Numerical simulation of nonlinear interactions in a naturally transitional flat plate boundary layer

Abstract

This paper presents numerical simulations of the natural laminar-turbulent transition in a flat plate boundary layer. Natural transition occurs in low disturbance environments and is triggered by the growth of boundary layer instabilities or disturbances. This contribution specifically aims at investigating the interaction of multiple disturbances and their effect on the transition mechanism. The numerical simulations employ a lattice Boltzmann method (LBM) in conjunction with a highly accurate cumulant collision operator and a shared memory multi-GPU framework. The numerical approach is validated by comparing the growth of single Tollmien-Schlichting (T-S) waves with results of the linear stability theory (LST) prior to transition. Moreover, a comprehensive comparison with available direct numerical simulation results (DNS) for the post transition and the fully turbulent regime confirms the validity of the employed numerical approach. Subsequently, the influence of disturbances on the transition process are investigated in detail and for different disturbance frequencies and amplitudes. Two types of natural transition scenarios (H- & K-type transition) are analyzed and the LBM results are compared to predictions of the classical eN-method. Both approaches are found to reproduce a similar frequency influence. Higher frequency T-S waves trigger an earlier transition until a critical frequency is reached, above which the boundary layer is stable. In addition, it is observed that in case of multiple interacting disturbances, the laminar-turbulent transition occurs earlier than predicted by simplified methods that ignore the nonlinear interactions between disturbances. A spectral analysis of the velocity field confirms that secondary disturbances are crucial for the resonance transition and can significantly accelerate the transition process. The paper offers a comparison of linear and nonlinear results using a classical LST map and furthermore the laminar-turbulent natural transition is comprehensively investigated using the LBM.