Advertisement

Euler Angle and Axis—“Fingerprints” of a Subgrid-Scale Stress Model

  • Zixuan Yang
  • Bing-Chen Wang
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 165)

Abstract

The concepts of Euler angle and axis are utilized to investigate the relative rotation between the eigenframes of the deviatoric subgrid-scale (SGS) stress tensor \(-\tau _{ij}^d\) and the resolved strain rate tensor \(\bar{S}_{ij}\). Both Euler angle and axis are “natural invariants” of fluid tensors, which uniquely describe the relative rotation between eigenframes of two tensors. The Euler angle and axis can be regarded as “fingerprints” of a SGS stress model and have a profound implication for structural modeling of the SGS stress tensor. As an application, three SGS models are tested in the context of turbulent channel flows. The proposed Euler angle and axis are proven to be effective for demonstrating geometrical properties of a SGS stress model.

Keywords

Large Eddy Simulation Direct Numerical Simulation Euler Angle Viscous Sublayer Turbulent Channel Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Tao, B., Katz, J., Meneveau, C.: Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements. J. Fluid Mech. 457, 35–78 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Wang, B.-C., Yee, E., Bergstrom, D.J.: Geometrical description of subgrid-scale stress tensor based on Euler axis/angle. AIAA J. 44, 1106–1110 (2006)CrossRefGoogle Scholar
  3. 3.
    Lilly, D.K.: A proposed modification of the Germano subgrid scale closure method. Phys. Fluids A. 4(3), 633–635 (1992)Google Scholar
  4. 4.
    Morinishi, Y., Vasilyev, O.V.: A recommended modification to the dynamic two-parameter mixed subgrid scale model for large eddy simulation of wall bounded turbulent flow. Phys. Fluids. 13(11), 3400–3410 (2001)CrossRefzbMATHGoogle Scholar
  5. 5.
    Wang, B.-C., Bergstrom, D.J.: A dynamic nonlinear subgrid-scale stress model. Phys. Fluids. 17(3), 035109 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of ManitobaWinnipegCanada

Personalised recommendations