Laminar natural convection and interfacial heat flux distributions in pure water-ice systems

Experimental and numerical investigations of laminar natural convection and interfacial heat flux distributions in pure water-ice systems are presented. The main goals are: (i) Resolution of several issues related to steady, two-dimensional, laminar natural convection in pure water near its density inversion temperature; and (ii) development, testing, and demonstration of a nonintrusive experimental/numerical method for the determination of interfacial heat flux distributions in steady, two-dimensional, pure water-ice systems.; Attention was found on pure water and water-ice systems contained in a long cylindrical enclosure of square cross-section. One wall was maintained at a constant temperature equal to or less than {dollar}0spcirc{dollar}C; the opposite wall was maintained at a constant temperature above the density inversion temperature of water; the other two walls of the cross-section were essentially adiabatic. Several angles of inclination, {dollar}Theta ,{dollar} of the hot and cold walls, with respect to the gravitational acceleration vector, were considered: {dollar}Theta = 0spcirc , 30spcirc , 45spcirc ,{dollar} and {dollar}{lcub}-{rcub}45spcirc .{dollar} For these conditions, the natural convection in water is governed by three nondimensional parameters: the Rayleigh number, Ra; a density inversion parameter, R; and the Prandtl number, Pr. The following ranges of these parameters were investigated: {dollar}10sp3le Rale 3.37times 10sp7; 0.1le Rle 0.9;{dollar} and {dollar}6.74le Prle 12.4.{dollar}; A complete rig was designed and constructed. The water-ice interface positions were obtained using shadowgraphy and computer-aided image processing techniques. In the complementary numerical work, a staggered-grid finite volume method (FVM) and a co-located, equal-order, control-volume finite element method (CVFEM) were formulated and used.; In the first investigation, variable- and constant-property models (VPM and CPM) were used. Results of the VPM and CPM were found to be similar, except when the values of R are in the vicinity of 0.5, where significant differences in the flow patterns, but only minor changes in the overall Nusselt number, {dollar}overline{lcub}Nu{rcub},{dollar} were observed. It was demonstrated that the fluid flow is extremely sensitive to changes in the value of R in the vincinity of 0.5. A correlation that gives the {dollar}overline{lcub}Nu{rcub}{dollar} as a function of Ra and R has been proposed for the vertical enclosure {dollar}(Theta = 0spcirc ).{dollar}; In the proposed experimental/numerical technique to determine the interfacial heat flux distributions, the interface position obtained by the shadowgraphy and image processing techniques was used as an input to the CVFEM. The CVFEM was then used to solve the heat conduction problem in the ice and obtain the interfacial heat flux distribution. It was found that if the raw digitized interface position data are directly inputted to the CVFEM simulations of heat conduction in the ice, the interfacial heat flux distributions exhibit physically untenable fluctuations. The reasons for this difficulty were identified and successfully overcome using appropriate data filtering techniques. (Abstract shortened by UMI.)...