Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Impact of non-normality in a local stability analysis of Poiseuille-Rayleigh-Benard flow
Submission Author:
Gabriel Yudi Ragni Hamada , SP
Co-Authors:
Gabriel Yudi Ragni Hamada, William Wolf, Diogo B. Pitz
Presenter: Gabriel Yudi Ragni Hamada
doi://10.26678/ABCM.COBEM2021.COB2021-0097
Abstract
This work presents a temporal local stability analysis of a Poiseuille-Rayleigh-Bénard (PRB) flow, which is important in several industrial applications such as chemical vapor deposition studies and cooling of electronic equipment. The linearized Navier-Stokes equations are solved assuming the Oberbeck-Boussinesq approximation. The wall-normal derivatives appearing in the linearized equations are discretized using a fourth-order finite difference scheme, while a Fourier mode decomposition is used in the streamwise and spanwise directions. Then, the resulting system is solved by a generalized eigenvalue problem. Initially, the modal approach is used to understand the flow stability properties in an infinite time horizon, i.e., following the definition of Lyapunov through analysis of the eigenvalue spectra. Since the modal analysis cannot provide insights of the non-normal properties of the flow, a non-modal approach is also considered. To employ this analysis, it is first necessary to establish an energy norm of the linear operator and, then, rewrite it into the matrix exponential form, which is solved by a singular value decomposition (SVD). Transient growth, resolvent and input-output analyses are employed to understand the flow behavior in a finite time. Results demonstrate that the increase of the non-dimensional parameters such as Reynolds and Rayleigh numbers enhance the effects of energy growth in both transient growth and input-output analyses.
Keywords
Poiseuille-Rayleigh-Benard, Input-Output Analysis, Linear Hydrodynamic Stability, Resolvent Analysis
