Rarefied gas flow
Rarefied gas flow
Flow of gases below standard atmospheric pressure, sometimes called low-pressure gas flow. The flow may be confined to pipes between a chamber or vessel to be evacuated and a pump, or it may be the beam of molecules issuing from an orifice into a large evacuated chamber or the plume of exhaust gases from a rocket launched into the upper atmosphere, for example. The flow velocity is measured with respect to a fixed boundary such as the wall of a pipe, the surface of a rocket or jet plane, or a model in a wind tunnel. See Fluid flow, Molecular beams
For flow through ducts, the gases concerned are initially those of the original atmosphere inside a chamber that must be evacuated. However, even after the bulk of the original gas has been removed, the pumps must continue to remove gas evolved from surfaces and leaking in through imperfections in the walls. In some cases, gas is introduced through valves at a controlled rate as part of the process being carried out at a low pressure.
Since the flow through pipes involves an interaction or drag at the walls, a pressure drop is generated across the entrance and exit of the pipe. Also, gaseous impurities from the pump may flow toward the chamber when the pressure is very low. Proper design of the duct system therefore involves selecting pipes and valves of adequate internal diameter to ensure a minimal pressure drop and the insertion of baffles or traps to prevent impurities from the pumps from entering the process chamber.
The resistance due to the walls depends on the mass flow velocity, and may depend on the gas viscosity and the pressure or density of the gas. The mean free path of molecules is the distance between collisions with other molecules in the gas. See Kinetic theory of matter, Mean free path, Viscosity
The analysis of low-pressure flow is divided into three or four flow regimes depending on the value of the Knudsen number Kn, defined as the ratio of the mean free path to a characteristic length, and the dimensionless Reynolds number. The characteristic length may be chosen as the mean pipe diameter in the case of confined flow or as some length associated with a test model suspended in a wind tunnel, for example. See Gas dynamics, Knudsen number, Reynolds number
Another dimensionless number used in gas flow dynamics is the Mach number (Ma), defined as the ratio of the mass flow velocity to the local velocity of sound in the gas. See Mach number
When the mean free path is much smaller than the pipe diameter (Kn < 0.01), the gas flows as a continuous viscous fluid with velocity near the axis of the pipe at locations well beyond the pipe entrance much higher than the velocity in gas layers near the wall. The velocity profile as a function of radial distance from the axis depends on the distance from the entrance and the viscosity of the gas. When the Reynolds number is less than 2000, the profile is a simple curved surface so that the flow is laminar (laminar flow regime). When the mean free path becomes greater than about 0.01 times the diameter, the profile is distorted by boundary-layer effects, and the velocity near the wall does not approach zero (sometimes referred to as slip flow). See Laminar flow
For Reynolds numbers above the critical value (approximately 2100), the flow is subject to instabilities depending on the geometry of the boundary and at high Reynolds numbers becomes turbulent (turbulent flow regime). See Turbulent flow
When the mean free path is about equal to or greater than the pipe diameter (Kn ≥ 1), the gas molecules seldom collide with each other, but can either pass through the pipe without striking the wall or scatter randomly back and forth between various points on the wall and eventually escape through the exit or pass back through the entrance. This type of gas flow is known as free-molecule flow (molecular flow regime). The transition region (0.01 < Kn < 1) between the laminar flow regime and the molecular flow regime is referred to as the Knudsen or transition flow regime.
The flow may also be classified by the boundary conditions or by the Mach number. For example, Couette flow involves the flow of rarefied gas between two surfaces that are moving with respect to each other with different parallel tangential velocities. For hypersonic flow, Ma ≥ 5.