Abstract

The initial stage of transition phenomena is investigated by numerically solving the complete Navier-Stokes equations for incompressible temporally evolving boundary layer flows on a flat plate. To force transition, the present investigation uses sufficiently small amplitude periodic perturbations at the inflow boundary and asymptotically decaying perturbation velocities and never-ending open boundary conditions at the far-field and outflow boundaries respectively. An initial steady state solution of the Navier-Stokes equation is assumed throughout the computational domain followed by the introduction of disturbances into the flow field. The reaction of this flow to such disturbances is studied by directly solving the Navier-Stokes equations using a highly accurate modal spectral element scheme developed by Niewiadomski [36]. The numerical scheme is recast to simulate our problem by incorporating various numerical algorithms. Furthermore, the computational results are discussed for a test case and several other simulation cases are considered to justify the initial stage of transition process. Finally, a demonstration of the suitability of the three dimensional aspect of the numerical method for the investigation of the temporal development of the two dimensional perturbations in the downstream locations is presented where the results are in fairly close agreement with the known numerical results of Fasel [05]