Mathematical modeling of cold cap
The ultimate goal of studies of cold cap behavior in glass melters is to increase the rate of glass processing in an energy-efficient manner. Regrettably, mathematical models, which are ideal tools for assessing the responses of melters to process parameters, have not paid adequate attention to the cold cap. In this study, we consider a cold cap resting on a pool of molten glass from which it receives a steady heat flux while temperature, velocity, and extent of conversion are functions of the position along the vertical coordinate. A one-dimensional mathematical model simulates this process by solving the differential equations for mass and energy balances with appropriate boundary conditions and constitutive relationships for material properties. The sensitivity analyses on the effects of incoming heat fluxes to the cold cap through its lower and upper boundaries show that the cold cap thickness increases as the heat flux from above increases, and decreases as the total heat flux increases. We also discuss the effects of foam, originating from batch reactions and from redox reactions in molten glass, and argue that models must represent the foam layer to achieve a reliable prediction of the melting rate as a function of feed properties and melter conditions.
DETERMINATION OF HLW GLASS MELT RATE USING X-RAY COMPUTED TOMOGRAPHY
The purpose of the high-level waste (HLW) glass melt rate study is two-fold: (1) to gain a better understanding of the impact of feed chemistry on melt rate through bench-scale testing, and (2) to develop a predictive tool for melt rate in support of the on-going frit development efforts for the Defense Waste Processing Facility (DWPF). In particular, the focus is on predicting relative melt rates, not the absolute melt rates, of various HLW glass formulations solely based on feed chemistry, i.e., the chemistry of both waste and glass-forming frit for DWPF. Critical to the successful melt rate modeling is the accurate determination of the melting rates of various HLW glass formulations. The baseline procedure being used at the Savannah River National Laboratory (SRNL) is to; (1) heat a 4 inch-diameter stainless steel beaker containing a mixture of dried sludge and frit in a furnace for a preset period of time, (2) section the cooled beaker along its diameter, and (3) measure the average glass height across the sectioned face using a ruler. As illustrated in Figure 1-1, the glass height is measured for each of the 16 horizontal segments up to the red lines where relatively large-sized bubbles begin to appear. The linear melt rate (LMR) is determined as the average of all 16 glass height readings divided by the time during which the sample was kept in the furnace. This 'visual' method has proved useful in identifying melting accelerants such as alkalis and sulfate and further ranking the relative melt rates of candidate frits for a given sludge batch. However, one of the inherent technical difficulties of this method is to determine the glass height in the presence of numerous gas bubbles of varying sizes, which is prevalent especially for the higher-waste-loading glasses. That is, how the red lines are drawn in Figure 1-1 can be subjective and, therefore, may influence the resulting melt rates significantly. For example, if the red lines are drawn too low, a significant amount of glassy material interspersed among the gas bubbles will be excluded, thus underestimating the melt rate. Likewise, if they are drawn too high, many large voids will be counted as glass, thus overestimating the melt rate. As will be shown later in this report, there is also no guarantee that a given distribution of glass and gas bubbles along a particular sectioned plane will always be representative of the entire sample volume. Poor reproducibility seen in some LMR data may be related to these difficulties of the visual method. In addition, further improvement of the existing melt rate model requires that the overall impact of feed chemistry on melt rate be reflected on measured data at a greater quantitative resolution on a more consistent basis than the visual method can provide. An alternate method being pursued is X-ray computed tomography (CT). It involves X-ray scanning of glass samples, performing CT on the 2-D X-ray images to build 3-D volumetric data, and adaptive segmentation analysis of CT results to not only identify but quantify the distinct regions within each sample based on material density and morphologies. The main advantage of this new method is that it can determine the relative local density of the material remaining in the beaker after the heat treatment regardless of its morphological conditions by selectively excluding all the voids greater than a given volumetric pixel (voxel) size, thus eliminating much of the subjectivity involved in the visual method. As a result, the melt rate data obtained from CT scan will give quantitative descriptions not only on the fully-melted glass, but partially-melted and unmelted feed materials. Therefore, the CT data are presumed to be more reflective of the actual melt rate trends in continuously-fed melters than the visual data. In order to test the applicability of X-ray CT scan to the HLW glass melt rate study, several new series of HLW simulant/frit mixtures were melted in the Melt Rate Furnace (MRF) and the contents of each cooled but un-sectioned beaker were CT scanned and analyzed. For comparison purposes, a cross-sectional X-ray image of each sample was used to estimate the melt rate using the visual method. In order to see the impact of feed chemistry on melt rate more clearly, a total of ten frit-only glasses (i.e., no waste) were also made, CT scanned and analyzed. In addition, two historical glass series which were previously sectioned were re-joined and CT scanned; the results were then compared to the visual data obtained earlier. All the work performed on these historical samples will be documented separately in another report. This report describes the methodologies used to interpret and apply the results of X-ray CT scans to the HLW melt rate study and further highlights some of the key results on the compositional dependence of melt rate and the cross-comparison of the visual and CT results.
The effect of free convection on the dissolution of a spherical particle in a viscous melt
Mise en place d'une equation qui tient compte de la composition et de la densite de la fonte. Etude de l'effet du nombre de Rayleigh sur la cinetique de dissolution