Effect Of Mach Number, Attack Angle And Sweep Angle On The Stability And Transition In A Swept-wing Boundary Layer

The research of hydrodynamic instability in a swept-wing boundary layer has important value to the design and optimization and the drag reduction of airfoil. The swept-wing boundary layer is a typical 3D boundary layer, whose transition is mainly caused by the cross-flow instability. While the inlet Mach number, attack angle and sweep angle are the key parameters that have important influence on the cross-flow instability of the swept-wing boundary layer.In this paper, the NACA0012 swept-wing model is established and the grid is generated by modeling software, and the mean flow of the swept-wing boundary layer is calculated by numerically solving the three-dimensional compressible Navier-Stokes equation under an airworthiness status, then the neutral curve and the growth curve of unstable T-S wave are obtained by solving the O-S equation to study the effect of the Mach number, attack angle and sweep angle on the stability of the swept-wing boundary layer, finally the transition position is predicted by applying eN method.Through the research of the effect of three parameters, the main conclusions can be drawn as follows:In the range of subsonic speed, the cross-flow in the swept-wing boundary layer is enhanced as the increase of Mach number. With the increase of Mach number, the range of the unstable wave frequency increases gradually, except the variation of the range in the stream-wise direction. The neutral curve of the stationary wave( ω =0) is insensitive to the variation of Mach number. At the leading edge of the wing, the growth rate is large and the N-factor increases rapidly. The maximum growth rate of the disturbance for small Mach number decreases faster than that for high Mach number, leading to that the N-factor of the flow with high Mach number is larger than that with small Mach number.The disturbance is inhibited in the leeward but enhanced in the windward when the attack angle is nonzero. The maximum position of the neutral curve in the stream-wise direction linearly increases in the windward and decreases in the leeward with the increase of attack angle. Transition firstly occurs in the windward, and the transition position predicted by eN method will shift to the leading edge of the swept-wing with the increase of the attack angle.With the increase of the sweep angle, both of the strength of the cross-flow and the amplification factor n of the disturbance amplitude increase first and then decrease, and the strength of the cross-flow reaches its peak value when the sweep angle is in the range of 40°~50°. The N factor predicted by eN method is the largest one when the sweep angle is about 50°, implying that with which angle, the inducing disturbance with a small amplitude can easily lead to the occurrence of transition.