[en] In the U.S. Department of Energy (DOE) complex, 100 million gallons of radioactive and chemical wastes from plutonium production are stored in 281 underground storage tanks. Retrieval of the wastes from the tanks is the first step in its ultimate treatment and disposal. Because billions of dollars are being spent on this effort, waste retrieval demands a strong scientific basis for its successful completion. As will be discussed in Section 4.2, complex interactions among waste chemical reactions, rheology, and mixing of solid and liquid tank waste (and possibly with a solvent) will occur in DSTs during the waste retrieval (mixer pump) operations. The ultimate goal of this study was to develop the ability to simulate the complex chemical and rheological changes that occur in the waste during processing for retrieval. This capability would serve as a scientific assessment tool allowing a priori evaluation of the consequences of proposed waste retrieval operations. Hanford tan k waste is a multiphase, multicomponent, high-ionic strength, and highly basic mixture of liquids and solids. Wastes stored in the 4,000-m3 DSTs will be mixed by 300-hp mixer pumps that inject high-speed (18.3 m/s) jets to stir up the sludge and supernatant liquid for retrieval. During waste retrieval operations, complex interactions occur among waste mixing, chemical reactions, and associated rheology. Thus, to determine safe and cost-effective operational parameters for waste retrieval, decisions must rely on new scientific knowledge to account for physical mixing of multiphase flows, chemical reactions, and waste rheology. To satisfy this need, we integrated a computational fluid dynamics code with state-of-the-art equilibrium and kinetic chemical models and non-Newtonian rheology (Onishi (and others) 1999). This development is unique and holds great promise for addressing the complex phenomena of tank waste retrieval. The current model is, however, applicable only to idealized tank waste conditions-solids are crystals, not hydrates; kinetic rates are fast; the slurry has simple rheology; and the water mass is constant. Thus, this idealized reactive transport model, ARIEL could provide a basis for addressing potentially crippling waste retrieval issues associated with hydrated mineral formation by systematically expanding its modeling capabilities

[en] Integral relations based on boundary layer theory are derived to study the motion of an isolated, two-dimensional thermal plume through a viscous mantle containing polymorphic phase changes. Analytical results are obtained which show that phase transitions alter average mangle convective velocities by less than 50%. In particular we find that the olivine-spinel transition, approximated as univariant, can enhance the circulation velocity of upper mantle convection by 30--40%, while it can enhance the overall amplitude of whole mantle convection by a few percent only. Our calculations demonstrate that a possible endothermic phase change located at 650 km will not prevent deep mantle convection by 30--40%, while it can enhance the overll amplitude of whole mantle convection by a few percent only. Our calculations demonstrate that a possible endothermic phase change located at 650 km will not prevent deep mantle convection unless the Clapeyron slope defining the transition exceeds -0.3 kbar/⁰K. This large value is more than one order of magnitude greater than what has been proposed for the 650-km discontinuity. We then extend the method to include compositional buoyancy and effects of the divariant nature of the olivine-spinel transition. Analysis of the motion of a compositionally buoyant plume (one having an anomalous Mg/Fe ratio relative to the ambient mantle) reveals that the chemical plume locally distorts the transition in a way which contributes buoyancy and enhances convective amplitudes by 10% or less. Finally, we combine thermal and compositional buoyancy to investigate the interaction between a thermochemical plume and a compositionally induced density interface

[en] The principle of local similarity, which has been used to model the two-dimensional boundary layers in the oceanic upper mantle, permits calculation of the temperature, velocity, and stress fields with essentially analytic techniques. Finite difference numerical methods are hard pressed to resolve the detail required by the large variation of viscosity between the lithosphere and the asthenosphere. In this paper the local similarity approximation has been justified by quantitatively evaluating the effect of nonsimilarity due to viscous heating, nonlinear temperature- and pressure-dependent rheology, buoyancy, adiabatic cooling, etc. Nonsimilar effects produce only small modifications of the locally similar boundary layers; important geophysical observables such as surface heat flux and ocean floor topography are given to better than 10% by the locally similar solution. A posteriori evaluations of the term neglected in the boundary layer simplification of the complete equations have been conducted on the locally similar temperature and velocity profiles close to the spreading ridge. The boundary layer models are valid to depths of 100 km at 3 m.y. and 10 km at 0.3 m.y

[en] The principle of local similarity, which has been used to model the two-dimensional boundary layers in the oceanic upper mantle, permits calculation of the temperature, velocity, and stress fields with essentially analytic techniques. Finite difference numerical methods are hard pressed to resolve the detail required by the large variation of viscosity between the lithosphere and the asthenosphere. In this paper the local similarity approximation has been justified by quantitatively evaluating the effect of nonsimilarity due to viscous heating, nonlinear temperature- and pressure-dependent rheology, buoyancy, adiabatic cooling, etc. Nonsimilar effects produce only small modifications of the locally similar boundary layers; important geophysical observables such as surface heat flux and ocean floor topography are given to better than 10% by the locally similar solution. A posteriori evaluations of the term neglected in the boundary layer simplification of the complete equations have been conducted on the locally similar temperature and velocity profiles close to the spreading ridge. The boundary layer models are valid to depths of 100 km at 3 m.y. and 10 km at 0.3 m.y

[en] The effects due to departures from local similarity in steady-state boundary layers ascending through a fluid with strongly variable viscosity are examined with the local-nonsimilarity method. Both the absolute temperature and the hydrostatic pressure appear in the argument of an exponential in the viscosity function. The fluid-dynamical system studied here is that which characterizes plume structures in the Earth's mantle. By means of an iterative approach, two successive nonlinear boundary value problems are solved simultaneously and the errors incurred in the locally similar solutions are then assessed from a comparison between the first (locally similar) and the second level of a system of truncated equations. Three different sources of nonsimilarity have been considered: 1) localized radiogenic hearting within the plume, 2) ambient thermal stratification, 3) pressure dependence of mantle rheology. Of particular interest is an appraisal of the degree of accuracy of the locally similar solutions as a function of viscosity contrast within the boundary layer. For the range of viscosity contrast examined, up to 10₈, the velocity and temperature fields between the first- and second-level solutions differ at most by 20 to 30%, for the rheological parameter values relevant to the Earth's mantle

[en] This paper reports on the characteristics of heat-transfer in strongly time-dependent thermal convection for base-heated, infinite Prandtl number fluids within the Boussinesq approximation. The range of the Rayleigh number studied lies between 5 x 10⁵ and 10⁸. Typically, flows at Rayleigh number around 10⁶ consist of large-scale cells with intermittent boundary-layer instabilities. For Ra greater than 10⁷ the heat-transfer mechanism changes from one, characterized by mushroom-like plumes, to one consisting of disconnected upward rising instabilities. The Nusselt numbers of the time-dependent flows are smaller than the steady-state values. This discrepancy between the steady-state and time-dependent Nusselt numbers increases with Ra and reaches around 30% for Ra = 10⁸

[en] Fully two-dimensional analytic boundary layer solutions are used to model the thermodmechanical structure of the oceanic upper mantle when a shallow horizontal return flow helps balance the lithospheric transport of mass from ridge to trench. The following are all incorporated in the solutions: horizontal and vertical advection of heat, vertical heat conduction, viscous dissipation, adiabatic heating and cooling, buoyancy, and the pressure- and temperature-dependent nonlinear rheology of olivine. Depth profiles of horizontal and vertical velocities, temperature, and shear stress are calculated for several ages of ocean floor. Such solutions are used to construct accurate isotherm and streamline patterns within the rigid lithosphere and high-shear, return flow asthenosphere of the oceanic upper mantle boundary layer. Ocean floor topography is inferred from the thermal contraction of the cooling lithosphere and asthenosphere and from the adverse horizontal pressure gradient required by the dynamics to drive the shallow return flow