关键词: magnetoelasticity, bifurcation, limit point, numerical method, straight rod carrying electric current, three-dimensional boundary layer, ray tracing theory, transition prediction, e^N method

Abstract:

In order to extend the e^N method to general three-dimensional boundary layers, the conservation law of the imaginary parts for the wave parameters with a fixed wave vector is deduced. The compatibility relationship (CR) and the general theory of ray tracing (RT), which have been extensively used in conservative systems, are applied to a general three-dimensional boundary layer belonging to non-conservative systems. Two kinds of e^N methods, i.e., the e^N-CR method and the e^N-RT method, are established. Both the two kinds of methods can be used to predict the evolutions of the spanwise wavenumber and the amplitude of the disturbances in general three-dimensional boundary layers. The reliability of the proposed methods is verified and validated by performing a direct numerical simulation (DNS) in a hypersonic general three-dimensional boundary layer over an aircraft model. The results are also compared with those obtained by other e^N methods, indicating that the proposed methods have great potential applications in improving the transition prediction accuracy in general three-dimensional boundary layers.

Key words: magnetoelasticity, bifurcation, limit point, numerical method, straight rod carrying electric current, e^N method, three-dimensional boundary layer, transition prediction, ray tracing theory