Relaxation Effects in Small Critical Nozzles

Abstract

We computed the flow of four gases (He, N2, CO2, and SF6) through a critical flow venturi (CFV) by augmenting traditional computational fluid dynamics (CFD) with a rate equation that accounts for τrelax, a species-dependent relaxation time that characterizes the equilibration of the vibrational degrees of freedom with the translational and rotational degrees of freedom. Conventional CFD (τrelax=0) underpredicts the flow through small CFVs (throat diameter d=0.593mm) by up to 2.3% for CO2 and by up to 1.2% for SF6. When we used values of τrelax from the acoustics literature, the augmented CFD underpredicted the flow for SF6 by only 0.3%, in the worst case. The augmented predictions for CO2 were within the scatter of previously published experimental data (±0.1%). As expected, both conventional and augmented CFD agree with experiments for He and N2. Thus, augmented CFD enables one to calibrate a small CFV with one gas (e.g., N2) and to use these results as a flow standard with other gases (e.g., CO2) for which reliable values of τrelax and the relaxing heat capacity are available.