Signature of linear instability in transition zone measurements in boundary layer

Abstract

The hydrodynamic stability and transition in the boundary layer over a flat plate is a largely discussed topic and various researches have been done on the same with fairly accurate results. This is an important area of research because it can be used to approximate boundary layer over streamlined objects with very large radius of curvature, like airfoils. For such approximations, the development of boundary layer in favorable as well as adverse pressure gradients has to be thoroughly studied. Transition to turbulence is a result of growth of instabilities in the transition region. Hydrodynamic stability of laminar boundary layer when developed in the mathematical framework gives us insight into the wavenumber and frequency of unstable modes, which are responsible for transition. Because of its stochastic nature, it is impossible to develop a mathematical theory for transition zone, and therefore, we rely on experimental measurements and numerical simulations. In this work, we studied the relation between laminar instability and transition measurements. We then studied zero and adverse pressure gradient boundary layers to establish the connection. Orr-Sommerfeld equation deals with instability in parallel flows when the instabilities are in its linear stage. This equation is solved using Chebychev collocation method to determine the most unstable modes. We measured the transient wall pressure in the transition zone to establish a direct relation with laminar instability wave characteristics. Primary results indicate that the relation is prominent in adverse pressure gradient boundary layers, while it is obscured in Blassius boundary layers.