arXiv subjects

Alexander Gelfgat

Publications and source records attributed to Alexander Gelfgat.

At least 19 recordsLinked to original sources

arXiv2026

Validation of quasi-two-dimensional model of convection in a transverse magnetic field

In this study we examine applicability of the quasi-two-dimensional (Q2D) model of natural convection in a laterally heated rectangular box subject to a transverse magnetic field. For this purpose, results obtained using the Q2D model are compared with fully three-dimensional calculations for rectangular boxes with a square cross-section and horizontally elongated ones with the length to height ratio 8. The width to height ratio is varied from 1 to 10. It is argued that the Q2D model is valid under certain conditions, which include perfect thermal and electrical insulation of the spanwise boundaries and reflection symmetry with respect to the spanwise midplane. It is shown that under these conditions, the Q2D model yields quantitatively correct results for boxes with square cross-section, as well as for horizontally elongated cavities, independently on the width to height ratio. Three-dimensional results obtained for boxes with perfectly conducting walls exhibit asymptotics at gradually increasing width ratio, which, however, does not agree with the predictions of an amended Q2D model. It is shown also that when is applicable, the Q2D model can correctly predict steady-oscillatory transition of three-dimensional flows. It is proposed to seek for extensions of the Q2D model for cavities with perfectly conducting spanwise boundaries.

physics.flu-dyn↗

arXiv2026

Two-phase stratified MHD flows in rectangular ducts

The characteristics of two-phase stratified magnetohydrodynamic (MHD) flow in horizontal rectangular ducts are investigated for a system consisting of a conductive liquid and a non-conductive gas. Numerical and analytical solutions of the governing equations for the velocity and induced magnetic field intensity of fully developed laminar MHD flow are obtained for various combinations of bottom- and side-wall conductivities and for different orientations of an externally applied transverse magnetic field. The relevant set of dimensionless parameters governing the problem is identified. Unlike in single-phase MHD flows, the presence of a non-conductive gas layer breaks the flow symmetry, leading to a significantly different dependence of the flow characteristics on duct aspect ratio, wall-conductivity configuration, and the strength and orientation of the applied magnetic field. Using mercury-air flow as a representative test case, the solutions are employed to quantify the influence of the gas phase on the in-situ liquid holdup, velocity field, pressure gradient, flow lubrication, and pumping-power requirements. It is shown that, regardless of the magnetic Reynolds number, these characteristics are strongly affected by the wall-conductivity configuration and by the orientation of the external magnetic field.

physics.flu-dyn↗

arXiv2025

Long-wave instability of stratified two-phase MHD flow

Instability of a stratified two-phase MHD parallel flow between two infinite plates is addressed. We examine the effect of the transverse magnetic field on the base flow and long wave instability of a two-layer system consisting of conductive liquid and non-conductive gas. Both perfectly insulating and perfectly conducting boundaries are considered. To capture the behavior at small but finite wavenumbers, the conventional first-order long-wave stability analysis is extended to higher order terms. Using mercury-air system as a representative test case, the results demonstrate distinct and non-similar base flow and disturbance profiles, as well as different stability maps for insulating versus conducting boundaries. The stability diagrams reveal a non-monotonic influence of the magnetic field on flow stability, showing that, in addition to its expected stabilizing effect, the field can also induce destabilization under certain conditions. Inspection of the disturbance profiles indicates that despite the strong damping of mercury flow by the magnetic field, interaction of the two fluids at the interface and the shear-induced instabilities in the gas layer dominate and can lead to flow destabilization as the magnetic field strength increases.

physics.flu-dyn↗

arXiv2025

Two-phase stratified MHD flows in wide rectangular ducts: analytical and numerical solutions

This study explores the effects of a non-conductive gas layer flowing concurrently with a conductive liquid on the two-phase flow characteristics in wide horizontal ducts under a constant vertical magnetic field. To this end, analytical solutions for the velocity profile and induced magnetic field are presented for laminar gas-liquid stratified magnetohydrodynamic (MHD) flow between two infinite plates of various conductivities. The contributions of the Lorentz force and wall shear stresses to the pressure gradient are examined. To the best of our knowledge, it is shown for the first time that, unlike the single-phase Hartmann flow, the velocity profiles in two-phase flow differ significantly depending on whether the bottom wall is conducting or insulating. In the case of an insulating bottom wall, the gas lubrication effect and potential pumping power savings are significantly greater, regardless of the magnetic Reynolds number. This conclusion also holds for gas-liquid MHD flows in rectangular ducts with finite width-to-height aspect ratios. To assess the applicability of the Two-Plate (TP) model to wide ducts, numerical solutions of the two-dimensional problem are used to investigate the influence of side walls on the two-phase flow characteristics, considering various combinations of bottom and side wall conductivities. In all cases, the results for high aspect ratios converge to the analytical solution obtained from the TP model with the same bottom wall conductivity. However, the influence of insulating side walls remains significant even at large aspect ratios when the bottom wall is conducting. Unexpectedly, in such cases, the change in the induced magnetic field due to the presence of side walls has a dramatic effect on the velocity profile, leading to a reduced pressure gradient compared to that predicted by the TP model.

physics.flu-dyn↗

arXiv2024

Flow of a shear-thinning fluid in a rectangular duct

We address the problem of steady laminar flow of a shear-thinning fluid in rectangular ducts, which is encountered in many systems, in particular, in microfluidic and biomedical devices. However, an exact solution for the flow of non-Newtonian fluids that considers a realistic shear-thinning rheological behavior is not available in the literature. In this study, an accurate solution for the case of Carreau fluid is obtained and investigated numerically. The numerical solution allows us to analyze the effects of the fluid rheology and the aspect ratio of the rectangular duct on the velocity field and pressure gradient that drives the flow. The relationship between the pressure gradient and the Carreau number is found to follow the rheological curve of the shear-thinning fluid. The analysis shows that the fluid rheology and the aspect ratio have independent contributions to the integral flow characteristics. Moreover, separate consideration of these contributions allows us to arrive at universal scaling and general formulae for the pressure gradient and friction factor for various rheological parameters of the fluid and aspect ratios of rectangular ducts.

physics.flu-dyn↗

arXiv2024

Instability of stratified air-water flows in circular pipes

This work deals with stability of two-phase stratified air-water flows in horizontal circular pipes. For this purpose, we performed a linear stability analysis, which considers all possible three-dimensional infinitesimal disturbances and takes into account deformations of the air-water interface. The main results are presented in form of stability maps, which compare well with the available experimental data. The neutral stability curves are accompanied by the corresponding wavenumbers and wave speeds of the critical perturbations, as well as by spatial patterns of their velocity components. Accordingly, several modes of the critical perturbation are revealed. Long waves are found to be the critical perturbation over part of the stability boundary, and they are affected by the surface tension due to the confinement effect of the lateral direction. Exploring the effect of pipe diameter on the stability boundary and critical perturbations shows that for small water holdups (i.e., thin water film) the scaling of the critical gas velocity by the gas Froude number is valid for pipe diameters larger than about 0.1m, where the surface tension effects due to the lateral confinement become negligible. Comparing results obtained in pipe, square duct, and two-plate geometries, we show that there are cases where the simplified geometry of two parallel plates can be employed to model the realistic geometry reasonably well.

physics.flu-dyn↗

arXiv2024

Generation of interfacial waves by rotating magnetic fields

Interfacial waves arising in a two-phase swirling flow driven by a low-frequency rotating magnetic field (RMF) are studied. At low RMF frequencies, of the order of 1-10 Hz, the oscillatory part of the induced Lorenz force becomes comparable to the time-averaged one, and cannot be neglected. In particular, when free surfaces or two-liquid stably stratified systems are subject to a low-frequency RMF, induced pressure variations necessarily excite free-surface/interfacial waves, which can improve mass transfer in different metallurgical processes. In this paper, we formulate a linear wave model and derive explicit analytical solutions predicting RMF-driven wave patterns that closely resemble hyperbolic paraboloids. These theoretical predictions are validated against experiments based on a non-intrusive acoustic measurement technique, which measures liquid-liquid interface elevations in a two-phase KOH-GaInSn stably stratified system. A good quantitative agreement is found for non-resonant wave responses in the vicinity of the fundamental resonance frequency. The experiments reveal the additional excitation of several higher harmonics superimposing the fundamental wave oscillation, which are visible even in the linear wave regime.

physics.flu-dyn↗

arXiv2023

A numerical framework for linear stability analysis of two-phase stratified pipe flows

A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the interface between two fluids, are considered. The proposed numerical framework is based on a finite-volume method and allows solving the problem numerically in bipolar cylindrical coordinates. In these coordinates, both the pipe wall and the unperturbed interface (of a constant curvature, e.g., plane interface, as considered in this work) coincide with the coordinate surfaces. Thereby, the no-slip as well as the interfacial boundary conditions can be imposed easily. It also enables investigation of the local behavior of the flow field and shear stresses in the vicinity of the triple points, where the interface contacts the pipe wall. The results obtained in the bipolar coordinates are verified by an independent numerical solution based on the problem formulation in Cartesian coordinates, where the pipe wall is treated by the immersed boundary method. Two representative examples of gas-liquid and liquid-liquid flows are included to demonstrate the applicability of the proposed numerical technique for analyzing the flow stability.

physics.flu-dyn↗

arXiv2022

Sequence of bifurcations of natural convection of air in a laterally heated cube with perfectly insulated horizontal and spanwise boundaries

A sequence of three steady - oscillatory transitions of buoyancy convection of air in a laterally heated cube with perfectly thermally insulated horizontal and spanwise boundaries is studied. The problem is treated by Newton and Arnoldi methods based on Krylov subspace iteration. The finite volume grid is gradually refined from 100^3 to 256^3 finite volumes. It is shown that the primary instability is characterized by two competing eigenmodes, whose temporal development results in two different oscillatory states that differ by their symmetries. Bifurcations due to both modes are subcritical. These modes develop into different oscillatory and then stochastic flow states, which, at larger Grashof number, stabilize and arrive to single stable steady flow. With further increase of the Grashof number this flow loses it stability again. It is argued that in all the three transitions, the instabilities onsets, as well as reinstatement of stability, take place owing to an interaction between a destabilizing centrifugal mechanism and stabilizing effect of thermal stratification.

physics.flu-dyn↗

arXiv2022

Effect of interface dynamic deformations on instabilities of buoyancy-thermocapillary convection in a two-fluid two-layer system

Effect of interfacial disturbances on instabilities of buoyant/thermocapillary convective flows in rectangular cavities is studied in a series of numerical experiments. The computations are carried out for several two-liquid two-layer systems taking into account properties of liquids used in previously published experiments. Relation between the interface deformations and the Boussinesq approximation is discussed. It is shown that in some systems, including the interface disturbances in the model can alter the critical temperature difference by approximately 10%, producing either destabilizing, or stabilizing effect. The interface oscillations appear as standing or travelling waves whose wavelength can vary from short wave lengths to a single wave occupying all the available space. Rough estimations show that in some liquid-liquid systems the interface oscillations amplitude can reach several tens of microns. Patterns of the most unstable disturbances are presented and discussed. It is argued that instabilities in some two layer systems develop similarly to the Holmboe instabilities in stratified mixing layers.

physics.flu-dyn↗

arXiv2020

Instability of stratified two-phase flows in rectangular ducts

The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the associated eigenproblem. The neutral stability boundary and the corresponding critical wave number are obtained for liquid - liquid and air - water systems. Depending on the problem parameters, the instability sets in owing to short, intermediate, of long wave most unstable perturbations. Patterns of the most unstable disturbances are reported and discussed. It is shown that the instability arises due to shear, or interfacial mechanisms. Effects of the surface tension and of width/height aspect ratio are also studied. The results support the premise that the stability analysis of stratified two-phase flow in the simpler geometry of two-infinite plates can provide a reasonable estimation of the conditions for which this flow pattern can be considered to be linearly stable.

physics.flu-dyn↗

arXiv2020

Instability of steady flows in helical pipes

A parametric numerical study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out. The computations are performed by a numerical approach verified against independent experimental and numerical results in a previous study. The results are reported as dependences of the critical Reynolds number, critical wavenumber and the critical frequency on the dimensionless pipe curvature and torsion. A multiplicity of different disturbance modes becoming most unstable at different values of the governing parameters, is observed. Patterns of the most unstable modes are reported and classified. Different routes to instability including viscous and inviscid mechanisms, locally developing boundary and mixing layers, interaction between the Dean vortices and the through flow are described.

physics.flu-dyn↗

arXiv2019

A comparative study on instability of steady flows in helical pipes

A computational study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out for the first time. The problem is formulated in Germano coordinates in two equivalent but different forms of the momentum equation, so that results obtained using both formulations cross verify each other. An additional formulation in the cylindrical coordinates is applied for a limiting case of the toroidal pipe. The calculations are performed by the finite volume and finite difference methods. Grid independence of the results is established for both steady flows, the eigenvalues associated with the linear stability problem, and the critical parameters. The calculated steady flows agree well with experimental measurements and previous numerical results. The computed critical Reynolds numbers corresponding to the onset of oscillatory instability agree well with the most recent experimental results, but disagree with the earlier ones. Novel results related to the parametric stability study are reported.

physics.flu-dyn↗

arXiv2019

Instability of natural convection in a laterally heated cube with perfectly conducting horizontal boundaries

Oscillatory instability of buoyancy convection in a laterally heated cube with perfectly thermally conducting horizontal boundaries is studied. The effect of the spanwise boundaries on the oscillatory instability onset is studied. The problem is treated by Krylov-subspace-iteration based Newton and Arnoldi methods. The Krylov basis vectors are calculated by a novel approach that involves the SIMPLE iteration and a projection onto a space of functions satisfying all linearized and homogeneous boundary conditions. The finite volume grid is gradually refined from 1003 to 2563 finite volumes. A self-sustaining oscillatory process responsible for the instability onset is revealed, visualized and explained.

physics.flu-dyn↗

arXiv2018

Non-modal stability analysis of stratified two-phase channel flows

The non-modal transient growth of perturbations in horizontal and inclined channel flows of two immiscible fluids is studied. 3D perturbations are examined in order to find the optimal perturbations that attain the maximum amplification of perturbation energy at relatively short times. Definition of the energy norm is extended to account for the gravitational potential energy along with the kinetic energy and interfacial capillary energy. Contrarily to the fastest exponential growth, which is reached by essentially 2D perturbations, the maximal non-modal energy growth is attained mostly by three-dimensional spanwise perturbations. Significant transient energy growth is found to occur in linearly stable flow configurations, which, similarly to single phase shear flows, may trigger non-linear destabilizing mechanisms within one of the phases. It is shown that the transient energy growth in linearly stable cases can be accompanied by noticeable interface deformations. Therefore, flow pattern transition due to non-modal transient growth and reduction of the range of operational conditions for which stratified-smooth flow remains stable cannot be ruled out.

physics.flu-dyn↗

arXiv2018

On acceleration of Krylov-subspace-based Newton and Arnoldi iterations for incompressible CFD: replacing time steppers and generation of initial guess

We propose two techniques aimed at improving the convergence rate of steady state and eigenvalue solvers preconditioned by the inverse Stokes operator and realized via time-stepping. First, we suggest a generalization of the Stokes operator so that the resulting preconditioner operator depends on several parameters and whose action preserves zero divergence and boundary conditions. The parameters can be tuned for each problem to speed up the convergence of a Krylov-subspace-based linear algebra solver. This operator can be inverted by the Uzawa-like algorithm, and does not need a time-stepping. Second, we propose to generate an initial guess of steady flow, leading eigenvalue and eigenvector using orthogonal projection on a divergence-free basis satisfying all boundary conditions. The approach, including the two proposed techniques, is illustrated on the solution of the linear stability problem for laterally heated square and cubic cavities.

physics.comp-ph↗

arXiv2018

Global Galerkin method for stability studies in incompressible CFD and other possible applications

In this paper the author reviews a version of the global Galerkin that was developed and applied in a series of earlier publications. The method is based on divergence-free basis functions satisfying all the linear and homogeneous boundary conditions. The functions are defined as linear superpositions of the Chebyshev polynomials of the first and second klinds that are combined into divergence free vectors. The description and explanations of treatment of boundary conditions inhomogeneities and singularities are given. Possible implementation for steady state solvers, path-continuation, stability solvers and straight-forward integration in time are discussed. The most important results obtained using the approach are briefly reviewed and possible future applications are discussed.

physics.flu-dyn↗

arXiv2017

Time-dependent modelling of oscillatory instability of three-dimensional natural convection of air in a laterally heated cubic box

Transition from steady to oscillatory buoyancy convection of air in a laterally heated cubic box is studied numerically by straight-forward time integration of Boussinesq equations using a series of gradually refined finite volume grids. Horizontal and spanwise cube boundaries are assumed to be either perfectly thermally conducting or perfectly thermally insulated, which results in four different sets of thermal boundary conditions. Critical Grashof numbers are obtained by interpolation of numerically extracted growth/decay rates of oscillations amplitude to zero. Slightly supercritical flow regimes are described by time-averaged flows, snapshots, and spatial distribution of oscillations amplitude. Possible similarities and dissimilarities with two-dimensional instabilities in laterally heated square cavities are discussed. Break of symmetries and sub- or super-critical character of bifurcations are examined. Three consequent transitions from steady to oscillatory regime, from oscillatory to steady, and finally to oscillatory flow, are found in the case of perfectly insulated horizontal and spanwise boundaries. Arguments for grid and time step independence of the results are given.

physics.flu-dyn↗