TITLE:
Mathematical Formulation of Bubble Formation after Compressible Boundary Layer Separation: Preliminary Numerical Results
AUTHORS:
Michail A. Xenos
KEYWORDS:
Laminar Separation Bubble, Compressible Boundary Layer, Fluid Mechanics, Computational Fluid Dynamics
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.12 No.4,
December
15,
2022
ABSTRACT: Laminar boundary layer (BL), under adverse pressure gradient, can separate. The separated shear layer reattaches to form a laminar separation bubble. Such bubbles are usually observed on gas turbine blades, on low Reynolds number wings and close to the leading edges of airfoils. Presence of bubbles has a weakening effect on the performance of a fluid device. The understanding of the prevailing mechanism of the separation bubble and ways to control it are essential for the efficient design of these devices. This is due to the significance of drag reduction in these various aerodynamic devices, such as gas turbines, re-entry space vehicles and airfoils. This study introduces a two-dimensional mathematical formulation of bubble formation after flow separation. The laminar BL equations with appropriate boundary conditions are dimensionalized using the Falkner-Skan transformation. Additionally, using the Keller-box method, the nonlinear system of partial differential equations (PDEs) is numerically solved. This study presents preliminary numerical results of bubble formation in low Mach numbers. These results reveal that after separation, a laminar bubble is formed in all studied cases, for Mach numbers, M = 0.2, 0.33 and 1.0. The flow after separation reverses close to the wall and finally reattaches downstream, in a new location. As the Mach number increases, this effect is more intense. After reattachment, the BL is again established in a lower energy level and the velocity field is substantially reduced, for all cases.