Rarefied gas flow

Since the middle of the 1990s, another computation method, direct simulation Monte Carlo (DSMC), has been employed in analysis of ultra-thin film gas lubrication problems [13-15]. DSMC is a particle-based simulation scheme suitable to treat rarefied gas flow problems. It was introduced by Bird [16] in the 1970s. It has been proven that a DSMC solution is an equivalent solution of the Boltzmann equation, and the method has been effectively used to solve gas flow problems in aerospace engineering. However, a disadvantageous feature of DSMC is heavy time consumption in computing, compared with the approach by solving the slip-flow or F-K models. This limits its application to two- or three-dimensional gas flow problems in microscale. In the... 

Figure 2.3 Model geometry used for the study of surface-roughness effects on rarefied gas flows in micro channels.

Theoretical and experimental investigation of rarefied gas flow in molecular pumps... 

Analogy in molecular system Rarefied gas flow Molecular theory of liquids or kinetic theory of gas... 

In the absence of any significant body of experimental data for rarefied, hypersonic flows, vehicle design has depended greatly on computational modeling. In this section, we briefly review continuum approaches for computing rarefied gas flows. We then pass on to a more complete description of the methods and models associated with a particle formulation. Hybrid methods that combine continuum and particle methods are reviewed briefly. 

In case of rarefied gas flow, there is a finite temperature difference between the wall temperature and the fluid temperature at the wall. A temperature jump coefficient has been proposed as ... 

Beskok, A., Kamiadakis, G. E., (1997a) Modeling Separation in Rarefied Gas Flows, 28 " AIAA Fluid Dynamics Conference, ALAA Shear Flow Control Conference, June 29-July 2. 

Gaseous flow has usually been investigated by theoretical means. Some experiments were also performed to verify the theoretical results. When gases are at low pressures, or are flowing in small geometries, the interaction of the gas molecules with the wall becomes as frequent as intermolecular collisions, which makes the boundaries and the molecular structure more effective on flow. This type of flow is known as rarefied gas flow. 

Another characteristie of rarefied gas flow is that there is a finite difference between the fluid temperature at the wall and the wall temperature. Temperature jump is first proposed to be... 

Struchtrup, H. 2005 Macroscopic Transport Equations for Rarefied Gas Flows. Berlin Springer. 

With this correction, aspect ratios of 1, 2, and 4 ducts correspond to 42.17%, 68.60%, and 84.24% of the theoretical two-dimensional channel volumetric flowrate for no-slip flows, respectively. According to the new model, the volumetric flowrate for rarefied gas flows in ducts is... 

The investigations of Hertz were given a new impetus only a few decades later in the studies of Knudsen [20] and Langmuir [21]. The interest of Knudsen in vaporization was prompted by his studies of thermal conductivity and rarefied gas flow, as well as by the possibility of development of the effusion... 

Tunc and Bayazitoglu [3] have calculated for the T case the fully developed Nusselt numbers for microtubes through which a rarefied gas flows by taking into account the viscous dissipation but neglecting axial conduction in the fluid and the flow work. They defined the Brinkman number (Eq. 20) with ATref = Te — Tip and used in the slip boundary conditions (Eqs. 8 and 19) (x = = a., = a, = 1. The values of the Nusselt... 

In order to simulate fluid flow, heat transfer, and other related physical phenomena over various length scales, it is necessary to describe the associated physics in mathematical terms. Nearly all the physical phenomena of interest to the fluid dynamics research community are governed by the principles of continuum conservation and are expressed in terms of first- or second-order partial differential equations that mathematically represent these principles (within the restrictions of a continuum-based firamework). However, in case the requirements of continuum hypothesis are violated altogether for certain physical problems (for instance, in case of high Knudsen number rarefied gas flows), alternative formulations in terms of the particle-based statistical tools or the atomistic simulation techniques need to be resorted to. In this entry, we shall only focus our attention to situations in which the governing differential equations physically originate out of continuum conservation requirements and can be expressed in the form of a general differential equation that incorporates the unsteady term, the advection term, the diffusion term, and the source term to be elucidated as follows. 

Free-molecular regime Internal rarefied gas flows Slip flow regime Transitional regime... 

Sharipov F (1997) Rarefied gas flow through a long tube at arbitrary pressure and temperature drops. J Vac Sci Technol A 15(4) 2434-2436... 

Sharipov F (2003) Application of the Cercignani-Lampis scattering kernel to calculations of rarefied gas flows. II. Slip and jump coefficients. Eur J Mech B/Fluid 22 133-143... 

Sharipov F, Seleznev V (1998) Data on intmnal rarefied gas flows. J Phys Chem Ref Data 27(3) 657-706... 

Shaiipov F (1999) Rarefied gas flow through a long rectangular channel. J Vase Sci Technol A 17(5) 3062-3306... 

The DSMC method is a molecule-based statistical simulation method for rarefied-gas flows introduced by Bird [3]. The method solves the dynamical equations for the gas flow numerically, using thousands of simulated molecules. Each simulated molecule represents a large number of real molecules. Assuming molecular chaos and a rarefied gas, only binary collisions need be considered, and so the molecular motion and the collisions are uncoupled if the computational time step is smaller than the physical collision time. Interactions with botmdaries and with other... 

Both microscale gas flows and rarefied-gas flows have three dimensionless numbers that characterize the flow the Reynolds number Re, the Mach number Ma, and the Knudsen number Kn. However, these three parameters are not independent in rarefied-gas flows but instead are related by... 

Several researchers have used this relationship for rarefied-gas flows in the analysis of microscale gas flows [2], However, this relationship has limited application to microscale gas flows. Wang and Li [15] found that Eq. (11) is based on a relationship between the viscosity and the mean free path. On the basis of the kinetic theory of gases, when the gas molecules are treated as smooth, rigid spheres with only a repelling force, the kinetic viscosity can be simply related to the molecular mean free path by... 

With this assumptimi for Eq. (12), if the gas is a perfect gas, the three dimensionless numbers are not independent As a result, gas flows at different scales can be similar (if other similarity conditions are also satisfied, such as similar geometries and boundary conditions). Since rarefied-gas flows have been studied extensively, owing to their important applications in astronautics and aeronautics, many theories and much experimental data can be used for the analysis of microscale gas flow by making use of this similarity, which has been numerically validated by a series of standard DSMC simulations [15]. 

The DSMC method often used in micro-gas flow simulations was originally developed for high Knudsen number rarefied gas flow. The procedures involved in applying DSMC to steady and unsteady flow problems are presented in Fig. 1 [2, 5]. 

Meghadadi Isfahan AH, Soleimani A (2012) Thermal lattice Boltzmann simulation of rarefied gas flows nanochannels for wide range of Knudsen number. Adv Mater Res 403-408 5313-5317... 

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