Frequency response of pressure sensor configurations in slip-flow conditions

摘要

A dynamic model is presented for pneumatic tubing and pressure sensor configurations in rarefied or slip-flow conditions. The model uses the linearized Navier-Stokes equations, with the boundary conditions extended to allow for rarefied conditions. At low pressure levels, the modified wall boundary condition allows fluid elements to slip when directly in contact with the tubing wall. This slippage effectively lowers fluid viscosity. Dynamic effects of the rarefied-flow extension are demonstrated by comparing rarefied-flow solutions to equivalent solutions generated using continuum-flow models. Lower viscosity resulting from rarefied flow causes the configuration response to be less damped than for similar conditions without molecular effects. Comparing steady-state response to data from a series of laboratory experiments validates the range of the rarefied-flow model. When pneumatic tubing is heated unevenly, rarefied flow forces the tube hot end to have higher pressure than the cold end, with no net flow along the tube. This pressure difference results in a dc offset in the measured pressure reading. Comparisons of the steady-state model to experimental data show that the slip-flow model is generally applicable for Knudsen numbers up to approximately 0.65. Beyond 0.7 Knudsen number, molecular effects dominate, and the model is no longer applicable to the problem physics. References: 17