Role of diffusion on molecular tagging velocimetry technique for rarefied gas flow analysis

Abstract

The molecular tagging velocimetry (MTV) is a well-suited technique for velocity field measurement in gas flows. Typically, a line is tagged by a laser beam within the gas flow seeded with light emitting acetone molecules. Positions of the luminescent molecules are then observed at successive times and the velocity field is deduced from the analysis of the tagged line displacement and deformation. However, the displacement evolution is expected to be affected by molecular diffusion, when the gas is rarefied. Therefore, there is no direct and simple relationship between the velocity field and the measured displacement of the initial tagged line. This paper addresses the study of tracer molecules diffusion through a background gas flowing in a channel delimited by planar walls. Tracer and background species are supposed to be governed by a system of coupled Boltzmann equations, numerically solved by the direct simulation Monte Carlo (DSMC) method. Simulations confirm that the diffusion of tracer species becomes significant as the degree of rarefaction of the gas flow increases. It is shown that a simple advection–diffusion equation provides an accurate description of tracer molecules behavior, in spite of the non-equilibrium state of the background gas. A simple reconstruction algorithm based on the advection–diffusion equation has been developed to obtain the velocity profile from the displacement field. This reconstruction algorithm has been numerically tested on DSMC generated data. Results help estimating an upper bound on the flow rarefaction degree, above which MTV measurements might become problematic

Molecular tagging velocimetry by direct phosphorescence in gas microflows: Correction of Taylor dispersion

“…(1). The first step of the reconstruction method consists in approximating the velocity profile () The application of this reconstruction method to DSMC simulations [62] has shown a very accurate velocity reconstruction from displacements, for Knudsen numbers lower than 0.05, i.e. within the continuum and slip flow regimes.…”

“…Although diffusion is much less significant in liquids, the authors showed that the velocity close to the walls could be overestimated due to the combination of molecular diffusion and shear stress. They demonstrated that this error, limited to a near wall region of a few micrometers thick, could be Regarding Taylor dispersion in gas microflows, a Direct Simulation Monte Carlo (DSMC) study, led by Frezzotti et al, showed that even in the continuum regime, the tagged molecules are subject to significant molecular diffusion [62]. In case of slip flow, the mechanism illustrated in Fig.…”

Velocity Measurements in Channel Gas Flows in the Slip Regime by means of Molecular Tagging Velocimetry

“…In step (d), MTV images are passed through a proper noise filter to make the fitting procedure of step (e) more robust. Finally, step (f) consists in the actual measurement of the velocity profile by means of the reconstruction method [13]. All the operations described below were implemented by means of Matlab ® software (The MathWorks Inc., Natick, MA, USA) and were systematically applied to all the recorded images.…”

“…Subsequently, we have proposed a numerical method based on the advection-diffusion equation that was able to correctly reconstruct the velocity profile from the displacement of the tagged line. In a first step, the reliability of the method was proven by applying it to direct simulation Monte Carlo (DSMC) numerical experiments [13]. Later on, the method was proven to be valid also in the case of physical MTV experiments in confined non-rarefied flows.…”

“…In Section 3, the experimental methodology used for acquiring MTV images in slow-varying thermodynamic gas flow conditions is thoroughly explained and the advantages and disadvantages of this approach are critically discussed. Section 4 describes the sequence of used post-processing operations, from the recorded MTV images to the extraction of the displacement profile data to be used in the reconstruction method developed in [13]. In Section 5, the experimental results of this work are reported.…”