Two Reynolds-averaged Navier-Stokes models with full Reynolds-stress transport (RST) and tensor eddy viscosity are presented. These new models represent RST extensions of the $$k−2L−a−\mathscr{C}$$ and $$k−ϕ−L−a−\mathscr{C}$$ models by Morgan. Self-similarity analysis is used to derive constraints on model coefficients required to reproduce expected growth parameters for a variety of canonical flows, including Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) mixing layers. Both models are then applied in one-dimensional simulation of RT and KH mixing layers, and the expected self-similar growth rates and anisotropy are obtained. Next, models are applied in two-dimensional simulation of the so-called “tilted rocket rig” inclined RT experiment and in simulation of a shock-accelerated localized patch of turbulence. Here it is found that RST is required to capture the qualitative growth of the shock-accelerated patch, and an anisotropic eddy viscosity provides substantial improvement over a Boussinesq treatment for the tilted rocket rig problem.
Morgan, Brandon E., et al. "Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity." Physical Review. E, vol. 108, no. 5, Nov. 2023. https://doi.org/10.1103/physreve.108.055104
Morgan, Brandon E., Ferguson, Kevin, & Olson, Britton J. (2023). Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity. Physical Review. E, 108(5). https://doi.org/10.1103/physreve.108.055104
@article{osti_2274884,
author = {Morgan, Brandon E. and Ferguson, Kevin and Olson, Britton J.},
title = {Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity},
annote = {Two Reynolds-averaged Navier-Stokes models with full Reynolds-stress transport (RST) and tensor eddy viscosity are presented. These new models represent RST extensions of the $k−2L−a−\mathscr{C}$ and $k−ϕ−L−a−\mathscr{C}$ models by Morgan. Self-similarity analysis is used to derive constraints on model coefficients required to reproduce expected growth parameters for a variety of canonical flows, including Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) mixing layers. Both models are then applied in one-dimensional simulation of RT and KH mixing layers, and the expected self-similar growth rates and anisotropy are obtained. Next, models are applied in two-dimensional simulation of the so-called “tilted rocket rig” inclined RT experiment and in simulation of a shock-accelerated localized patch of turbulence. Here it is found that RST is required to capture the qualitative growth of the shock-accelerated patch, and an anisotropic eddy viscosity provides substantial improvement over a Boussinesq treatment for the tilted rocket rig problem.},
doi = {10.1103/physreve.108.055104},
url = {https://www.osti.gov/biblio/2274884},
journal = {Physical Review. E},
issn = {ISSN 2470-0045},
number = {5},
volume = {108},
place = {United States},
publisher = {American Physical Society (APS)},
year = {2023},
month = {11}}
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 190, Issue 1023, p. 534-550https://doi.org/10.1098/rspa.1947.0095
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 201, Issue 1065, p. 192-196https://doi.org/10.1098/rspa.1950.0052