Ivan Korotkin

Two-phase flow analogy as an effective boundary condition for modelling liquids at atomistic resolution

A hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework based on the analogy with two-phase hydrodynamics has been extended to dynamically tracking the feature of interest at all-atom resolution. In the model, the hydrodynamics description is used as an effective boundary condition to close the molecular dynamics solution without resorting to standard periodic boundary conditions. The approach is implemented in a popular Molecular Dynamics package GROMACS and results for two biomolecular systems are reported. A small peptide dialanine and a complete capsid of a virus porcine circovirus 2 in water are considered and shown to reproduce the structural and dynamic properties compared to those obtained in theory, purely atomistic simulations, and experiment.

Thermo-Electrical Regime of a Vertical Electrolyzer: Estimates of the Effects of Electric Conductivity and Gas Evolution

Some estimates of the distribution of the electric field and current in a vertical electrolyzer are made. The homogeneity criterion, connecting electrode sizes, working space thickness, electrolyte conductivity, and electrode conductivity is obtained. This criterion is verified in numerical calculations. The effects of the gas phase in a vertical electrolyzer are estimated under homogeneous and nonhomogeneous distributions of the potential with height in the working space. It is shown that, under conditions when two-phase models of a liquid with bubbles can be used, the effect of the gas phase on the potential and current distributions with height is insignificant in a number of cases. The research results can be used to select proper electrode materials and to verify and interpret the results of numerical modeling of two-phase electrolyte hydrodynamics in the working space of a vertical electrolyzer.

Thermoelectrical regime of a vertical electrolyzer. Part 2: Numerical modeling of two-phase electrolyte convection

The results of numerical modeling of two-phase electrolyte thermo-and hydrodynamics in the working space of a separate electrolyzer cell with vertical electrode arrangement are presented. The problem is solved in a self-consistent formulation taking into account the electric current, Joule heat evolution, gas evolution, gas and liquid flows, and electric conductivity of the disperse phase. Within the framework of the proposed two-liquid approach, near-wall bubbly flow is calculated using a model of expanding gas plume, which is based on the introduction of an effective force acting upon the gas phase. The results of several variants of such calculations are compared. The numerical solution is also compared to approximate analytical solutions of the problem. The results of this study can be used to calculate estimations of the electrical and thermal regimes of vertical electrolyzers.

Parameter-free numerical method for modeling thermal convection in square cavities in a wide range of Rayleigh numbers

Some computational results for the two and three-dimensional Davis benchmark are presented. This benchmark represents thermal convection in a square (cubical) cavity with vertical active walls in a wide range of Rayleigh numbers (104to 1014), which covers both laminar and highly turbulent flows. A turbulence model with parameters that depend on a Rayleigh number and require adjustment is usually used to describe turbulent flows. An alternative is Direct Numerical Simulation (DNS) methods, but they demand extremely large computational grids. Recently there has been an increasing interest in DNS methods with incomplete resolution, which are able to provide in some cases acceptable results without resolving Kolmogorov scales. On the basis of such an approach the so-called parameter-free computational techniques have been developed. These methods cover wide range of Rayleigh numbers and allow computing various integral properties of heat transport on relatively coarse computational grids. In this paper, a new numerical method based on the CABARET scheme is proposed for solving Navier-Stokes equations with Boussinesq approximation. This turbulent model-free technique includes no additional parameters and has a second-order approximation scheme in time and space on uniform and non-uniform computational grids with minimal computational stencil. Testing of the technique on the Davis benchmark and the sequence of refined grids shows that the method allows one to compute integral heat fluxes with a high degree of accuracy both for laminar and highly turbulent flows. For the Rayleigh numbers up to 1014, a several percent accuracy has been achieved on an extremely coarse grid consisting of 20×20 cells refined toward boundary. There is no a definite and comprehensive explanation of this computational phenomenon. Cautious optimism exists regarding the perspectives of using the new method of thermal convection computations for low Prandtl numbers typical of liquid metals.Представлены результаты численного решения двумерной и трехмерной задачи Дэвиса — задачи термоконвекции в квадратной (кубической) каверне с вертикальной подогреваемой стенкой при числах Рэлея от 10 до 10. В этот диапазон попадают как ламинарные течения, так и сильно развитые турбулентные. Для описания турбулентных течений обычно используются модели турбулентности, параметры которых зависят от числа Рэлея и нуждаются в настройке. Альтернативой являются методы прямого численного моделирования (DNS), требующие экстремально больших расчетных сеток. В последнее время усилился интерес к методам DNS с неполным разрешением, которые в ряде случаев позволяют получать приемлемые результаты на масштабах больших, чем колмогоровские. На основе такого подхода строятся так называемые «беспараметрические» вычислительные алгоритмы, охватывающие широкий диапазон чисел Рэлея и предназначенные для расчета интегральных характеристик теплопереноса на относительно грубых сетках. В работе описан новый численный метод решения уравнений Навье–Стокса в приближении Буссинеска на основе схемы КАБАРЕ. Этот метод не опирается на какие-либо модели турбулентности и не содержит настроечных параметров. Он обладает вторым порядком аппроксимации как по времени, так и по пространству на неравномерных расчетных сетках и довольствуется минимально возможным шаблоном разностной схемы. Тестирование метода на задаче Дэвиса и последовательности сгущающихся сеток показало, что он обладает способностью с высокой точностью находить интегральные тепловые потоки для ламинарных и сильно турбулентных течений. При этом точность в несколько процентов при числах Рэлея до 10 достигается на рекордно грубой, сгущающейся к границам области сетке размерностью 20×20 ячеек. Однозначного и исчерпывающего объяснения этого вычислительного феномена пока не найдено. Выражается осторожный оптимизм относительно перспектив применения нового метода для расчетов термоконвекции при малых числах Прандтля, присущих жидким металлам.

A multi-resolution particle/fluctuating hydrodynamics model for hybrid simulations of liquids based on the two-phase flow analogy

A triple-scale model of a molecular liquid, where atomistic, coarse-grained, and hydrodynamic descriptions of the same substance are consistently combined, is developed. Following the two-phase analogy method, the continuum and discrete particle representations of the same substance are coupled together in the framework of conservation laws for mass and momentum that are treated as effective phases of a nominally two-phase flow. The effective phase distribution, which governs the model resolution locally, is a user-defined function. In comparison with the previous models of this kind in the literature which used the classical Molecular Dynamics (MD) for the particulate phase, the current approach uses the Adaptive Resolution Scheme (AdResS) and stochastic integration to smoothen the particle transition from non-bonded atom dynamics to hydrodynamics. Accuracy and robustness of the new AdResS-Fluctuating Hydrodynamics (FH) model for water at equilibrium conditions is compared with the previous implementation of the two-phase analogy model based on the MD-FH method. To demonstrate that the AdResS-FH method can accurately support hydrodynamic fluctuations of mass and momentum, a test problem of high-frequency acoustic wave propagation through a small hybrid computational domain region is considered.

Modeling of Turbulent Natural Convection in Enclosed Tall Cavities

It was shown in our previous work (J. Appl. Mech. Tech. Phys 57 (7), 1159–1171 (2016)) that the eddy-resolving parameter-free CABARET scheme as applied to two-and three-dimensional de Vahl Davis benchmark tests (thermal convection in a square cavity) yields numerical results on coarse (20 × 20 and 20 × 20 × 20) grids that agree surprisingly well with experimental data and highly accurate computations for Rayleigh numbers of up to 1014. In the present paper, the sensitivity of this phenomenon to the cavity shape (varying from cubical to highly elongated) is analyzed. Box-shaped computational domains with aspect ratios of 1: 4, 1: 10, and 1: 28.6 are considered. The results produced by the CABARET scheme are compared with experimental data (aspect ratio of 1: 28.6), DNS results (aspect ratio of 1: 4), and an empirical formula (aspect ratio of 1: 10). In all the cases, the CABARET-based integral parameters of the cavity flow agree well with the other authors’ results. Notably coarse grids with mesh refinement toward the walls are used in the CABARET calculations. It is shown that acceptable numerical accuracy on extremely coarse grids is achieved for an aspect ratio of up to 1: 10. For higher aspect ratios, the number of grid cells required for achieving prescribed accuracy grows significantly.