Starting vortex, separation bubbles and stall: a numerical study of laminar unsteady flow around an airfoil

Abstract

The stalling characteristics of an airfoil in laminar viscous incompressible fluid are investigated. The governing equations in terms of the vorticity and stream function are solved using an implicit finite-difference scheme and point successive relaxation procedure. The development of the impulsively started flow, the initial generation of circulation, and the behaviour of the forces at large times are studied.Following the impulsive start, the lift is at first very large and then it rapidly drops. The subsequent growth of circulation and lift is associated with the starting vortex. After incipient separation, the lift increases owing to enlargement of the separation bubble and intensification of the flow rotation in it. The extension of this bubble beyond the trailing edge causes it to rupture and brings about the stalling characteristics of the airfoil. Subsequently, new bubbles are formed near the upper surface of the airfoil and are swept away. The behaviour of the lift acting on the airfoil is explained in terms of the strength and sense of these bubbles. The lift increases when attached clockwise bubbles grow and when counterclockwise bubbles are swept away and vice versa.

Application of multi-block approach in the immersed boundary–lattice Boltzmann method for viscous fluid flows

“…In the present study, the calculated Strouhal number is 0.20, while the value given by Mehta and Lavan [26] is 0.2162. Fig.…”

Analysis of Two-Dimensional Incompressible Flow Past Airfoils Using Unsteady Navier-Stokes Equations

“…Instead, only some relevant studies using the Navier-Stokes equations approach and a couple of very recent experimental and analytical studies are cited here. Mehta and Lavan [3] studied the incompressible flow past a 9 percent thick Joukowski airfoil at Re = 1000, and angle of incidence, a = 15°, using the NavierStokes equations, and provided accurate results for the stall characteristics. Care was exercised in determining the far-field boundary condition which was placed at a finite distance from the airfoil.…”

Numerical Study of Incompressible Slightly Viscous Flow Past Blunt Bodies and Airfoils

“…The flow due to an impulsive start of an airfoil at an angle of attack equal to -n/12 radians, in a fluid of Reynolds number 1000, has been previously studied by Metha and Lavan [34] and by Wu, Sampath and Sankar [56]. The former solved the problem numerically using a finite difference method while the latter used an integra-differential formulation.…”