Research on Molecule Distribution during Transmission Process in Molecular Flow
|Course||Fluid Machinery and Engineering|
|Keywords||molecular flow molecular gas dynaics beaming effect cosineemission law numerical integration Monte Carlo simulation|
The theory of molecular flow have been researched by Knudsen and Clausing ever since the beginning of last centry. However, up to present still there is need to discuss molecular flow theory more deeply, such as moleucle distribution in tube in molecular flow. Choosing the molecule distribution as pointcut, this paper aims to reveal the principles of molecular flow charactors. The research of molecule distribution can also make some vacuum theoritical calculation preciser, such as sucking speed of cryopump and transmission probability of series connection.Aiming at the problem of gas molecules passing through the cylindrical tube in free molecular flow, the gas molecules are divided into "directly passing" ones which fly directly from inlet to outlet and "reflective" ones which are reflected from the inner wall of the tube to inlet or outlet. The geometrical models are respectively established for two kinds of molecules. Based on the Knudsen cosine law, the formulae and simulation results of both positional and directional (angular) distribution of gas molecules at any position of orifices are obtained by means of theoretical derivation and numerical integration.As the base of calculation, the relative incident rate along the tube is deduced and computed for the first time, which means the ratio of tube wall local reflectivity to inlet original incident rate. For molecular positional distribution, a criterion v is defined as the ratio of local molecular density to the average density on the whole orifice section, and its expression is given for each kind of molecules. The numerical simulation results demonstrated that, after entering the inlet uniformly, molecules shows "positional beaming effect" at outlet,(e.g. when L=0.5d, v (0)=1.1353in center and v (0.5)=0.8313in edge). Meanwhile, the distribution of molecules returning to inlet shows that the central area is sparse and the edge area is dense. Inlet positional distribution and outlet positional distribution are complementary with each other, i.e. the superposition of them at corresponding points becomes uniform precisely regardless of length-diameter ratio of the tube.For molecular angular distribution, the directional distribution graphs at different positions are drawn as the curved surfaces within a unit sphere which corresponds to the cosine distribution style. In the graphs, the "directly passing" molecules occupies an eccentric cone part around the normal line, while the "reflecting" molecules occupies the other part out of the cone. Calculating results demonstrate that angular distribution depends on not only the length-diameter ratio, but also the position on orifice. At the outlet, the molecules are dense in small angle range and sparse in large angular range. Whether for the molecules emitting from one point or the whole outlet cross section, the distribution all shows "angular beaming effect". While at inlet, the angular distribution is that molecules are sparse in small angle range and dense in large angular range, which is opposite to the distribution at outlet. For either the corresponding points or the whole section of the inlet and the outlet, the angular distributions are complementary with each other, i.e. the superposition of them obeys the cosine distribution.Besides cylinder which is the most common tube style in vacuum system, this paper also analytically researched the molecular flow in tube of rectangular cross section by the same method with cylinders. by obtaining the relative incident rate which is more complicated than that of cylinder, the "positional beaming effect" at outlet and divergent distribution at inlet are testified. Meanwhile, the angular distributions of molecules emitting from any point of orifice are obtained.For molecular flow in elbow tube which is difficult to solve by analytic method, this paper researched elbow tube by means of a widely applicable method-Monte Carlo simulation. Using Visual Basic to prepare a procedure, the process that molecules uniformly enter from inlet according to cosine emission law and flying in the tube to escape is simulated, and the parameters at orifice are recorded. The "postional beaming effect" at outlet is summarized by statistical results. Meanwhile, the Monte Carlo simulating procedure is also a convenient tool to obtain transmission probability of different dimensions. In addition, Monte Carlo simulation is applied to rectangular cross section tube. Compared with analytical results, the similar data and consistent conclusion are achieved.