Physics of internal microstructure fluid flows plays important role both due to their applications as well as their more general research field. In most occasions this type of fluid flow problems are treated with discrete models that are both computational costly as well as unable to shed light into the more general physics of the problem. In this sense a continuous model in the Eulerian frame is adopted here that consists a generalization of the incompressible Navier-Stokes equation. The present model introduces an extra tensor in the governing equations that accounts for the angular velocity of the internal microstructure, namely the micropolar model.
The micropolar set of equations is implemented in the open-source finite volume solver OpenFoam, where the micropolar model is tested in a fully turbulent case. The Reynolds number is fixed while the micropolar viscosity ratio is varied for values between 0 and 0.9. For the usual channel geometry, the micropolar model shows excellent agreement with the Newtonian case, when the angular velocity tensor is disregarded. Furthermore, when the extra tensor of angular velocity is taken into account, higher wall values are observed due to friction velocity increment which lead to drag enhancement. The micropolar equation stress analysis indicated that the micropolar stress term becomes significant in the near-wall area intensifying turbulence.
Finally, a range of Reynolds numbers is investigated in order to study the effect of the micropolar model as turbulence increases. Once again, higher friction velocity and drag coefficients are observed as compared to the Newtonian case. However, turbulence seems to attenuate in the near wall region for cases of high micropolar viscosity ratio and Reynolds, as compared to cases of lower values of these parameters. This interesting effect is further supported by the analysis of additional quantities such as root mean square velocity (rms) and stress balance analysis. The turbulent kinetic energy balance analysis reveals that the energy injection to the system stemming from the micropolar term becomes comparable to the Newtonian one, as micropolar viscosity ratio and Reynolds number take higher values. Thus, it seems that the extra force acting on the flow, becomes significant enough in order to suppress turbulence activity in the near-wall region.
George Sofiadis is a Postodoctoral Researcher/Adjunct Assistant Professor at the University of West Attica, Athens, Greece.