Modeling boundary-layer transition in direct and large-eddy simulations using parabolized stability equations.

Area of Science:

• Fluid Dynamics
• Turbulence Modeling
• Computational Fluid Dynamics

Background:

• Turbulence transition is crucial for understanding complex fluid flows.
• Accurate prediction of transition onset and development is computationally demanding.
• Existing methods often rely on empirical correlations or computationally expensive simulations.

Purpose of the Study:

• To evaluate the nonlinear parabolized stability equations (PSE) for accurate and efficient modeling of H-type transition to turbulence.
• To demonstrate PSE's capability in capturing nonlinear interactions leading to turbulence breakdown.
• To establish PSE as a suitable inflow condition for subsequent simulations.

Main Methods:

• Application of nonlinear parabolized stability equations (PSE) to model the pretransitional flow region.
• Coupling PSE with direct numerical simulations (DNS) to validate results.
• Integration of PSE with wall-resolved and wall-modeled large-eddy simulations (LES).

Main Results:

• PSE accurately captures nonlinear interactions driving turbulence transition without empirical correlations.
• A combined PSE-DNS approach successfully reproduces skin-friction distribution and turbulent statistics.
• Significant reduction in computational cost (several orders of magnitude) compared to full DNS when using PSE with LES.

Conclusions:

• Nonlinear PSE offer a computationally efficient and accurate method for studying turbulence transition.
• PSE provide a natural and non-physical transient-free inflow condition for DNS and LES.
• The PSE-LES approach presents a powerful tool for reducing the computational burden of turbulent flow simulations.