Showing papers on "Mixture theory published in 1991"

Modeling of dendritic solidification systems: Reassessment of the continuum momentum equation and application to solidification of a lead-tin alloy

Abstract: In recent years there has been renewed interest in modeling transport phenomena associated with the dendritic solidification of binary mixtures. Solidification occurs in a two-phase (mushy) region characterized by complex, solid-liquid interfacial geometries, and development of a model which is amenable to solution dictates the use of continuum (mixture theory) assumption and/or volume-averaging procedures. A review of the recent literature would suggest that solidification models developed from mixture theory assumptions are less valid and less general than similar models based on volume-averaging, particularly with regard to the respective momentum equations which describe interdendritic fluid flow. In this report, these different approaches are shown to yield identical macroscopic conservation equations, and the continuum momentum equation is reconsidered in an effort to reconcile matters which have lead to confusion about the validity of the continuum model. Consistency between recently presented momentum equations is demonstrated. Using a continuum model for conservation of total mass, momentum, energy and species, numerical simulations of a binary metal alloy (Pb-Sn) undergoing solidification phase-change are performed. The system is contained in an axisymmetric, annular mold, which is cooled along its outer vertical wall. Results show that thermosolutal convection in the melt and mush zones is strongly coupled landmore » that macrosegregation is reduced with increased cooling rate. For low cooling rates, solutally induced convection in the mushy zone favors the development of channels, which subsequently spawn macrosegregation in the form of A-segregates. With increasing solidification rate, however, thermosolutal interactions in the melt contribute to reducing the formation of channels and A-segregates. 61 refs., 14 figs., 1 tab.« less

Physics-Based Models of Snow

Abstract: This chapter is a review of current physics-based techniques for modeling snowmelt Mixture theory is used to develop the equations of conservation of mass, momentum and energy for snow treated as a two-component, three-phase mixture of ice, water, water vapor, and air The constitutive laws and boundary conditions required to complete a general snowmelt model are then described, with particular attention to the energy balance at the upper boundary of a snowpack

High-Order Mixture Homogenization of Fiber-Reinforced Composites

Abstract: : An asymptotic mixture theory of fiber-reinforced composites with periodic microstructure is presented for rate-independent inelastic responses, such as elastoplastic deformation. Key elements are the modeling capability of simulation critical interaction across material interfaces and the inclusion of the kinetic energy of microdisplacement. The construction of the proposed mixture model, which is deterministic, instead of phenomenological, is accomplished by resorting to a variational approach. The principle of virtual work is used for total quantities to derive mixture equations of motion and boundary conditions, while Reissner's mixed variational principle (1984, 1986), applied to the incremental boundary value problem yields consistent mixture constitutive relations. In order to assess the model accuracy, numerical experiments were conducted for static and dynamic loads. The prediction of the model in the time domain was obtained by an explicit finite element code. DYNA2D is used to furnish numerically exact data for the problems by discretizing the details of the microstructure. On the other hand, the model capability of predicting effective tangent moduli was tested by comparing results with NIKE2D. In all cases, good agreement was observed between the predicted and exact data for plastic, as well as, elastic responses. Keywords: Fiber reinforced composites; Mixture theory; Structural properties. (kt)

Steady flow of a fluid-solid mixture between parallel plates

Abstract: In Part I, a mathematical description for a flowing mixture of solid particulates and a fluid is developed within the context of Mixture Theory. Specifically, the equations governing the flow of a two-component mixture of a Newtonian fluid and a granular solid are derived. These relatively general equations are then reduced to a system of coupled ordinary differential equations describing steady flow of the mixture between flat plates. The resulting boundary value problem is solved numerically and results are presented for cases in which drag and lift interactions are important. Part II gives an overview of the methods used to obtain the numerical solutions. Multiple shooting, finite difference, and collocation methods for solving boundary value problems involving ordinary differential equations are discussed. A method for applying integral boundary conditions is then presented. Finally, the relative efficiency and effectiveness of the methods is discussed.

Steady flow of a fluid-solid mixture in a circular cylinder

Abstract: A mathematical description for a flowing mixture of solid particulates and a fluid similar to a coal-water slurry, is developed within the context of Mixture Theory. Specifically, the equations governing the flow of a two-component mixture of a Newtonian fluid and a granular solid are derived. These relatively general equations are then reduced to a system of coupled ordinary differential equations describing steady flow of the mixture through a pipe. The resulting boundary value problem is solved numerically and results are presented for cases in which drag and lift interactions are important. 44 refs.

Thermomechanical Behavior of Anisotropic Inelastic Composites: A Micromechanical Theory

Abstract: The first section of this paper deals with thermomecanical relations, the second with a first order mixture theory used for the micromechanical determination of the stiffness tensor of a metal matrix composite, the third with the discrepancies between analytical and calculated values