Abstract
The Mach–Zehnder interferometer with the finite fringe method is applied for the first time to diagnose the three-dimensional density field of a shock-containing microjet issued from a convergent nozzle with an inner diameter of 1 mm at the exit. Experiments are performed at a nozzle pressure ratio of 4.0 to produce an underexpanded free jet with a Mach disk in the first shock-cell where the Reynolds number, based upon the diameter and flow properties at the nozzle exit, is . Interferogram analyses for reconstructing the jet density fields are performed using the Abel inversion method, in which the analysis of the phase shift of the deformed fringe relative to the background fringe is carried out by the Fourier transform method. In addition to experiments, the flow field of the shock-containing microjet is simulated by solving the Reynolds-averaged Navier–Stokes equations with the SST – turbulence model for a quantitative mutual comparison between the simulation and the experiment. The detailed variation of the density field associated with the Mach disk, the slip streams and the outer shear layers near the jet boundaries are successfully captured. Furthermore, the density profile along the jet centreline obtained by the present experiment is quantitatively compared with those from prior quantitative visualization studies, such as rainbow schlieren deflectometry, background oriented schlieren, moire schlieren and Mach–Zehnder interferometer. The three-dimensional contour map coloured by the magnitude of the density gradient vector inside the microjet reveals the flow topology of the near-field shock systems and elucidates the spatial variation of the shock strength.
Highlights
There has been considerable research on the subject of the dynamics of a supersonic microjet for the application of microscale devices, including a small satellite thruster in space engineering (Bayt & Breuer 2001; Lempert et al 2003), a critical nozzle for obtaining mass flow rate at a low Reynolds number (Nakao & Takamoto 2000), and a micro-propulsion nozzle (Louisos & Hitt 2007)
The Mach–Zehnder interferometer (Born & Wolf 2011) is utilized to investigate the three-dimensional density fields of a microjet with a Mach disk, which could be useful for the computational fluid dynamics (CFD) community as validation data against their numerical simulations of shock-containing microjets
When the test beam passes through a free jet with a variable refractive-index field, the background fringes are changed into the deformed fringe patterns because of the phase shift caused by the variations of the light speed as the beam passes through the test field
Summary
There has been considerable research on the subject of the dynamics of a supersonic microjet for the application of microscale devices, including a small satellite thruster in space engineering (Bayt & Breuer 2001; Lempert et al 2003), a critical nozzle for obtaining mass flow rate at a low Reynolds number (Nakao & Takamoto 2000), and a micro-propulsion nozzle (Louisos & Hitt 2007). The structure of supersonic microjets was systematically studied for the first time by Scroggs & Settles (1996), who made axisymmetric nozzles with exit Mach numbers ranging from 1.0 to 2.8 and two different inner diameters of 600 μm and 1200 μm at the nozzle exit They measured the Pitot pressures along the jet centreline by impinging the jet upon a flat plate, including a pressure port of 0.2 mm in diameter with a pressure sensor attached to the reverse side. An axisymmetric convergent nozzle with an exit diameter = 1 mm is used as the first step for obtaining three-dimensional density fields of a supersonic microjet that shows complex shock structures To this aim, the Mach–Zehnder interferometer (Born & Wolf 2011) is utilized to investigate the three-dimensional density fields of a microjet with a Mach disk, which could be useful for the CFD community as validation data against their numerical simulations of shock-containing microjets. Quantitative comparisons among the present experiment and the previous visualization studies for the jet centreline density profiles are performed in order to investigate the effects of the measuring methods on the density profiles and the nozzle dimensions
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