The nonequilibrium flows of gases appear in different technological domains like the vacuum equipment, high altitude aerodynamics and in a relatively new field as the microelectromechanical systems (MEMS). The deviation of a gas from its local equilibrium state can be characterized by the Knudsen number, which presents the ratio between the molecular mean free path and the characteristic length of the problem. For the relatively large values of the Knudsen number the classical continuum approach fails to describe the gas behavior and the kinetic equations, like the Boltzmann equation or model kinetic equations, must be solved to simulate the gas flows.
The gas flow through a thin orifice is a problem of a large practical interest for the design of the vacuum equipment, space or the microfluidic applications. The under-expanded jets through the orifices are predominately used by particle analyzer systems to separate and isolate molecules, ions of substances for analyzing their physical and chemical properties. The time dependent characteristics of these jets are important for the investigation of the response time of the vacuum gauges developed for the measurements of the rapid pressure changes [1].
The steady state flows through the orifice, slit and short tube have been successfully studied applying the DSMC method and the kinetic equations [2], [3]. However, only a few results on the transient rarefied flows through an orifice [4] or a slit [5] may be found in open literature.
The transient properties of gas flow through an orifice, induced by various values of the pressure ratio, are studied over a broad range of gas rarefaction. The unsteady nonlinear S-model kinetic equation is solved numerically by Discrete Velocity Method (DVM) to obtain the mass flow rate and macroscopic parameters as a function of time.
The simulations are conducted from the free molecular to hydrodynamic regimes for four values of pressure ratio between reservoirs. The mass flow rate evolution in time is analyzed and it is found that the time to reach the steady state mass flow rate depends essentially on the pressure ratio between the reservoirs and on the gas flow regime in the left reservoir. For several pressure ratios between the reservoirs the particular flow behavior is observed: the spatial cell structure of axisymmetric mildly under-expanded jet appears, formed by the system of incident and reflected shock and compression waves.
REFERENCES
1. K. Jousten et al A standard to test the dynamics of vacuum gauges in the millisecond range, Vacuum 100 (2014) 14--17.
2. T.Lilly et al. Measurements and computations of mass flow and momentum flux through short tubes in rarefied gases, Phys. Fluids 18~(9) (2006) 093601.1--11.
3. V. Aristov et al. Simulations of pressure-driven flows through channels and pipes with unified flow solver, Vacuum 86 SI~(11) (2012) 1717--1724.
4. F.Sharipov, Transient flow of rarefied gas through an orifice, J. Vac. Sci. Technol. A 30(2) (2012) 021602.1--5.
5. A.Polikarpov, I.Graur, Unsteady rarefied gas flow through a slit, Vacuum 101(2014) 79 -- 85.
