In the last 30 days

• Open/close Nonlinear steady hydromagnetic convection in mushy layers during alloy solidification

  D N Riahi 2011 Fluid Dyn. Res. 43 045501 Tag this article

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  We consider the problem of nonlinear steady convection in a horizontal mushy layer, which is subjected to a vertical magnetic field, during alloy solidification. Under near-eutectic approximation and the limit of large far-field temperature, we determine the finite-amplitude solutions to the weakly nonlinear problem by using a perturbation technique. We obtain specific information about convective flow solutions in the form of rolls, squares, rectangles, down-hexagons with down-flow at the cells' centers and up-flow at the cells' boundaries and up-hexagons with up-flow at the cells' centers and down-flow at the cells' boundaries. The stability of these solutions is also investigated with respect to arbitrary disturbances. We found, in particular, that only up-hexagons or supercritical rolls can be stable. No subcritical non-hexagonal pattern convection was found to exist. The subcritical domain of stable hexagons and the supercritical domain of stable rolls were found to be enhanced by the magnetic field as well as by the non-uniformity of the permeability of the medium, but the magnetic field narrows down the supercritical domain for the stable hexagons. The magnetic field appears to reduce the tendency for chimney formation at the nodes of up-hexagons, while such a tendency is enhanced by the magnetic field at the nodes of down-hexagons.

• Open/close The dynamics and rheology of a dilute suspension of periodically forced neutrally buoyant spherical particles in a quiescent Newtonian fluid at low Reynolds numbers

  T R Ramamohan et al 2011 Fluid Dyn. Res. 43 045502 Tag this article

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  We study the effects of both convective and unsteady inertia on the dynamics and rheology of a dilute suspension of periodically forced neutrally buoyant spherical particles, at low Reynolds numbers, in a quiescent Newtonian fluid. The inclusion of inertia results in additional terms in the equation governing the dynamics of the particle that represent a fading memory of the entire history of the particle motion. The inclusion of convective inertia in the low Reynolds number limit makes the memory term nonlinear. Several tests were performed to show that the results presented in this paper are physically reasonable and correct. A perturbation analysis of the problem yields strong evidence that the results of our simulations are correct. It is observed that there is a preferred direction in this system which manifests itself in the properties of the solution. This preferred direction is identified as the direction of the initial motion of the particle. We present here results on the behavior of various parameters with respect to Reynolds numbers and the amplitude of the periodic force. These include phase-space plots between particle displacement and particle velocity and the variation of a rheological parameter, namely a 'normal stress' with respect to Reynolds number and the amplitude of the periodic force. We believe that our results may be technologically important since the rheological parameter depends strongly on controllable parameters such as the Reynolds number and the amplitude of the periodic force. Further, this system is one of the simplest systems whose rheology shows non-Newtonian behavior, such as the presence of a normal stress. In addition, this system represents a physically realizable system for experimentally testing the frameworks developed to calculate the collective behavior of systems of oscillators with memory.

• Open/close Damping of surface waves in a brimful circular cylinder with a contaminated free surface

  Rangachari Kidambi 2011 Fluid Dyn. Res. 43 035504 Tag this article

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  We consider the effect of insoluble surfactants on the frequency and damping of surface waves on a viscous liquid in a circular cylinder. The contact line is assumed to be pinned and the surfactants are characterized by an elastic film of Marangoni elasticity γ. The natural complex viscous eigenfunctions for cylindrical geometry are used to obtain a nonlinear eigenvalue problem for the complex frequencies by projecting the governing equations onto an appropriate basis. This is then solved to obtain the modal frequencies as a function of the Reynolds number Re, elasticity γ, Bond number Bo and liquid depth h. Comparison with the theoretical results of Henderson and Miles (1994  J. Fluid Mech. 275 285) for the case of an inextensible film (γ = ∞) showed that there is good agreement. Comparison with the experimental results of Henderson and Miles (1994  J. Fluid Mech. 275 285) and the semi-analytical results of Nicolás and Vega (2000  J. Fluid Mech. 410 367) for the (1, 0), (2, 0), (3, 0) and (4, 0) modes, with an assumed value of γ = 100, also showed good agreement. Results are also presented for a four decadal range of γ. For all modes, a maximum in the damping rate is observed at an intermediate γ. The case of soluble surfactants is briefly considered as well; these results seem to be new. The method can be used for a wide range of parameters; results are presented here for the cases of low Re and shallow depth.

• Open/close A computational study of the dynamic motion of a bubble rising in Carreau model fluids

  Mitsuhiro Ohta et al 2010 Fluid Dyn. Res. 42 025501 Tag this article

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  We present the results of three-dimensional direct numerical simulations of the dynamic motion of a gas bubble rising in Carreau model fluids. The simulations are carried out by a coupled level-set/volume-of-fluid (CLSVOF) method, which combines some of the advantages of the volume-of-fluid (VOF) method with the level-set (LS) method. In our study, it is shown that the motion of a rising gas bubble largely depends on the Carreau model parameters, n and B ( n, the slope of decreasing viscosity and B, time constant). Both the model parameters, n and B, have considerable influence on the bubble rise motion. Using numerical analysis, we can understand in detail the bubble morphology for non-Newtonian two-phase flow systems. We also discuss bubble rise motion in shear-thinning fluids in terms of the effective viscosity, η _eff, the effective Reynolds number, Re _eff and the effective Morton number, M _eff.

• Open/close Influence of liquid and gas compressibility on the growth of waves in thin liquid sheets

  T John Tharakan and K Ramamurthi 2010 Fluid Dyn. Res. 42 035508 Tag this article

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  The growth of waves along the direction of motion of viscous compressible liquid sheets in inviscid compressible gas streams was investigated. Gas streams were considered to move at different velocities relative to the liquid sheet. A dispersion relation was derived for the spatial growth of longitudinal waves in the presence of lateral wave modes. The solution of the dispersion relation showed that the incorporation of gas compressibility increases the growth of paraantisymmetric waves. Compressibility in liquid, such as obtained by the dispersion of gas bubbles, has a much lower influence on the growth of paraantisymmetric waves. The presence of lateral wave modes did not influence longitudinal wave growth when the compressibility of liquid and gas was considered in the model.

• Open/close Molecular dynamics simulations of nanodroplet spreading on solid surfaces, effect of droplet size

  Nahid Sedighi et al 2010 Fluid Dyn. Res. 42 035501 Tag this article

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  Molecular dynamics simulations were performed to study the spreading characteristics of nano-sized droplets on solid surfaces. The spreading behavior was analyzed in terms of the temporal evolution of the dynamic contact angle and spreading diameter for wettable, partially wettable and non-wettable surfaces. The computational model was validated through qualitative comparison with the measurements of Bayer and Megaridis, and through comparison with existing correlations. The comparison based on the ratio of relevant time scales indicated that for the conditions investigated, the spreading dynamics is governed by inertial and surface forces, with negligible influence of viscous forces. In addition, the simulation results indicated that the dynamic contact angle and spreading diameter, as well as the advancing and receding time periods, exhibit strong dependence on droplet size. These results were further analyzed to obtain correlations for the effect of droplet size on these spreading parameters. The correlations indicated that the normalized spreading diameter and contact angle scale with drop diameter as D _m / D ₀ ∝ D ₀ ^0.5 and θ _R ∝ D ₀ ^0.5, while the advancing and receding time periods scale as t∝ D ₀ ^2/3. Global kinetic energy and surface energy considerations were used to provide a physical basis for these correlations. The correlations were also found to be generally consistent with the experimentally observed spreading behavior of macroscopic droplets.

• Open/close Numerical simulation of droplets, bubbles and waves: state of the art

  Daniel Fuster et al 2009 Fluid Dyn. Res. 41 065001 Tag this article

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  This work presents current advances in the numerical simulation of two-phase flows using a volume of fluid (VOF) method, balanced-force surface tension and quad/octree adaptive mesh refinement (AMR). The simulations of the atomization of a liquid sheet, the capillary retraction of a liquid sheet and two- and three-dimensional wave breaking all for air/water systems are used to show the potential of the numerical techniques. New simulations of atomization processes for air/water conditions are allowing us to investigate the processes leading to the appearance of instabilities in the primary atomization zone in real conditions. For the retracting liquid sheet, the new simulations show that two different regimes can be encountered as a function of the Ohnesorge number. For large values, a laminar flow is encountered inside the rim and a steady state is reached after a quick transient state. For small values, a turbulent flow is generated inside the rim, which is responsible for large oscillations in the rim size and neck thickness. The breaking wave case study demonstrates the orders-of-magnitude efficiency gains of the AMR method.

• Open/close A study of mixing in coherent vortices using braiding factors

  M R Turner and M A Berger 2011 Fluid Dyn. Res. 43 035501 Tag this article

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  This paper studies the use of braiding fluid particles to quantify the amount of mixing within a fluid flow. We analyze the pros and cons of braid methods by considering the motion of three or more fluid particles in a coherent vortex structure. The relative motions of the particles, as seen in a space–time diagram, produce a braid pattern, which is correlated with mixing and measured by the braiding factor.

  The flow we consider is a Gaussian vortex within a rotating strain field that generates cat's eyes in the vortex. We also consider a modified version of this strain field that contains a resonance frequency effect that produces multiple sets of cat's eyes at different radii. As the thickness of the cat's eyes increases, they interact with one another and produce complex Lagrangian motion in the flow that increases the braiding of particles, hence implying more mixing within the vortex.

  It is found that calculating the braiding factor using only three fluid particles gives useful information about the flow, but only if all three particles lie in the same region of the flow, i.e. this gives good local information. We find that we only require one of the three particles to trace a chaotic path to give an exponentially growing braiding factor. i.e. a non-zero 'braiding exponent'. A modified braiding exponent is also introduced which removes the spurious effects caused by the rotation of the fluid.

  This analysis is extended to a more global approach by using multiple fluid particles that span larger regions of the fluid. Using these global results, we compare the braiding within a viscously spreading Gaussian vortex in the above strain fields, where the flow is determined both kinematically and dynamically. We show that the dynamic feedback of the strain field onto the flow field reduces the overall amount of braiding of the fluid particles.

• Open/close Flow structure generated from an axisymmetric natural air jet at a moderate Reynolds number

  Yassine Zaouali et al 2011 Fluid Dyn. Res. 43 035502 Tag this article

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  This paper reports on an experimental study of a free air jet evolving naturally and discharging from a round nozzle at a Reynolds number of 1600. By using flow visualization images and time-series analysis, the details of the flow behavior are clarified. In particular, the length of the transition zone of the jet is measured and its temporal evolution is investigated. We show that the vortex structures interact with each other, thus producing different sizes in the flow. The probability distribution and temporal evolution of the jet width at various distances from the nozzle exit are studied. The occurrence frequency of vortex rings and the Strouhal number of the jet were also determined at different positions from the nozzle exit. The results obtained are compared with those reported in the literature.

• Open/close Multi-functional Lagrangian flow structures in three-dimensional ac electro-osmotic micro-flows

  M F M Speetjens et al 2011 Fluid Dyn. Res. 43 035503 Tag this article

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  Flow forcing by ac electro-osmosis (ACEO) is a promising technique for the actuation and manipulation of micro-flows. Utilization to date mainly concerns pumping and mixing. However, emerging micro-fluidic applications demand further functionalities. The present study explores the first ways to systematically realize this in three-dimensional (3D) micro-flows using ACEO. This exploits the fact that continuity 'organizes' Lagrangian fluid trajectories into coherent structures that geometrically determine the transport properties. Lagrangian flow structures typically comprise families of concentric tubular structures, acting both as transport barriers and as transport conduits, embedded in chaotic regions. Numerical simulations of representative case studies demonstrate that ACEO, possibly in combination with other forcing mechanisms, has the potential to tailor these features into multi-functional Lagrangian flow structures that can fulfill various transport purposes. This may greatly enhance the functionality and versatility of labs-on-a-chip.