Totally analytical closure of space filtered Navier–Stokes for arbitrary Reynolds number: Part III. aFNS theory validation

ABSTRACT

For arbitrary Reynolds number Re, aFNS theory O(1; δ²; δ³) significance scaled state variable achieves analytical closure of rigorously space filtered thermal, multi-species Navier–Stokes (NS) conservation principle partial differential equation (PDE) system well-posed on bounded domains (Part I). Validation of boundary commutation error (BCE) and nonhomogeneous Dirichlet boundary condition (DBC) resolution strategies results in AD^h-GWS^h-BCE^h-DBC^h algorithm coupling with aFNS theory optimal Galerkin GWS^h + θTS CFD algorithm (Part II), including accuracy/convergence assessments. For Reynolds numbers ranging E+02 <Re < 2E+04, aFNS theory fully coupled k = 1 basis Galerkin CFD code generated a posteriori data enable theory quantitative validation. For assured laminar Re range, NS no-slip BC reduced and coupled aFNS theory code predicted quasi-steady thermal-velocity transition to periodic unsteady is validated via linear stability predicted critical Re. For Re exceeding assured laminar, theory coupled CFD data quantify spatial filtering annihilation of (laminar) NS predicted large wave number spectral content. For sufficiently large Re, coupled CFD code a posteriori data document first principles prediction of unsteady periodic wall attached velocity profile transitioning-from-laminar, then separation, fully turbulent profile reattachment followed by relaminarization. These large Re CFD data as well enable validation of perturbation theory O(1; δ²; δ³) significance scaled state variable, AD^h-GWS^h-DBC^h algorithm prediction of O(δ²) state variable non-homogeneous Dirichlet BC DOF data and in concert thoroughly quantify theory generated O(δ²; δ³) state variable distributions.

Acknowledgments

During the dissertation project the first author served as HPC Graduate Assistant in the Joint Institute for Computational Sciences (JICS), a collaboration between the US DOE Oak Ridge National Laboratory and the University of Tennessee/Knoxville (UTK). Reported a posteriori data were CFD code generated using the ORNL Kraken multi-parallel HPC facility, access to which is gratefully acknowledged. Dissertation project coordination was through the UTK College of Engineering CFD Laboratory.