Papers by Author: Andreas Ludwig

Abstract: As a response to “call for contribution to a numerical problem for 2D columnar solidification of binary alloys” [Bellet et al., Int. J. Therm. Sci., Vol. 48(11)(2009), p. 2013], the macrosegregation in a Pb-18wt.%Sn benchmark casting is numerically studied with a two-phase columnar solidification model developed by the current authors. The studies were done with 2D calculations in response to the call, and a 3D calculation was performed to confirm the consistency with the 2D case. A grid-sensitivity study was done to ensure the reliability and accuracy of the present results. The segregation mechanism due to thermosolutal convection was analyzed and the uncertainties resulting from the inaccurate thermophysical properties, modelling and process parameters are discussed. The numerical model was evaluated by comparison with experiments.

Abstract: In semi condinuous casting of technincal bronze alloys homogenuous microstructure is very important for the assurance of material properties. The improvement of the knowledge about both, thermodynamics of the ternary system Cu-Sn-P and the solidification process is of main interest for the involved industry. To describe solidification of these alloys, the ternary system Cu-Sn-P in the Cu-rich corner is experimentally investigated. DSC measurements, diffusion and annealing experiments have been performed and compared with computational thermodynamics based on the Calphad approach. The so defined thermodynamic information is coupled with solidification simulation. For this, CFD calculations are done with a two phase solidification model including mass, momentum, energy and concentration transfer and applied to semi-continuous casting of technical Bronze alloys. The predicted macrosegregation pattern is in good qualitative agreement with experimentally observed result.

Abstract: This paper deals with the validation of a volume averaged multiphase solidification model based on a benchmark experiment using NH4Cl-H2O as model alloy and Particle Image Velocimetry (PIV) as optical measurement method. For the numerical modelling of the solidification, different phases (e.g. liquid, equiaxed grains and columnar dendrite trunks) have been considered. The mass, momentum, energy conservation and species transport equations for each phase have been solved. The Eulerian-Eulerian model equations have been implemented in the commercial Finite Volume Method based software FLUENT-ANSYS v6.3 using User-Defined Functions (UDF). The mass transfer has been modelled by diffusion controlled crystal growth. The simulation of the NH4Cl-H2O solidification has been numerically investigated as a two-dimensional unsteady process in the cross-section of a 100 x 80 x 10 (mm3) experimental benchmark. Since during the experiment both columnar and equiaxed growth of NH4Cl have been observed, both phenomena have been considered in the simulation. The predicted distribution of the solidification front and the measured thickness of the mushy zone have been compared with the measurements.

Abstract: The present paper deals with the formation of macrosegregation in a benchmark ingot using (Fe-C-Cr) ternary alloy composition. The numerical investigation of complex multiphase phenomena is a difficult study, because the thermophysical properties depend strongly on the temperature, concentration, pressure and chemical composition as well. For the numerical modeling of solidification and melting processes different phases (e.g. liquid, equiaxed crystals and columnar dendrite trunks) have been considered. The mass, momentum, energy conservation and species conservation equations for each phase have been solved. The Eulerian-Eulerian model equations have been implemented in the commercial Finite Volume Method based FLUENT-ANSYS v6.3 CFD software using User-Defined Functions (UDF). The mass transfer has been modelled by diffusion controlled crystal growth by applying an advanced tip tracking algorithm for columnar solidification. The modeling of the grain density transport has been improved. The derivatives of the mass fraction quantities for each component appear in the nucleation rate term. It means that we obtain a new term of the right hand side of the grain density transport equation for using ternary alloy composition. This paper focuses on both the process and simulation parameters and their influence on the macrosegregation formation. The results show that the macrosegregation pattern does not change significantly above a well-chosen number of grid cells, and the computational time could be decreased, when the time step size has been increased.

Abstract: The Electro-Slag-Remelting (ESR) is an advanced technology for the production of components of e.g. high quality steels. In the present study a comprehensive computational model using the VOF technique for the prediction of the slag/pool interface is presented for axisymmetric and steady state conditions. In this model the distribution of the electric current is not constant in time, but is dynamically computed according to the evolution of the slag and steel phase distribution. The turbulent flow, created by the Lorentz and buoyancy forces, is computed by solving the time-averaged mass and momentum conservation equations. The turbulence effect is modelled by using a k-model. Two numerical simulations were performed, one assuming a flat interface, and a second leaving the interface free to find an equilibrium shape. The results are then analysed and compared for both cases.

Abstract: Up to date very few organic substances have been reported that show a non-faceted/non-faceted (nf/nf) peritectic phase diagram in a temperature range suitable for direct observation in a micro Bridgman furnace setup. Sturz et al. [1] and Barrio et al. [2] studied the peritectic phase diagram for the organic model alloy TRIS (Tris(hydroxymenthyl)aminomethane) - NPG (Neopentylglycol). The phase diagram is based on thermal analysis by means of DSC measurements [1, 2] and evaluation of lattice parameters measured with x-ray diffractometry [2]. In the current work we present investigations on the system TRIS – NPG that have been obtained by optical investigations of directional solidification in a micro Bridgman-furnace with various initial alloy concentrations and pulling rates in a fixed temperature gradient. The phase diagram [1, 2] was confirmed by direct comparison of DSC measurements and optical investigations. Furthermore we present in situ observations of solidification in the peritectic region. They show a solidification behavior that was clearly distinguishable from the solidification in hyper- and hypoperitectic regions of the phase diagram.

Abstract: A two-phase volume-averaging model developed for the simulation of the dynamic decomposition and solidification of hypermonotectic alloys was used to study the occurrence of convection phenomena during directional solidification of a hypermonotectic alloy (Al-10 wt.%Bi) under terrestrial condition. The model accounts for nucleation and growth of secondary phase droplets, Marangoni and Stokes forces, solute partitioning, heat release due to decomposition and solidification. It is shown that the appearance and growth of secondary droplets is accompanied with a continuous downwards motion of droplets, which rapidly becomes unstable. After relaxation of this dynamic motion the advancing solidification front freezes in the resulting non-uniform droplet distribution.

Abstract: 3D samples of NH4Cl-H2O solutions were solidified under defined experimental conditions. The occurring melt convection was investigated by Particle Image Velocimetry (PIV). The occurrence of NH4Cl crystals was observed optically and first attempts were made to quantitatively measure its number density, size distribution and sedimentation rate by PIV and Particle Tracking (PT). In order to prove the reproducibility of the results several experimental runs with equal and slightly modified conditions were analyzed.