three-dimensional flow and temperature distribution in ... - CiteSeerX

18TH UIT NATIONAL HEAT TRANSFER CONFERENCE CERNOBBIO, COMO, ITALY, 26-28 JUNE, 2000 THREE-DIMENSIONAL FLOW AND TEMPERATURE DISTRIBUTION IN RAYLEIGH-BENARD CONVECTION USING THERMOCHROMIC LIQUID CRYSTALS AND DIGITAL IMAGE PROCESSING F. Palazzolo, F. Magnasco and M. Ciofalo Dipartimento di Ingegneria Nucleare (DIN), Università di Palermo Viale delle Scienze, I-90128 Palermo, Italy Abstract The application of Thermochromic Liquid Crystals (TLC) suspended in glycerol to the investigation of Rayleigh-Bénard convection is described. Multiple-exposure images of TLC particles in cross sections parallel to the long and short sides of an enclosure are recorded on transparency film using a flash equipped with a collimator, yielding a thin light sheet. Images are then digitized and split into hue-saturation-intensity components; hue is converted into temperature using a previously obtained calibration curve, while the intensity component (B/W image) is processed by the AEA software VISIFLOW using a correlation method to give in-plane velocities. Planar distributions can then be interpolated to reconstruct the threedimensional flow and temperature fields, giving Tomographic Particle Image Velocimetry and Thermography (TPIVT). 1. INTRODUCTION The present work involves two independent fields of interest: the first is one of the most basic problems of fluid dynamics, Rayleigh-Bénard convection, while the second is the development of imaging techniques for the visualization and the quantitative characterization of flow and temperature fields in fluids. The fluid in a shallow cavity heated from below is a classic example of nonlinear systems exhibiting a sequence of transitions as a control parameter increases. Here, the control parameter is the Rayleigh number Ra=(gβ∆TH3)/(να), H being the cavity height, ∆T the temperature difference between the walls, g the acceleration due to gravity, and β, ν, α the fluid’s thermal expansion coefficient, kinematic viscosity, and thermal diffusivity. Despite the long time elapsed since the first contribution by Lord Rayleigh [1] and the many theoretical and experimental studies dedicated to the problem, it is still only partially understood. For shallow enclosures, the first instability (transition from conduction to convection) occurs at a Rayleigh number close to the theoretical value for infinite-aspect ratio cavities (~1708). According to the literature [2-3], flow patterns initially take the form of steady transverse rolls, parallel to the shorter side; as Ra increases, rolls orthogonal to the above appear near the short sides, where they are superimposed on the base transverse-roll pattern. A complex interface (“grain boundaries”) develops between the regions dominated by the two alternative flow patterns [4]. Further increases of Ra lead to a growth of the regions dominated by longitudinal rolls. Eventually, through different and complex mechanisms, steady-state flow becomes unstable and a fully three-dimensional and time-

dependent regime is established in the enclosure. For practical and theoretical reasons, our investigation has focused on moderate aspect ratios (e.g. height/width/length = 1/2/4 or 1/4/8) and Rayleigh numbers ranging from ~5000 to ~30,000. The experimental approach is based on thermochromic liquid crystals (TLC) suspended in glycerol. The use of TLC in heat transfer research is widespread [5], but applications of TLC in the suspended form are rare [6], and usually limited to the qualitative visualization of the flow and temperature distribution. The quantitative reconstruction of velocity and temperature fields, based on the use of suspended TLC droplets in glycerol and of a multiple-exposure photographic technique (PIVT, i.e. simultaneous Particle Image Velocimetry and Thermography) was demonstrated for free convection in rectangular enclosures in our previous work [7]. However, it was limited to a single plane or a few planes at most, which in the case of inclined or vertical enclosures - was justified by the flow being essentially twodimensional. The extraction of velocity vectors from the frames was performed by a rather crude - essentially manual - technique. The aim of the present work was to improve the above investigation by: - extending the study to three-dimensional flows, via the acquisition and post-processing of images for two families of orthogonal planes and the subsequent numerical interpolation of the results, yielding three-dimensional flow and temperature fields (Tomographic Particle Image Velocimetry and Thermography, or TPIVT); - using the dedicated software package VISIFLOW (AEA Technology, Harwell) to automatically extract in-plane velocity distributions from digitized pictures. A flow-chart of the whole method is reported in Fig.1. In the following, the various steps will be described. Results will also be presented for a 60×120×240 mm (1/2/4 aspect ratio) cavity subject to a temperature difference of 0.8°C, giving a Rayleigh number of ~7300. 2. TEST SECTION AND WORKING FLUID The test section includes two main walls, built of 20 mm thick, black-anodyzed aluminium plates which were made independently isothermal by forced circulation of water through milled grooves; a swinging support, provided with devices to close and tighten the cavity; and the associated hydraulic circuits. Details are given in ref.[8]. The cavity proper is delimited by the two isothermal walls and by a frame built from 11 mm-thick perspex, having the appropriate height H and side dimensions L, W, which provides the four (transparent) side walls. A separate frame was used for each geometrical configuration studied. Hot and cold water is provided by thermo-static laboratory baths, which include water circulators and keep the temperature within ±0.1°C with good precision and repeatability. Mercury thermometers, having a resolution of 0.1°C and located at the inlet and outlet sections of each plate, provide a reading of the heating/cooling water temperatures. For the configurations which have been tested or planned, the convective heat transfer through the cavity is low (