Design of de Laval nozzles for gas-phase molecular studies in uniform supersonic flow

Abstract

A method to design de Laval nozzles to generate uniform supersonic flows for gas-phase molecular studies at very low temperature is presented. The nozzle design is optimized for the flows in argon, helium, or nitrogen, up to Mach 5 and down to a few kelvin. Experimental results have shown that flows exhibit a good uniformity in terms of speed, temperature, and density, with the length of the uniformity of the supersonic flows up to 50 cm which corresponds to a kinetic time of about 1 ms in nitrogen for nozzles with a throat of about 1 cm in diameter. The design of the de Laval nozzles is concentrated at the diverging section. The method is based on the calculation of an isentropic core as described in Owen's work [J. M. Owen, "An improved method of supersonic nozzle design for rarefied gas flows,"Ph.D. thesis (University of California, 1950)] of supersonic nozzle design for rarefied gas flows. The determination of the isentropic nozzle wall is carried out by the method of characteristics following Cronvich's algorithm [L. Cronvich, "A numerical-graphical methods of characteristics for axially symmetric isentropic flow,"J. Aeronaut. Sci. 15, 156-162 (1948)]. The laminar boundary layer is corrected by employing Michel's integral method [R. Michel, "Aérodynamique: Couches limites, frottement et transfert de chaleur"(ENSAE, 1963)]. This approach has already largely shown its potency and had been widely used for 30 years in the field of experimental molecular physics or laboratory astrophysics [sometimes known under the french acronym CRESU for Cinetique de Réaction en Écoulement Supersonique Uniforme (reaction kinetics in uniform supersonic flow)]. Based on this approach, an in-house computer program with graphical user interface to design de Laval nozzles for kinetic studies is published for the first time.