Biorthogonal decomposition of the disturbance flow field generated by particle impingement on a hypersonic boundary layer

Abstract

The disturbance flow field in a hypersonic boundary layer excited by particle impingement was investigated with a focus on the first stage of the laminar-to-turbulent transition process, namely the receptivity process. A previously validated direct numerical simulation approach adopting disturbance flow tracking is used to simulate the particle-induced transition process. Particle impingement generates a highly complex disturbance flow field that can be characterised by a wide range of frequencies and wavenumbers. After providing some insight about the spectral characteristics of the disturbance flow field in the frequency and wavenumber domains, biorthogonal decomposition is employed to reveal the composition of the disturbance flow field consisting of different continuous and discrete eigenmodes that are triggered through particle impingement. The disturbance flow characteristics for different frequency and wavenumber pairs are discussed where large contributions in the disturbance flow spectrum are observed in the vicinity of the impingement location. A significant amount of the disturbance energy is diverted into the free stream leading to large coefficients of projection for the slow and fast acoustic branches while contributions to the entropy and vorticity branches are negligible. In addition to the continuous acoustic spectra, the first-, second- and other higher-order Mack modes are activated and provide large contributions to the disturbance flow field inside the boundary layer. Finally, it is demonstrated that the disturbance flow field in the vicinity of the impingement location can be reconstructed with a maximum relative error of $2.3\,\%$ by employing a theoretical biorthogonal eigenfunction system expansion and by considering contributions from fast and slow acoustic waves and at most four discrete modes only.