Three-dimensional free surface modelling in an unstructured mesh environment for metal processing applications

In the casting of metals, tundish flow, welding, converters, and other metal processing applications, the behaviour of the fluid surface is important. In aluminium alloys, for example, oxides formed on the surface may be drawn into the body of the melt where they act as faults in the solidified product affecting cast quality. For this reason, accurate description of wave behaviour, air entrapment, and other effects need to be modelled, in the presence of heat transfer and possibly phase change. The authors have developed a single-phase algorithm for modelling this problem. The Scalar Equation Algorithm (SEA) (see Refs. 1 and 2), enables the transport of the property discontinuity representing the free surface through a fixed grid. An extension of this method to unstructured mesh codes is presented here, together with validation. The new method employs a TVD flux limiter in conjunction with a ray-tracing algorithm, to ensure a sharp bound interface. Applications of the method are in the filling and emptying of mould cavities, with heat transfer and phase change.

Approximation Algorithms for a Symmetric Quadratic Knapsack Problem and its Scheduling Applications

We consider a knapsack problem to minimize a symmetric quadratic function. We demonstrate that this symmetric quadratic knapsack problem is relevant to two problems of single machine scheduling: the problem of minimizing the weighted sum of the completion times with a single machine non-availability interval under the non-resumable scenario; and the problem of minimizing the total weighted earliness and tardiness with respect to a common small due date. We develop a polynomial-time approximation algorithm that delivers a constant worst-case performance ratio for a special form of the symmetric quadratic knapsack problem. We adapt that algorithm to our scheduling problems and achieve a better performance. For the problems under consideration no fixed-ratio approximation algorithms have been previously known.

Microwave curing of thermosetting polymer materials in microelectronics applications

Thermosetting polymer materials are widely utilised in modern microelectronics packaging technology. These materials are used for a number of functions, such as for device bonding, for structural support applications and for physical protection of semiconductor dies. Typically, convection heating systems are used to raise the temperature of the materials to expedite the polymerisation process. The convection cure process has a number of drawbacks including process durations generally in excess of 1 hour and the requirement to heat the entire printed circuit board assembly, inducing thermomechanical stresses which effect device reliability. Microwave energy is able to raise the temperature of materials in a rapid, controlled manner. As the microwave energy penetrates into the polymer materials, the heating can be considered volumetric – i.e. the rate of heating is approximately constant throughout the material. This enables a maximal heating rate far greater than is available with convection oven systems which only raise the surface temperature of the polymer material and rely on thermal conductivity to transfer heat energy into the bulk. The high heating rate, combined with the ability to vary the operating power of the microwave system, enables the extremely rapid cure processes. Microwave curing of a commercially available encapsulation material has been studied experimentally and through use of numerical modelling techniques. The material assessed is Henkel EO-1080, a single component thermosetting epoxy. The producer has suggested three typical convection oven cure options for EO1080: 20 min at 150C or 90 min at 140C or 120 min at 110C. Rapid curing of materials of this type using advanced microwave systems, such as the FAMOBS system [1], is of great interest to microelectronics system manufacturers as it has the potential to reduce manufacturing costs, increase device reliability and enables new device designs. Experimental analysis has demonstrated that, in a realistic chip-on-board encapsulation scenario, the polymer material can be fully cured in approximately one minute. This corresponds to a reduction in cure time of approximately 95 percent relative to the convection oven process. Numerical assessment of the process [2] also suggests that cure times of approximately 70 seconds are feasible whilst indicating that the decrease in process duration comes at the expense of variation in degree of cure within the polymer.

Three-dimensional free surface modelling in an unstructured mesh environment for metal processing applications

In the casting of metals, tundish flow, welding, converters, and other metal processing applications, the behaviour of the fluid surface is important. In aluminium alloys, for example, oxides formed on the surface may be drawn into the body of the melt where they act as faults in the solidified product affecting cast quality. For this reason, accurate description of wave behaviour, air entrapment, and other effects need to be modelled, in the presence of heat transfer and possibly phase change. The authors have developed a single-phase algorithm for modelling this problem. The Scalar Equation Algorithm (SEA) (see Refs. 1 and 2), enables the transport of the property discontinuity representing the free surface through a fixed grid. An extension of this method to unstructured mesh codes is presented here, together with validation. The new method employs a TVD flux limiter in conjunction with a ray-tracing algorithm, to ensure a sharp bound interface. Applications of the method are in the filling and emptying of mould cavities, with heat transfer and phase change.