Flow features of underexpanded microjets emerging from a round convergent nozzle

Density measurements of underexpanded microjets that emerge from a round convergent nozzle with an inner diameter of 1 mm at the exit are taken using rainbow schlieren deflectometry to nonintrusively capture an extensive region from the nozzle exit to a downstream location of twenty times the nozzle exit diameter. Flow visualizations of the microjets are carried out at nozzle pressure ratios (NPRs) of 3.0, 4.0, 5.0, 6.0, and 7.0 and corresponding fully expanded jet Mach numbers (\(M_{j}\)) of 1.36, 1.56, 1.71, 1.83, and 1.93, where the NPR can be defined as the ratio of the stagnation pressure upstream of the nozzle to the back pressure. The three-dimensional density fields of the microjets are reconstructed at a spatial resolution of approximately 4 \(\mu\)m by the Abel inversion technique based upon the assumption of axisymmetric density fields. The flow topology of the near-field shock structure for each NPR is demonstrated with an elevated view of the density field, including the jet central axis. The location and flow Mach number of the first local minimum in the density profile along the jet central axis are experimentally provided for the first time as a function of the NPR to propose an empirical relation. An approximate expression for the flow Mach number on the jet central axis from the nozzle exit to the location where the isentropic process is established is also derived against the streamwise distance. In addition, the supersonic length of a shock-containing microjet, which is defined as the distance along the jet central axis from the nozzle exit to the location farthest downstream at which there exists a local flow Mach number of unity, is acquired from the density profile along the jet centerline and compared quantitatively with the experimental data from previous Pitot probe surveys as well as previous empirical relations. Furthermore, the microjet density fields from rainbow schlieren deflectometry are mutually compared with those from previous Mach–Zehnder interferometry under the same nozzle to investigate the effects of nonintrusive techniques on the density profiles along three representative locations: the jet centerline, intermediate line, and lipline.