Quantitative Flow Visualization of Slightly Underexpanded Microjets by Mach–Zehnder Interferometers

Abstract

The Mach–Zehnder interferometer with the finite fringe setting is applied for a shock-containing microjet issued from an axisymmetric convergent nozzle with an inner diameter of 1.0 mm at the exit. Experiments are performed at a nozzle pressure ratio of 3.0 to produce a slightly underexpanded sonic jet where the Reynolds number, based upon the diameter and flow properties at the nozzle exit, is $$4.45 \times 10^4$$ 4.45 × 10 4 . The reconstruction of the jet density field is performed using the Abel inversion method under the assumption of an axisymmetric flow as well as the Fourier transform method for the phase shift analyses of interferograms. The three-dimensional density field of a shock-containing microjet can be captured with a spatial resolution of 4 $$\upmu$$ μ m, and the near-field shock structure inside the jet plume is shown in the density contour plot at the cross-section including the jet centerline. In addition, the density field of the microjet is illustrated with various techniques, including representation such as the vertical-knife-edge schlieren, the horizontal-knife-edge schlieren, the bright-field schlieren, and the shadowgraphy. In addition to experiments, the Reynolds averaged Navier–Stokes (RANS) simulation with the SST k–$$\omega$$ ω turbulence model is carried out to model the microjets, and a quantitative comparison with the experiments is performed. The jet centerline density profile obtained by the present experiment is quantitatively compared with those from the previous Mach–Zehnder interferometer, the background oriented schlieren, as well as the RANS simulation.

Study of Rectangular Underexpanded Microjets

“…The pressure-based compressible RANS equations are numerically solved. The Menter's SST k-ω turbulence model is employed because Sugawara et al [11] [12] showed that the RANS simulations with this turbulence model for round shock-containing microjets are in good quantitative agreement with experimental density fields captured by the Mach-Zehnder interferometry. The NPR is held constant at 5.0 where p os and p b are 500 kPa and 100 kPa, respectively, and the plenum temperature T os upstream of the nozzle is specified at 300 K. The dry air is assumed to follow the perfect gas law with a constant specific heat ratio of γ = 1.4, and the coefficient of viscosity is calculated by using the Sutherland's formula.…”

“…The projections of the magnitude of the density gradient vector onto the zy and zx planes are shown in Figure 5(a) and Figure 5(b), respectively. These are sometimes called the bright field schlieren [12] [14] or the circular-cutoff schlieren, which corresponds to schlieren with a disc-shaped filter.…”