LAMINAR STABILITY ANALYSIS IN BOUNDARY LAYER FLOW

Abstract

This study presents a numerical study concerning the flow control by suction and injection. The case study is over a symmetrical airfoil with suction and injection slots. The angle of attack is 3 degree with the Mach number 0.12. Introduction This paper aims to study the stability of incompressible laminar boundary layer by numerical simulation carried out on an aerodynamic profile with suction and injection flow. The method purpose in this paper for the study of laminar stability is based on small disturbance theory in witch a small sinusoidal disturbance is imposed on a given steady laminar flow to see whether the disturbance will amplify or decay in time. If the disturbance decays, the flow will stay laminar, if the disturbance amplifies sufficiently the flow become turbulent. n e The small disturbance theory does not predict the details of the nonlinear process by which the flow changes from laminar to turbulent. It establishes which shapes of velocity profiles are unstable, identifies those frequencies that amplify fastest and indicates how the parameters governing the flow can be changed to delay transition process. Mathematical Model Let be , , u v p a solution of the incompressible laminar boundary layer equations. Over this solution assign a disturbance . , , u v p ′ ′ ′ ; ; u u u v v v p p p ′ ′ = + = + = + ′ (1) Since the basic solution , , u v p and sizes u,v,p satisfy the boundary layer equations, following equations are obtained for disturbance: 0 y v x u = ∂ ′ ∂ + ∂ ′ ∂ (2)