Rarefied gas flows have a central role in microfluidic devices for many applications in various scientific fields. Local thermodynamic non-equilibrium at the wall-gas interface produces macroscopic effects, one of which is a velocity slip between the gas flow and the solid surface. Local experimental data able to shed light on this physical phenomenon are very limited in the literature. The molecular tagging velocimetry (MTV) could be a suitable technique for measuring velocity fields in gas micro flows. However, the implementation of this technique in the case of confined and rarefied gas flows is a difficult task: the reduced number of molecules in the system, which induces high diffusion, and the low concentration of the molecular tracer both drastically reduce the intensity and the duration of the exploitable signal for carrying out the velocity measures. This work demonstrates that the application of the 1D-MTV by direct phosphorescence to gas flows in the slip flow regime and in a rectangular long channel is, actually, possible. New experimental data on phosphorescence emission of acetone and diacetyl vapors at low pressures are presented. An analysis of the optimal excitation wavelength is carried out to maximize the intensity and the lifetime of the tracer emission. The experimental results demonstrate that a little concentration of about 5-10 % of acetone vapor excited at 310 nm or of diacetyl vapor excited at 410 nm in a helium mixture at pressures on the order of 1 kPa provides an intense and durable luminescent signal. In a 1-mm deep channel, a gas flow characterized by these thermodynamic conditions is in the slip flow regime. Moreover, numerical experiments based on DSMC simulations are carried out to demonstrate that an accurate measurement of the velocity profile in a laminar pressure-driven flow is possible for the rarefied conditions of interest.

This work presents a novel numerical procedure for reconstructing volumetric density and velocity fields from planar laser-induced fluorescence (PLIF) and stereoscopic particle image velocimetry (SPIV) data. This new method is theoretically and practically demonstrated to provide more accurate 3D vortical structures and density fields in high shear flows than reconstruction methods based on the mean convective velocity. While Taylor’s hypothesis of frozen turbulence is commonly applied by using the local mean streamwise velocity, the proposed algorithm uses the measured local instantaneous velocity for data convection. It consists of a step-by-step reconstruction based on a mixed Lagrangian–Eulerian solver that includes the 3D interpolation of scattered flow data and that relaxes the Taylor’s hypothesis by iterative enforcement of the incompressibility constraint on the velocity field. This methodology provides 3D fields with temporal resolution, spatial resolution, and accuracy comparable to that of real 3D snapshots, thus providing a practical alternative to tomographic measurements. The procedure is validated using numerical data of the constant-density channel flow available on the Johns Hopkins University Turbulence Database (JHTDB), showing the accurate reconstruction of the 3D velocity field. The algorithm is applied to an experimental dataset of PLIF and SPIV measurements of a variable-density jet flow, demonstrating its capability to provide 3D velocity and density fields that are more consistent with the Navier–Stokes equations compared to the mean flow convective method. Graphic abstract

Simulated and experimental molecular tagging velocimetry (MTV) images have been analyzed with a technique commonly used to process grid images on surfaces, the windowed Fourier transform with local spectrum analysis (WFT-LSA). A systematic synthetic image study of the modulation transfer function (MTF) and error tendencies of the WFT-LSA was performed and compared with a PIV-style cross-correlation algorithm to see if advanced strategies such as iterative image deformation can improve analysis of gridded images with high noise levels. Testing of single-pass algorithms showed that in typical MTV images, the WFT-LSA yields significantly lower bias errors than cross-correlation (CC) at displacements greater than 1 pixel but slightly higher random error at all displacements and image conditions. Analysis of the MTF shows that CC provided better resolution of spatial fluctuations than the WFT-LSA in many combinations of grid size and interrogation window. Tests of image deformation algorithms showed that the gap in performance between CC and WFT-LSA is maintained even as both methods improve. Additionally, WFT-LSA and CC methods are applied to real MTV experiments in high-speed gas jet flows. A preliminary analysis of phosphorescence lifetime provided by acetone vapor excited at 266 nm is used for assessing the required gas speeds for making MTV application feasible. The application of WFT-LSA to real MTV images demonstrates the ability of the algorithm to handle further real-world effects that could not be considered in the synthetic image analysis, like reduced signal-to-noise ratio and non-uniform intensity of the tagging grid across the image introduced by the actual laser beam energy distribution. With experimental images, CC is more accurate with shear flows but less robust to high noise levels than WFT-LSA, as predicted by the synthetic image analysis.

Direct measurements of the slip velocity in rarefied gas flows produced by local thermodynamic non-equilibrium at the wall represent crucial information for the validation of existing theoretical and numerical models. In this work, molecular tagging velocimetry (MTV) by direct phosphorescence is applied to argon and helium flows at low pressures in a 1-mm deep channel. MTV has provided accurate measurements of the molecular displacement of the gas at average pressures of the order of 1 kPa. To the best of our knowledge, this work reports the very first flow visualizations of a gas in a confined domain and in the slip flow regime, with Knudsen numbers up to 0.014. MTV is cross-validated with mass flowrate measurements by the constant volume technique. The two diagnostic methods are applied simultaneously, and the measurements in terms of average velocity at the test section are in good agreement. Moreover, preliminary results of the slip velocity at the wall are computed from the MTV data by means of a reconstruction method.

Over the last few years, superhydrophobic (SH) surfaces have been receiving an increasing attention in many scientific areas by virtue of their ability to enhance flow slip past solid walls and reduce the skin-friction drag. In the present study, a global linear-stability analysis is employed to investigate the influence of the SH-induced slip velocity on the primary instability of the 2D flow past a circular cylinder. The flow regions playing the role of 'wavemaker' are identified by considering the structural sensitivity of the unstable mode, thus highlighting the effect of slip on the global instability of the considered flow. In addition, a sensitivity analysis to slip-induced base-flow modifications is performed, revealing which areas of the cylinder surface provide a stabilising/destabilising effect when treated with a SH coating.

This work presents reconstructions of 3D pressure fields starting from 2D3C stereoscopic-PIV (SPIV) measurements. In Fratantonio et al. (2021), we presented a new reconstruction algorithm, the “Instantaneous convection” method, capable of producing 3D velocity fields from time-resolved SPIV measurements. For reconstructions in flows with strong shear layers and high turbulence intensity, this method is able to provide time-resolved 3D velocity volumes that are more accurate than those that can be obtained from the more frequently employed reconstruction method based on the Taylor’s hypothesis and on the use of a mean convective field. Here we investigate the possibility of reconstructing the 3D pressure field from the timeresolved series of reconstructed 3D velocity data. A pseudo-tracking method is employed for computing the velocity material derivative, and the pressure field is then reconstructed by solving the 3D Poisson equation. The velocity and pressure reconstructions are validated on the Direct Numerical Simulation data of the turbulent channel flow taken from the John Hopkins Turbulence Database (JHTDB), and an application to experimental SPIV measurements of an air jet flow in coflow carried out at the Turbulent Mixing Tunnel (TMT) facility at Los Alamos National Laboratory is presented.

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