METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 27B, DECEMBER 1996—1015 A One-Phase Model of the Mixing of Al-SiC Composite Melt D. KOCAEFE and R.T. BUI Good mixing of silicon carbide (SiC) particles with liquid aluminum is an important component of the fabrication process of Al-SiC composites and the casting of mechanical parts from composite melts. A one-phase flow model has been built in which the mixture is considered as one fluid, and the SiC flow is differentiated from the main mixture flow by a slip velocity, calculated from the balance of forces exerted on the particles. The impeller blades’ action on the fluid is seen as a quadratic source of momentum. Sedimentation is simulated by imposing an increased viscosity on the fluid and setting gravity to zero once the SiC volume fraction reaches a critical value. The model is first applied to a water-SiC system for which some experimental data exist permitting a validation of the model. It is then applied to a Al-SiC system for which some parameter studies are carried out. Compared to the two-phase flow model published earlier, this one-phase model offers two advantages: it takes much less computing time and can accommodate a distribution of particle sizes instead of being limited to one size. I. INTRODUCTION REINFORCING aluminum with particulate materials such as silicon carbide (SiC) particles yields composites with improved mechanical properties that enhance its in- dustrial use at relatively low cost. Thus, high strength, high modulus, and high wear resistance are obtained as com- pared to conventional aluminum alloys. The quality and reliability of the composite depend on the uniform distribution of the particles inside the metal matrix. Particles, however, tend to settle due to density dif- ference. Mixing is therefore a critical part of the composite manufacturing and casting process. Mathematical models properly built and duly validated can serve as tools to improve or optimize the mixing pro- cess. This helps significantly reduce the experimental work in either real or pilot furnaces and, consequently, the cost of design. In a previous study, a steady-state, two-phase model was developed [1] to simulate the mixing of Al-SiC melts. The general-purpose fluid-dynamics code PHOENICS (CHAM Ltd., London) was used [2] for the solution of the two-phase problem. PHOENICS is based on the finite volume method in which the physical domain to be computed is discretized into small volumes referred to as ‘‘cells.’’ In that two-phase model, liquid aluminum was the first phase, whereas the SiC had a particle size small enough to be treated as a second phase. It was assumed that the par- ticles behave as a nonviscous continuous phase until a crit- ical value of solid concentration is reached; at this point, the viscous term of the solid-phase momentum equation is reactivated, a high viscosity is assigned to the solid phase, and gravity is set to zero in order to simulate the sedimen- tation. No interphase mass transfer is assumed to occur, whereas an interphase momentum transfer takes place through a drag force exerted by the liquid on the particles. The two-phase approach called for the solution of two sets of momentum equations and a volume fraction equation. D. KOCAEFE and R.T. BUI are Professors with the Department of Applied Science, Universite ´ du Que ´bec a ` Chicoutimi, Chicoutimi, P.Q. Canada, G7H2B1. Manuscript submitted June 14, 1995. The required computing time on the HP* 730 was over 16 *HP is a trademark of Hewlett-Packard Company, Colorado Springs, CO. hours for each simulation. This long computation is due to the large number of equations to be solved simultaneously. The present work is motivated by the often expressed need to decrease this time to make the model more suitable for industrial use. In this work, a one-phase model is developed. It treats the mixture of liquid and solid as one single continuous medium. The main advantage is that only one set of mo- mentum transfer equations is to be solved together with the mass fraction equations for the particles; as a consequence, less computing time is required, thus making it possible in practice to do several simulation runs required, for example, in parametric studies which constitute indeed an important class of industrial application problems. There is the need to differentiate the solid flow from the main flow of the mixture; this is done by determining a slip velocity, i.e., the relative velocity of the solid particles with respect to the mixture surrounding them. Slip velocity is determined by an algorithm referred to as the algebraic slip model (ASM) incorporated in PHOEN- ICS. [3] A description of this algorithm will be given later when the model is presented. A first version of the present work was recently presented at a conference, [4] with emphasis on the general modeling concept and some of the results obtained. The present ar- ticle reports on improvements that were since brought to the mathematical model and focuses on the physical impli- cations of the assumptions made in the modeling work, as well as the predictive capabilities of the model. II. THE PHYSICAL SYSTEM Figure 1(a) shows the geometry of the rectangular mix- ing tank to be modeled. It is equipped with three flat-blade impellers, tilted at 17 deg and placed close to the tank bottom. The speed and direction of rotation of each impeller can be changed.