E.D. Koronaki

Enabling stability analysis of tubular reactor models using PDE/PDAE integrators

Abstract We discuss the construction of computational superstructures enabling time-dependent process simulation codes to perform stability, continuation and bifurcation calculations—tasks in principle not accessible to them—directly. The basis of the approach is the so-called Recursive Projection Method of Shroff and Keller (SIAM Journal of Numerical Analysis 31). We discuss its implementation and performance for the detection of different types of bifurcations (with emphasis on Hopf bifurcations) as well as slight modifications appropriate for index 1 partial differential/algebraic equations (PDAE) simulators. Tests that help discriminate between physical and numerical (spurious) bifurcations detected in the process are discussed and illustrated through the standard example of a tubular reactor with a single irreversible exothermic reaction.

Enabling a commercial computational fluid dynamics code to perform certain nonlinear analysis tasks

Abstract In this work we enable the commercial computational fluid dynamics code Fluent, to successfully trace a complete solution branch, even past turning points. Here the so-called Recursive Projection Method (RPM) is implemented as a computational shell “wrapped” around Fluent, in conjunction with a pseudo-arc-length method for convergence on the unstable branch. The case study is a mixed convection flow in a stagnation point chemical vapor deposition (CVD) reactor. Multiple steady states coexist over a range of inlet Reynolds numbers, due to the competition of the two dominant physical mechanisms: forced and free convection. Continuation on the solution branch reveals a curve consisting of a stable branch, dominated by free convection, followed, past the first turning point, by an unstable branch. Past a second turning point, follows another stable branch dominated by forced convection. Taking the problem a step further, it is augmented with a chemical model describing the deposition of silicon (Si) from silane (SiH 4 ), silylene (SiH 2 ) and hydrogen (H 2 ). The solution branch does not alter since the gas mixture is dilute and the carrier gas, in this case nitrogen (N 2 ), and the precursor, in this case SiH 4 , are of similar molar masses; the concentration differences cannot lead to solutal convection. Results for the mass fraction distribution inside the reactor and the film growth rates are reported in all parts of the solution branch.

Current-induced wave propagation on surfaces of voids in metallic thin films with high symmetry of surface diffusional anisotropy

We report results of a systematic theoretical analysis of the electromigration driven morphological evolution of voids in metallic thin films based on self-consistent numerical simulations according to a fully nonlinear surface transport model that accounts for surface diffusional anisotropy. The analysis focuses on film planes with high symmetry of surface diffusional anisotropy. The simulations indicate that under very low anisotropy strengths, there is indeed the possibility of current driven wave propagation on the void surface. Specifically, surface waves appear prior to film failure over a broad range of electric field strengths: from very weak to quite strong. These interesting phenomena appear only at negative misorientation angles between the electric field direction and fast directions of surface diffusion for very low anisotropy strengths. However, for a slight increase in the anisotropy strength, current-induced wave propagation is observed also in the case of positive misorientation angles.