Equations Of One-dimensional Gas Flow Research Articles

Modeling of large cluster synthesis

The original idea of the ionized cluster beam thin film deposition technique was based upon producing, ionizing and accelerating beams of atoms clusters from vaporized material onto a substrate in a vacuum environment using a supersonic jet source. However, the conditions and nozzles for this cluster synthesis found so far require rather high stagnation pressures (more than 1 atm) which is impractical for many materials with lower vapor pressures than, for example, zinc. Simulation of this process using classical nucleation theory and one-dimensional gas flow equations is described here. This approach is an extension of previous methods used for simulation of condensation of water vapor during supersonic expansion in nozzles and the simulation mechanism of large clusters from vaporized solid materials. Zinc cluster sizes predicted by the model are in qualitative and quantitative agreement with our experimental results. Simulation results are discussed in terms of the best nozzle geometry which will result in larger clusters at a lower stagnation pressure. Novel nozzle designs simulated in this work show that clusters may be formed at lower pressures which would extend the method to a much wider range of materials. Thus development of such new nozzles for use at lower pressure and temperature would significantly impact this method.

SU(3) symmetry of the equations of unidimensional gas flow, with arbitrary entropy distribution

We have shown in an earlier work that, assuming a particular class of equations of state, the Euler equations of one-dimensional gas flow are invariant under an SU(3) group of transformations, and in fact admit of a Lie group of symmetry of infinite order; they, therefore, possess an infinite number of conservation laws. We show in the present work that the SU(3) symmetrical formalism still brings about tremendous simplification and analytical order in the most general case where the equation of state is arbitrary. The six characteristic equations assume a vector form and relate two conjugate, three-dimensional vectors U and X. The SU(3) symmetry is only broken to a minor extent through the occurrence of a multiplicative factor Γ in the equations. The conservation laws take the form of the Cauchy integrability condition for the elements of a traceless second rank tensor εij and, taken all together, form an SU(3) octet; in the most general case, however, there exist four conservation laws only (five if the gas is monatomic) as a result of the breaking of symmetry. Application of these results to the theory of self-similar flow is also discussed. Finally, we show the invariance of the equations of monatomic gas flow under Lorentz transformations in a three-dimensional Minkowski space; that raises the question of whether a geometrical relation may exist between the Minkowski light cones and characteristics.