Volume 28, Issue 8, August 2016

Large eddy simulation (LES) is carried out to study the vortex dynamics in the nearfield of a starting turbulent square jet as well as its evolution into a developed steady jet. Simulations are conducted at Reynolds numbers (Re = UjD/υ) of 8000 and 45 000 based on the nozzle hydraulic diameter and jet velocity (Uj). A Reynolds stress model was used to simulate the internal flow in the nozzle which provided the inlet conditions for the LES of the jet. To validate the simulations, turbulence statistics are compared with experimental results available for a steady square jet. Evaluation of the probability density function, skewness, and flatness of the centerline streamwise velocity (Uc) shows deviation from the Gaussian distribution in the nearfield. Evolution of the selfinduced deformation of the leading vortex ring is investigated to further clarify the role of axisswitching. The axisswitching is initiated earlier at low Reynolds number while the completion of the axisswitching process occurred at the same dimensionless time for both Reynolds numbers. The role of pressure distribution on vortex ring deformation is investigated. It is shown that the influence of pressureinduced azimuthal instability tends to deform a twodimensional vortex ring topology into a threedimensional one and revert back to a twodimensional character again. The breakdown and diffusion of the tip of the vortex are also studied. Evolution of the shear layer from a starting jet to a developed jet is studied in terms of the vorticity field. For a starting jet, entrainment is shown to occur in the presence of corner hairpin vortices.
 LETTERS


A transport equation for reaction rate in turbulent flows
View Description Hide DescriptionNew transport equations for chemical reaction rate and its mean value in turbulent flows have been derived and analyzed. Local perturbations of the reaction zone by turbulent eddies are shown to play a pivotal role even for weakly turbulent flows. The meanreactionrate transport equation is shown to involve two unclosed dominant terms and a joint closure relation for the sum of these two terms is developed. Obtained analytical results and, in particular, the closure relation are supported by processing two widely recognized sets of data obtained from earlier direct numerical simulations of statistically planar 1D premixed flames associated with both weak largescale and intense smallscale turbulence.

Contribution of velocityvorticity correlations to the frictional drag in wallbounded turbulent flows
View Description Hide DescriptionThe relationship between the frictional drag and the velocityvorticity correlations in wallbounded turbulent flows is derived from the mean vorticity equation. A formula for the skin friction coefficient is proposed and evaluated with regards to three canonical wallbounded flows: turbulent boundary layer, turbulent channel flow, and turbulent pipe flow. The frictional drag encompasses four terms: advective vorticity transport, vortex stretching, viscous, and inhomogeneous terms. Dragreduced channel flow with the slip condition is used to test the reliability of the formula. The advective vorticity transport and vortex stretching terms are found to dominate the contributions to the frictional drag.

Mixedderivative skewness for high Prandtl and Reynolds numbers in homogeneous isotropic turbulence
View Description Hide DescriptionThe mixedderivative skewness S uθ of a passive scalar field in high Reynolds and Prandtl numbers decaying homogeneous isotropic turbulence is studied numerically using eddydamped quasinormal Markovian closure, for Re λ ≥ 10^{3} up to Pr = 10^{5}. A convergence of S uθ for Pr ≥ 10^{3} is observed for any high enough Reynolds number. This asymptotic high Pr regime can be interpreted as a saturation of the mixing properties of the flow at small scales. The decay of the derivative skewnesses from high to low Reynolds numbers and the influence of large scales initial conditions are investigated as well.
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 ARTICLES

 Biofluid Mechanics

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution
View Description Hide DescriptionThe present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the arterial system and the possible malfunction of the aorta.
 Micro and Nanofluid Mechanics

Nanoflow over a fractal surface
View Description Hide DescriptionThis paper investigates the effects of surface roughness on nanoflows using molecular dynamics simulations. A fractal model is employed to model wall roughness, and simulations are performed for liquid argon confined by two solid walls. It is shown that the surface roughness reduces the velocity in the proximity of the walls with the reduction being accentuated when increasing the roughness depth and wettability of the solid wall. It also makes the flow threedimensional and anisotropic. In flows over idealized smooth surfaces, the liquid forms parallel, wellspaced layers, with a significant gap between the first layer and the solid wall. Rough walls distort the orderly distribution of fluid layers resulting in an incoherent formation of irregularly shaped fluid structures around and within the wall cavities.

Permeability and effective slip in confined flows transverse to wall slippage patterns
View Description Hide DescriptionThe pressuredriven Stokes flow through a plane channel with arbitrary wall separation having a continuous pattern of sinusoidally varying slippage of arbitrary wavelength and amplitude on one/both walls is modelled semianalytically. The patterning direction is transverse to the flow. In the special situations of thin and thick channels, respectively, the predictions of the model are found to be consistent with lubrication theory and results from the literature pertaining to free shear flow. For the same patternaveraged slip length, the hydraulic permeability relative to a channel with noslip walls increases as the pattern wavenumber, amplitude, and channel size are decreased. Unlike discontinuous wall patterns of stickslip zones studied elsewhere in the literature, the effective slip length of a sinusoidally patterned wall in a confined flow continues to scale with both channel size and the patternaveraged slip length even in the limit of thin channel size to pattern wavelength ratio. As a consequence, for sufficiently small channel sizes, the permeability of a channel with sinusoidal wall slip patterns will always exceed that of an otherwise similar channel with discontinuous patterns on corresponding walls. For a channel with one noslip wall and one patterned wall, the permeability relative to that of an unpatterned reference channel of same patternaveraged slip length exhibits nonmonotonic behaviour with channel size, with a minimum appearing at intermediate channel sizes. Approximate closedform estimates for finding the location and size of this minimum are provided in the limit of large and small pattern wavelengths. For example, if the pattern wavelength is much larger than the channel thickness, exact results from lubrication theory indicate that a worst case permeability penalty relative to the reference channel of ∼23% arises when the average slip of the patterned wall is ∼2.7 times the channel size. The results from the current study should be applicable to microfluidic flows through channels with hydrophobized/superhydrophobic surfaces.

Microscopic molecular dynamics characterization of the secondorder nonNavierFourier constitutive laws in the Poiseuille gas flow
View Description Hide DescriptionThe secondorder nonNavierFourier constitutive laws, expressed in a compact algebraic mathematical form, were validated for the forcedriven Poiseuille gas flow by the deterministic atomiclevel microscopic molecular dynamics (MD). Emphasis is placed on how completely different methods (a secondorder continuum macroscopic theory based on the kinetic Boltzmann equation, the probabilistic mesoscopic direct simulation Monte Carlo, and, in particular, the deterministic microscopic MD) describe the nonclassical physics, and whether the secondorder nonNavierFourier constitutive laws derived from the continuum theory can be validated using MD solutions for the viscous stress and heat flux calculated directly from the molecular data using the statistical method. Peculiar behaviors (nonuniform tangent pressure profile and exotic instantaneous heat conduction from cold to hot [R. S. Myong, “A full analytical solution for the forcedriven compressible Poiseuille gas flow based on a nonlinear coupled constitutive relation,” Phys. Fluids 23(1), 012002 (2011)]) were reexamined using atomiclevel MD results. It was shown that all three results were in strong qualitative agreement with each other, implying that the secondorder nonNavierFourier laws are indeed physically legitimate in the transition regime. Furthermore, it was shown that the nonNavierFourier constitutive laws are essential for describing nonzero normal stress and tangential heat flux, while the classical and nonclassical laws remain similar for shear stress and normal heat flux.

Nanoscale roughness effect on Maxwelllike boundary conditions for the Boltzmann equation
View Description Hide DescriptionIt is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwelllike kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of monoenergetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified twodimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a threedimensional configuration. Finally, the case of nonelastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics of gassurface interaction, at a reasonable computing cost, to improve kinetic simulations of micro and nanoflows.

Passive nanofluidic diode using nonuniform nanochannels
View Description Hide DescriptionIn this work, we propose a nanofluidic diode for simple fluids using nonuniform nanochannels. Molecular dynamics simulations show that the fluidic diode allows water flows in the forward direction and blocks flows in the backward direction in a wide range of pressure drops. The unidirectional water flows are owing to the distinct activation pressures in different directions. In the forward (converging) direction, the activation pressure is small because of the relatively low capillary pressure and the water coalescence at the exit. In the backward direction, the activation pressure is high due to the high infiltration pressure. The pressure drop range for the fluidic diode can be varied by modifying the surface wettability, channel height, and/or the tilt angle of the channel. The fluidic diode can be used for flow control in integrated micro and nanofluidic devices.
 Interfacial Flows

High fidelity simulation and analysis of liquid jet atomization in a gaseous crossflow at intermediate Weber numbers
View Description Hide DescriptionRecent advances in numerical methods coupled with the substantial enhancements in computing power and the advent of high performance computing have presented first principle, high fidelity simulation as a viable tool in the prediction and analysis of spray atomization processes. The credibility and potential impact of such simulations, however, has been hampered by the relative absence of detailed validation against experimental evidence. The numerical stability and accuracy challenges arising from the need to simulate the high liquidgas density ratio across the sharp interfaces encountered in these flows are key reasons for this. In this work we challenge this status quo by presenting a numerical model able to deal with these challenges, employing it in simulations of liquid jet in crossflow atomization and performing extensive validation of its results against a carefully executed experiment with detailed measurements in the atomization region. We then proceed to the detailed analysis of the flow physics. The computational model employs the coupled level set and volume of fluid approach to directly capture the spatiotemporal evolution of the liquidgas interface and the sharpinterface ghost fluid method to stably handle high liquidair density ratio. Adaptive mesh refinement and Lagrangian droplet models are shown to be viable options for computational cost reduction. Moreover, high performance computing is leveraged to manage the computational cost. The experiment selected for validation eliminates the impact of inlet liquid and gas turbulence and focuses on the impact of the crossflow aerodynamic forces on the atomization physics. Validation is demonstrated by comparing column surface wavelengths, deformation, breakup locations, column trajectories and droplet sizes, velocities, and mass rates for a range of intermediate Weber numbers. Analysis of the physics is performed in terms of the instability and breakup characteristics and the features of downstream flow recirculation, and vortex shedding. Formation of “Λ” shape windward column waves is observed and explained by the combined upward and lateral surface motion. The existence of RayleighTaylor instability as the primary mechanism for the windward column waves is verified for this case by comparing wavelengths from the simulations to those predicted by linear stability analyses. Physical arguments are employed to postulate that the type of instability manifested may be related to conditions such as the gas Weber number and the inlet turbulence level. The decreased column wavelength with increasing Weber number is found to cause enhanced surface stripping and early depletion of liquid core at higher Weber number. A peculiar “threestreaktwomembrane” liquid structure is identified at the lowest Weber number and explained as the consequence of the symmetric recirculation zones behind the jet column. It is found that the vortical flow downstream of the liquid column resembles a von Karman vortex street and that the coupling between the gas flow and droplet transport is weak for the conditions explored.

Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder
View Description Hide DescriptionWe discuss the behavior of partially wetting liquids on a rotating cylinder using a model that takes into account the effects of gravity, viscosity, rotation, surface tension, and wettability. Such a system can be considered as a prototype for many other systems where the interplay of spatial heterogeneity and a lateral driving force in the proximity of a first or secondorder phase transition results in intricate behavior. So does a partially wetting drop on a rotating cylinder undergo a depinning transition as the rotation speed is increased, whereas for ideally wetting liquids, the behavior only changes quantitatively. We analyze the bifurcations that occur when the rotation speed is increased for several values of the equilibrium contact angle of the partially wetting liquids. This allows us to discuss how the entire bifurcation structure and the flow behavior it encodes change with changing wettability. We employ various numerical continuation techniques that allow us to track stable/unstable steady and timeperiodic film and drop thickness profiles. We support our findings by timedependent numerical simulations and asymptotic analyses of steady and timeperiodic profiles for large rotation numbers.

A nonlinear flowtransition criterion for the onset of slugging in horizontal channels and pipes
View Description Hide DescriptionIn this work, the interfacial instability and transition of a twofluid flow from a stratified state to large amplitude waves or slugs is considered. By combining an asymptotic approximation of the linear OrrSommerfeld analysis with nonlinear resonant wave interaction theory, a novel nonlinear slugtransition criterion is derived. This criterion corresponds to a bounding condition on the upper fluid’s velocity in order to limit the amount of energy (provided by the linear instability) which is transferred to long waves through resonant wave interactions. It is proposed that such a condition can predict the formation of largeamplitude long waves and/or slugs. Quantitative comparisons of the onset of slugging are made between the prediction by the nonlinear transition criterion and the experimental measurements carried out in a horizontal square channel. Good agreement is observed. An additional heuristic model is developed which generalizes the transition criterion to flow through horizontal pipes. Comparisons are made for flows through different pipe diameters and over a wide range of fluid properties. Good agreement between the present theoretical predictions and the experimental measurements is also observed.

The RichtmyerMeshkov instability of a “V” shaped air/helium interface subjected to a weak shock
View Description Hide DescriptionThe RichtmyerMeshkov instability of a “V” shaped air/helium gaseous interface subjected to a weak shock wave is experimentally studied. A soap film technique is adopted to create a “V” shaped interface with accurate initial conditions. Five kinds of air/helium “V” shaped interfaces with different vertex angles (60°, 90°, 120°, 140°, and 160°), i.e., different amplitudewavelength ratios, are formed to highlight the effects of initial conditions, especially the initial amplitude, on the flow characteristics. The interface morphologies identified by the highspeed schlieren photography show that a spike is generated from the vertex after the shock impact, and grows constantly with time accompanied by the occurrence of the phase reversal. As the vertex angle increases, vortices generated on the interface become less noticeable, and the spike develops less pronouncedly. The linear growth rate of the interface mixing width of a heavy/light interface configuration after compression phase is estimated by a linear model and a revised linear model, and the latter is proven to be more effective for the interface with high initial amplitudes. It is found for the first time in a heavy/light interface configuration that the linear growth rate of interface width is a nonmonotonous function of the initial perturbation amplitudewavelength ratio. In the nonlinear stage, it is confirmed that the width growth rate of interface with high initial amplitudes can be well predicted by a model proposed by Dimonte and Ramaprabhu [“Simulations and model of the nonlinear RichtmyerMeshkov instability,” Phys. Fluids 22, 014104 (2010)].

Studies on dispersive stabilization of porous media flows
View Description Hide DescriptionMotivated by a need to improve the performance of chemical enhanced oil recovery (EOR) processes, we investigate dispersive effects on the linear stability of threelayer porous media flow models of EOR for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in the available parameter space of capillary number, Peclet number, longitudinal and transverse dispersion, and the viscous profile of the middle layer. The stabilization capacity of each of these two interfaces is explored numerically and conditions for complete dispersive stabilization are identified for each of these two types of interfaces. Key results obtained are (i) threelayer porous media flows with permeable interfaces can be almost completely stabilized by diffusion if the optimal viscous profile is chosen, (ii) flows with impermeable interfaces can also be almost completely stabilized for short time, but become more unstable at later times because diffusion flattens out the basic viscous profile, (iii) diffusion stabilizes short waves more than long waves which leads to a “turning point” Peclet number at which short and long waves have the same growth rate, and (iv) mechanical dispersion further stabilizes flows with permeable interfaces but in some cases has a destabilizing effect for flows with impermeable interfaces, which is a surprising result. These results are then used to give a comparison of the two types of interfaces. It is found that for most values of the flow parameters, permeable interfaces suppress flow instability more than impermeable interfaces.

Asymmetric bursting of Taylor bubble in inclined tubes
View Description Hide DescriptionIn the present study, experiments have been reported to explain the phenomenon of approach and collapse of an asymmetric Taylor bubble at free surface inside an inclined tube. Four different tube inclinations with horizontal (30°, 45°, 60° and 75°) and two different fluids (water and silicon oil) are considered for the experiment. Using high speed imaging, we have investigated the approach, puncture, and subsequent liquid drainage for reestablishment of the free surface. The present study covers all the aspects in the collapse of an asymmetric Taylor bubble through the generation of two films, i.e., a cap film which lies on top of the bubble and an asymmetric annular film along the tube wall. Retraction of the cap film is studied in detail and its velocity has been predicted successfully for different inclinations and fluids. Film drainage formulation considering azimuthal variation is proposed which also describes the experimental observations well. In addition, extrapolation of drainage velocity pattern beyond the experimental observation limit provides insight into the total collapse time of bubbles at different inclinations and fluids.

Liquid film flow along a substrate with an asymmetric topography sustained by the thermocapillary effect
View Description Hide DescriptionWe investigate flow in a thin liquid film over a “thick” asymmetric corrugated surface in a gasliquid bilayer system. Using longwave approximation, we derive a nonlinear evolution equation for the spatiotemporal dynamics of the liquidgas interface over the corrugated topography. A closedform expression indicating a nonzero value for a liquid flow rate is derived in a steady state of the system. Through numerical investigations we study the nonlinear dynamics of the liquidgas interface with respect to topographical variations of the solid surface, different thermal properties of the liquid and the solid, and different values of the Marangoni number. We find the existence of a critical value for the Marangoni number Mc, so that for M > Mc, the liquid film ruptures, whereas for M < Mc, the interface will remain continuous. In a broad variety of parameters, the interface attains a deformed steady state with a nonzero average flow rate through the system, thus the described mechanism may be used as a means of transport in microfluidic devices. We carry out the Floquet stability analysis of periodic steady states with respect to spatial replication and show that in the framework of the timeindependent evolution equation, the system is unstable to long wave perturbations. We demonstrate that in a finite periodic setting, the system may evolve within a certain parameter range into a metastable state which may be manipulated by varying the Marangoni number M in time in order to increase, control, and sustain the average flow rate through the system. We also show that in the case of a solid substrate with the thermal conductivity lower than that of the liquid, the flow rate through the system may be significantly increased with respect to the opposite case.

Hydrodynamic effects on phase separation morphologies in evaporating thin films of polymer solutions
View Description Hide DescriptionWe examine effects of hydrodynamics on phase separation morphologies developed during drying of thin films containing a volatile solvent and two dissolved polymers. CahnHilliard and FloryHuggins theories are used to describe the free energy of the phase separating systems. The thin films, considered as Newtonian fluids, flow in response to Korteweg stresses arising due to concentration nonuniformities that develop during solvent evaporation. Numerical simulations are employed to investigate the effects of a Peclet number, defined in terms of system physical properties, as well as the effects of parameters characterizing the speed of evaporation and preferential wetting of the solutes at the gas interface. For systems exhibiting preferential wetting, diffusion alone is known to favor lamellar configurations for the separated phases in the dried film. However, a mechanism of hydrodynamic instability of a short length scale is revealed, which beyond a threshold Peclet number may deform and break the lamellae. The critical Peclet number tends to decrease as the evaporation rate increases and to increase with the tendency of the polymers to selectively wet the gas interface. As the Peclet number increases, the instability moves closer to the gas interface and induces the formation of a lateral segregation template that guides the subsequent evolution of the phase separation process. On the other hand, for systems with no preferential wetting or any other property asymmetries between the two polymers, diffusion alone favors the formation of laterally separated configurations. In this case, concentration perturbation modes that lead to enhanced Korteweg stresses may be favored for sufficiently large Peclet numbers. For such modes, a second mechanism is revealed, which is similar to the solutocapillary Marangoni instability observed in evaporating solutions when interfacial tension increases with the concentration of the nonvolatile component. This mechanism may lead to multiple length scales in the laterally phase separated configurations.
 Viscous and NonNewtonian Flows

Fluid mobility over corrugated surfaces in the Stokes regime
View Description Hide DescriptionAn exact solution is found for laminar fluid flow along the grooves of a family of surfaces whose shape is given by the Lambert Wfunction. This simple solution allows for the slip length in the direction parallel to the grooves to be calculated exactly. With this analytical model, we establish the regime of validity for a previously untested perturbation theory intended for calculating the surface mobility tensor of arbitrary periodic surfaces, finding that it compares well to the exact expression for nearly all choices of parameters of the conformal map. To test this perturbation theory further, the mobility tensor is evaluated for a simple sinusoidal surface for flow both parallel and perpendicular to the grooves, finding that the perturbation theory is less accurate in the latter of these two cases.
 Particulate, Multiphase, and Granular Flows

Direct numerical simulation of a particle attachment to an immersed bubble
View Description Hide DescriptionA numerical extension of the “smooth profile method” is presently suggested to simulate the attachment of a colloidal particle to the surface of an immersed bubble. In this approach, the two fluidparticle boundaries and the fluidic boundary are replaced with diffuse interfaces. The method is tested under various capillary numbers. Upon attachment to a stable bubble, it is found that the method is capable of reproducing the three microprocesses associated with the particle attachment. The change in the trajectory as the particle approaches the fluidic interface, the collision process, and the sliding down the bubble surface are all captured. Potential application of the present method shows great promise in the field of froth flotation, where the capture of hydrophobic particles by rising bubbles is of primary importance.

Microscopic origin of selfsimilarity in granular blast waves
View Description Hide DescriptionThe selfsimilar expansion of a blast wave, wellstudied in air, has peculiar counterparts in dense and dissipative media such as granular gases. Recent results have shown that, while the traditional Taylorvon NeumannSedov (TvNS) derivation is not applicable to such granular blasts, they can nevertheless be well understood via a combination of microscopic and hydrodynamic insights. In this article, we provide a detailed analysis of these methods associating molecular dynamics simulations and continuum equations, which successfully predict hydrodynamic profiles, scaling properties, and the instability of the selfsimilar solution. We also present new results for the energy conserving case, including the particlelevel analysis of the classic TvNS solution and its breakdown at higher densities.