Three dimensional flow in a continuous casting mould

Abstract

The study of three dimensional fluid motion is becoming increasingly important to industry. Knowledge of fluid movement not only increases understanding of the particular physical process but often allows changes to be made which optimise the process. The problem of interest in this research was the study of fluid flow in an industrial continuous steel casting machine. This is a device into which molten steel is poured and solid sections withdrawn continuously from the bottom of the caster. The process is one in which fluid flow and heat transfer phenomena are fundamental to the outcome. Slab and bloom caster mould geometries fed by nozzles comprised of two horizontally opposed exit ports form the flow geometry of interest. This method of steel supply to the mould creates two inlet jets of fluid which drive a three dimensional flow structure. Observations from two physical models in the Literature revealed that these jets are comprised of two counter-rotating vortices which stretch through the ports of the Submerged Entry Nozzle (SEN). Understanding of the three dimensional flow structure in the mould and the effect of the inlet rotation on this was one of the primary aims of this research and was investigated utilising a numerical model of the flow. Previous three dimensional numerical models of this flow oversimplified the complex mould inlet and employed questionable representations of the turbulent flow. The work described in this thesis was based on a laminar model, avoiding the associated computation and complexity of turbulence modelling, enabling Iow Reynolds number flow fields to be calculated in fine detail. These revealed the three dimensional structure of the flow and its dependence on SEN internal flows. The flow equations were solved in vorticity vector potential form. This formulation eliminated pressure from the system and guaranteed satisfaction of continuity. Several features of the method required rationalising before adequate solutions could be obtained. The correct boundary conditions on the vector potential, enabling representation of the inlet, were determined. In addition, the use of a Staggered computational mesh in conjunction with careful evaluation of the boundary conditions on vorticity ensured that the calculated vorticity was solenoidal. Convective effects were represented numerically using the QUICK scheme. This scheme was shown to be more accurate than the central difference and upwind schemes whilst maintaining adequate stability for the calculation of laminar mould flow. The vorticity vector potential based mould flow model was validated by comparison with results obtained from a commercial fluid dynamics package (PHOENICS). The vorticity based code provided numerically equivalent velocity fields and generally required less grid points than PHOENlCS to achieve mesh independent results. The bulk of the computational load in evaluating the fluid flow code was associated with numerically resolving the system of linear equations. Techniques were studied for implementing the line relaxation and Samarskii-Andreyev Alternating Direction Implicit (ADI) numerical solution algorithms in shared and local memory parallel computing environments. For the Iine relaxation method the order of operations was altered and alternate slabs of mesh points updated simultaneously to effect parallel execution. This affected the integrity of the original scheme but had no adverse effect on convergence. The Samarskii-Andreyev ADI scheme required no alteration as it is made up of inherently independent substructures. Parallel elements could be relatively small for adequate performance improvement in the shared memory environment, but had to be grouped into larger blocks in the local memory environment. The vorticity vector potential code was implemented in the local memory parallel computing environment using a domain splitting technique to spread the computational load, and adapting the parallel Samarskii-Andreyev algorithm above. This resulted in an efficient parallel algorithm that incurred no performance degradation, in terms of convergence per iteration, relative to the scalar algorithm from which it was derived. Laminar flow in a representative casting mould was investigated using the vorticity based numerical mould model. The mould inlet was specified using a separate numerical model describing flow in the SEN. The appropriateness of calculated mould flow fields was verified by comparison with a low Reynolds number physical model. This was achieved by visually comparing the propagation of dye injected into the flow. At low Reynolds number both simulations showed that the dye streams from the SEN ports split into upward and downward moving components. This is a consequence of jet rotation transporting dye across and up the outside, as well as out, of the port. The effect of the magnitude of this inlet rotation was studied by applying various vorticity fields at the mould inlet assuming a fully developed, fixed inlet velocity profile. This study showed that rotation caused each jet to spread, reducing its momentum, and to deflect downwards on an angle below the horizontal. The effects of other parameters on laminar mould flow were investigated. As mould aspect ratio is increased the three dimensional flow behaviour weakens. Raising the SEN compresses the upper zones of circulation causing SEN jet angle and strength to decrease. The effects of various SEN design parameters were also calculated. The initial jet strength is affected by the peak velocity attained in the SEN bore, this being a function of the flowrate and the bore area. The rate of jet decay can be increased, at least for laminar flow, by raising the speed of the counter rotating vortices, and may be achieved by increasing the velocity gradients and hence vorticity across the SEN pipe flow. This is affected by the width across the port of the SEN. Decreasing this width maximises the appropriate vorticity component. Thus the jet characteristics may be tailored by changing the SEN bore area and aspect ratio. The enhanced understanding of the effect of SEN design parameters on mould flow developed during this study is significant for continuous casting. Engineers may use these simple observations to optimise SEN shape for particular casting requirements.