A Mathematically Exact and Well-Determined System of Equations to Close Reynolds-Averaged Navier–Stokes Equations

Abstract

Since Sir Osborne Reynolds presented the Reynolds-averaged Navier–Stokes (RANS) equations in 1895, the construction of complete closure for RANS equations has been regarded as extremely challenging. Taking into account that the Navier–Stokes equations are not coherent for instantaneous and mean flows, a body of knowledge outside the scope of classical mechanics may be amenable to the closure problem. In this regard, the methodology of physics-to-geometry transformation, which is coherent for both flows, is applied to RANS equations to construct six additional equations. The proposed equations stand out from existing RANS closure models and turbulence quantity transport equations in two respects: they are mathematically exact and well-determined.