A numerical simulation of combined radiation and natural convection heat transfer in a square enclosure heated by a centric circular cylinder

A numerical simulation of combined natural convection and radiation in a square enclosure heated by a centric circular cylinder and filled with absorbing-emitting medium is presented. The ideal gas law and the discrete ordinates method are used to model the density changes due to temperature differences and the radiation heat transfer correspondingly. The influence of Rayleigh number, optical thickness and temperature difference on flow and temperature fields along with the natural convection, radiation and total Nusselt number at the source surfaces is studied. The results reveal that the radiation heat transfer as well as the optical thickness of the fluid has a distinct effect on the fluid flow phenomena, especially at high Rayleigh number. The heat transfer and so the Nusselt number decreases with increase in optical thickness, while increases greatly with increase in temperature difference. The variation in radiation heat transfer with optical thickness and temperature difference is much more obvious as comparison with convection heat transfer.     

Factors affecting temperature measurement using phase measurement interferometry in small scale devices

This paper presents full-field temperature measurements of buoyancy opposing mixed convection flow within a miniscale fluidic geometry. The technique used is phase measurement interferometry and a Mach–Zehnder layout is employed. The popular two-dimensional microfluidic geometry of three streams merging at a junction is chosen for this analysis. The apparatus set-up is described and measures taken to limit experimental errors discussed. Also presented, are corresponding flow visualization images for comparison with the interferometric results. The results are compared for similar boundary conditions over the range of Richardson numbers of 0.5–1.7. The results of the interferometric study are presented in the form of full-field temperature maps depicting the type of thermal plume structure present through isotherms and are seen to compare well with the results of the flow visualization study. Some factors affecting the measurement technique at this scale are then discussed. These include the effect of using different transparent materials for sealing the fluidic device and temporal vibrations caused by either varying boundary conditions or by slight pulsations in the flow supplied. Also, due to discrepancies that exist in the literature for the temperature coefficient of the refractive index of the working fluid, thermocouples are embedded in the flow field and used to convert the measured phase change to a corresponding temperature change. The corresponding values of refractive index change with temperature are discussed and compared to published values. Overall, PMI is demonstrated to provide excellent full-field temperature plots that can be used to measure local heat transfer rates from this non-intrusive measurement technique.     

Interferometric investigation of convection in plexiglas boxes

Real-time holographic interferometry is used to study free convection in cavities heated from below and bounded by Plexiglas windows. Advantages and shortcomings of this visualization technique applied to such Plexiglas boxes are discussed. As Plexiglas has a high temperature-dependent refractive index, temperature fields in the windows and the fluid layer are visualized. These visualizations furnished proof of a pronounced thermal influence of the walls on the flow pattern based on what we call “thermal memory” of Plexiglas.     

Numerical study on magneto-convection of cold water in an open cavity with variable fluid properties

The aim of the present study is to understand the problem of buoyancy and thermocapillary induced convection of cold water near its density maximum in an open cavity with temperature dependent properties in the presence of uniform external magnetic field. The governing equations are solved by the finite volume method. The results are discussed for various values of reference temperature parameter, density inversion parameter, Rayleigh, Hartmann and Marangoni numbers. It is observed that the temperature of maximum density leaves strong effects on fluid flow and heat transfer due to the formation of bi-cellular structure. Convection heat transfer is enhanced by thermocapillary force when buoyancy force is weakened.     

Mixed convective heat transfer characteristics and mechanisms in structured packed beds

The structured packed bed is considered a promising reactor owing to its low pressure drop and good heat transfer performance. In the heat transfer process of thermal storage in packed beds, natural convection plays an important role. To obtain the mixed convective heat transfer characteristics and mechanisms in packed beds, numerical simulations and coupling analyses were carried out in this study on the unsteady process of fluid flow and heat transfer. A three-dimensional model of the flow channel in the packed bed was established, and the Navier–Stokes equations and Laminar model were adopted for the computations. The effects of the driving force on fluid flow around a particle were studied in detail. The differences in velocity and density distributions under different flow directions due to effect of the aiding flow or opposing flow were intuitively demonstrated and quantitatively analyzed. It was found that the driving force strengthens the fluid flow near the particle surface when aiding flow occurs and inhibits the fluid flow when opposing flow occurs. The boundary layer structure was changed by the natural convection, which in turn influences the field synergy angle. For the aiding flow, the coordination between the velocity and density fields is higher than that for the opposing flow. By analysis the effects of physical parameters on mixed convective heat transfer, it is indicated that with an increase in the fluid-solid temperature difference or the particle diameter, or a decrease in the fluid temperature, the strengthening or inhibiting effect of natural convection on the heat transfer became more significant.     

Numerical and experimental study of free convection above a sinusoidal horizontal plate

A numerical and experimental analysis is performed to study the laminar free convection above a horizontal plate facing upward subjected to an uniform heat flux. The surface of the plate, in contact with the fluid, is described by a sinusoidal profile. The natural convection equations are discretized, using an implicit finite difference technique, based on the finite volume approach. The SIMPLE algorithm assumes the linkage between velocities and pressure fields. The top and the lateral boundaries of the space, where free convection is developing, are determined by using an iterative procedure. The temperature fields of the fluid, over the plate, are visualized by an experimental device, which can realize a simultaneous measurement of the temperature and the position. Qualitative information about the natural convection flow above the plate is obtained by using a laser tomography technique. The numerical results show that the flow and the heat transfer are strongly affected by the amplitude, the period of the sinusoidal profile and the type of fluid. Comparisons between numerical and experimental results show a good qualitative agreement.     

Flow pattern recognition in heated vertical channels: Steady and transient conditions

Experimental work was carried out to determine the flow pattern map in vertical heated pipes under steady-state and transient conditions, using Freon 12 in forced convective flow as working fluid and optical probes for the measurements Existing maps are based on adiabatic tests, steady-state conditions, and fluids different from Freon 12. Signals from optical probes (whose response is based on the variations in fluid refractive index) are analyzed in terms oflocal void fraction, using either the probability density function (PDF) or the ratio between the average and maximum values of the signal. From the analysis of the experimental measurements the definition of a map for annular and intermittent flow regimes was achieved. The map turned out to be in good agreement with the Weisman and Kang map developed in adiabatic, steady-state conditions Qualitative results for the transient conditions are also presented.     

The onset of penetrative double-diffusive convection

The onset of double-diffusive convection in a horizontal fluid layer is studied. The density is assumed to depend quadratically on the temperature and linearly on the solute concentration. Under the Boussinesq approximation, the linear stability of the conduction state is investigated with respect to the oscillatory and steady convection modes. For steady onset, the critical thermal Rayleigh number is found to be a double-valued function of the solutal Rayleigh number as long as the relative maximum of the density profile exists within the fluid layer. Driving mechanisms of the steady convections are discussed.     

Full-field Measurement of Topography and Curvature by Coherent Gradient Sensing Method at High Temperature

Coherent gradient sensing (CGS) method, a real time, full-field optical technique, is insensitive to vibrations and able to provide slope and curvature maps and surface topographies, to investigate non-uniform deformations. In this paper, we analyze the thermal effects on the optical path in CGS due to air convection, and the influence of grating thickness and refractive index on the measurement accuracy. A modified governing equation is derived considering the grating thickness, which is demonstrated by testing a standard sample. Finally, we apply CGS method to measure the full-field deformation of a specimen at high temperature.     

Heat transfer by combined free and forced convection in vertical tubes

The influence of free convection on forced convection heat transfer becomes important in laminar flows. Numerical methods have been applied for a study of mixed convection in vertical tubes for the following conditions: temperature-dependent fluid density, constant wall temperature and parabolic profile of axial velocity at the tube entrance. Both cases: heating and cooling have been considered.     

Evolution of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid

The problem of the stabilization of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid is solved using both asymptotic and numerical methods. The analytical solution describes the structure of the main convective cells, including thin meridional jets flowing along the surface and plumes spreading from the flow convergence regions above the upper and lower poles of the sphere which gradually return the fluid particles to the neutral buoyancy horizon. The total width of the flows adjacent to the surface exceeds the thickness of the salinity deficit layer or the density boundary layer. The numerical solution of the complete problem in the nonlinear formulation describes the main convective cells and two systems of unsteady integral waves formed in the vicinity of the sphere poles. At large times, out of the entire system of internal waves only those nearest to the neighborhood of their horizon of formation remain clearly defined. The calculated flow patterns are in agreement with each other and the data of shadow visualization of the stratified fluid structure near a submerged obstacle at rest.     

A large-scale matched index of refraction flow facility for LDA studies around complex geometries

Useage of laser-Doppler anemometry (LDA) requires optical access to the flow field of interest. This has not always proved easy, as in the case of complex geometries or very near-wall boundary layer measurements. One solution is to employ a solid material and fluid with the same refractive index. In this case, there is no optical interference of the solid with the LDA. Although this technique is not new, previous studies have been limited to small flow apparatus and relatively unpleasant fluids. A large-scale flow tunnel has now been constructed, permitting matched index of refraction LDA measurements in difficult geometries, higher Reynolds numbers, and increased spatial resolution in the measurements. This paper describes the facility and fluid flow quality, and presents some preliminary results for very near-wall measurements of a transitional boundary layer behind a roughness element. Received: 13 March 2000/Accepted: 30 July 2000     

The Sensitivity of Thermohaline Groundwater Circulation to Flow and Transport Parameters: A Numerical Study Based on Double-Diffusive Convection above a Salt Dome

This article explores double-diffusive convective fluid motion in an aquifer above a salt dome. Aside from the ambient regional flow regime, the hydraulic conditions in an aquifer connected with a salt formation are determined by differences in salinity. Whereas density-driven flow patterns induced by the effect of salt have been studied before we focus on the additional effect of temperature. For the model setup, we select typical parameter values that are characteristic of not only the lowlands in Germany and Poland. For the computation of flow in a vertical cross-section, we use numerical modeling with COMSOL Multiphysics. The size and strength of eddies in the high salinity region above the aquifer base are strongly influenced by thermal effects. A sensitivity study shows a wide range of convection phenomena, ranging from the absence of convective motions via steady and oscillating circulation to unsteady fluctuating patterns. The flow and transport parameters show the highest sensitivity to the thermal Rayleigh number.     

Particle image velocimetry in a variable density flow: application to a dynamically evolving microburst

A fondamental difficulty in the experimental study of gravity-driven flows using particle image velocimetry (PIV) and other optical diagnostic techniques is the problem associated with variations in thé refractive index within the fluid. This paper discusses a method by which the refractive indices of two fluids are matched while maintaining density differences of up to 4%. Aqueous solutions of glycerol and potassium phosphate are used to achieve precise index matching in the presence of mixed and unmixed constituents. The effectiveness of the method is verified in a PIV study of a laboratory-scale model of an atmospheric microburst where planes of two-dimensional velocity vectors are obtained in thé evolving flow field.This work was sponsored by the National Science Foundation under grant CTS-9209948. We also thank TSI, Inc. for the use of its facility     

Transient conjugate mixed convection from a sphere in a porous medium saturated with cold pure or saline water

In this paper, a numerical investigation of the transient conjugate mixed convection flow about a sphere embedded in a porous medium saturated with pure or saline water is carried out. The effect of density extremum is considered by using the nonlinear dependence of density on the temperature. The salinity effects are considered by assuming uniform saline concentration over the domain considered. The direction of the natural convection is changed either to aiding or to opposing the upcoming flow direction simulating the sphere is either hot or cold relative to the surrounding temperature. Results show that the initial temperature differences as well as the saline concentration alter the transient heat transfer rate in conceivable degree. It was found that the heat capacity ratio between the sphere and the surrounding media has more significant effect on the calculated heat transfer rate than the thermal conductivity ratio. The study is performed by using six nondimensional parameters and results are discussed in detail. Received on 10 November 1997     

Penetrative convection in thawing subsea permafrost

Penetrative convection is investigated in a porous medium bounded above by the ocean bed and below by the interface of the thawing permafrost ground. The thermal equation of state relating the density, temperature and salinity is assumed to be that of ocean water as proposed by the UNESCO formula. Employing the Boussinesq approximated Darcy-flow equations with such a realistic density formula in the buoyancy term, the problem of convective motion of brine is studied. Such convection flow is observed off the coast of Alaska. The field variables in question are the brine-velocity field, the temperature and the salinity, although we simplify the problem by imposing a temperature field that is linear in the depth variable. For this simplified system we study the continuous dependence of the velocity and salinity on the initial data, develop a linear instability analysis and, additionally, present a fully nonlinear three-dimensional stability analysis. This nonlinear analysis necessitates the introduction of a generalised energy (or Lyapunov function) due to the extra terms present in the realistic equation of state. Numerical results indicate that values of the critical Rayleigh numbers are smaller than when these extra terms are omitted. Received: March 10, 1997     

Unobstructed particle image velocimetry measurements within an axial turbo-pump using liquid and blades with matched refractive indices

Performing PIV measurements within complex turbomachinery with multiple blade rows is difficult due to the optical obstruction to the illuminating sheet and to the camera caused by the blades. This paper introduces a refractive index matched facility that overcomes this problem. The rotor and stator blades are made of transparent acrylic, and the working fluid has the same optical refractive index as the blades. A 64% by weight solution of sodium iodide in water is used for this purpose. This liquid has a kinematic viscosity of about 1.1᎒^-6 m²/s, which is almost the same as that of water enabling operation at high Reynolds numbers. Issues related to operating with this fluid such as chemical stability, variations in transmittance and solutions to these problems are discussed. This setup allows full optical access to the entire rotor and stator passages both to the laser sheet and the camera. The experiments are conducted at different streamwise locations covering the entire flow fields around the rotor, the stator, the gap between them, and the wakes behind. Vector maps of the instantaneous and phase-averaged flow fields as well as the distribution of turbulent kinetic energy are obtained. Measurements at different magnifications enable us to obtain an overview of the flow structure, as well as detailed velocity distributions in the boundary layers and in the wakes.     

Effects of a barrier on temperature structure and mixing in thermally stratified water cooled from above

A Mach-Zehnder interferometer was used to study the unsteady temperature structure in radiation stratified water cooled from above. Temperature distribution measurements in a test cell filled with distilled water provide conclusive evidence that the thermal structure between the air-water interface and the stable region is controlled by buoyancy induced natural convection. The cooling from above produces a complex vertical temperature profile which can be divided into several distinct regimes. Introduction of a thin, rigid transparent (glass) plate into the water before thermal stratification by radiation and cooling confines the natural convection driven flow and reduces the intensity of mixing. As a result, the energy transport from the interior of the water layer to the interface is decreased. However, under the experimental conditions tested use of rigid, horizontal plates introduced in the fluid were not very effective in reducing the transport of heat from the warm interior to the cooler interface.     

An experimental study of the effect of wall temperature nonuniformity on natural convection in an enclosure heated from the side

An experimental study of natural convection in a parallelepipedal enclosure induced by a single vertical wall is described. The upper half of this wall was warm and the lower half cold. The other enclosure walls were insulated. The temperature and flow measurements were performed in the high Rayleigh number regime (10¹⁰<Ra<5×10¹⁰) by using water as the working fluid. The Rayleigh number was based on the enclosure height and the temperature difference between the warm and the cold part of the driving wall. The flow field featured two flat cells, one filled with warm fluid along the top horizontal wall, and the other filled with cold fluid along the bottom horizontal wall. Each of these cells was surrounded by an additional cell as tall as half the enclosure height. The above flow structure prohibited extensive thermal contact between warm and cold fluid, thus limiting the role of convection on the heat transfer process in the cavity. The findings of this study differ significantly from the findings of previous studies based on the ‘classical’ enclosure model possessing two isothermal vertical walls, the one warm and the other cold, and support the view that the use of ‘more realistic‘ temperature boundary conditions in enclosure natural convection needs careful examination.     

Experimental techniques in natural convection

Experimental techniques in natural convection heat transfer employed in the author's laboratory are introduced. The techniques are mostly related to visualization of flow, temperature field, and heat flux distribution in fluids. Three topics are presented, the first being natural convection in a horizontal rectangular liquid layer driven by surface tension and buoyancy. The patterns of flow were visualized by suspending fine aluminum flakes in the liquid. At the same time, the distribution of the temperature gradient in the liquid was visualized by an optical method making use of the refraction of light. The second topic is the onset of oscillatory convection in the Czochralski growth melt. In this case a forced flow due to rotation of the crystal and the vessel is superimposed on the buoyancy convection, resulting in an oscillatory flow under certain circumstances. The flow pattern and the temperature distribution in the liquid were visualized simultaneously by suspending in the liquid a microencapsulated temperature-sensitive liquid crystal. Periodical oscillation of the flow and the temperature was clearly recognized. The third topic is the rollover of double liquid layers that were stratified stably due to a density difference. A small-scale experiment was carried out to clarify the basic mechanism of rollover. The tracer method was used to visualize boundary layer flow along the vertical side wall and the shadowgraph technique to visualize the density distribution in the liquid layers. The article emphasizes the importance of visual observation in the investigation of natural convection phenomena.