchical equations for different orders of the expansion is derived. Accordingly, the zeroth-order fields in Reynolds number satisfy the Stokes equation, which is accurately solved in the presence of the spherical particle and the cylindrical conduit. Then, recognizing that in narrow vessels Stokesian scattered fields from the sphere decrease exponentially in the axial direction, a simpler regular perturbation scheme is used to quantify the first-order inertial correction to hydrodynamic quantities. Consequently, it is possible to obtain two results. First, the sphere is assumed to follow the axial motion of a freely suspended sphere in a Stokesian condition, and the radial lift force on it due to the presence of fluid inertia is evaluated. Then, the approximate motion is determined for a freely suspended body on which net hydrodynamic force including first-order inertial lift is zero. The results agree well with the available experimental results. Thus, this study along with the measured data would precisely describe particle dynamics inside narrow tubes.

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Khayat, Roger E., and Byung Chan Eu. "Generalized hydrodynamics and linear stability analysis of cylindrical Couette flow of a dilute Lennard–Jones fluid." Canadian Journal of Physics 71, no. 11-12 (November 1, 1993): 518–36. http://dx.doi.org/10.1139/p93-081.

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Linear stability analysis is carried out for cylindrical Couette flow of a Lennard–Jones fluid in the density range from the dense liquid to the dilute gas regime. Generalized hydrodynamic equations are used to calculate marginal stability curves and compare them with those obtained by using the Navier–Stokes–Fourier equations for compressible fluids and also for incompressible fluids. In the low Reynolds or Mach number regime, if the Knudsen number is sufficiently low, the marginal stability curves calculated by the generalized hydrodynamic theory coincide, within numerical errors, with those based on the Navier–Stokes theory. But there are considerable deviations between them in the regimes beyond those mentioned earlier, since nonlinear effects manifest themselves in the laminar mean flow through the nonlinear dissipation term and normal stresses. There are three marginal stability curves obtained in contrast to the Navier–Stokes theory, which yields only two. The previously observed phase-transition-like behavior in fluid variables and the slip phenomenon are found to occur beyond the hydrodynamic stability point. The disturbance entropy production associated with the Taylor–Couette vortices is calculated to first order in disturbances in flow variables and is found to decrease as the number of vortices increases and thereby the dynamic structure is progressively more organized.

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Journal articles on the topic 'Low Reynolds number hydrodynamics'

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