Efficient tracing and stability analysis of multiple stationary and periodic states with exploitation of commercial CFD software

• Published in: Chemical engineering science Vol. 150; pp. 26 - 34
• Main Authors: Koronaki, E.D., Gakis, G.P., Cheimarios, N., Boudouvis, A.G.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 21-08-2016
• Subjects: CFD software; Chemical vapor deposition; Computation; Computational fluid dynamics; Computer programs; Cylinders; Hopf bifurcation; Mathematical models; Matlab; Multiple solutions; Periodic states; Software; Multiple solutions; Periodic states; CFD software; Hopf bifurcation; Chemical vapor deposition
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/j.ces.2016.04.043

A computational approach is presented that enables commercial Computational Fluid Dynamics (CFD) codes to detect Hopf bifurcations and with necessary adjustments, compute the frequency and amplitude of the periodic orbits that arise from the Hopf point. The proposed computational framework, which combines a homemade Matlab code with Ansys/Fluent, is an extension of a previously presented methodology for the efficient tracing of solution branches that contain turning points. The need for the special attention to periodic orbits springs from recently published results that indicate that time-periodic states occur in industrial-scale Chemical Vapor Deposition (CVD) reactors. Nevertheless the method presented here is not limited to deposition processes; in fact it treats the CFD process model as a “black box” and requires no alteration of the commercial software. To prove the effectiveness of the computational framework, it is implemented here on the benchmark case of laminar flow around a cylinder, where Hopf bifurcations have been identified via eigenvalue analysis. Once the method is validated, it is implemented on a rotating-disk commercial CVD reactor model in the region of parameter space where Hopf points are observed. In both the benchmark and the industrial-scale CVD cases, stable and unstable, stationary and periodic states are computed for the same parameter values.
•Solution branch tracing and stability analysis performed with Fluent.•Benchmark is the 2D flow around a cylinder with known Hopf point.•Application to a CVD reactor model reveals transition to periodic states.•Solution branches of stable and unstable stationary states are computed.•Period and amplitude of periodic states is computed over a range of parameters.