Laminar gas jets in high-temperature atmospheres

Abstract

Numerical and asymptotic methods are used to describe the structure of low-temperature laminar gas jets discharging into a hot atmosphere of the same gas in the limit of small jet-to-ambient temperature ratios " = Tj/To 1. In the limit " ! 0, heat conduction cannot modify significantly the temperature in the cold gas, leading to a two-region flow structure consisting of a neatly defined unperturbed cold jet for r < rf (x), where T = T0/To = " and u = U0/Uj = 1, surrounded by a hot gas. These two region are separated by a transition layer where T − " " and 1 − u 1. In planar jets the front thickens with distance achieving thickness of order unity at axial distances x "−(1+)Rea forcing the near-axis fluid to change slowly its velocity and temperature, being necessary distances x "−2Rea to reach values of T and 1−u of order unity. In round jets the front remains at r = a up to distances x "−(1−)(log "−1)2 where the front is forced to move radially towards the axis of the jet, reaching r = 0 at x "−1 log "−1Rea. The arrival of the front forces the change of the velocity and temperature in the near-axis region, reaching values of order unity in a far field region of characteristic length x "−1 log "−1Rea, distance comparable to that needed by the front to achieve the axis. In both geometries, the distance necessary for the fully development of the cold jet is considerably longer than that required by the isothermal jet x Rea.