Volume 26, Issue 6, June 2014
Index of content:
The present work investigates the influence of the primary filter resolution on various turbulence statistics and the representation of vortical structures in Large-Eddy Simulation (LES) of homogeneous isotropic turbulent flow. The resolution effects are investigated both analytically and numerically for an ideal LES solution with negligible modeling and numerical errors, and as such equivalent to filtered direct numerical simulation data. The Taylor-Green vortex is considered for the numerical investigation. Several resolution criteria, found in the literature, which prescribe the filter width requirements for LES, are investigated and their effect on various turbulent statistics is evaluated analytically. Further, the resolution effect on vortical structures is evaluated numerically using the Taylor-Green vortex. Finally, an optimal resolution for LES is derived via a multi-objective optimization, maximizing the resolved fractions of specifically chosen turbulent quantities while minimizing the computational overhead in comparison with a reference simulation. The optimum resolution criterion was found to be . However, a more practical quasi-optimal criterion κ e λ ≈ π is proposed resulting in an acceptable trade-off between accuracy and computational overhead.
- Biofluid Mechanics
26(2014); http://dx.doi.org/10.1063/1.4878338View Description Hide Description
Magnetic microbubbles are a relatively recent development with the potential to greatly improve the efficacy of the minimally invasive drug-delivery procedure sonoporation. However, very little is known about the dynamics of magnetic microbubbles, in general. In this paper, a novel mathematical model and numerical method are developed to simulate the dynamics of non-spherical magnetic microbubbles in vitro. The ambient fluid is assumed to be inviscid and the flow irrotational, enabling a generalized Bernoulli equation to be derived that includes surface tension effects and the effect of the applied magnetic field. The governing equations are solved using the boundary element method in which both the bubble surface and the velocity potential are represented by cubic splines. Results show that magnetic microbubble dynamics are highly dependent on the magnetic susceptibility difference, Δχ, between the bubble and the ambient fluid, with the sign and magnitude of Δχ dictating the direction and velocity of any formed liquid jets. Importantly, it is shown that the magnetic field can provide an additional means of flow control to the experimental investigator: in the presence of surface tension, weak magnetic fields do not generate jets. However, increasing the magnitude of the magnetic field can instigate jet formation, and increase the maximum and time-averaged jet velocities. Experimentally relevant parameter values are also considered, and results suggest that a combined application of magnetic and ultrasound fields is required to generate the high-speed bubble collapse events most likely to maximise cell poration and drug delivery.
26(2014); http://dx.doi.org/10.1063/1.4882263View Description Hide Description
We present a numerical investigation of peristaltic pumping in the presence of suspended drops, the latter serving as a model for deformable obstructions. We impose a sinusoidal motion to an elastic tube thereby driving flow. Inertial and curvature effects are both accounted for, and we track streamlines and transport within the tube. It is found that drops of radius less than half that of the tube have little effect on the overall flow. Larger drops are found to become more easily trapped by the traveling wave and therefore to enhance transport. Inertial effects are seen to increase the size of the trapped region, but to limit the regime in which fluid may be trapped at all.
26(2014); http://dx.doi.org/10.1063/1.4884130View Description Hide Description
Dynamically stretching and retracting wingspan has been widely observed in the flight of birds and bats, and its effects on the aerodynamic performance particularly lift generation are intriguing. The rectangular flat-plate flapping wing with a sinusoidally stretching and retracting wingspan is proposed as a simple model for biologically inspired dynamic morphing wings. Numerical simulations of the low-Reynolds-number flows around the flapping morphing wing are conducted in a parametric space by using the immersed boundary method. It is found that the instantaneous and time-averaged lift coefficients of the wing can be significantly enhanced by dynamically changing wingspan in a flapping cycle. The lift enhancement is caused by both changing the lifting surface area and manipulating the flow structures responsible to the vortex lift generation. The physical mechanisms behind the lift enhancement are explored by examining the three-dimensional flow structures around the flapping wing.
- Micro- and Nanofluid Mechanics
26(2014); http://dx.doi.org/10.1063/1.4880214View Description Hide Description
The behavior of an ellipsoidal particle subjected to a vertical optical force by a loosely focused laser beam in a uniform flow was studied numerically. The fluid flow and the particle motion were separately solved and coupled using the penalty immersed boundary method, and the optical force was calculated using the dynamic ray tracing method. The optical force and optically induced torque on the ellipsoidal particle varied according to the aspect ratio and initial inclination angle. The ellipsoidal particle, whose major axis was initially aligned with the laser beam axis, was more migrated as the aspect ratio increased. The migration distance also depended on the initial inclination angle, even for a given ellipsoidal particle shape. As the laser beam power increased and the flow velocity decreased, the effect of the initial inclination angle increased. The ellipsoidal particles with different aspect ratios could be effectively separated if the rotation along the spanwise direction was suppressed. Moreover, the migration distance could be predicted analytically by introducing a new dimensionless number S c to represent the ratio of the optical force to the viscous force for the ellipsoidal particles.
26(2014); http://dx.doi.org/10.1063/1.4881940View Description Hide Description
An experimental study of nearly isothermal rarefied gas flow near the sudden contraction junction of a tube is presented in this paper. The measurements are performed with nitrogen gas flowing at low pressures in conventional tubes with sudden contraction area ratios of 1.48, 3.74, 12.43, and 64. The flow is dynamically similar to gas flow in a microchannel as the Knudsen number (0.0001 < Kn < 0.032) falls in the slip flow regime. The Reynolds number in the smaller section (Re s ) ranges between 0.2 and 837. The static pressure measurements are analyzed to understand the flow behavior. The static pressure variation along the wall and uniform radial pressure profile near the junction indicates absence of flow separation and vena contracta. The static pressure variation in both the tubes approaches the pressure variation as that of an isolated straight tube at a certain critical Knudsen number for a given area ratio. The velocity field is obtained through a momentum balance and using the flow measurements. The effect of larger momentum diffusivity and slip at the wall, restricts any deviation in velocity profile from its parabolic nature at the junction and suppresses flow separation and vena contracta. The larger inertia force at the sudden contraction junction causes larger acceleration of the flow near the junction in the smaller tube as compared to that of the straight tube. The larger pressure drop in the sudden contraction is a result of the extent of flow compression and additional acceleration near the junction in the smaller tube as compared to the straight tube. This paper reports a set of new results that are expected to help in improving understanding of gaseous slip flows.
26(2014); http://dx.doi.org/10.1063/1.4884369View Description Hide Description
Existing studies on sound wave propagation in rarefied gases examine sound generation by actuated boundaries subject to isothermal boundary conditions. While these conditions are simple to analyze theoretically, they are more challenging to apply in practice compared to heat-flux conditions. To study the effect of modifying the thermal boundary conditions, the present work investigates the impact of replacing the isothermal with heat-flux conditions on propagation of acoustic waves in a microchannel. The linearized problem is formulated for an ideal hard-sphere gas, and the effect of heat-flux prescription is demonstrated through comparison with counterpart results for isothermal boundaries. Analytical solutions are obtained for a gas at collisionless (highly rarefied) and continuum-limit conditions, and validated through comparison with direct simulation Mote Carlo predictions. Remarkably, it is found that prescription of heat flux at the walls, altering the energy balance within the medium, has a significant effect on acoustic wave propagation in the gas. In particular, when optimized with respect to the boundary acoustic signal applied, the heat flux condition may be used to achieve “acoustic cloaking” of the moving wall, a much desired property in classical acoustics.
26(2014); http://dx.doi.org/10.1063/1.4884955View Description Hide Description
We use confocal microscopy to directly visualize the simultaneous flow of both a wetting and a non-wetting fluid through a model three-dimensional (3D) porous medium. We find that, for small flow rates, both fluids flow through unchanging, distinct, connected 3D pathways; in stark contrast, at sufficiently large flow rates, the non-wetting fluid is broken up into discrete ganglia. By performing experiments over a range of flow rates, using fluids of different viscosities, and with porous media having different geometries, we show that this transition can be characterized by a state diagram that depends on the capillary numbers of both fluids, suggesting that it is controlled by the competition between the viscous forces exerted on the flowing oil and the capillary forces at the pore scale. Our results thus help elucidate the diverse range of behaviors that arise in two-phase flow through a 3D porous medium.
- Interfacial Flows
Numerical study of drop motion on a surface with stepwise wettability gradient and contact angle hysteresis26(2014); http://dx.doi.org/10.1063/1.4880656View Description Hide Description
In this work, the motion of a two-dimensional drop on a surface with stepwise wettability gradient (WG) is studied numerically by a hybrid lattice-Boltzmann finite-difference method. We incorporate the geometric wetting boundary condition that allows accurate implementation of a contact angle hysteresis (CAH) model. The method is first validated through a series of tests that check different constituents of the numerical model. Then, simulations of a drop on a wall with given stepwise WG are performed under different conditions. The effects of the Reynolds number, the viscosity ratio, the WG, as well as the CAH on the drop motion are investigated in detail. It was discovered that the shape of the drop in steady motion may be fitted by two arcs that give two apparent contact angles, which are related to the respective contact line velocities and the relevant contact angles (that specify the WG and CAH) through the relation derived by Cox [“The dynamics of the spreading of liquids on a solid surface. Part 1. viscous flow,” J. Fluid Mech.168, 169–194 (1986)] if the slip length in simulation is defined according to Yue et al. [“Sharp-interface limit of the Cahn-Hilliard model for moving contact lines,” J. Fluid Mech.645, 279–294 (2010)]. It was also found that the steady capillary number of the drop is significantly affected by the viscosity ratio, the magnitudes of the WG, and the CAH, whereas it almost shows no dependence on the Reynolds number.
26(2014); http://dx.doi.org/10.1063/1.4879827View Description Hide Description
A long and narrow solid strip coated with a thin liquid layer is used as a model of a generic fluid mass probe in a spacecraft propellant tank just after a small thruster firing. The drainage dynamics of the initial coating layer into the settled bulk fluid affects the interpretation of probe measurements as the sensors' signal depends strongly on whether a sensor is in contact with vapor or with liquid. We analyze the drainage under various conditions of zero-gravity (i.e., capillary drainage) and with gravity aligned with the strip length, corresponding to the thruster acceleration. Long-time analytical solutions are found for zero and non-zero gravity. In the case with gravity, an approximate solution is found using matched asymptotics. Estimates show that a thrust of 10−3 g 0 significantly reduces drainage times.
Derivation of a continuum model and the energy law for moving contact lines with insoluble surfactants26(2014); http://dx.doi.org/10.1063/1.4881195View Description Hide Description
A continuous model is derived for the dynamics of two immiscible fluids with moving contact lines and insoluble surfactants based on thermodynamic principles. The continuum model consists of the Navier-Stokes equations for the dynamics of the two fluids and a convection-diffusion equation for the evolution of the surfactant on the fluid interface. The interface condition, the boundary condition for the slip velocity, and the condition for the dynamic contact angle are derived from the consideration of energy dissipations. Different types of energy dissipations, including the viscous dissipation, the dissipations on the solid wall and at the contact line, as well as the dissipation due to the diffusion of surfactant, are identified from the analysis. A finite element method is developed for the continuum model. Numerical experiments are performed to demonstrate the influence of surfactant on the contact line dynamics. The different types of energy dissipations are compared numerically.
26(2014); http://dx.doi.org/10.1063/1.4882264View Description Hide Description
This is a transient two-dimensional numerical study of double-diffusive salt fingers in a two-layer heat-salt system for a wide range of initial density stability ratio (R ρ0) and thermal Rayleigh numbers (Ra T ∼103 − 1011). Salt fingers have been studied for several decades now, but several perplexing features of this rich and complex system remain unexplained. The work in question studies this problem and shows the morphological variation in fingers from low to high thermal Rayleigh numbers, which have been missed by the previous investigators. Considerable variations in convective structures and evolution pattern were observed in the range of Ra T used in the simulation. Evolution of salt fingers was studied by monitoring the finger structures, kinetic energy, vertical profiles, velocity fields, and transient variation of R ρ(t). The results show that large scale convection that limits the finger length was observed only at high Rayleigh numbers. The transition from nonlinear to linear convection occurs at about Ra T ∼ 108. Contrary to the popular notion, R ρ(t) first decrease during diffusion before the onset time and then increase when convection begins at the interface. Decrease in R ρ(t) is substantial at low Ra T and it decreases even below unity resulting in overturning of the system. Interestingly, all the finger system passes through the same state before the onset of convection irrespective of Rayleigh number and density stability ratio of the system.
26(2014); http://dx.doi.org/10.1063/1.4878095View Description Hide Description
We analyse the force balance on a cylindrical drop in a Hele-Shaw cell, subjected to a Marangoni flow caused by a surface tension gradient. Depth-averaged Stokes equations, called Brinkman equations, are introduced and a general closed form solution is obtained. The validity of the averaging procedure is ascertained by considering a linear surface tension gradient acting on a cylindrical flattened drop. The Marangoni-driven flow field and resulting force predicted by the Brinkman model are seen to match well a full three-dimensional direct numerical simulation. A closed form expression of the force acting on the drop is obtained, calculated from contributions due to the normal viscous stress, tangential viscous stress, and pressure fields, integrated on the drop perimeter. This expression is used to predict the force balance when a stationary droplet is submitted to both a carrier flow and a Marangoni flow. We show that previous results in the literature had underestimated by a factor two the Marangoni-induced force.
Modeling the interaction of microbubbles: Effects of proximity, confinement, and excitation amplitude26(2014); http://dx.doi.org/10.1063/1.4883482View Description Hide Description
The interaction of closely spaced microbubbles (MBs) exposed to a transient external pressure field is relevant for a variety of industrial and medical applications. We present a computational framework employing an interface tracking approach to model the transient dynamics of multiple, interacting, insonated MBs in arbitrary settings. In particular, this technique allows studying the effects of mutual proximity, confinement, and variations in excitation amplitude on the translatory motion of pairs of differently sized MBs. Domains of mutual repulsion or attraction are observed for closely spaced MBs in the investigated range of excitation frequencies. The repulsion domain widens and shifts to lower frequencies with increasing excitation pressure amplitude. When the MBs are confined in rigid tubes of decreasing diameters, we observe a shift of the translatory patterns towards lower frequencies, accompanied by a change in relative strength of the two translation modes. This effect is correlated to a decrease of the resonance frequency due to confinement which causes changes in oscillation amplitude and phase shift between the bubble vibrations. Coupling to the viscous host liquid gives rise to phenomena such as collective MB drift, non-symmetric attraction or repulsion, and reversal of translation direction. A system comprising six MBs inside a narrow tube highlights the potential of the computational framework to treat complex setups with multiple bubbles.
- Viscous and Non-Newtonian Flows
26(2014); http://dx.doi.org/10.1063/1.4878842View Description Hide Description
In a recent letter [M. Cromer, M. C. Villet, G. H. Fredrickson, and L. G. Leal, “Shear banding in polymer solutions,” Phys. Fluids25, 051703 (2013)], we showed the existence of a steady shear-banded velocity profile for a model polymer solution with an underlying monotonic constitutive curve. The driving mechanism is the coupling of the polymer stress to an inhomogeneous concentration profile. To further understand this phenomenon, in this paper we investigate the underlying linear instability as well as probe the model parameters and their effect on transient and steady state solutions. The linear stability analysis of the steady, base homogeneous model shows that, in opposition to diffusion, the polymer concentration moves up stress gradients in a shear flow creating a critical balance such that, for a range of parameters, an instability occurs that drives the system away from homogeneity. The simulation of the full nonlinear equations in planar one-dimensional shear reveals a window within which the linear instability manifests itself as a shear-banded flow. Unlike the case for a nonmonotonic constitutive curve for which two bands are predicted, there is no apparent selection process for a monotonic curve that sets the number of bands in planar shear. Thus, we find the possibility of greater than two bands, the number of which is determined by the ratio of the polymer correlation length to the channel width. In addition to steady shear banding, transient phenomena are also probed revealing a complicated band transition (i.e., number of bands changing in time) as well as elastic recoil in a Taylor-Couette cell, each of which have been observed in experiment. Finally, as we showed in our letter, a nonlinear subcritical instability exists resulting in multiple steady states depending upon the wall ramp speed. Here, we show that this phenomenon can occur for realistic parameter values, in particular those obtained for a particular polymer solution that has shown this multiple steady state behavior experimentally.
- Particulate, Multiphase, and Granular Flows
26(2014); http://dx.doi.org/10.1063/1.4882265View Description Hide Description
The lateral migration of microspheres across streamlines induced by elasticity and inertia in a square microchannel flow of viscoelastic fluids is investigated using a holographic microscopy technique. We experimentally demonstrate the exact particle positions driven by the elasticity of fluid in the channel cross-section. The effects of the blockage ratio, flow rate, and shear-thinning property of the viscoelastic fluids on particle migration are evaluated. In particular, the focusing patterns of microspheres in three-dimensional volume are analyzed under different conditions, namely, dominant inertia, dominant elasticity, and the combined effects of inertia and elasticity.
26(2014); http://dx.doi.org/10.1063/1.4881942View Description Hide Description
In this study, the slip velocity between rigid fibers and a viscous carrier fluid is investigated for the reference case of turbulent channel flow. The statistical moments of the slip velocity are evaluated modelling fibers as prolate spheroids with Stokes number, St, ranging from 1 to 100 and aspect ratio, λ, ranging from 3 to 50. Statistics are compared one-to-one with those obtained for spherical particles (λ = 1) to highlight effects due to fiber elongation. Comparison is also made at different Reynolds numbers (Re τ =150, 180, and 300 based on the fluid shear velocity) to discuss effects due to an increase of turbulent fluctuations. Results show that elongation has a quantitative effect on slip velocity statistics, particularly evident for fibers with small St. As St increases, differences due to the aspect ratio tend to vanish and the relative translational motion between individual fibers and surrounding fluid is controlled by fiber inertia through preferential concentration. A clear manifestation of inertial effects is the different distribution of slip velocities for fibers trapped in sweep/ejection events and for fibers segregated in near-wall fluid streaks. The corresponding conditional probability distribution functions, shown here for the streamwise and wall-normal slip velocity components, are found to be non-Gaussian, thus suggesting that fiber motion relative to the fluid in high-shear flow regions may not be modelled as a pure diffusion process with constant diffusion coefficient. For the range of simulation parameters investigated, no significant Reynolds number effects are observed, indicating that fiber dynamics exhibit a scaling behavior with respect to the shear velocity up to Re τ =300.
- Laminar Flows
26(2014); http://dx.doi.org/10.1063/1.4880135View Description Hide Description
The flow characteristics of the vortex-induced vibration of an elastically mounted circular cylinder with a hinged flat plate are investigated numerically in this study. By fixing the Reynolds number, the mass ratio, the damping ratio, and the plate length, we systematically examine the influence of the reduced velocities of cylinder and plate as well as the ratio of moment of inertia on the flow behaviors. With the help of the hinged plate, the cylinder vibration and the force fluctuations can be efficiently suppressed. Meanwhile, the drag force can also be reduced significantly compared to the situation of an isolated cylinder. Moreover, because of the large pitching angle of the hinged plate, smoother vortex shedding can be observed.
Characterisation and analysis of flow over two side by side cylinders for different gaps at low Reynolds number: A numerical approach26(2014); http://dx.doi.org/10.1063/1.4883484View Description Hide Description
Numerical simulations were performed for two-dimensional viscous incompressible flow past two stationary side by side circular cylinders at Reynolds number (Re) 100 by varying centre to centre distance between the cylinders from 1.1 to 8 times the diameter (D) of a cylinder. The incompressible Navier-Stokes equations were solved using a finite volume method. Five different flow regimes were observed in the flow as the distance between the cylinders was increased systematically. An attempt has been made to characterise the different flow regimes using different numerical tools like Proper Orthogonal Decomposition (POD), λ2 criterion, instantaneous streamwise normal stress produced due to periodic variation of flow, frequency spectrum analysis and phase diagrams. All these tools confirm the clear existence of five different regimes in the flow when the gap between the cylinders is varied over the above stated range.
- Instability and Transition
26(2014); http://dx.doi.org/10.1063/1.4880038View Description Hide Description
We consider the classical problem of the Marangoni instability in a liquid layer with a deformable free surface atop a substrate heated from below. The linear stability analysis is performed numerically in order to extend the recent asymptotic results [S. Shklyaev, M. Khenner, and A. A. Alabuzhev, “Oscillatory and monotonic modes of long-wave Marangoni convection in a thin film,” Phys. Rev. E 82, 025302 (2010)] to finite-wavenumber perturbations. In spite of detailed analyses by many researchers, we have obtained novel computational results confirming the existence of the oscillatory mode for heating from below. Moreover, numerical simulations indicate that the oscillatory mode is critical in a wider range of parameters, than it is predicted by the asymptotic analysis. Additionally, we provide guiding data for the experimental observation of the oscillatory regime.
Three-dimensional instabilities in a discretely heated annular flow: Onset of spatio-temporal complexity via defect dynamics26(2014); http://dx.doi.org/10.1063/1.4881435View Description Hide Description
The transition to three-dimensional and unsteady flow in an annulus with a discrete heat source on the inner cylinder is studied numerically. For large applied heat flux through the heater (large Grashof number Gr), there is a strong wall plume originating at the heater that reaches the top and forms a large scale axisymmetric wavy structure along the top. For Gr ≈ 6 × 109, this wavy structure becomes unstable to three-dimensional instabilities with high azimuthal wavenumbers m ∼ 30, influenced by mode competition within an Eckhaus band of wavenumbers. Coexisting with some of these steady three-dimensional states, solution branches with localized defects break parity and result in spatio-temporal dynamics. We have identified two such time dependent states. One is a limit cycle that while breaking spatial parity, retains spatio-temporal parity. The other branch corresponds to quasi-periodic states that have globally broken parity.