High-order Spectral Difference Solution of Unsteady Compressible Micropolar Equations on Moving and Deformable Grids

Compressible Navier-Stokes equations have been widely used for computational aerodynamics. Classical continuum theory, where the Newtonian Navier-Stokes equations come from, is short of a mechanism of characterizing the spinning motion, i.e. vortices. A common practice is to use vorticity (a mathematical definition which is not consistent with vortex physically) for characterizing vortex dynamics. Micropolar Fluid Dynamics (MFD) equations are derived from a continuum theory taking into account the interaction of macromotion and micromotion of fluid particles. A continuous collection of finite size particles constitutes a Micropolar continuum. Each finite size particle consists of three rotational degrees of freedom, named as gyration vector, in addition to three conventional translational degrees of freedom. Gyration vector is a natural choice to determine the spinning rotation of a group of fluid molecules or that of a single fluid molecule. Such spinning effect is missed in the classical Navier-Stokes equations. Similar to the classical continuum theory, Micropolar theory is derived from the thermodynamic balance laws and therefore can be easily rearranged in a fully conservative form. By comparing the linear constitutive equations of Micropolar and Newtonian fluids, their distinct differences are asymmetrical Cauchy stress and existence of moment stress due to the effect of gyrations. Chen et. al. [1] initiated the development of a numerical solver for MFD equations by incorporating finite difference method and time-centered split method (TCSM). However such study is restricted only for incompressible flow and second order accuracy on structured grids.

The present study extends the high order spectral difference (SD) method [2] to simulate unsteady MFD problems on unstructured moving and deformable grids for compressible viscous flows. A series of simulations of unsteady flow past plunging and pitching airfoils were conducted as we are motivated by the application of oscillating wing wind power generator.

References

[1] J. Chen, C. Liang and J. D. Lee, Theory and Simulation of Micropolar Fluid Dynamics, Journal of Nanoengineering and Nanosystems, 224, 31-40, 2011.

[2] C. Liang, A. Jameson and Z. J. Wang. Spectral Difference method for two-dimensional compressible flow on unstructured grids with mixed elements. Journal of Computational Physics, vol 228, pp 2847-2858, 2009.

Speaker Bio: Dr Chunlei Liang obtained his PhD in Mechanical Engineering from University of London, UK. He joined George Washington University in 2010 as an assistant professor after three years’ postdoctoral research in Stanford University. He is a senior member of American Institute of Aeronautics and Astronautics.

Presentation Slides: PPT

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.