Global stability analysis of spatially developing boundary layers

by Ramesh BhoraniyaPh.D

Evaluation of the outflow boundary conditions for Bi-Global stability analysis of axisymmetric boundary layer

The numerical solution of the Bi-Global stability problem in the axisymmetric boundary layers required boundary conditions in the axial and radial directions. It is very dif- ficult to impose physically meaningful boundary conditions in the streamwise direction at inflow and outflow. The twodimensional eigenvalue problem is considered for the BiGlobal stability analysis of the axisymmetric boundary layer. The extrapolated boundary conditions are imposed as an outflow condition with the Homogeneous Dirichlet conditions at the inflow boundary. The temporal and spatial properties are computed with the linear, quadratic and cubic order of extrapolation at the outflow boundary condition. The Linear extrapolation yields the largest temporal and spatial growth than that of quadratic and cubic extrapolation.by Ramesh Bhoraniya and Vinod Narayana

Global stability analysis of axisymmetric boundary layers

Global stability analysis of axisymmetric boundary layers RAMESHKUMAR BHORANIYA, VINOD NARAYANAN, Mechanical Engineer- ing, Indian Institute of Technology, Gandhinagar, India — Global stability analysis of the axisymmetric boundary layer flow explores the stability features of a nonpar- allel flow. Consider an incompressible flow past a cylinder, where flow direction is parallel to the axis of cylinder. The ensuing boundary layer is axisymmetric but non-similar. Due to the boundary layer growth, the velocity profile is two dimen- sional. This work aims to understand the nonparallel effects of an axisymmetric boundary layer using a biglobal stability analysis. The linearized biglobal stability equations are derived in polar cylindrical coordinates. The resulting stability equa- tions along with boundary conditions form an eigenvalue problem, which is solved using Chebyshev spectral collocation method. Arnoldi’s algorithm is used to com- pute selective eigenvalues and eigenfunctions. The results show that the nonparallel effects are considerable at very moderate Reynolds numbers. More detailed results will be presented at the time of conferenceby Rameshkumar Bhoraniya and Vinod Narayana