Neutral+Stability+Curves+on+a+Flat+Plate

The transition from laminar to turbulent flow over an airfoil leads to greatly increased aerodynamic drag. In many instances, transition is initiated by small periodic velocity disturbances in the airfoil’s boundary layer. While most disturbances are damped, some amplify as they travel downstream and ultimately result in turbulence.

The Orr-Sommerfeld equation (OSE) describes the instability conditions for a viscous, parallel flow. With the OSE, disturbance frequency and Reynolds number can be plotted for varying values of an amplification factor. A neutral stability curve (NSC) is the locus for which the amplification factor is zero, separating the unstable and stable disturbances.

Because the OSE cannot be analytically solved for general flows, this project's aim is to use computational fluid dynamics (CFD) as an alternative method for obtaining the NSC for flow over a 2D flat plate. With CFD, disturbed flows can be simulated at specific Reynolds numbers and frequencies to determine their stability. These simulations can be repeated with different combinations of the aforementioned inputs to approximate the NSC. A reliable, fast, and efficient method to obtain the NSC with CFD would greatly aid the investigation of stability in more complicated flows.