Linear stability of solutal convection in solidifying mushy layers: permeable mush–melt interface

The linear stability theory is used to investigate analytically the effect of a permeable mush–melt boundary condition on the stability of solutal convection in a mushy layer of homogenous permeability at the near eutectic (solid) limit. The results clearly show that, in contrast to the impermeable mush–melt interface boundary condition, the application of the permeable mush–melt interface boundary condition destabilizes the convection in a mushy layer.     

Two-dimensional cellular metals as multifunctional structures: topology optimization

Highly porous two-dimensional (2D) cellular metals have multifunctional attributes, with tailorable structures to achieve multifunctional performance. The focus of this study is to explore the optimal cellular topology of 2D cellular metals for heat dissipation, and to investigate the eligibility of different heat enhancement techniques for more efficient heat dissipation. An analytical approach for the optimal design of metallic 2D cellular materials, cooled by single-phase laminar forced convection in various flow configurations, is proposed and validated by comparison with full numerical simulations. The optimal design is characterized by two subsidiary dimensionless parameters: one reflecting the trade-off between convection and fluid friction, and the other reflecting the optimal balance between conduction and convection. A heat transfer enhancement technique––boundary layer redevelopment––is subsequently introduced and its feasibility examined experimentally. Future research directions in specific areas are discussed.     

Separation of mixtures in connected channels

The stationary modes of thermal convection of a binary mixture in connected channels of finite height were studied experimentally and theoretically. The effects of positive and negative thermal diffusion on the convection were examined. The ranges of parameters corresponding to the modes of soft and rigid initiation of convection were determined. Vertical distributions of the temperature and concentration fields were found for various values of the thermal diffusion parameter. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 68–77, January–February, 2009.     

Linear and nonlinear stability of double diffusive convection in a couple stress fluid–saturated porous layer

The linear and nonlinear stability of double diffusive convection in a layer of couple stress fluid–saturated porous medium is theoretically investigated in this work. Applying the linear stability theory, the criterion for the onset of steady and oscillatory convection is obtained. Emphasizing the presence of couple stresses, it is shown that their effect is to delay the onset of convection and oscillatory convection always occurs at a lower value of the Rayleigh number at which steady convection sets in. The nonlinear stability analysis is carried out by constructing a system of nonlinear autonomous ordinary differential equations using a truncated representation of Fourier series method and also employing modified perturbation theory with the help of self-adjoint operator technique. The results obtained from these two methods are found to complement each other. Besides, heat and mass transport are calculated in terms of Nusselt numbers. In addition, the transient behavior of Nusselt numbers is analyzed by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta–Gill method. Streamlines, isotherms, and isohalines are also displayed.     

'T-RANS' Simulation of Deterministic Eddy Structure in Flows Driven by Thermal Buoyancy and Lorentz Force

The paper reports on the application of the Time-dependent Reynolds-Averaged Navier–Stokes (T-RANS) approach to analysing the effects of magnetic force and bottom-wall configuration on the reorganisation of a large coherent structure and its role in the transport processes in Rayleigh–Bénard convection. The large-scale deterministic motion is fully resolved in time and space, whereas the unresolved stochastic motion is modelled by a `subscale' model for which the conventional algebraic stress/flux expressions were used, closed with the low-Re number (k)-(ε)-(θ²) three-equation model. The applied method reproduces long-term averaged mean flow properties, turbulence second moments, and all major features of the coherent roll/cell structure in classic Rayleigh–Bénard convection in excellent agreement with the available DNS and experimental results. Application of the T-RANS approach to Rayleigh–Bénard convection with wavy bottom walls and a superimposed magnetic field yielded the expected effects on there organisation of the eddy structure and consequent modifications of the mean and turbulence parameters and wall heat transfer. This revised version was published online in August 2006 with corrections to the Cover Date.     

Combined effect of thermal modulation and rotation on the onset of stationary convection in a porous layer

The stability of a fluid-saturated horizontal rotating porous layer subjected to time-periodic temperature modulation is investigated when the condition for the principle of exchange of stabilities is valid. The linear stability analysis is used to study the effect of infinitesimal disturbances. A regular perturbation method based on small amplitude of applied temperature field is used to compute the critical values of Darcy–Rayleigh number and wavenumber. The shift in critical Darcy–Rayleigh number is calculated as a function of frequency of modulation, Taylor number, and Darcy–Prandtl number. It is established that the convection can be advanced by the low frequency in-phase and lower-wall temperature modulation, where as delayed by the out-of-phase modulation. The effect of Taylor number and Darcy–Prandtl number on the stability of the system is also discussed. We found that by proper tuning of modulation frequency, Taylor number, and Darcy–Prandtl number it is possible to advance or delay the onset of convection.     

Hysteresis phenomenon in turbulent convection

Coherent large-scale circulations of turbulent thermal convection in air have been studied experimentally in a rectangular box heated from below and cooled from above using Particle Image Velocimetry. The hysteresis phenomenon in turbulent convection was found by varying the temperature difference between the bottom and the top walls of the chamber (the Rayleigh number was changed within the range of 10⁷–10⁸). The hysteresis loop comprises the one-cell and two-cells flow patterns while the aspect ratio is kept constant (A=2–2.23). We found that the change of the sign of the degree of the anisotropy of turbulence was accompanied by the change of the flow pattern. The developed theory of coherent structures in turbulent convection (Phys Rev E 66:1–15, 2002, Boundary-Layer Meteorol, 2005) is in agreement with the experimental observations. The observed coherent structures are superimposed on a small-scale turbulent convection. The redistribution of the turbulent heat flux plays a crucial role in the formation of coherent large-scale circulations in turbulent convection.     

Vibrational Convection in the Hele-Shaw Cell. Theory and Experiment

The influence of high-frequency horizontal vibrations on convection in the Hele-Shaw cell located in a uniform gravity field is considered experimentally and theoretically. Nonlinear regimes of vibrational convection in the supercritical region are examined. It is shown that horizontal vibrations (directed toward the wide sides of the cell) decrease the threshold of quasi-equilibrium stability. Regions of existence of one- and two-vortex steady flows are found, and unsteady regular and random regimes of thermal vibrational convection are considered. New random regimes in the Hele-Shaw cell are found, which result from nonlinear interaction of the “lower” modes responsible for the formation of regular supercritical convective regimes. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 40–48, March–April, 2006.     

Filtration convection in a high-frequency vibration field

The effect of high-frequency translational vibrations on the occurrence of filtration convection in a plane horizontal layer of a viscous incompressible liquid saturating a porous medium is studied. Constant temperature is maintained at the boundaries of the layer. It is established that for any vibration direction different from the vertical (transverse) direction, convection in gravity and thermal gravitational convection under both heating from above and heating from below can arise. In the case of reduced gravity, values of the vibration parameter that lead to transition to zero gravity are established. The results are obtained from an analysis of the averaged equations of filtration convection, derived for an arbitrary region. This work was presented at the joint X European and VI Russian Symposium on Physical Sciences in Microgravity (St. Petersburg, June 15–20, 1997). Rostov State university, Rostov-on-Don 344090. Rostov State Academy of Building, Rostov-on-Don 344022. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 22–29, May–June, 1999.     

Effect of vapor condensation on forced convection heat transfer of moistened gas

The forced convection heat transfer with water vapor condensation is studied both theoretically and experimentally when wet flue gas passes downwards through a bank of horizontal tubes. Extraordinarily, discussions are concentrated on the effect of water vapor condensation on forced convection heat transfer. In the experiments, the air–steam mixture is used to simulate the flue gas of a natural gas fired boiler, and the vapor mass fraction ranges from 3.2 to 12.8%. By theoretical analysis, a new dimensionless number defined as augmentation factor is derived to account for the effect of condensation of relatively small amount of water vapor on convection heat transfer, and a consequent correlation is proposed based on the experimental data to describe the combined convection–condensation heat transfer. Good agreement can be found between the values of the Nusselt number obtained from the experiments and calculated by the correlation. The maximum deviation is within ±6%. The experimental results also shows that the convection–condensation heat transfer coefficient increases with Reynolds number and bulk vapor mass fraction, and is 1∼3.5 times that of the forced convection without condensation.     

Rotating Brinkman–Lapwood Convection with Modulation

The purpose of this article is to analyze, theoretically, the effect of modulation on rotating Brinkman–Lapwood convection, i.e., buoyancy-driven convection in a sparse porous medium subjected to rotation. Darcy–Brinkman momentum equation with Coriolis term has been used to describe the flow. The system is considered rotating about an axis with non-uniform rotation speed. In particular, we assume that the rotation speed is varying sinusoidally with time. A linear stability analysis has been performed to find the critical Rayleigh number in modulated case. The effect of modulated rotation speed is found to have a stabilizing effect on the onset of convection for different values of modulation frequency and the other physical parameters involved.     

Multiphase Thermohaline Convection in the Earth’s Crust: II. Benchmarking and Application of a Finite Element – Finite Volume Solution Technique with a NaCl–H2O Equation of State

We present the benchmarking of a new finite element – finite volume (FEFV) solution technique capable of modeling transient multiphase thermohaline convection for geological realistic p-T-X conditions. The algorithm embeds a new and accurate equation of state for the NaCl–H₂O system. Benchmarks are carried out to compare the numerical results for the various component-processes of multiphase thermohaline convection. They include simulations of (i) convection driven by temperature and/or concentration gradients in a single-phase fluid (i.e., the Elder problem, thermal convection at different Rayleigh numbers, and a free thermohaline convection example), (ii) multiphase flow (i.e., the Buckley–Leverett problem), and (iii) energy transport in a pure H₂O fluid at liquid, vapor, supercritical, and two-phase conditions (i.e., comparison to the U.S. Geological Survey Code HYDROTHERM). The results produced with the new FEFV technique are in good agreement with the reference solutions. We further present the application of the FEFV technique to the simulation of thermohaline convection of a 400°C hot and 10 wt.% saline fluid rising from 4 km depth. During the buoyant rise, the fluid boils and separates into a high-density, high-salinity liquid phase and a low-density, low-salinity vapor phase.     

Fully Coupled THMC Modeling of Wellbore Stability with Thermal and Solute Convection Considered

Wellbore stability analysis is an important topic in petroleum geomechanics. Analytical and numerical analysis of wellbore stability involves the study of interactions among pressure, temperature and chemical changes, and the mechanical response of the rock, a coupled thermal–hydraulic–mechanical–chemical (THMC) process. Thermal and solute convection have usually been overlooked in numerical models. This is appropriate for shales with extremely low permeability, but for shales with intermediate and high permeability (e.g., shale with a disseminated microfissure network), thermal and solute convection should be considered. The challenge of considering advection lies in the numerical oscillation encountered when implementing the traditional Galerkin finite element approach for transient advection–diffusion problems. In this article, we present a fully coupled THMC model to analyze the stress, pressure, temperature, and solute concentration changes around a wellbore. In order to overcome spurious spatial temperature oscillations in the convection-dominated thermal advection–diffusion problem, we place the transient problem into an advection– diffusion-reaction problem framework, which is then efficiently addressed by a stabilized finite element approach, the subgrid scale/gradient subgrid scale method (SGS/GSGS).     

Onset of Buoyancy-driven Instability in Porous Media Melted from Below

When a nonhomogeneous solid is melting from below, convection may be induced in a thermally–unstable melt layer. In this study, the onset of buoyancy-driven convection during time-dependent melting is investigated by using similarly transformed disturbance equations. The critical Darcy–Rayleigh numbers based on the melt-layer thickness, Ra _H,c, are found numerically for various conditions. For small superheats, the present predictions show that Ra _H,c is located between 27.1 and 4π ² and it approaches the well-known results of the original Horton–Rogers–Lapwood problem. However, for high superheats, it is dependent on the phase change rate λ and the relation of Ra _H,c λ = 25.89 is shown.     

Heat transfer by laminar flow in a vertical and horizontal pipe with twisted-tape inserts

 This article presents the results of laboratory research on heat exchange while heating water in horizontal and vertical tubes with twisted-tape inserts. The scope of the research: 70 ≤ Re ≤ 4000 3.6 ≤ Pr ≤ 5.9 8.6 ≤ Gz ≤ 540 The research was held for three cases: – horizontal experimental tube – vertical experimental tube, the direction of flow according to the free convection vector – vertical experimental tube, the direction of flow not in accordance with the free convection vector For such cases the correlation equation was defined Nu_T=f(Gz; y), Nu = f(Gz) and the proportion Nu_T/Nu was analysed. Received on 30 March 2000     

Equations of convective instability of a two-phase medium with modulation of the gravity force

Thermal convection in a heterogeneous medium consisting of a fluid and solid particles is studied under conditions of finite-frequency vibrations. Equations of convection are derived within the framework of the generalized Boussinesq approximation, and the problem of stability of a horizontal layer to infinitesimal perturbations under the condition of vertical vibrations is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 21–28, March–April, 2008.     

The nature of near-wall convection velocity in turbulent channel flow

A novel notion of turbulent structure the local cascade structure-is introduced to study the convection phenomenon in a turbulent channel flow. A space-time cross-correlation method is used to calculate the convection velocity. It is found that there are two characteristic convection speeds near the wall, one associated with small-scale streaks of a lower speed and another with streamwise vortices and hairpin vortices of a higher speed. The new concept of turbulent structure is powerful to illustrate the dominant role of coherent structures in the near-wall convection, and to reveal also the nature of the convection-the propagation of patterns of velocity fluctuations-which is scale-dependent.     

The Onset of Darcy–Brinkman Electroconvection in a Dielectric Fluid Saturated Porous Layer

The combined effect of a vertical AC electric field and the boundaries on the onset of Darcy–Brinkman convection in a dielectric fluid saturated porous layer heated either from below or above is investigated using linear stability theory. The isothermal bounding surfaces of the porous layer are considered to be either rigid or free. It is established that the principle of exchange of stability is valid irrespective of the nature of velocity boundary conditions. The eigenvalue problem is solved exactly for free–free (F/F) boundaries and numerically using the Galerkin technique for rigid–rigid (R/R) and lower-rigid and upper-free (F/R) boundaries. It is observed that all the boundaries exhibit qualitatively similar results. The presence of electric field is emphasized on the stability of the system and it is shown that increasing the AC electric Rayleigh number R _ea is to facilitate the transfer of heat more effectively and to hasten the onset of Darcy–Brinkman convection. Whereas, increase in the ratio of viscosities Λ and the inverse Darcy number Da ⁻¹ is to delay the onset of Darcy–Brinkman electroconvection. Besides, increasing R _ea and Da ⁻¹ as well as decreasing Λ are to reduce the size of convection cells.     

Effect of Rotation on Thermal Convection in an Anisotropic Porous Medium with Temperature-dependent Viscosity

A linear stability analysis is performed for mono-diffusive convection in an anisotropic rotating porous medium with temperature-dependent viscosity. The Galerkin variant of the weighted residual technique is used to obtain the eigen value of the problem. The effect of Taylor–Vadasz number and the other parameters of the problem are considered for stationary convection in the absence or presence of rotation. Oscillatory convection seems highly improbable. Some new results on the parameters’ influence on convection in the presence of rotation, for both high and low rotation rates, are presented.     

Numerical and experimental study of the heat transfer and fluid flow by thermocapillary convection around gas bubbles

 At liquid–gas or liquid–liquid interfaces thermocapillary or Marangoni convection develops in the presence of a temperature or concentration gradient along the interface. This convection was not paid much attention up to now, because under terrestrial conditions it is superimposed by the strong buoyancy convection. In a microgravity environment, however, it is the remaining mode of natural convection. During boiling in microgravity it was observed at subcooled conditions. Therefore the question arises about its contribution to the heat transfer. Thus the thermocapillary convection was intensively studied at single gas bubbles in various liquids both experimentally and numerically. Inside a temperature gradient chamber, the overall heat transfer around single bubbles of different volume was measured with calorimetry and the liquid flow with PIV and LDV. In parallel to the experiment, a 2-dimensional mathematical model was worked out and the coupled heat transfer and fluid flow was simulated with a CV-FEM method both under earth gravity level and under microgravity. The results are described in terms of the dimensionless Nusselt-, Peclet-, Marangoni-, Bond- and Prandtl-number. Received on 23 August 1999