Vortex Flow in a Convergent-Divergent Nozzle

Introduction I N certain geometries, supersonic swirling jets mix more rapidly (in a shorter axial distance) with the surrounding gas than nonswirling jets and, thus,may Ž nd applicationin the Ž elds of combustion and propulsion.Experiments in which pressure-matchedsupersonic swirling jets dischargedinto stagnantair demonstratedgreater mixing layer growth rate in the near Ž eld,which could be correlated with mean streamline curvature.1;2 These studies also found that, if the jets were operated overexpanded, vortex breakdown occurred, leading to a substantial increase in mixing.A later study considered the injection of a supersonic swirling jet at 30 deg into a supersonic duct  ow.3 Other work includes that of Naughtonet al.4 and the referencesquoted therein.Critical to the implementationof the studies in Refs. 1–3 was the developmentof a simple, approximatemethod for the calculation of the  ow of a vortex in an axisymmetric nozzle.Thismethodassumessteady,quasi-one-dimensional (negligible radial velocity), irrotational, isentropic  ow with a line vortex (singularity)on theaxis and (itwas subsequentlyfound) is equivalent,in many respects, to the method ofMager. The purposeof this Note is to present the method and to establish its validity in this application by comparing the results of calculations to those of experiment.