The Bridgman furnace is widely used in industry and research. This paper outlines a working 1-dimensional model for tracking the columnar solidification front in a Bridgman furnace where the pulling velocity, and hence front position, change as a function of time. The front tracking model is applied to a fixed grid of control volumes using an explicit numerical finite difference scheme to solve the heat equation over a finite domain. The model is demonstrated by way of a notional scenario, namely, Bridgman furnace solidification of a 16-mm diameter rod of Al7wt.%Si. The results show how the evolution of temperature distribution, thermal history, and front position are affected by a step change in pulling velocity.

Direct measurement of heat flux and heat transfer coefficients in a Bridgman furnace is not always possible using traditional methods. This study characterised a vertical tubular Bridgman furnace using experimental data so that the estimated heat flux and heat transfer coefficients may be used in simulations of future experiments using the same furnace. An experimental-numerical method is presented where a discrete proportional integral derivative controller manipulates the radial heat flux in a front tracking solidification model so that the output temperature profile matches experimental data. The method is applicable for other experimentalists and modellers and its usefulness is demonstrated by example. Highlights A combined experimental-numerical method to estimate heat flux and heat transfer coefficients in a Bridgman furnace is outlined in detail.  The inverse heat transfer problem is solved using a discrete proportional integral derivative controller in series with a front tracking solidification model.  The usefulness of the method is demonstrated by example.

During casting often a dendritic microstructure is formed, resulting in a columnar or equiaxed grain structure, or leading to a transition from columnar to equiaxed growth (CET). Especially the detailed knowledge of the critical parameters for CET is important, because the microstructure determines significantly the materials properties. To provide unique data for testing of fundamental theories of grain and microstructure formation, solidification experiments in microgravity environment were performed within the ESA MAP project CETSOL. Reduced gravity allows for pure diffusive solidification conditions, i.e., suppressing melt flow and sedimentation and floatation effects. On-board the International Space Station ISS Al-7wt%Si alloys with and without grain refiners were solidified in different temperature gradients and with different cooling conditions. Detailed analysis of the microstructure and the grain structure showed columnar growth in case of non-refined alloy. CET was detected 2 only for refined alloys, either as a sharp CET in case of a sudden increase of the solidification velocity, or as a progressive CET in case of a continuous decrease of the temperature gradient. The unique experimental data were used for numerical modelling of CET with three different approaches: (i) a front tracking model using an equiaxed growth model, (ii) a 3D CAFE model, (iii) a 3D dendrite needle network (DNN) method. Each model allows predicting the columnar dendrite tip undercooling and the growth rate with respect time. Furthermore, the positions of CET and the spatial extent of the CET, being sharp or progressive, are in reasonably good quantitative agreement with experimental measurements.

Columnar to equiaxed transition (CET) was studied in a peritectic TiAl-based alloy with chemical composition Ti-45.1Al-4.9Nb-0.25C-0.2B (at.%). Solidification experiments were conducted in a Bridgman-type apparatus using cylindrical moulds made of high-purity Y2O3. The methodology containing appropriate etching and observations under flat light in stereo-microscope was used to identify the morphology of primary β phase grains and position of CET in the samples˰ All samples prepared by power down-technique showed sharp CET. The position of the CET measured from the beginning of the sample depends on the applied cooling rate and increases from approximately 65 to 115 mm by decreasing cooling rate from 50 to 15 K/min. Based on terrestrial experiments, the future work focused on microgravity and hypergravity CET experiments and numerical modeling is proposed. A Bridgman furnace front tracking method will be applied in future work to complement the experimental results here as part of the European Space Agency GRADECET programme. This modeling will input directly into planned microgravity and hypergravity CET experiments.

TiAl alloys are of interest to the aerospace and automotive industries (particularly for engine components) on account of their relatively low density and good mechanical properties at high temperatures. Processing routes involve melting and solidification of the alloy and require knowledge about the solidification morphology and microstructural texture evolution in the component. Among others, the Columnar-to-Equiaxed Transition (CET) of bcc β(Ti) dendrites is an issue of current interest. This article examines the results from solidification experiments where a combined Bridgman and power-down technique was implemented at four different cooling rates, using cylindrical samples of the TiAl alloy: Ti-45.5Al-4.7Nb-0.2C-0.2B (all at.%). Axial CET was observed in one of the samples and axial columnar to radial columnar microstructural transitions were observed in the others. A Bridgman Furnace Front Tracking Model (BFFTM), tailored specifically for use with the experiment apparatus, was used to estimate the transient thermal conditions and columnar growth conditions for CET and other microstructural transitions. An important link, due to the nature of the power-down technique, between the reversal of radial heat flow in the hot zone of the furnace and unwanted radial columnar growth, is explained using the model. Recommendations are made on how to avoid such growth, viz. use of low cooling rates and large sample diameters. K e y w o r d s : power-down technique, Bridgman furnace, gamma titanium aluminide, columnar to equiaxed transition, radial growth Nomenclature Across sectional area (mm 2) c-specific heat capacity at constant pressure (J kg −1 • C −1) C 0-original alloy composition (at.%) E-latent heat generated per unit volume (W m −3) G-axial temperature gradient (• C mm −1) h-heat transfer coefficient (W m −2 • C −1) p-perimeter (mm) Q-heat flow (W) r-radius (mm) t-time (s) T-temperature (• C) u-pulling rate (mm s −1) V tip-growth rate (mm s −1) x-axial position (mm) X-axial position with respect to the columnar dendrite tip (mm) ∆T tip-dendrite tip undercooling (• C) ρ-density (kg m −3) Sub-scripts H-hot zone l-liquidus s-solidus tip-dendrite tip ∞-infinity (far away)