Physics

The linear instability of a surfactant-laden two-layer falling film over an inclined slippery wall is analyzed under an influence of external shear which is imposed on the top surface of the flow. The free surface of the flow as well as the interface among the fluids are contaminated by insoluble surfactants. Dynamics of both the layers are governed by the Navier--Stokes equations, and the surfactant transport equation regulates the motion of the insoluble surfactants at the interface and free surface. Instability mechanisms are compared by imposing the external shear along and opposite to the flow direction. A coupled Orr--Sommerfeld system of equations for the considered problem is derived using the perturbation technique and normal mode analysis. The eigenmodes corresponding to the Orr--Sommerfeld eigenvalue problem are obtained by employing the spectral collocation method. The numerical results imply that the stronger external shear destabilizes the interface mode instability. However, a stabilizing impact of the external shear on the surface mode is noticed if the shear is imposed in the flow direction, which is in contrast to the role of imposed external shear on the surface mode for a surfactant laden single layer falling film. Moreover, the impression of shear mode on the primary instability is analyzed in the high Reynolds number regime with sufficiently low inclination angle. Under such configuration, dominance of the shear mode over the surface mode is observed due to the weaker impact of the gravitation force on the surface instability. The shear mode can also be stabilized by applying the external shear in the counter direction of the streamwise flow. Conclusively, the extra imposed shear on the stratified two-layer falling film plays an active role to control the attitude of the instabilities.

Low-level jets (LLJs) are the wind maxima in the lowest 50 to 1000 m of atmospheric boundary layers. Due to their significant influence on the power production of wind farms it is crucial to understand the interaction between LLJs and wind farms. In the presence of an LLJ, there are positive and negative shear regions in the velocity profile. The positive shear regions of LLJs are continuously turbulent, while the negative shear regions have limited turbulence. We present large-eddy simulations of wind farms in which the LLJ is above, below, or in the middle of the turbine rotor swept area. We find that the wakes recover relatively fast when the LLJ is above the turbines. This is due to the high turbulence below the LLJ and the downward vertical entrainment created by the momentum deficit due to the wind farm power production. This harvests the jet's energy and aids wake recovery. However, when the LLJ is below the turbine rotor swept area, the wake recovery is very slow due to the low atmospheric turbulence above the LLJ. The energy budget analysis reveals that the entrainment fluxes are maximum and minimum when the LLJ is above and in the middle of the turbine rotor swept area, respectively. Surprisingly, we find that the negative shear creates a significant entrainment flux upward when the LLJ is below the turbine rotor swept area. This facilitates energy extraction from the jet, which is beneficial for the performance of downwind turbines.

This paper is an attempt to study the effects of surface topography on the flow of a droplet (or a bubble) in a low Reynolds number flow regime. Multiphase flows through a constricted passage find many interesting applications in chemistry and biology. The main parameters which determine the flow properties such as flow rate and pressure drop, and govern the complex multiphase phenomena such as drop coalescence, break-up and snap-off in a straight channel flow are the viscosity ratio, droplet size and ratio of the viscous forces to the surface tension forces (denoted by Capillary number). But in flow through a constricted passage, in addition to the above-mentioned parameters, various other geometric parameters such as constriction ratio, length and shape of the constriction, phase angle, and spacing between the constrictions also start playing an important role. Most of the studies done on the problem of drop flow through a constricted passage have aimed to understand the role of physical parameters, with some studies extending their analysis to understand the variation of one or two geometric parameters. But no study could be found which explicitly evaluates the role of surface topography. An attempt has been made to unify the current literature as well as analyze the effect of the geometric parameters by understanding the physics and mechanisms involved. The non-dimensional numbers which govern this problem are then identified using the scaling analysis.

The existence of a quiescent core (QC) in the center of turbulent channel flows was demonstrated in recent experimental and numerical studies. The QC-region, which is characterized by relatively uniform velocity magnitude and weak turbulence levels, occupies about 40% of the cross-section at Reynolds numbers R e τ ranging from 1000 to 4000 . The influence of the QC region and its boundaries on transport and accumulation of inertial particles has never been investigated before. Here, we first demonstrate that a QC is unidentifiable at R e τ =180 , before an in-depth exploration of particle-laden turbulent channel flow at R e τ =600 is performed. The inertial spheres exhibited a tendency to accumulate preferentially in high-speed regions within the QC, i.e. contrary to the well-known concentration in low-speed streaks in the near-wall region. The particle wall-normal distribution, quantified by means of Voronoï volumes and particle number concentrations, varied abruptly across the QC-boundary and vortical flow structures appeared as void areas due to the centrifugal mechanism. The QC-boundary, characterized by a localized strong shear layer, appeared as a \emph{barrier}, across which transport of inertial particles is hindered. Nevertheless, the statistics conditioned in QC-frame show that the mean velocity of particles outside of the QC was towards the core, whereas particles within the QC tended to migrate towards the wall. Such upward and downward particle motions are driven by similar motions of fluid parcels. The present results show that the QC exerts a substantial influence on transport and accumulation of inertial particles, which is of practical relevance in high-Reynolds number channel flow.

Studies of flow through the human airway have shown that inhalation time (IT) and secondary flow structures can play important roles in particle deposition. However, the effects of varying IT in conjunction with respiratory rate (RR) on airway flow remain unknown. Using 3D numerical simulations of oscillatory flow through an idealized airway model consisting of a mouth inlet, glottis, trachea and symmetric double bifurcation at trachea Reynolds number ( Re ) of 4,200, we investigated how varying the ratio of IT to breathing time (BT) from 25% to 50% and RR from 10 breaths per minute (bpm) corresponding to Womersley number ( Wo ) of 2.37 to 1,000 bpm ( Wo =23.7) impacts airway flow characteristics. Irrespective of IT/BT, axial flow during inhalation at tracheal cross-sections was non-uniform for Wo =2.37 as compared to centrally concentrated distribution for Wo =23.7. For a given Wo and IT/BT, both axial and secondary (lateral) flow components unevenly split between left and right branches of a bifurcation. Irrespective of Wo , IT/BT and airway generation, lateral dispersion was stronger than axial flow streaming. Despite left-right symmetry of the lower airway in our model, the right-sided mouth-to-glottis portion generated turbulence in the upper airway. Varying IT/BT for a given Wo did not noticeably change flow characteristics. Discrepancy in the oscillatory flow relation Re / W o 2 =2 L / D ( L =stroke length; D =trachea diameter) was observed for IT/BT ??50%, as L changed with IT/BT. We developed a modified dimensionless stroke length term including IT/BT. While viscous forces and convective acceleration were dominant for lower Wo , unsteady acceleration was dominant for higher Wo .

Wildland fires are complex multi-physics problems that span wide spatial scale ranges. Capturing this complexity in computationally affordable numerical simulations for process studies and "outer-loop" techniques (e.g., optimization and uncertainty quantification) is a fundamental challenge in reacting flow research. Further complications arise for propagating fires where a priori knowledge of the fire spread rate and direction is typically not available. In such cases, static mesh refinement at all possible fire locations is a computationally inefficient approach to bridging the wide range of spatial scales relevant to wildland fire behavior. In the present study, we address this challenge by incorporating adaptive mesh refinement (AMR) in fireFoam, an OpenFOAM solver for simulations of complex fire phenomena. The AMR functionality in the extended solver, called wildFireFoam, allows us to dynamically track regions of interest and to avoid inefficient over-resolution of areas far from a propagating flame. We demonstrate the AMR capability for fire spread on vertical panels and for large-scale fire propagation on a variable-slope surface that is representative of real topography. We show that the AMR solver reproduces results obtained using much larger statically refined meshes, at a substantially reduced computational cost.

Resolvent analysis of the linearized Navier-Stokes equations provides useful insight into the dynamics of transitional and turbulent flows and can provide a model for the dominant coherent structures within the flow, particularly for flows with large gain separation. Direct computation of force and response modes using a singular value decomposition of the full resolvent matrix is feasible only for simple problems; despite recent progress, the cost of resolvent analysis for complex flows remains considerable. In this paper, we propose a new matrix-free method for computing resolvent modes based on integration of the linearized equations and the corresponding adjoint system in the time domain. Our approach achieves an order of magnitude speedup when compared to previous matrix-free time stepping methods by enabling all frequencies of interest to be computed simultaneously. Two different methods are presented: one based on analysis of the transient response, providing leading modes with fine frequency discretization; and another based on the steady-state response to a periodic forcing, providing optimal and suboptimal modes for a discrete set of frequencies. The methods are validated using a linearized Ginzburg-Landau equation and applied to the three dimensional flow around a parabolic body.

Three eigenvalue bounds are derived for the instability of ideal compressible stratified magnetohydrodynamic shear flows in which the base velocity, density, and magnetic field vary in two directions. The first bound can be obtained by combining the Howard semi-circle theorem with the energy principle of the Lagrangian displacement. Remarkably, no special conditions are needed to use this bound, and for some cases, we can establish the stability of the flow. The second and third bounds come out from a generalisation of the Miles-Howard theory and have some similarity to the semi-ellipse theorem by Kochar & Jain (J. Fluid Mech., vol. 91, 1979, 489) and the bound found by Cally (Astrophys. Fluid Dyn., vol. 31,1983, 43), respectively. An important byproduct of this investigation is that the Miles-Howard stability condition holds only when there is no applied magnetic field and, in addition, the directions of the shear and the stratification are aligned everywhere.

This study presents an extensive numerical investigation on the flow characteristics of wormlike micellar solutions past a single and vertically aligned two microcylinders placed in a microchannel in the creeping flow regime on the two-species Vasquez-Cook-McKinley (VCM) constitutive model, which takes into account both the breakage and reformation dynamics of micelles. For the case of single microcylinder, as the blockage ratio (ratio of the cylinder diameter to that of the channel height) is gradually varied, we find the existence of a flow bifurcation in the system, and also flow transits from steady to unsteady state. For the case of two microcylinders, we observe the presence of three distinct flow states in the system, namely, diverging (D), asymmetric-diverging (AD) and converging (C) states as the intercylinder spacing in between the two cylinders is varied. Similar types of flow states are also observed in the recent experiments dealing with wormlike micellar solutions. However, we show that either this transition from one flow state to another in the case of a single microcylinder or the occurrence of any flow state in the case of two microcylinders, is strongly dependent upon the values of the Weissenberg number and the nonlinear VCM model parameter \xi, which basically indicates how easy or hard to break a micelle. Based on the results and discussion presented herein for the single and two microcylinders, we ultimately provide the explanation for the formation of preferential paths or lanes during the flow of viscoelastic fluids through a porous media, which was seen in many prior experiments in the creeping flow regime.

We report that an electro-osmotic instability of concentration enrichment in curved geometries for an aqueous electrolyte, as opposed to the well-known one, is initiated exclusively at the enriched interface (anode), rather than at the depleted one (cathode). For this instability, the limitation of unrealistically high material Peclet number in planar geometry is eliminated by the strong electric field arising from the line charge singularity. In a model setup of concentric circular electrodes, we show by stability analysis, numerical simulation, and experimental visualization that instability occurs at the inner anode, below a critical radius of curvature. The stability criterion is also formulated in terms of a critical electric field and extended to arbitrary (2d) geometries by conformal mapping. This discovery suggests that transport may be enhanced in processes limited by salt enrichment, such as reverse osmosis, by triggering this instability with needle-like electrodes.