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Free Molecular Flow
Published in Randall F. Barron, Gregory F. Nellis, Cryogenic Heat Transfer, 2017
Randall F. Barron, Gregory F. Nellis
For gases at pressures near ambient and higher, the gas molecules travel extremely small distances between collisions. For example, for nitrogen gas at 101.3 kPa (14.7 psia) and 300 K (27°C or 80°F), a N2 molecule will travel a distance of 66 nm (2.6 × 10−6 in.) before it strikes another N2 molecule, on the average. The average N2 molecule would make 7.2 trillion collisions each second or 1 collision every 0.14 ns. In this case, the mass flow and energy transfer for the gas may be treated as if the gas were a continuous material; therefore, this flow regime is called continuum flow. As the gas pressure is decreased, the average distance that the molecules travel between collisions (i.e., the mean free path) also increases. If the gas pressure is reduced to sufficiently low values, the gas molecules interact much more often with the container surface than with each other. This type of flow is called free molecular flow. There is a range of gas pressures for which the flow has some continuum features (away from the container wall), but has discrete features in the region near the wall (within a distance on the order of the mean free path from the wall). This type of flow is called mixed or slip flow. The flow regimes are illustrated in Figure 9.1.
Gas Flow at Vacuum Conditions
Published in Igor Bello, Vacuum and Ultravacuum, 2017
In gases, we may recognize two major gas flow regimes with typical characteristics: the continuum gas flow and the molecular flow. The continuum gas flow is also called viscous flow, though in some specific circumstances gas viscosity is not involved. The regime of continuum (viscous) flow can be divided into viscous turbulent and viscous laminar flow. With lowering pressure, the later flow turns first to the intermediate flow and then to free molecular flow.
Study of Shock Structures Using the Unified Gas-Kinetic Wave-Particle Method with Various BGK Models
Published in International Journal of Computational Fluid Dynamics, 2022
Guochao Fan, Wenwen Zhao, Zhongzheng Jiang, Weifang Chen
The Knudsen number (Kn), defined as the ratio of the molecular mean free path to the object characteristic length, is used to preliminarily evaluate the degree of gas rarefaction and distinguish the flow regime from continuum flow to free molecular flow correspondingly. As Kn increases, beyond the hydrodynamic scale, the widely used Navier–Stokes equations with linear constitutive relations become incompetent in those non-equilibrium flows due to the breakdown of continuum assumption. For example, Navier–Stokes equations cannot correctly reproduce the behaviour of shock thickness for increasing Mach number (Gilbarg and Paolucci 1953). As the foundation of gas-kinetic theory, however, the Boltzmann equation is capable of describing the non-equilibrium processes from continuum flow to free molecular flow. After this kinetic equation is formed, the crucial problem in academia is how to solve it accurately and efficiently.