A Numerical Investigation On Inviscid Instability Of Streaky Structures In Incompressible Boundary Layer Flow

In the engineering designing, consisting of the design of the aircrafts and the engines, the transition location of the fluid is a necessary critical design parameter, especially on an airplane wing or a turbine blade. It need have a good analyse and good knowledge to the character of the transition and the stability of the flow. For high levels of free-stream turbulence, streaky structures in boundary layer with the spanwise variations alternating will be generated. As estimating the transition location, traditional method is useless. Therefore, it need having a description to the stability of the streaky structures in boundary layer.A numerical investigation is made for the effect of streaky structures in transition by inviscid linear disturbance equation with temporal mode consisting of Fourier expansions in horizontal discretization, Chebyshev collocation point in normal discretization and third-order difference schemes in temporal discretization. As initializing the disturbance with T-S wave, the instable wave, its growth rate, distribution, and the variation with the streamwise wave numbers can be received for a long enough time. The following conclusions are found:(1). Chebyshev collocation point in normal discretization for boundary layer is valid.(2). the waves exponential growing and periodic alternating are in existence in streaky structures in boundary layer.(3). for different streamwise wave numbers, eigenvalues are incremental at first and decremental later with the streamwise wave number increasing and the maximum rate of growth is in existence at near alpha=0.4; its frequency w is (0.2186 +0.001457i).(4). the distributions of eigenfunction with different streamwise wave numbers are received.