The paper presents the results of an experimental and numerical study of turbulent thermal convection in a rectangular box containing an extended immersed free-floating plate. Varying the values of control parameters, such as Rayleigh number, aspect ratio and vertical position of the plate, provides a wide range of possible modes, from immobile and purely periodic to stochastic. We have shown that stable periodic motions occur when the plate floats close to one of the heat exchangers. An increase in the distance between the plate and the heat exchanger breaks the periodic motion and (at moderate Rayleigh numbers) leads to a pronounced asymmetry, when the plate stays close to one of the walls most of the time, makes rare excursions to the opposite wall and immediately returns. As the Rayleigh number increases, the plate motions from one edge of the box to the other reappear, but always have an irregular character. Regarding the dependence of the system behaviour on the geometry of the box, both lower and upper limits of periodic plate motions were found in the experiments. In the numerical simulations, the upper limit was not achieved – the plate moves quasi-periodically through the chain of vortices of different signs even at the largest aspect ratio being considered. The heat-insulating floating plate provides the spatial and temporal variation of the heat flux and reduces the integral heat flux, but the reduction in heat flux depends significantly on the vertical position of the plate.

A mathematical model developed to describe the interaction of a thermal convective flow with a moving body is presented. The model was implemented within the framework of the SigmaFlow computational software package, which is based on computational fluid dynamics methods. The thermal convective flow is described by the Navier–Stokes equations in the Boussinesq approximation, and the moving body model is implemented using the immersed boundary method. The article presents the results of verification of the proposed mathematical model by solving the following test problems: unsteady laminar flow around the cylinder; natural convection in the channel between two cylinders; developed convective flow in a closed rectangular area with a fixed plate. The results of a numerical study of the plate motion in a thermal convective flow in a closed volume (cuvette) with hot lower and cold upper walls are presented. The calculations showed that the moving plate has an impact on the dynamics of formation of large-scale cells, the local distribution of heat flux density on the lower wall and the integral heat flux. In particular, they revealed a local decrease in the heat flux under the plate, an increase in the number of large vortices in the cuvette and the destruction of the horizontal temperature gradient observed in the case of a fixed plate. In addition, for a fixed plate, the value of heat flux under it depends on its position, and in the case of a moving plate – on the position and direction of its movement. A qualitative comparison of calculations for two different Rayleigh numbers with the experimental data obtained at the Institute of Continuous Medium Mechanics of the Ural Branch of the Russian Academy of Sciences showed that the behavior of the plate is governed by similar regularities. Представлена математическая модель, предназначенная для описания взаимодействия свободно-конвективного потока с подвижным телом. Модель реализована в рамках расчетного программного комплекса SigmaFlow, основанного на методах вычислительной гидродинамики. Свободно-конвективное течение описывается уравнениями Навье–Стокса в приближении Буссинеска, а модель подвижного тела реализована с помощью метода погруженных границ. В статье приведены результаты верификации предложенной математической модели на следующих тестовых задачах: нестационарное ламинарное обтекание цилиндра; естественная конвекция в канале между двумя цилиндрами; развитое конвективное течение в замкнутой прямоугольной области с неподвижной пластиной. Представлены результаты численного исследования движения пластины в свободно-конвективном потоке в замкнутом объеме (кювете) с горячей нижней и холодной верхней стенками. В результате расчетов обнаружено влияние подвижной пластины на динамику формирования крупномасштабных ячеек, на локальное распределение плотности теплового потока на нижней стенке и интегральный тепловой поток. В частности, выявлено локальное уменьшение теплового потока под пластиной, увеличение числа крупных вихрей в кювете и разрушение горизонтального градиента температуры, который наблюдается в случае закрепленной пластины. Кроме этого, для закрепленной пластины величина теплового потока под ней зависит от ее положения, а в случае подвижной пластины – от положения и направления ее движения. Качественное сравнение расчетов для двух разных чисел Релея c экспериментальными данными, полученными в Институте механики сплошных сред УрО РАН, показало, что поведение пластины имеет схожие закономерности.

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The two-dimensional motions of a disc submerged at a fixed depth but floating freely in an extended layer of liquid heated by a radiation flux falling from above are studied. The motion of a body in a convective layer depends on a number of factors such as the size of the body, the geometry of the cavity and the physical properties of the fluid and the body. The main focus of this work is to reveal the role of the degree of homogeneity of the distribution of heating of the underlying surface by incident radiation. Numerical simulations allowed us not only to describe the motion of the disc, but also to show the full three-dimensional structure of the convective flow for different regimes. Verification laboratory experiments confirmed the adequacy of the numerical simulations and clarified the role of the optical properties of the floating body. The simulation results showed the sensitivity of the system to the homogeneity of the radiation flux. A change in the radiation distribution leads to a change in the structure of the large-scale circulation. In the case of homogeneous distribution, a toroidal vortex is formed with the liquid sinking in the central part, and in the case of inhomogeneous distribution with maximum heating in the centre, on the contrary, a vortex appeared with the liquid rising in the centre. Since the motion of a floating body is determined by large-scale flows, their rearrangement leads to qualitative changes in the spatial and temporal characteristics of the disc motion. The experiments with discs of different radiation transparency demonstrated that, when the transparency coefficient reaches 0.4, the wandering of the disc stops.

Multiphase flows in porous media are widespread in nature and various technologies. One of the most common examples of this kind of task is the task of recovering oil from the rock. This article describes a mathematical model of the flow of a two-phase (immiscible) liquid based on a new approach of network hydrodynamics for a highly branched microchannel medium (simulating a porous space in the rock). The coupling of the flow and pressure fields in the network is performed using a well-proven SIMPLE algorithm in CFD problems; this approach allows us to use effective approaches to modeling 3D tasks. Phase transfer over the network is carried out by an explicit method with an adaptive time step. The article presents the results of verification of the model, with analytical calculations and in comparison with the results of experimental studies. As an experiment, the displacement of oil from a microchip (Dolomite: 3200284) simulating a porous medium was simulated. The good qualitative and quantitative compliance with the results calculated and the results of the experiment show the correct functioning of the model.