Effusion of neutral gas in vacuum

Fluid, gas and plasma mechanics


Kotel'nikov V. A.*, Kotelnikov M. V.*, Platonov M. A.**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: mvk_home@mail.ru
**e-mail: misiposhta@mail.ru


The neutral gas effusion into the vacuum space is studied by computer simulation methods. In General, this problem is six-dimensional in phase space (x,y,z,vx,vy,vz) and non-stationary. As a hole, it is proposed to consider a rectangle, which one side is much larger than the other. This model shape of the hole due to the shear symmetry will allow on the one hand to significantly reduce the dimension of the problem (in this case, in the phase space, the problem depends on x, y, vx, vy), and on the other hand to obtain all the main features of the distribution of gas parameters in the computational domain. The computational model of the problem is based on the method of successive iterations in time, when the transition process from the initial to the final stationary state is modeled, that is, the establishment of the distribution of gas parameters in the computational domain. The methods of characteristics were used to solve Vlasov equation. The calculation algorithm was implemented in the form of a computer program in C++ using the tools of the OpenGL graphic library. The size of computational domain was of 2 x 2 and contained 39942400 cells of the computational grid, the time step was of 0.01 ht dimensionless units. Control of the count end time was performed visually using a graphic window displayed on the screen during the account. According to the observations on the monitor, the following was observed:

  • The constant value of the gas particles flow crossing the computational domain, which indicated the establishment of a stationary solution to the problem

  • The practical coincidence of the gas particle flow from the orifice to the computational domain and the gas particle flow flowing from the computational domain, which indicates the implementation of the law of conservation of gas mass in the computational domain in a steady state.

These two conditions were fulfilled by the end of the calculation. Then the results were subjected to further analysis. The information on the parameters of the rarefied gas flowing from the effusion orifice to the vacuum is based on the distribution function f(t,x,y,vx,vy), which was studied in detail in the course of computational experiments. It follows from the graphs, that the distribution function changes its shape in a typical way when it is shifted from the hole to the boundary of the computational domain along the axis of the jet symmetry. The graphs show also the fields of velocities and concentrations of gas particles in the computational domain. The conducted researches may be useful to developers of portable devices for the small leakages diagnostics employed in the vacuum and space industry. Computer simulation of effusion of a rarefied gas in vacuum gave a presentation on the features of the gas distribution parameters in the computational domain, both during the transition process and in the final stationary state.


effusion, rarefied gas, Vlasov equation, method of characteristics, distribution function, depressurization, small leak, molecular flux


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