Marek Rebow

Combined Analytical and Numerical Front Tracking Approach to Modeling Directional Solidification of a TiAl-Based Intermetallic Alloy for Design of Microgravity Experiments

A three-step combined analytical and numerical approach to thermal modelling of a two-heater power-down furnace for controlled directional solidification of an intermetallic alloy is proposed. An analytical sensitivity analysis of the thermal model is carried out to show the effect of adiabatic zone length, and both hot-zone and cold-zone heater temperatures, on the initial thermal gradient in the sample and on the length of melt in the adiabatic zone. The subsequent axisymmetric front tracking method (FTM) simulations of directional solidification of a binary intermetallic Ti-46at.%Al alloy show that temperature gradient in the melt declines and velocity of the solid-liquid front increases with time, thus promoting good conditions for a columnar to equiaxed transition. The proposed analytical calculations combined with full-scale numerical FTM simulations provide a convenient and predictive optimization tool for the two-heater power-down furnace design and growth conditions for the future microgravity experiments.

A Front Tracking Model for Transient Solidification of Al–7wt%Si in a Bridgman Furnace

The Bridgman furnace is widely used in industry and research. This paper outlines a working one-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 Al–7wt%Si. The results show how the evolution of temperature distribution, thermal history, and front position are affected by a step change in pulling velocity.

The development of a microgravity experiment involving columnar to equiaxed transition for solidification of a Ti-Al based alloy

The authors are members of the integrated project Intermetallic Materials Processing in Relation to Earth and Space Solidification (IMPRESS), funded within the European Framework (FP6). One of the aims of IMPRESS is to develop new alloys and processes for the casting of TiAl-based turbine blades for the next generation of aero and industrial gas turbine engines. Within IMPRESS, two related issues have been identified during the primary solidification stage, namely, segregation and the columnar-to-equiaxed transition (CET). The authors have set out to isolate the effects of thermo-solutal convection, by designing a microgravity experiment to be performed on a European Space Agency platform. This experiment will investigate the CET formation during solidification. It is planned to use a sounding rocket providing a microgravity time of approximately twelve minutes. The results of this microgravity solidification experiment will be used as unique benchmark data for development and validation of new computational models of TiAl solidification. This in turn will produce accurate models and ultimately new robust industrial processes by project partners in the aerospace industry. The evolution of the design of the microgravity experiment is discussed and the results of preliminary ground reference experiments are presented. Future plans and objectives for the project are also highlighted.

A front tracking model of the MAXUS-8 microgravity solidification experiment on a Ti-45.5at.% Al-8at.%Nb alloy

On 26th March 2010 the MAXUS-8 sounding rocket was launched from the Esrange Space Center in Sweden. As part of the Intermetallic Materials Processing in Relation to Earth and Space Solidification (IMPRESS) project, a solidification experiment was conducted on a Ti-45.5at.%Al-8at.%Nb intermetallic alloy in a module on this rocket. The experiment was designed to investigate columnar and equiaxed microstructures in the alloy. A furnace model of the MAXUS 8 experiment with a Front Tracking Model of solidification has been developed to determine the macrostructure and thermal history of the samples in the experiment. This paper gives details of results of the front tracking model applied to the MAXUS 8 microgravity experiment. A model for columnar growth is presented and compared to experimental results for furnace A of the experiment module.

Economic Risk Assessment Using the Fractal Market Hypothesis

This paper considers the Fractal Market Hypothesis (FMH) for assessing the risk(s) in developing a financial portfolio based on data that is available through the Internet from an increasing number of sources. Most financial risk management systems are still based on the Efficient Market Hypothesis which often fails due to the inaccuracies of the statistical models that underpin the hypothesis, in particular, that financial data are based on stationary Gaussian processes. The FMH considered in this paper assumes that financial data are non-stationary and statistically self-affine so that a risk analysis can, in principal, be applied at any time scale provided there is sufficient data to make the output of a FMH analysis statistically significant.

A data centre air flow model for predicting computer server inlet temperatures

Data centres account for approx. 1.3% of the worlds electricity consumption, of which up to 50% of that power is dedicated to keeping the actual equipment cool. This represents a huge opportunity to reduce data centre energy consumption by tackling the cooling system operations with a focus on thermal management. This work presents a novel Data Centre Air Flow Model (DCAM) for temperature prediction of server inlet temperatures. The model is a physics-based model under-pinned by turbulent jet theory allowing a reduction in the solution domain size by using only local boundary conditions in front of the servers. Current physics-based modeling approaches require a solution domain of the entire data centre room which is expensive in terms of computation even if a small change occurs in a localized area. By limiting the solution domain and boundary conditions to a local level, the model focuses on the airflow mixing that affects temperatures while also simplifying the related computations. The DCAM model does not have the usual complexities of numerical computations, dependencies on computational grid size, meshing or the need to solve a full domain solution. The input boundary conditions required for the model can be supplied by the Building Management System (BMS), Power Distribution Units (PDU), sensors, or output from other modeling environments that only need updating when significant changes occur. Preliminary results validated on a real world data centre yield an overall prediction error of 1.2° C RMSE. The model can perform in real-time, giving way to applications for real-time monitoring, as input to optimize control of air conditioning units, and can complement sensor networks.

Two-dimensional Schrodinger Scattering and Electron Transport in Graphene

Two-dimensional Born scattering for the non-relativistic case is considered, the purpose being to investigate electron transport properties in mono-layer Graphene subject to an applied parallel electric eld. Solutions for the Probability Density Current (PDC) are obtained in the Fresnel zone which provides a model for simulating the PDC subject to membrane crumpling. In this context a Random Fractal Defect Model is considered which is used to assess the eect of (Fractal) crumpling on the PDC.