Rarefied Flow

Fig. 2.27 Influence of surface roughness on rarefied flow. Reprinted from Turner et al. (2004) with permission...

Henderson 575 presented a set of new correlations for drag coefficient of a single sphere in continuum and rarefied flows (Table 5.1). These correlations simplify in the limit to certain equations derived from theory and offer significantly improved agreement with experimental data. The flow regimes covered include continuum, slip, transition, and molecular flows at Mach numbers up to 6 and at Reynolds numbers up to the laminar-turbulent transition. The effect on drag of temperature difference between a sphere and gas is also incorporated. 

In the rarefied flow regime, all of these collisional mechanisms can also occur. Due to the reduced number of intermolecular collisions, however, all of the energy distributions may be in a state of nonequilibrium. This means that the rates of the kinetic processes cannot be described by the temperature-dependent forms usually employed in continuum models. Instead, models are required that describe these processes at the individual collision level. 

In this article, we begin by reviewing the variety of problems associated with laboratory and flight investigations of hypersonic rarefied flows. Then a complete review of computational methodologies is provided. This includes both continuum and particle methods. The focus is on particle methods and details are provided on general concepts. Then, several of the most commonly employed chemistry models are described in detail. There are two components to any chemistry model the rate of chemical reaction, and the mechanics of chemical reaction. These are discussed separately. Models for gas-surface interaction and hybrid methods that use both continuum and particle descriptions of the gas flow are also briefly reviewed. Results are reviewed for hypersonic conditions in air applicable to the Space Shuttle and to ballistic missiles where both dissociation and exchange reactions are important. The behavior of rarefled flow chemistry models is first considered in a test cell environment. Then, the models are applied to... 

When surface roughness is considered, the fully developed Nu increases with respect to the smooth channel value for rarefied flows, but not for continuum, for all values of Peclet number. The increase in Pe increases Nu more for low values of rarefaction. It appears that, for the range Kn considered in this work, the maximum heat transfer is observed for Kn =... 

At a low Reynolds number, the drag coefficient uniformly decreases with increasing Mach number and does not display a maximum value near unity. This is due to the prevalence of rarefied flow. 

There is no analytic nor numerical model available, which provides the particle drag coefficient for particles over all the regimes of rarefied flows. The earlier methods to correct for rarefied flow effects were based on a correction to Stokes drag, derived by Basset to account for velocity slip at the surface. In that case, the drag coefficient can be expressed as... 

Rarefied flows in the slip flow regime, rarefaction increases the hydrodynamic and thermal entrance lengths owing to slip at the walls (see Pressure-Driven Single-Phase Gas Flows ). 

In this section, the rarefied flow in step flows at different Knudsen numbers is considered [11]. Nitrogen flow in a channel with sudden expansion step geometry is considered. Pressure ratio along the channel is equal to 2, and wall and inlet gas temperature is 300 K. A grid with 100 X 60 structured meshes is used, and 25 particles are set in each cell. The simulations are performed for different Kn numbers in slip, transition, and free molecular regimes. Figure 8 shows the Mach number contours for different inlet Knudsen numbers. The step height is equal... 

Gas transport in nano-confinements can significantly deviate from the kinetic theory predictions due to surface force effects. Kinetic theory-based approaches based on the assumption of dynamic similarity between nanoscale confined and rarefied flows in low-pressure environments by simply matching the Knudsen and Mach numbers are incomplete. Molecular dynamics simulations of nanoscale gas flows in the early transition and free-molecular flow regimes reveal that the wall force field penetration depth should be considered as an important length scale in nano-confined gas flows, in addition to the channel dimensions and gas mean free path. 

A pressure-driven gas flow is generated by applying a pressure difference between the inlet and the outlet of a fluidic system, for example, a channel. Due to very small hydraulic diameters, pressure-driven gas flows in microchannels are laminar. Gas microflows are distinct from gas macroflows by rarefaction effects which appear as soon as the mean free path of the molecules is no longer negligible compared with the hydraulic diameter of the microchannel. For such rarefied flows, the classic Poiseuille model is no longer valid, and other models should be used, according to the rarefaction level, which is quantified by the Knudsen number. 

The JCnudsen layer plays a fundamental role in the slip flow regime. This thin layer, between one and two molecular mean free paths in thickness, is a region of local nonequilibrium which is observed in any gas flow near a surface. In non rarefied flows, the Knudsen layer is too thin for having any significant influence, but in the slip flow regime, it should be taken into account. 

---