CFD Capability Advancement Unstagnation

What is it about?

For 5+ decades, computational fluid dynamics (CFD) prediction of turbulent flowfields relies on “physics-based models” to define the action of the Reynolds stress tensor and heat/mass flux vectors embedded in time-averaged (RaNS) or spatial filtered (LES) Navier-Stokes (NS) PDE systems. That CFD algorithms written on these modeling closed RaNS/LES PDE systems lack sufficient prediction accuracy for rigorously detailed engineering design optimization remains a fundamental liability. The chronic absence of code prediction fidelity improvements engendered the observation, “... recently perceived stagnation of CFD capability advancement ... “ in AIAA Aerospace America in 2014. The 2014 NASA report “CFD Vision 2030 Study: a Path to Revolutionary Computational Aerosciences,” identified current practice RaNS/LES code prediction fidelity key inadequacies: • “... single most critical issue .. adequately predict viscous turbulent flows, ... boundary layer transition ... flows with separation present.” • “... a theoretically based, hybrid RaNS/LES turbulence simulation capability.” AIAA technical literature-cited inadequacies for the NPARC Alliance WIND-US RaNS/LES government/industry CFD code include: • “... prediction sensitivity to . . . turbulent scalar transport model constants, ...” • “... turbulent Prandtl and Schmidt number models ... “ Elimination of these closure modeling inadequacies requires heurism replacement with mathematical rigor. A fundamental CFD unstagnation advancement is documented - a totally analytical closure theory for the rigorously space-filtered thermal, multi-species NS PDE system. The theory closed PDE system is applicable for all Reynolds numbers (Re) as the derivation makes no assumption on flowfield state. Thus is enabled, herein documented, generation of a posteriori data quantifying first principles (modeling-free!) prediction of: • unsteady thermal wall layer velocity laminar profile transition to insipient turbulent, then separation, turbulent profile reattachment and relaminarization • theory state variable-specific momentum/thermal transport predictions quantify turbulent Prandtl number model fidelity liability. Both achievements are explicitly responsive to bulleted CFD inadequacy resolutions.

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Photo by Pawel Czerwinski on Unsplash

Photo by Pawel Czerwinski on Unsplash

Why is it important?

Elimination of CFD closure modeling inadequacies requires heurism replacement with mathematical rigor. A fundamental CFD unstagnation advancement is documented - a totally analytical closure theory for the rigorously space filtered thermal, multi-species NS PDE system. The theory closed PDE system is applicable for all Reynolds numbers (Re) as the derivation makes no assumption on flowfield state. Analytical filtered NS (aFNS) theory CFD advancement unstagnation is documented in three parts. Theory derivation, including resolution of numerous mathematical issues for aFNS theory PDE system to be bounded domain well-posed constitutes Part I. Key is handling filter penetration of domain boundaries leading to boundary commutation error (BCE) integral and non-homogeneous Dirichlet boundary condition (DBC) algorithms, validations for which are Part II detailed. Part III documents comprehensive validation of complete aFNS theory-resolutions coupled algorithm code for Reynolds number specifications ranging 100 < Re < 12,000.

Perspectives