Uncertainty analysis of computed flow rates and pressure differences in rarefied pressure and temperature driven gas flows through long capillaries

Abstract

Abstract The computation of the mass flow rate in the Poiseuille and thermal creep flows and of the pressure difference in the thermomolecular pressure difference (TPD) flow through long capillaries is well-known and available in the literature. Here, the uncertainty in the solution due to induced uncertainties in the input data, namely, the capillary radius and length, the pressure and/or temperature imposed at the capillary ends and the accommodation coefficient of the Maxwell diffuse-specular boundary conditions, is investigated. The uncertainty analysis is performed by the Monte Carlo Method. Conducting the required number of trials the distribution function of the output quantity and its associated uncertainty are obtained. In most cases, the uncertainty in the input quantity driving the flow has the largest effect on the output uncertainties. This is always true in the TPD flow and for small pressure and temperature differences in the Poiseuille and thermal creep flows respectively. In the case of large driving thermodynamic forces, in the latter two flows, the radius becomes the most important source of uncertainty. The accommodation coefficient uncertainty is always the less important one. Documenting the expected effect of the uncertainty in each input parameter is certainly beneficial in computational as well as experimental work.