Eddy-Resolving Simulation of Turbulent Transition and Transition Control in High-Speed Boundary Layers

Abstract

Laminar-to-turbulent transition on a high-speed vehicle is one of critical phenomena associated with the aerothermodynamic performance of the vehicle. Large aerodynamic heating and viscous drag in turbulent boundary layer underscores the precise prediction and control of turbulent transition. In this study, a cost-effective and high-fidelity method for predicting turbulent transition in high-speed boundary layers is proposed first. Subsequently, the control of turbulent transition in hypersonic boundary layers is investigated by utilizing the proposed method.

Full-scale eddy-resolving simulations require substantial computational resources to resolve turbulent transition accurately. In response, a novel computational approach is proposed to accurately resolve transitional boundary layer with affordable computational cost. This approach combines eddy-resolving simulation with stability analysis, which provides major instability modes in the pre-transition region efficiently. Combination of eddy-resolving simulation and stability analysis is pursued via unsteady inlet condition for eddy-resolving simulation; instability modes from stability analysis are introduced at the inlet with the undisturbed laminar solution. By assigning major instability modes as inlet condition of eddy-resolving simulation, the computational domain of eddy-resolving simulation can be reduced, reducing the overall computational cost. The combined approach is demonstrated in high-speed boundary layer at Mach 3. Detailed flow features associated with the turbulent transition are compared well with previous direct numerical simulation (DNS) studies, including the development of instability modes in the pre-transition region and statistics in the turbulent boundary layer. It is clearly shown that the combined approach can accurately resolve transitional boundary layer with significantly reduced computational cost, compared to the relevant DNS cost.

The combined approach is extended to hypersonic boundary layers to explore the control of turbulent transition using porous surfaces. Initially, the effect of porous surfaces on the Mack second mode, which is the most unstable mode in hypersonic boundary layers, is investigated. Here, porous surfaces are designed to absorb the Mack second mode effectively. It is demonstrated that the designed porous surfaces effectively suppress the Mack second mode without compromising other mean aerothermodynamic characteristics. Furthermore, eddy-resolving simulation with stability analysis is conducted to assess the effect of porous surfaces on the whole transition process. It is shown that the turbulent transition involving the Mack second mode can be effectively delayed by the designed porous surfaces. The comprehensive investigation provides crucial insights into turbulent transition control mechanisms in high-speed flows.

Furthermore, a novel strategy for designing nonuniform porous surfaces is proposed. The analysis of linear stability theory (LST) is utilized to design and examine nonuniform porous surfaces. The unstable Mack second modes are identified by their amplification factor N, obtained from the LST analysis. Conventional uniform porous surface is solely designed to stabilize the most unstable Mack second mode with the largest N. However, other Mack second modes with smaller but non-negligible N continue to grow and may initiate turbulent transition downstream. To further delay the transition, the current strategy integrates various porous surfaces along the streamwise direction. It is demonstrated that the nonuniform porous surfaces suppress not only the most unstable Mack second mode but also other instability modes, underscoring their the potential of nonuniform porous surfaces to enhance transition control in hypersonic boundary layers.