Multiscale modelling of dendrite growth during vacuum arc remelting

Vacuum Arc Remelting (VAR) is the accepted method for producing homogeneous, fine microstructures that are free of inclusions required for rotating grade applications. However, as ingot sizes are increasing INCONEL 718 becomes increasingly susceptible to defects such as freckles, tree rings, and white spots increases for large diameter billets. Therefore, predictive models of these defects are required to allow optimization of process parameters. In this paper, a multiscale and multi-physics model is presented to predict the development of microstructures in the VAR ingot during solidification. At the microscale, a combined stochastic nucleation approach and finite difference solution of the solute diffusion is applied in the semi-solid zone of the VAR ingot. The micromodel is coupled with a solution of the macroscale heat transfer, fluid flow and electromagnetism in the VAR process through the temperature, pressure and fluid flow fields. The main objective of this study is to achieve a better understanding of the formation of the defects in VAR by quantifying the influence of VAR processing parameters on grain nucleation and dendrite growth. In particular, the effect of different ingot growth velocities on the microstructure formation was investigated. It was found that reducing the velocity produces significantly more coarse grains.

A hybrid Laplace transform/finite difference boundary element method for diffusion problems

The solution process for diffusion problems usually involves the time development separately from the space solution. A finite difference algorithm in time requires a sequential time development in which all previous values must be determined prior to the current value. The Stehfest Laplace transform algorithm, however, allows time solutions without the knowledge of prior values. It is of interest to be able to develop a time-domain decomposition suitable for implementation in a parallel environment. One such possibility is to use the Laplace transform to develop coarse-grained solutions which act as the initial values for a set of fine-grained solutions. The independence of the Laplace transform solutions means that we do indeed have a time-domain decomposition process. Any suitable time solver can be used for the fine-grained solution. To illustrate the technique we shall use an Euler solver in time together with the dual reciprocity boundary element method for the space solution

Explicit finite volume modeling of aircraft anti-icing and de-icing

In this paper, a runback water and ice prediction model is extended to anti-icing and thermal de-icing situations. The resulting coupled equations that govern thin-film flow, ice accretion, and heat conduction in the multilayered system substrate-ice-water are solved using an explicit finite volume approach. The procedure is implemented in the three-dimensional icing code ICECREMO2, and both structured and unstructured grids can be considered. Numerical results are presented to compare the present code simulations to some data provided by other ice prediction codes and to show the capabilities of the present numerical tool.

On information rates of time-varying fading channels modeled as finite-state Markov channels

We study information rates of time-varying flat-fading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR lsim 12 dB) and at medium to fast normalized fading rates (0.01 lsim fDT lsim 0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT lsim 0.01.