Reynolds stress and turbulence energy spectra analysis of <italic>Re</italic>-understanding the turbulence constitutive equation DNS data in square and rectangular annular ducts

Abstract

Through systematic Direct Numerical Simulation (DNS) of the fully-developed turbulence inside a square annular and rectangular annular ducts, the current research established detailed turbulence statistics database, which included: (1) the mean flow field (mean streamwise velocity and turbulence-driven secondary flow or historically the secondary flow of Prandtl second kind); (2) the turbulent Reynolds stresses; and (3) the turbulence energy spectra. The current paper presented the characteristics of the complete Reynolds stress fields, including uu , vv , ww , uv , uw , vw , and provided a convincing validation of these results using the existing experimental measurements from Cheesright (1990) and the DNS data of Gavrilakis (1992). The DNS predicted Reynolds stress fields made it possible to conduct in-depth interrogation of the mechanisms of turbulence-driven secondary flow near the 90° convex corner. The current paper raised a fundamental issue of the isotropic assumption implicitly contained in the conventional constitutive equation of turbulence based on the analogy between the turbulence and molecular motions. Via in-depth observation of the characteristics of Reynolds stresses and turbulence energy spectra, the paper put forward the proposal to develop new constitutive equation of turbulence using the tensor form of eddy viscosity. The research is targeted to provide a capability to fully understand the anisotropic properties of turbulence in engineering practices and to further develop a high-fidelity RANS-based turbulence-closure model using more and more reliable DNS data.