Structure Of Convective Flows Research Articles

A hybrid discrete exterior calculus and finite difference method for anelastic convection in spherical shells

The present work develops, verifies, and benchmarks a hybrid discrete exterior calculus and finite difference (DEC-FD) method for density-stratified thermal convection in spherical shells. Discrete exterior calculus (DEC) is notable for its coordinate independence and structure preservation properties. The hybrid DEC-FD method for Boussinesq convection has been developed by Mantravadi et al. (2023). Motivated by astrophysics problems, we extend this method assuming anelastic convection, which retains density stratification; this has been widely used for decades to understand thermal convection in stars and giant planets. In the present work, the governing equations are splitted into surface and radial components and discrete anelastic equations are derived by replacing spherical surface operators with DEC and radial operators with FD operators. The novel feature of this work is the discretization of anelastic equations with the DEC-FD method and the assessment of a hybrid solver for density-stratified thermal convection in spherical shells. The discretized anelastic equations are verified using the method of manufactured solution (MMS). We performed a series of three-dimensional convection simulations in a spherical shell geometry and examined the effect of density ratio on convective flow structures and energy dynamics. The present observations are in agreement with the benchmark models.

Unifying heat transport model for the transition between buoyancy-dominated and Lorentz-force-dominated regimes in quasistatic magnetoconvection

In magnetoconvection, the flow of an electromagnetically conductive fluid is driven by a combination of buoyancy forces, which create the fluid motion due to thermal expansion and contraction, and Lorentz forces, which distort the convective flow structure in the presence of a magnetic field. The differences in the global flow structures in the buoyancy-dominated and Lorentz-force-dominated regimes lead to different heat transport properties in these regimes, reflected in distinct dimensionless scaling relations of the global heat flux (Nusselt number $Nu$ ) versus the strength of buoyancy (Rayleigh number $Ra$ ) and electromagnetic forces (Hartmann number $Ha$ ). Here, we propose a theoretical model for the transition between these two regimes for the case of a static vertical magnetic field applied across a convective fluid layer confined between two isothermal, a lower warmer and an upper colder, horizontal surfaces. The model suggests that the scaling exponents $\gamma$ in the buoyancy-dominated regime, $Nu\sim Ra ^\gamma$ , and $\xi$ in the Lorentz-force-dominated regime, $Nu\sim (Ha^{-2}Ra)^\xi$ , are related as $\xi =\gamma /(1-2\gamma )$ , and the onset of the transition scales with $Ha^{-1/\gamma }Ra$ . These theoretical results are supported by our direct numerical simulations for $10\leq Ha\leq 2000$ , Prandtl number $Pr=0.025$ and $Ra$ up to $10^9$ and data from the literature.

Экспериментальное исследование процесса смешения жидкостей в проточном микроканале в условиях развития неустойчивости Рэлея–Тейлора

This study experimentally investigates the influence of Rayleigh-Taylor instability on the liquid mixing process in a flow-type microchannel. We investigated a two-layer liquid-liquid system consisting of a denser aqueous solution of potassium permanganate (upper layer) and less dense pure water (lower layer) with a fixed density gradient. A colorimetric method based on the dependence of light absorption by solutions on the concentration of the dissolved substance was used to reconstruct the two-dimensional concentration field. Based on the obtained data, we analyzed the spatial structure of convective flows and the degree of liquid mixing along the channel. The studies were carried out at low Reynolds numbers, which precludes the development of turbulent flow, and across a wide range of Richardson numbers that indicate the ratio of buoyancy to inertial forces in the formation of convective structures. We found that at high Richardson numbers, the development of Rayleigh-Taylor instability ensures almost complete mixing of liquids within five calibers from the channel inlet. Reducing the Richardson number by increasing the flow rate through the channel leads to a slowdown in the instability development and, consequently, in a significant decrease in mixing efficiency along the channel. We demonstrated that with optimal values of governing parameters, the characteristic liquid mixing length can be reduced by an order of magnitude compared to pure diffusive mixing scenarios. The obtained results demonstrate the effectiveness of convective instability mechanisms in controlling mass transfer processes in flow-type microchannel systems.

Soret-induced convection of ternary fluid in a horizontal porous layer heated from below

The present paper deals with the investigation of the Soret-induced convection of a three-component mixture of hydrocarbons in a horizontal porous layer. This problem is important for geological applications. The first part of the paper is devoted to the linear stability of the conductive state. The longwave instability is studied analytically by the expansion into the power series with respect to the wave number. A new long-wave oscillatory instability mode existing at negative separation ratios is found out. It is shown that this mode is more dangerous than the long-wave monotonic instability mode in the entire range of its existence. The instability to the perturbations with nonzero wave numbers is studied numerically by the shooting method. Stability map is obtained. The results confirm the predictions of the longwave analysis. In the second part of the paper, the nonlinear convection regimes are studied by the finite difference method. The calculations give the results consistent with the linear stability analysis. It is found that the primary bifurcation as a result of which the conductive state losses its stability is supercritical. The transformations of the convective flow structure with the change in the Rayleigh–Darcy number are accompanied by the hysteresis phenomena.

Analysis of the intermittent laser-induced thermocapillary convection of the melt by the method of short-time correlation

Online video diagnostics was used in the process of laser metal deposition. The method of short-time correlation was applied to analyse fluctuations in the size of the molten pool. Power distributions of the cross correlation of the breadth and length of the pool depending on the intensity of laser irradiation up to 30 kW/cm2 are obtained. The intermittency in parameters of the molten pool is associated with changes in the structure of convective Marangoni flows in the melt during the formation of the bead. It is shown to decrease the duration of the regular changes in the parameters of the molten pool with the increase in the intensity of laser irradiation.

Morphology evolution of a melting solid layer above its melt heated from below

We numerically study the melting process of a solid layer heated from below such that a liquid melt layer develops underneath. The objective is to quantitatively describe and understand the emerging topography of the structures (characterized by the amplitude and wavelength), which evolve out of an initially smooth surface. By performing both two-dimensional (achieving Rayleigh number up to$Ra=10^{11}$) and three-dimensional (achieving Rayleigh number up to$Ra=10^9$) direct numerical simulations with an advanced finite difference solver coupled to the phase-field method, we show how the interface roughness is spontaneously generated by thermal convection. With increasing height of the melt the convective flow intensifies and eventually even becomes turbulent. As a consequence, the interface becomes rougher but is still coupled to the flow topology. The emerging structure of the interface coincides with the regions of rising hot plumes and descending cold plumes. We find that the roughness amplitude scales with the mean height of the liquid layer. We derive this scaling relation from the Stefan boundary condition and relate it to the non-uniform distribution of heat flux at the interface. For two-dimensional cases, we further quantify the horizontal length scale of the morphology, based on the theoretical upper and lower bounds given for the size of convective cells known from Wanget al.(Phys. Rev. Lett., vol. 125, 2020, 074501). These bounds agree with our simulation results. Our findings highlight the key connection between the morphology of the melting solid and the convective flow structures in the melt beneath.

THERMAL EFFECT IN THE EVAPORATION PROCESS FROM THE INTERFACE OF THE HORIZONTAL LIQUID LAYER UNDER A SHEAR GAS FLOW

This manuscript presents the experimental study of interfacial motion and convection in a horizontal liquid layer (ethanol and HFE 7100) evaporating from a localized surface (10 × 10 mm<sup>2</sup>) into the gas flow (dry air). The novel IR-Schlieren system has been developed. The system can almost simultaneously maintain the gas-liquid interface in a flat position in a confined square area and perform thermal imaging of the volatile liquid surface by IR camera. We consider the thermal effect of gas and liquid temperature (20°C-50°C) for various gas velocities (0.0138-0.138 m/s) on interfacial liquid motion and their influence on the convective flow structure within the liquid layer. It is found that the influence of the gas flow action on the Marangoni convection at the interface is reduced with an increase in temperature. We explain this fact by the growth of the diffusion resistance for the gas flow under a strong evaporation from the interface.

Magnetoconvection in a rotating spherical shell in the presence of a uniform axial magnetic field

ABSTRACT We report simulations of thermal convection and magnetic-field generation in a rapidly-rotating spherical shell, in the presence of a uniform axial magnetic field of variable strength. We consider the effect of the imposed field on the critical parameters (Rayleigh number, azimuthal wavenumber and propagation frequency) for the onset of convection, and on the relative importance of Coriolis, buoyancy and Lorentz forces in the resulting solutions. The imposed field strength must be of order one (corresponding to an Elsasser number of unity) to observe significant modifications of the flow; in this case, all the critical parameters are reduced, an effect that is more pronounced at small Ekman numbers. Beyond onset, we study the variations of the structure and properties of the magnetically-modified convective flows with increasing Rayleigh numbers. In particular, we note the weak relative kinetic helicity, the rapid breakdown of the columnarity, and the enhanced heat transport efficiency of the flows obtained for imposed field strengths of order one. Furthermore, magnetic and thermal winds drive a significant zonal flow in this case, which is not present with no imposed field or with stronger imposed fields. The mechanisms for magnetic field generation (particularly the lengthscales involved in the axisymmetric field production) vary with the strength of the imposed field, with three distinct regimes being observed for weak, order one, and stronger imposed fields. In the last two cases, the induced magnetic field reinforces the imposed field, even exceeding its strength for large Rayleigh numbers, which suggests that magnetically-modified flows might be able to produce large-scale self-sustained magnetic field. These magnetoconvection calculations are relevant to planets orbiting magnetically active hosts, and also help to elucidate the mechanisms for field generation in a strong-field regime.

The effect of Marangoni convection on mass transfer in a rising droplet with surface reaction

Dispersing of the medium from which the desired component is extracted is still one of the main approaches to liquid extraction. However, despite its high efficiency, this approach is still of empirical nature, since the choice of the main parameters - the average drop diameter and the residence time of the drop in the surrounding liquid (the extractant) - is determined by experiment in relation to the initial concentration of the extracted substance (reagent). The main difficulty with a full-scale theoretical treatment and numerical simulation is a three-dimensional shape of the droplet and, accordingly, the lack of experimental data on the structure of convective flows and the dynamics of reagent concentration fields in the moving droplet. The situation can get worse when the extracted component is a surfactant or reactive against the extractant. The paper presents the results of an experimental study of the structure and evolution of flows and distribution of a reagent (acetic acid) diffusing from a rising cylindrical droplet with an insoluble base component into a chemically active medium (aqueous sodium hydroxide solution). The motion of the droplet is accompanied by the development of Marangoni convection and neutralization reaction on the droplet surface.

Experimental and numerical investigations on heat transfer and flow behavior of flow blockage in narrow rectangular channel with protrusions

The safety analysis of flow blockage accident is significant for plate-type fuel reactor, especially swelling of cladding, which is resulted from irradiation damage in high burnup condition and needs to be paid more attention. In this study, experimental and numerical researches have been conducted to study the convective heat transfer and flow structure within narrow rectangular channel, where exists different numbers and arrangements of spherical crown protrusions. Compared with the experimental data of single protrusion condition, the overall heat transfer capacity even deteriorates more than 20% when protrusions are aligned in streamwise direction. In contrast, the global Nu is nearly 10% higher when three protrusions are located in spanwise direction. Conclusions can be drawn that existence of protrusion can also significantly change convective flow condition in narrow channel, and the laminar flow is altered to transitional/quasi-turbulent even though Re is only nearly 1600. Besides, the local information, such as flow boundary layer separation, low-speed recirculation and vortex evolution etc., can also be acquired by the Computational Fluid Dynamics (CFD) method comprehensively. Combined with experimental data and numerical results, the distinct heat transfer behaviors and flow structures for different flow blockage conditions can be explained in detail. In summary, conclusions about the flow and thermal processes influenced by protrusions in narrow rectangular channel are fundamental to safety analysis and design criteria of plate-type fuel assembly for flow blockage condition. Besides, it also can be applied in other industry scene during convective laminar flow within narrow rectangular channel.

Influence of horizontal heat-insulating plates on the structure of convective flows and heat transfer in a closed cavity

The influence of horizontal insulating plates of different sizes on the structure of a convective flow and on the total heat flux in a cavity with aspect ratio 5 is studied numerically. Direct numerical simulations have been performed using the open source software OpenFoam 4.1 at Prandtl number 6.12 and for two Rayleigh numbers: 3.9·107and 3.9·108. In all calculations the plates are of the same thickness. It is found that the location and size of the plate strongly influence the structure of the flow. Changes in the mean flow structure have little effect on the heat flux in the case of a small plate. Increasing the plate size leads to little change in the heat flux, except for the plate location near the lower boundary. In this case, the Nusselt number is 25% less compared to Rayleigh-Bénard convection. It is found that the values of kinetic energy and Nusselt number do not correlate with each other. As the Rayleigh number increases, the influence of the plate on the heat flux decreases. It is shown that an insulating plate has no significant effect on the heat flux if the height of the plate location is significantly larger (10 times or more) than the thickness of the temperature boundary layer. It has been established that the presence of plates in the fluid volume significantly affects the integral values of velocity and temperature fluctuations.

Динамика конвективной системы с плавающим протяженным теплоизолятором

The paper presents an experimental study of a convective flow in a rectangular cell of length L, width W and depth H, filled with water, heated from the bottom and cooled from the top, with a heat-insulating disk floating at a fixed height h (the disk diameter is slightly smaller than the cavity width). Such a system exhibits a range of modes, including periodic movements of the float along the cavity, chaotic motions of various types, and drift of the disk to the edge of the cavity without further movements. In addition to the Rayleigh, Prandtl numbers and the cavity dimension ratio (L/H), usual for convective systems, the structure of convective flows in the cavity depends on geometric parameters associated with the floating disk: the relative height of the body position (h/H) and the body size to the cavity length ratio (D/L). Experiments were performed for fixed W=100mm, H=40mm, D=98mm, and h=4mm, but different lengths 170mm < L < 500mm. It is shown that periodic motions occur only in a limited range of the body size to the cavity size ratio. As the length of the cavity increases, a chaotic mode of intermittent motion of the disc occurs; at the maximum cavity length considered, the disk is shifted to the extreme position and remains there. The structure of the convective flow at different phases of periodic motions has been reconstructed by PIV (particle image velocimetry) technique.

The effect of controlled vibrations on Rayleigh-Benard convection

The paper presents the results of a numerical study of convective heat transfer in a long horizontal layer heated from below with and without the vibration effect of the lower wall. The simulation was carried out on the basis of solving the Navier-Stokes 2D equations for an incompressible fluid in the Boussinesq approximation. It is shown that the influence of vibrations of the lower heated wall on the wave number of the convective flow roll structure, on the time and on the critical Rayleigh number of convection. The influence of controlled harmonic vibrations of wall on the structure of convective flow in the Rayleigh-Benard problem has been investigated. It is shown that the wave number of the periodic convective structure, the critical Rayleigh number, and the time of occurrence of Rayleigh-Benard convection under the vertical vibration effect on the horizontal layer from the lower wall are reduced.

Heat transfer analysis of jet impinging on a curved surface

The detailed study on convection heat transfer and flow structure characteristic of air-jet studied with impinging vertically on a hemisphere plate. The inner surface of the cylindrical-shaped plate is subject to constant heat flux boundary conditions. Hemispherical plate subjected to comparative computations with Reynolds number (Re) ranging from 3000, 6000, and 9000 for the round nozzle impinging jet.

Experimental Study of Thermal Convection in a Cylindrical Layer with a Longitudinal Partition at Modulated Rotation

Thermal convection of a liquid in a simply connected horizontal cylindrical layer rotating at a variable velocity is investigated experimentally. The inner boundary of the layer has a higher temperature. The cavity rotates rapidly and the liquid is stably stratified in a centrifugal force field. The parameters of the experiment correspond to the conditions when inertial waves are not excited (the modulation frequency is more than twice the cavity rotation frequency). The excitation thresholds of thermal convection and the structure of convective flows are studied depending on the rotation velocity and the parameters of the rotational vibrations of the cavity. It is found that the thermal convection is excited in a threshold way and its excitation is not associated with the manifestation of the mechanism of pendulum vibrational convection. A system of toroidal rolls with a spatial period commensurate with the layer thickness is observed in the cavity.

Numerical analysis of the performance enhancement of a latent heat storage shell and tube unit using finned tubes during melting and solidification

The present study deals with the numerical analysis of the melting and solidification processes in three horizontal storage units for Latent Heat Thermal Storage (LHTS) using water, around its density-temperature inversion point as phase change material (PCM) and a water/glycol solution as the Heat Transfer Fluid (HTF). One of these storage units, made of a plain tube and a shell is used in this study as the reference against which the other two configurations, made respectively of longitudinal and radial finned tube and shell are compared at constant heat transfer surface, compactness and PCM volume. The objective is to improve the thermal performance of the reference unit, and therefore the charge and discharge rates using surface extension. The effect of adding longitudinal or radial fins to the tube on the local mechanism of melting and solidification is studied. The major phenomena involved in these mechanisms such as natural convection are highlighted and their effects during melting and solidification processes are analysed using the CFD code Star CCM + V12.02. Quantitative analysis including the temporal evolution of the PCM average temperature and the solid volume fraction are analysed and compared for the three configurations. This study exhibits a complex natural convective flow structure in the three storage units due to the inversion of the buoyancy forces in the PCM for the considered temperature range −4 °C to 4 °C. During the solidification process, natural convection intensively develops at the earlier stages of the process and, as the time goes, its effect on the solidification becomes negligible as compared to the one due to conduction. During the melting process, heat is transferred to the PCM first by conduction and later by natural convection. The use of fins significantly increases the solidification and melting rates, especially for the configuration with longitudinal fins for which performance are found to be superior to the two other configurations.

Tectonic depressions on the East-European and Siberian platforms: numerical modeling of convection beneath the Eurasian continent

In modern concepts, the upper mantle of the Earth is a highly viscous incompressible liquid, and its flow is described using the Navier – Stokes equations in the Oberbeck – Boussinesq and geodynamic approximations. Convective flows in the upper mantle play a decisive role in the kinematics of lithospheric plates and the geological history of continental regions. Mathematical modeling is a basic method for studying convective processes in the mantle. Our paper presents a numerical model of convection, which is based on the implicit artificial compressibility method. This model is tested in detail by comparing our calculation results with the results of a well-known international test. It is demonstrated that the Fedorenko grids sequence method is highly efficient and reduces the computing time almost by a factor of eight. The numerical model is generalized in order to state the problem in a spherical system of coordinates. It is used to analyse the distribution of convective flows in the upper mantle underneath the Eurasian continent. The analysis shows that the thickness and geometrical parameters of the lithospheric blocks are the factors of significant influence on the distribution of convective flows in the upper mantle. The resulting structure of convective flows is manifested in the surface topography of large platform areas wherein the lithosphere thickness is increased. Thus, the locations of extended downward convection flows under the East European and Siberian platforms are clearly comparable to syneclises observed in the study area.

Crustal Reservoir Flow Simulation for Long-Range Spatially-Correlated Random Poroperm Media

In interest of accurately modelling wellbore production in convective geothermal systems, we draw attention to two approaches to numerical simulation of crustal fluid flow. The historical ‘’strong’’ approach simulates the fluid mass conservation condition on a localised finite difference mesh approximation to poroelastic continua. The more flexible ‘’weak’’ approach globally enforces fluid mass conservation by in effect integrating over all numerical mesh cells. Strong formulation crustal flow simulation emerged from numerical simulations of mathematically tractable conductive heat flow in media typified by normally-distributed/spatially-uncorrelated thermal property distributions. Strong formulation numerical stability problems quickly intrude, however, when confronted with the lognormally-distributed/spatially-correlated crustal permeability distributions that pervade the ambient crust. Weak flow conservation solver formulations accurately handle abrupt wide-ranging crustal permeability spatial fluctuations arising from these crustal permeability structures. We use two Matlab-based weak formulation flow simulation schemes to model wellbore-centric production fluid connectivity within large-scale spatially erratic convective geothermal flow structures described by the empirical poroperm relation k(x,y,z) ~ exp(αφ(x,y,z)) acting over cm-to-km scale lengths. Through weak formulation reservoir flow modelling of convective geothermal systems, the advancing ability to support large-scale crustal flow structure models with multi-channel surface seismic data acquisition/processing can guide geothermal field exploration and developmental drilling via feedback loops between crustal flow imaging data and accurate wellbore production modelling data.

Free-fall velocities and heat transport enhancement in liquid metal magneto-convection

Abstract

Theoretical and experimental substantiation of the system of local removal of harmful substances during the combustion of candles in the worship hall of Orthodox churches and cathedrals

The analysis of the features of Orthodox churches, temples and cathedrals, elements of the design of the halls of worship, and their preservation. The types of hazards generated during the burning of candles and the parishioners and staff present are systematized. Thermal imaging surveys of convective flows formed during candle combustion were carried out. A technique for conducting experiments and a diagram of an experimental setup for measuring the temperature and air velocity in a convective jet have been developed. The diagram of the convective flow structure is presented, which consists of individual jets from each candle. The results of the study have been obtained, which make it possible to determine the area of stable convective flow and the place of installation of the exhaust hood above the candlestick, as well as the distance between the burning candles and the edge of the bottom of the umbrella. A local mechanical exhaust ventilation system with umbrellas has been developed to trap and remove harmful substances from the worship hall and provide comfortable conditions for parishioners and preserve the decoration elements of the halls. The characteristics and conditions for the efficient operation of the hoods in the local exhaust ventilation system and the factors influencing their operation are given.