Sensitivity of linear stability analysis of measured separated shear layers

Abstract

Linear stability analysis is commonly performed on measured mean velocity profiles in experimental studies on transitional separation bubbles; however, the results of such an analysis are sensitive to both the analysis approach and to experimental data scatter. In this investigation, the sensitivity of linear stability analysis of measured separated shear layer profiles is examined in order to identify reliable analysis approaches and to quantify the uncertainty in the results due to experimental data scatter and the method of analysis. Analysis approaches are compared based on their predictions for a simulated velocity profile without data scatter, profiles with simulated data scatter, and several published experimental separated shear layer profiles. Both viscous and inviscid analyses are considered. The predicted maximum disturbance amplification rates between the viscous and inviscid solutions are found to agree to within 15% for several measured separated shear layer profiles. It is shown that, for the level of data scatter typical of hot-wire measurements over flat plates and airfoils, the measured mean velocity profile should not be used directly in the stability equation, and therefore curve fitting the base velocity profile is necessary. Three curve fits are identified that provide stability predictions with relatively low sensitivity to mean profile data scatter. Stability predictions obtained using these fits are found to be more sensitive to the type of curve fit used in the analysis than to experimental data scatter, with the predicted maximum disturbance growth rate and corresponding frequency varying by approximately 35% between fits. The results of this investigation provide a means of estimating the uncertainty in linear stability predictions for measured separated shear layer profiles.