Stability Analysis of Boundary Layer Fluid Flow Under Variable Pressure Gradients
Keywords:
Boundary Layer Flow, Stability Analysis, Pressure Gradient, Similarity Solution, Laminar FlowAbstract
This study is a mathematical exploration of the stability properties of two-dimensional laminar flow in the boundary layers under the conditions of variable pressure gradient. Flow of an incompressible Newtonian fluid over a flat plate is taken into consideration and the governing boundary layer equations are developed under the usual considerations of the boundary layers. With a power-law change of the external velocity, similarity transformations are used to simplify the governing partial differential equations to the Falkner Skan type ordinary differential equation of the simplest flow profile. The linear stability theory is then used through superimposition of small perturbation onto the fundamental flow and the equations governing the flow are then linearized giving an eigenvalue problem similar to the Orr Sommerfeld formulation. The stability behavior is examined in the form of the parameter of pressure gradient that controls the nature of the external flow. The findings indicate that positive pressure gradients yield rounded velocity fields and inhibit the growth of disturbances which, in turn, increases the stability of flows but adverse pressure gradients promote the growth of disturbances and makes it more likely that the separation of the boundary layer will take place. The discussion is of the importance of pressure gradients in the control of stability of the boundary layer and offers theoretical knowledge applicable in aerodynamic design, control of flow dynamics, as well as prediction of transition effects in viscous flow.
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