Open AccessA Discrete Linear Stability Analysis of Two-dimensional Laminar Flow Past a Square Cylinder
Author(s) -
Nitin Kumar,
Sachin Tejyan,
Sunil Chamoli,
Pawan Kumar Pant
Publication year - 2021
Publication title -
wseas transactions on fluid mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.234
H-Index - 11
eISSN - 2224-347X
pISSN - 1790-5087
DOI - 10.37394/232013.2021.16.11
Subject(s) - reynolds number , laminar flow , mathematics , discretization , lattice boltzmann methods , flow (mathematics) , vortex shedding , vortex , cylinder , potential flow around a circular cylinder , mathematical analysis , mechanics , geometry , open channel flow , physics , turbulence
The present study focuses on the development of a numerical framework for predicting the onset of vortex sheading due to flow past a square cylinder. For this a discrete linear stability analysis framework for two-dimensional laminar flows have used. Initially the frame work is validating by using the analysis of thermal stability of flows in the discrete numerical sense. The two-dimensional base flow for various values of the controlling parameter (Reynolds number for flow past a square cylinder and Rayleigh number for double-glazing problem) is computed numerically by using the lattice Boltzmann method. The governing equations, discretized using the finite-difference method in two-dimensions and are subsequently written in the form of perturbed equations with two-dimensional disturbances. These equations are linearized around the base flow and form a set of partial differential equations that govern the evolution of the perturbations. The eigenvalues, stability of the base flow and the points of bifurcations are determined using normal mode analysis. The eigenvalue spectrum predicts that the critical Reynolds number is 52 for the flow past a square cylinder. The results are consistent with the previous numerical and experimental observations.