Bifurcations of transonic flow past simple airfoils with elliptic and wedge-shaped noses

Abstract

A turbulent transonic flow past two symmetric airfoils with flat midparts is studied numerically. Using the Reynolds-averaged Navier-Stokes equations, we analyze the flow past a 9% thick airfoil with an elliptic nose. A range of the free-stream Mach number M ∞ , in which flow bifurcations occur, is determined. Values of M ∞ that give rise to significant changes in the lift coefficient with variations of the angle of attack are specified. Flow bifurcations are also revealed for a thin double wedge, i.e., a sort of a hexagon.

Mathematical Modelling and Numerical Investigations on the Coanda Effect

“…domains A and D, which correspond to the solution obtained by starting with a uniform flow at an angle of 0 0 ; -domains B and C, which correspond to the solution obtained by starting with the initial solution at 1 0 and M  =0.86. The nonlinear flow equations, the initial solution used for the numeric computations and the length of the airfoil midpart with a small or zero curvature are the principal factors for the onset of flow bifurcations [40,41].…”

“…Extreme values of the lift coefficient CL as function of the Mach number M∞ for self-sustained flow oscillations about the particular symmetric airfoil (relative airfoil thickness h = 0.09) at 0 0 incidence and Re = 1.1 e+7: domains A, B,C and D describes the flow regimes with different location of supersonic regions[40].…”

Bifurcation of Transonic Flow in a Channel With a Central Body

“…At the moment of coalescence of two regions the pressure distribution and the lift force abruptly change. This phenomenon takes place for a number of symmetrical airfoils, and for an asymmetrical airfoil whose upper surface is nearly flat in the midchord region [1,2].…”