Convective structures in a thin layer of an evaporating liquid under an airflow

Evolution of convective structures in a thin layer of an evaporating liquid (ethanol) located under a turbulent boundary layer of an airflow is studied experimentally and theoretically. Evolution of the structures is examined under conditions of an increased flow velocity. A transition is found from convective cells formed in the absence of the flow to convective rolls elongated in the streamwise direction. The theoretical analysis is performed within a two-dimensional model of the flow in the liquid layer. The boundary conditions on the liquid surface are obtained with the use of self-similar solutions for mean fields in the airflow. The onset and evolution of a periodic system of rolls are simulated numerically. Theoretical conclusions are compared with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 3–14, July–August, 2007.     

湍流池湍流特征研究

在用于激光束传输和控制模拟实验的湍流池中温度脉动测量结果表明,原始温度变化曲线上有明显的斜坡（ｒａｍｐ）结构,温度三阶及五阶结构函数和理论预计一致和大气对流边界层的测量相似,斜坡结构的出现对二阶结构函数的影响较小,加热面和冷却附近有明显的猝发现象出现,温度脉动的峰度系数大于３,表现了较大的间歇性。     

The coupling between turbulent,penetrative convection and internal waves

Experiments aimed at exploring the coupling of penetrative convection with internal waves in the adjoining, stable layer were performed in a long convection cell. The experiments are motivated by preliminary theoretical results suggesting that an intrinsic phase instability may exist in the coupled system in which case long internal waves modulate the height and strength of convective plumes. Using a temperature-controlled, stably stratified experimental apparatus, measured temperature data reveal the presence of long internal wave modes that persist for many convective time scales. The frequencies of these waves increase linearly in time during the energy transfer between the convective and stratified regions as the depth of the stratified region diminishes and the depth of the mixed layer increases. Temporal variations in the heat flux, interface rise characteristics, and frequencies of internal wave motions are reported. A natural temporal modulation of the thickness of the transition layer separating the mixed layer from the stratified layer occurs following commencement of heating, with the amplitude and frequency of the modulation varying with the initial stratification. Temperature variance data suggest that a fairly strong interaction between convection and internal waves occurs, especially when the interface region is midway between the upper and lower boundaries of the cell and the no-slip boundary conditions play a less influential role on the dynamics of the coupling.     

Modeling of convective structures in a thin layer of silicone oil in air flow under heating

Numerical simulation was performed to study convective structures in a thin silicone oil layer heated from below, whose free surface is exposed to air flow generating drift flow. The basic equations are transformation to a form suitable for spectral methods. The steady flow velocity profile obtained in a laboratory experiment is calculated. It is shown that increasing the Reynolds number leads to the transition from polygonal convective cells to longitudinal rolls (elongated along the flow). The dependence of the transition Reynolds number on the temperature on the lower boundary of the layer is obtained. The calculation results are compared with experimental data.     

The ultrasonic velocity profile measurement of flow structure in the near field of a square free jet

 Coherent structures in the near field of a three-dimensional jet have been investigated. Experiments were carried out for a free jet issuing from a square nozzle using a water channel. Instantaneous velocity profiles were obtained in the axial and radial directions by using an ultrasonic velocity profile (UVP) monitor. Axial variations of dominant time-scales of vortex structures were examined from one-dimensional wavelet spectra. Wavenumber-frequency spectra were calculated by two-dimensional Fourier transform along the axial direction in a mixing layer, and it was found that a convective velocity of flow structures was nearly constant independently of their scales in space and time. Coherent structures in the axial direction were investigated in terms of proper orthogonal decomposition (POD). Eigenfunctions are similar to a sinusoidal wave, and reconstructed velocity fields by the lower-order and higher-order POD modes demonstrate large-scale and smaller-scale coherent structures, respectively. Received: 8 May 2000/Accepted: 23 January 2001 Published online: 29 November 2001     

Investigation of convection in a horizontal cylindrical layer of a saturated porous medium

The structures of the convective motions and the nature of the heat transfer in a horizontal cylindrical layer are studied numerically for the Forchheimer model of a porous medium in the Boussinesq approximation. New asymmetric solutions of the equations of convection flow through a porous medium are found. Their development, domains of existence, and stability are investigated. One consists of a multivortex structure with asymmetric vortices in the near-polar region. Another asymmetric solution is realized at large Grashof numbers in the form of a convective plume deflected from the vertical. The threshold Grashof number of formation of the asymmetric motions depends on the Prandtl number and the cylindrical layer thickness.     

Localized convective flows in a nonuniformly heated liquid layer

Within the class of exact solutions of the thermal-convection equations in the Oberbeck-Boussinesq approximation, which assumes a linear dependence of the temperature and the vertical velocity component on the height, a non-self-similar behavior of localized disturbances of a special type in a nonuniformly heated liquid layer is studied. It is shown that in an unstably stratified medium these disturbances can evolve to isothermal vortex structures of Burgers type. In the conditions of stable stratification or uniform heating of the layer, the disturbances considered tend to the state of rest in an oscillating or monotonic manner. New solutions describing self-similar convective vortices are found.     

Convective stability of a nonisothermal fluid in a rotating horizontal coaxial gap

The thermal fluid convection in a coaxial horizontal gap uniformly rotating about its axis is investigated. The threshold above which convective flows are excited and the structure of these flows are studied. It is found that convection ensues irrespective of whether the inner or outer boundary temperature is higher. Convection manifests itself in the threshold development of rolls elongated in the direction of the rotation axis and is determined by two different mechanisms. If the layer is heated from outside, the centrifugal convection mechanism plays a leading part and the diameter of the convective rolls is comparable with the layer thickness. If the higher is the temperature of the inner boundary of the layer, the centrifugal inertia force has a stabilizing effect and convection development is related with the action of thermal vibrational mechanism. The latter is determined by gravity-generated oscillations of the nonisothermal fluid relative to the cavity. The wave number of the vibrational convective structures is several times smaller than under centrifugal convection. The results obtained broaden our understanding of thermal convection in systems rotating in external static force fields.     

High-speed cinematography of compressible mixing layers

Experiments are performed using high-speed film cinematography to temporally resolve compressible planar mixing layer structures using shadowgraphs and planar light sheet visualization. The technique is relatively inexpensive and allows multiple images. The time-dependent shadowgraph and Mie scattering images are documented with a rotating mirror camera operating at approximately 350 kHz. The results show the presence of large scale structures in the mixing layer which flatten as they convect downstream. Both spatial and temporal covariances have been obtained through digital image processing which yield, on average, elliptical structures with convective speeds above the isentropic prediction, and non-isotropic streamwise and transverse scalar transport fluctuations.     

Effect of the nonmonotonic temperature dependence of water density on convection under uniform heating

This paper presents the results of an experimental study of free convection in a closed rectangular tank with fresh water whose initial temperature is lower than the constant temperature of air outside the tank. Convective instability is shown to play a significant role in the process of heat transfer from the boundary layers on the walls to the bulk of water. In the case where the initial water temperature is higher than the temperature at which the density is maximal (about 4°C), convective instability occurs only in the boundary layer at the bottom of the tank. At a water temperature below 4°C convective instability also exists for some time in the boundary layer on the cover. Quantitative information is given on the variations in temperature and water density in time and on the vertical coordinate.     

Experimental Study of the Effect of Gas-Phase Thickness On Stability and Structure of the Flow in a Two—Layer Liquid—Gas System

The stability of a two-layer liquid—gas system with a variable ratio of layer thicknesses is experimentally studied. It is found that the critical value of the Marangoni number and the characteristic size of convective structures depend on the ratio of thicknesses of the gas and liquid phases. For ratios higher than ten, the gas layer can be considered as infinite.     

Computational analysis of convective instabilities in a liquid layer subjected to an inclined gradient of temperature

A 3D numerical study of convective instabilities in a horizontal liquid layer (silicone oil with a Prandtl number Pr = 102) with an upper free surface is presented. The liquid layer is subjected to an inclined gradient of temperature. The influence of both gravity and thermocapillary forces on the formation of convective patterns is studied for different values of the liquid layer depth. Numerical results are found to be in good agreement with experimental data of other authors.     

Planar solidification of a warm flowing-liquid under different boundary conditions

Planar solidification of a warm flowing liquid with the convective heat transfer to the growing solid layer, has been analysed for the boundary conditions of constant temperature, constant heat flux and convective heat flux at the surface respectively. The mathematical formulation of the problem resulted in a coupled set of two differential equations in temperature and solid thickness as function of position, time and the problem parameters. Analytical expressions for the temperature distribution within the growing solid layer, the rate of solidification and the solidification time are obtained. The perturbation techniques employed here is simple and straight forward in contrast with the earlier techniques. Good agreement between the experimental results and the present solutions is obtained for the convective heat flux boundary condition. The results of this analysis are useful in the design and analysis of experiments dealing with freezing/melting in one dimension. The role of the parameter Stefan number which is small for phase change materials, is discussed in context with the storage of thermal energy.     

Flow and heat transfer of nanofluids over stretching sheet taking into account partial slip and thermal convective boundary conditions

The effect of flow slip on the nanofluid boundary layer over a stretching surface is studied. The present results provide a basic understanding on the effects of the slip boundary condition on heat and mass transfer of nanofluids past stretching sheets subject to a convective boundary condition from below. The results show that an increase of thermophoresis parameter or slip factor would decrease the reduced Nusselt number in some cases.     

Mixed Convection in a Darcy–Brinkman Porous Medium with a Constant Convective Thermal Boundary Condition

The characteristics of the boundary layer flow past a plane surface adjacent to a saturated Darcy–Brinkman porous medium are investigated in this paper. The flow is driven by an external free stream moving with constant velocity. The surface is heated with a convective boundary condition with constant heat transfer coefficient. The problem is non-similar and is investigated numerically by a finite difference method. The problem is governed by four non-dimensional parameters, that is, the convective Darcy number, the convective Grashof number, the Prandtl number, and the axial distance along the plate. The influence of these parameters on the results is investigated, and the results are presented in tables and figures. The Darcy term and the Grashof term in the momentum equation contradict each other and this contradiction makes the problem complicated. However, the wall shear stress and the wall temperature increase continuously along the plate and the wall temperature always tends to 1.     

受对流边界层影响的过山气流

建立了一个自由大气与对流边界层相耦合的解析模式，利用该模式系统地讨论了对流边界层对过山气流的影响。     

Physical modeling of heat and mass transfer in large crystal growth by high-temperature horizontal directional crystallization

The conditions of heat and mass transfer in a growth container in horizontally oriented crystallization of refractory oxides are studied by means of physical modeling. It is found that increasing the thickness of the fluid layer has no significant impact on the character and intensity of mass transfer in the near-surface and near-bottom areas, but it contributes to an increase in the width of the central zone, in which the convective mass transfer is substantially limited.     

Forced convective flow and heat transfer over a?porous plate in a?Darcy-Forchheimer porous medium in presence of?radiation

A mathematical model is presented for analyzing the boundary layer forced convective flow and heat transfer of an incompressible fluid past a plate embedded in a Darcy-Forchheimer porous medium. Thermal radiation term is considered in the energy equation. The similarity solutions for the problem are obtained and the reduced nonlinear ordinary differential equations are solved numerically. It is noticed that the boundary layer decreases with an increase in the value of inertial parameter and in this case the temperature profile is found to decrease smoothly within the boundary layer. In case of porous plate, fluid velocity increases whereas non-dimensional temperature decreases for increasing values of suction parameter. The rate of heat transfer increases with the increasing values of Prandtl number. The effect of thermal radiation on temperature field is also analyzed.     

Quasiperiodic structures in the problem of fluid convection between horizontal planes

A steady flow induced by quasiperiodic temperature distributions at the boundaries is considered with reference to the example of fluid convection in a plane horizontal layer heated from below. A spectral-finite-difference method is employed to obtain convective vortex structures varying quasiperiodically along the horizontal coordinate. The properties of the quasiperiodic solutions, together with their spectra and integral characteristics (Nusselt number) are studied as functions of the Grashof number and the boundary conditions of the problem.