Simulation of interfacial instabilities during solidification-I. Conduction and capillarity effects

A combined Eulerian-Lagrangian numerical method is developed for simulating deformed interfaces arising in the solidification of pure materials. The interface tracking procedure employs marker particles and is the Lagrangian component of the calculation. The field equations are solved in a fixed Eulerian framework, so that the interface passes through the grid layout. Information from the explicitly tracked interface is used to apply boundary conditions at the exact interface location in each computational cell, in contrast with other Eulerian schemes. Consistent with the the established theory, in the absence of surface tension, the present simulations result in different types of behavior such as tip-splitting and cusp formation. For low surface tensions, due to the lack of physical length scales, the solutions are qualitatively affected by grid resolution with no unique solution available. In contrast, with substantial surface tension values the initial perturbation grows to form long fingers. The finger shapes reflect the stabilizing effects of capillarity. Unique solutions can be reached with nonzero surface tension. © 1995

Modeling solidification processes at morphological scales

The goal of the research detailed herein is to develop a theoretical model capable of predicting heat and mass transport during the solidification process and their effects on morphological development at the phase boundaries and on macrosegregation. The issue of scaling and its implication on modeling and experimentation is addressed. To complement a macroscopic model recently developed to account for the interaction between phase change and transport processes including turbulence effects, a microscopic model at the morphological scale is presented here. The model tracks the development of the interface explicitly with the inclusion of surface tension, supercooling, and local convection effects, and yields information on the solidification characteristics resulting from their interaction. The model presented here will be a major component for developing a comprehensive model containing the important mechanisms at both macroscopic and microscopic levels

Grid-supported marker particle scheme for interface tracking

A methodology is presented to simulate the growth and interaction of unstable fronts. Such fronts are found to be important in instabilities arising in several natural and industrial processes, such as solidification, spray dynamics, and bubble growth. The numerical simulation of such phenomena is challenging on account of the highly distorted moving boundary at which, often, curvature-dependent boundary conditions need be applied in each phase. Herein is presented a numerical technique to capture highly distorted interfaces. The interface is represented employing marker particles. Joining successive markers with circular arcs yields values of curvatures and normals on the interface. The markers are followed over an underlying Cartesian grid and new marker particles are generated at each time step by an intersection procedure. The issue of mergers of interfaces is also attacked and use of cells permits the simulation of merger-breakup processes. Thus, the method presented here, unlike previous marker particle-based schemes, can handle particle depletion/accumulation and merger/breakup issues with good accuracy. Results are presented, employing velocity functions modeled to mimic the actual instability phenomena, to demonstrate the accuracy and capability of the scheme developed

ELAFINT: a computational method for fluid flows with free and moving boundaries

A computational technique called ELAFINT has been developed to handle the existence of highly deformed moving and free boundaries. These boundaries or interfaces cut through an underlying cartesian grid, leading to irregularly shaped control volumes in the vicinity of the interface. Also, a method to reassemble these control volumes to maintain flux conversion has been designed, and the accuracy of the methods at each stage of the development assessed. Currently highly deformed, moving interfaces with phase change can be tracked in conjunction with an implicit pressure-based Navier-Stokes equation solver. This methodology can be applied to solve fluid flow problems in complex geometries

Optimal cure cycles for thermoset composites manufacture

This paper addresses the problem of determining time-optimal cure cycles for the manufacture of thermoset composites. The cure cycle is considered to be a series of heating and cooling zones, and the optimal values of the end-point temperature and duration of each zone are obtained using numerical optimization techniques, combined with a process model to simulate the cure. The optimal cure schedules incorporate constraints on the maximum material temperatures, the maximum heating and cooling rates, and the maximum difference in the temperatures across the composite cross section. The optimization results are shown to improve significantly upon the cure cycles recommended in the literature and by the manufacturers. Parametric studies are presented in terms of dimensionless groups in order to assess the effects of the product and process variables on the optimal cure cycles

A high accuracy sequential solver for simulation and active control of a longitudinal combustion instability

A high accuracy convection scheme using a sequential solution technique has been developed and applied to simulate the longitudinal combustion instability and its active control. The scheme has been devised in the spirit of the TVD concept with special source term treatment. Due to the substantial heat release effect, a clear delineation of the key elements employed by the scheme, i.e. the adjustable damping factor and the source term treatment has been made. By comparing with the first-order upwind scheme previously utilized, the present results exhibit less damping and are free from spurious oscillations, offering improved quantitative accuracy while confirming the spectral analysis reported earlier. A simple feedback type of active control has been found to be capable of enhancing or attenuating the magnitude of the combustion instability. © 1993

Scaling procedure and finite volume computations of phase-change problems with convection

In this paper, solidification problems are investigated from two angles, namely, the issue of wide disparity of important length scales present in phase change processes, and the finite volume based computational techniques developed to simulate such processes. To appropriately handle phase change phenomena, a scaling analysis is presented to bring out the relevant physics at the macroscopic and morphological scales. It is demonstrated that an appropriate choice of the scale is necessary to obtain numerical solutions economically. Two different finite volume techniques are described in this paper. The first technique involves a mixed Eulerian/Lagrangian approach, where the interface is explicitly tracked by means of marker particles, and the field equations are solved on an underlying fixed, finite volume grid. The other approach is an enthalpy model which incorporates the interface information in a field variable called the phase-fraction. This volume averaged technique enables the implicit handling of the interface as part of the solution procedure at the cost of smearing out the discontinuity. Two different phase-fraction update techniques are presented and their relative effectiveness and performance discussed. A continuous ingot casting problem modelled by accounting for the interaction of phase-change and turbulent transport is also presented and compared with experimental results. © 1995

Adaptive unstructured grid for three-dimensional interface representation

Moving-boundary problems arise in numerous important physical phenomena, and often form complex shapes during their evolution. The ability to track the interface in such cases in two dimensions is well established. However, modifying the grid representing the interface as it evolves in three-dimensional space introduces additional issues. In the current work, three-dimensional interfaces are represented by adaptive unstructured grids. The grids are restructured and refined based on the shape and size of the triangular elements in the grid that forms the interfaces. As the interface deforms, points are automatically added to ensure that the accuracy of interface representation remains consistent. Results are presented to show how complex interface features, including surface curvatures and normals, can be captured by modifying an existing method that uses an approximation to the Dupin indicatrix

Control of longitudinal oscillations in a constant area combustor: Numerical simulation

The phenomenon of combustion driven oscillations has long held the interest of scientists and engineers. In the present model, instead of specifying the unsteady heat release at every point in time and space, the heat release rate at the gutter is coupled directly to the velocity fluctuation with a time delay incorporated in it. The transport of this heat is modeled through a heat convection and the heat release at the downstream locations calculated. This way, the fluid dynamic and combustion mechanisms are treated in a coupled and nonlinear manner