Assessment of Bhatnagar-Gross-Krook Approaches for Near Continuum Regime Nozzle Flows

Abstract

Accurate and numerically efficient modeling of low-to-moderate Reynolds number nozzle flow expansions to vacuum can be difficult due to the presence of multiple flow length scales. Such simulations are important for the prediction of propulsive thrust as well as spacecraft contamination, both of which can be difficult to measure in ground-based facilities. To that end, conical nozzle flows were studied for Reynolds numbers of 1230 and 12,300 using the direct simulation Monte Carlo method, Navier―Stokes with velocity slip and temperature jump boundary conditions, and statistical and deterministic approaches to the solution of the Bhatnagar―Gross―Krook and ellipsoidal-statistical Bhatnagar―Gross―Krook equations. The deterministic and statistical solutions of the Bhatnagar―Gross―Krook equation were found to be in good agreement with the benchmark direct simulation Monte Carlo results. Statistical Bhatnagar―Gross―Krook and ellipsoidal-statistical Bhatnagar―Gross―Krook methods were also found to be more efficient methods than direct simulation Monte Carlo in the continuum and near-continuum regime, and more accurate than the Navier―Stokes equations in the portions of the flow with rarefaction, such as the boundary layer and the flow around the nozzle lip.