UNCERTAINTY AND MEASUREMENT ERRORS

Errors in the experimental data are associated with misalignment of the apparatus with respect to the light beam, noise generated at different stages of the experiment, including the imperfections of the optical components, and the intrinsic unsteadiness of the convection process itself. All experiments were conducted several times to establish the repeatability of the convective patterns, for the parameter range of interest. A quantitative assessment of errors and uncertainty was possible in experiments on convection in a rectangular cavity because of knowledge of the lower and upper surface temperatures.

A series of cross-checks have been enforced to validate the quantitative results obtained from experiments in the rectangular cavity. These include predicting the temperature of the cold top wall by starting from the lower hot wall, as well as comparing steady heat transfer rates across the cavity against published correlations.  For example, an interferometry experiment with hot and cold temperatures of 305.5 K and 300.5 K yielded the cold wall temperature as 300.2 K. For temperatures of 300 and 320 K, the hot wall temperature was predicted to be 319.65 K.  In schlieren, temperatures of 300 and 320 K were predicted as 301 and 319 K. The errors were considerably smaller at lower temperature differences across the cavity where the flow field was clearly steady. The comparison with correlations of average heat fluxes across the cavity for various temperature differences is discussed in Section Benchmark Experiment.

In experiments with air, the time-dependent movement of the fringes during interferometry and the time-wise change in intensity for schlieren were not severe enough at the lower end of temperature differences, specifically the lower end of the Rayleigh number range. For Ra>51,000 unsteadiness was a source of uncertainty in the local temperature profiles as well as the wall heat transfer rates. Quite often, unsteadiness was a source of measurement uncertainty in air. It was less serious in water as well as the aqueous solution of KDP. Analysis of convection patterns in the KDP solution could be carried out under conditions of mild unsteadiness by averaging a time-sequence of images. The results obtained in the present work can be taken to be quantitatively meaningful for the lower range of Rayleigh numbers. For very high Rayleigh numbers, the images are purely representative of the instantaneous thermal/solutal fields in the fluid region.

An additional check carried out in the crystal growth experiments was one of solutal mass balance. Since the convective field was imaged from various angles, it was possible to independently determine the average concentration of KDP on a given plane. These averages were within 0.1% of each other as long as the convection plume was steady. Larger discrepancies were seen in those experiments where the convection process was strongly unsteady. Only those images that satisfied the mass balance check were used for tomographic reconstruction.