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

TL;DR

This paper reveals that rarefaction effects, often overlooked, can significantly impact turbulence simulations, exposing limitations of Navier Stokes equations in high-speed aerodynamics and planetary exploration.

Contribution

It demonstrates that rarefaction effects can dominate shear layers, causing errors in Navier Stokes predictions, highlighting the need for alternative modeling approaches.

Findings

Rarefaction effects can become dominant in shear layers.

Navier Stokes equations can produce significant errors in turbulent regimes.

Turbulence reveals fundamental limits of traditional flow models.

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.