Structure of low-density supersonic jet

Free underexpanded jets in a quiescent medium: A review

“…Among the available papers, experimental [62,30,12,64,123,124,90], theoretical [96,29,[98][99][100]107] or numerical [132,114,41,115], it is difficult to find quantitative results concerning the passage between regular and singular reflection. However, it seems that the boundary layer behavior and consequently the velocity field and the structure of the first cell are influenced by the shape of the nozzle (especially for CV-DV ones) [62,56,30].…”

“…16] or [11,Chap. 7] but the moment when this phenomenon occurs is quantitatively poorly known, especially the dependency (and interactions) on the pressure [96,29,62,30,[98][99][100]12,64,123,43,124,84,13,107,90,54]. Nonetheless, among the theoretical studies, the Mach disk location has been supposed to appear at a position such that the conservation equations are satisfied for the section perpendicular to the axis [95].…”

“…However, it seems that the boundary layer behavior and consequently the velocity field and the structure of the first cell are influenced by the shape of the nozzle (especially for CV-DV ones) [62,56,30]. Thus, it is usually admitted that the singular reflection, that is to say the apparition of a Mach disk, occurs for a wider pressure range if the exit Mach number increases [30,12,114,124,90,54]; γ is increased [84,13].…”

“…This feature has clearly been less studied than the Mach disk position, however it appears that it is mainly governed by the pressure ratio [62,56,30,[67][68][69]74,81,43,124,128,14,85,129]; apparently decreased when the exit Mach number increases [30,68,12,114,43,90], as discussed below in Section 4.1.3, yet some authors disagree with this conclusion [124,51,52]; different for various gases [74,125,84,13] and inversely proportional to γ; strongly dependent on the nozzle geometry and shape [62,30,[67][68][69]81,14]. It seems that for convergent nozzles it decreases with increasing nozzle angle [56] whereas for convergent-divergent nozzles it increases with the nozzle angle [30].…”

“…Among the huge amount of studies, it appears that the Mach disk location is mainly governed by the pressure ratio [29,30,62,[67][68][69][70]72,[74][75][76][124][125][126][127][128][129]12,57,78,64,81,43,105,[83][84][85][86][87]121,[89][90][91][92]109 independent of the fluid [67,74,78,83,43]; not clearly influenced by the exit nozzle angle since some studies show no noticeable effects [62,[68][69][70]74,78] while others present some influence [29,56,30,126,…”