Prediction of Onset of Laminar to Turbulent Transition Point for the flow around an Airfoil with NumericalSolution of the Orr-Sommerfeld Equationusing Numerical Profiles

The onset of laminar to turbulent transition point over airfoils in 2D flows has been determined. For this purpose، the hydrodynamic stability analysis of fluid flow is required which has been done by solving the Orr-Sommerfeld equation. An efficient and accurate finite difference method has been utilized to solve the Orr-Sommerfeld equation. The velocity profiles and their derivatives within the boundary layer are required at all sections in streamwise direction for solving the Orr-Sommerfeld equation which are obtained by a flow solver. A CFD code using an implicit TVD scheme was used to solve 2D Navier-Stokes equations. To determine the onset of transition location from laminar to turbulent regime، the eN method was used. This method based on the linear stability theory uses the eigenvalues of Orr-Sommerfeld equation for determining the amplification rates of disturbance waves. The solution to the Orr-Sommerfeld equation was in good agreement with the other numerical and analytical solutions thanks to the efficient algorithm used. Moreover، extracting the velocity profiles from viscous flow solution leads in the satisfying prediction of the transition point for the flow around a NACA0012 airfoil.