Small Rarefaction, Large Consequences: Limits of Navier Stokes Turbulence Simulations

Abstract

We conduct numerical simulations of rocket plume impingement on a lunar landing surface using two complementary frameworks: the Boltzmann equation, which naturally captures rarefied gas dynamics, and the Navier Stokes (NS) equations, the conventional workhorse for turbulent flow simulations. We show that subtle rarefaction effects, long considered negligible in turbulent regimes, can become locally dominant within shear layers where viscous stresses predicted by the NS constitutive relation undergo sign reversals. This phenomenon, which we term constitutive degeneracy, produces order-one relative errors in predicted surface shear stress and heat flux. Our results demonstrate that turbulence can expose hidden limits of NS equations with broad implications for high-speed aerodynamics and planetary exploration.

Figures (2)

• Figure 1: (a) The density gradient and streamlines. (b) Shear stress at the ground surface. (c) The turbulent-to-laminar viscosity ratio $\mu_r$ and the local Knudsen number $\text{Kn}_{gll}$, in the left and right half-domains, respectively. (d) Heat flux at the ground surface. (e) Contour of the NS shear stress $\sigma_\text{12,Linear}=\sigma_\text{12,NS}+\sigma_\text{12,SST}$. (f) The laminar, turbulent, and non-equilibrium stresses at $x_2=-0.3$ m.
• Figure 2: Direct numerical simulation of the Boltzmann equation using the transient GSIS solver in turbulent-model-free mode Zeng2023GSIS. (a,b) The NS and Boltzmann shear stress, and their relative strength. (c) The Reynolds shear stress $R_{12}$ and the turbulence production term $\text{Prod}_\text{k}$. (d) The laminar, Reynolds, and non-equilibrium stresses at $x_2=-0.3$ m.