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Register a new userParticle-Pair Relative Velocity Measurement in High-Reynolds-Number Homogeneous and Isotropic Turbulence Using 4-Frame Particle Tracking Velocimetry
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The radial relative velocity between particles suspended in turbulent flow plays a critical role in droplet collision and growth. We present a simple and accurate approach to RV measurement in isotropic turbulence - planar 4-frame particle tracking velocimetry - using routine PIV hardware. This study demonstrates the feasibility of accurately measuring RV using routine hardware and verifies, for the first time, the path-history and inertial filtering effects on particle-pair RV at large particle separations experimentally.
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The effects of Reynolds number and Stokes number on particle-pair relative velocity (RV) were investigated systematically using a recently developed planar four-frame particle tracking technique in a novel homogeneous and isotropic turbulence chamber.
The collision rate of particles suspended in turbulent flow is critical to particle agglomeration and droplet coalescence. The collision kernel can be evaluated by the radial distribution function (RDF) and radial relative velocity (RV) between particles at small separations $r$. Previously, the smallest $r$ was limited to roughly the Kolmogorov length $eta$ due to particle position uncertainty and image overlap. We report a new approach to measure RDF and RV near contact ($r/a: approx$ 2.07, $a$ particle radius) overcoming these limitations. Three-dimensional particle tracking velocimetry using four-pulse Shake-the-Box algorithm recorded short particle tracks with the interpolated midpoints registered as particle positions to avoid image overlap. This strategy further allows removal of mismatched tracks using their characteristic false RV. We measured RDF and RV in a one-meter-diameter isotropic turbulence chamber with Taylor Reynolds number $Re_lambda=324$ with particles of 12-16 $mu$m radius and Stokes number $approx$ 0.7. While at large $r$ the measured RV agrees with the literature, when $r<20eta$ the first moment of negative RV is 10 times higher than direct numerical simulations of non-interacting particles. Likewise, when $r>eta$, RDF scales as $r^{-0.39}$ reflecting RDF scaling for polydisperse particles in the literature , but when $rlessapproxeta$ RDF scales as $r^{-6}$, yielding 1000 times higher near-contact RDF than simulations. Such extreme clustering and relative velocity enhancement can be attributed to particle-particle interactions. Uncertainty analysis substantiates the observed trends. This first-ever simultaneous RDF and RV measurement at small separations provides a clear glimpse into the clustering and relative velocities of particles in turbulence near-contact.
Multiscale statistical analyses of inertial particle distributions are presented to investigate the statistical signature of clustering and void regions in particle-laden incompressible isotropic turbulence. Three-dimensional direct numerical simulations of homogeneous isotropic turbulence at high Reynolds number ($Re_lambda gtrsim 200$) with up to $10^9$ inertial particles are performed for Stokes numbers ranging from $0.05$ to $5.0$. Orthogonal wavelet analysis is then applied to the computed particle number density fields. Scale-dependent skewness and flatness values of the particle number density distributions are calculated and the influence of Reynolds number $Re_lambda$ and Stokes number $St$ is assessed. For $St sim 1.0$, both the scale-dependent skewness and flatness values become larger as the scale decreases, suggesting intermittent clustering at small scales. For $St le 0.2$, the flatness at intermediate scales, i.e. for scales larger than the Kolmogorov scale and smaller than the integral scale of the flow, increases as $St$ increases, and the skewness exhibits negative values at the intermediate scales. The negative values of the skewness are attributed to void regions. These results indicate that void regions at the intermediate sales are pronounced and intermittently distributed for such small Stokes numbers. As $Re_lambda$ increases, the flatness increases slightly. For $Re_lambda ge 328$, the skewness shows negative values at large scales, suggesting that void regions are pronounced at large scales, while clusters are pronounced at small scales.
This article describes two independent developments aimed at improving the Particle Tracking Method for measurements of flow or particle velocities. First, a stereoscopic multicamera calibration method that does not require any optical model is described and evaluated. We show that this new calibration method gives better results than the most commonly-used technique, based on the Tsai camera/optics model. Additionally, the methods uses a simple interpolant to compute the transformation matrix and it is trivial to apply for any experimental fluid dynamics visualization set up. The second contribution proposes a solution to remove noise from Eulerian measurements of velocity statistics obtained from Particle Tracking velocimetry, without the need of filtering and/or windowing. The novel method presented here is based on recomputing particle displacement measurements from two consecutive frames for multiple different time-step values between frames. We show the successful application of this new technique to recover the second order velocity structure function of the flow. Increased accuracy is demonstrated by comparing the dissipation rate of turbulent kinetic energy measured from the second order structure function against previously validated measurements. These two techniques for improvement of experimental fluid/particle velocity measurements can be combined to provide high accuracy 3D particle and/or flow velocity statistics and derived variables needed to characterize a turbulent flow.
We use direct numerical simulations to investigate the interaction between the temperature field of a fluid and the temperature of small particles suspended in the flow, employing both one and two-way thermal coupling, in a statistically stationary, isotropic turbulent flow. Using statistical analysis, we investigate this variegated interaction at the different scales of the flow. We find that the variance of the fluid temperature gradients decreases as the thermal response time of the suspended particles is increased. The probability density function (PDF) of the fluid temperature gradients scales with its variance, while the PDF of the rate of change of the particle temperature, whose variance is associated with the thermal dissipation due to the particles, does not scale in such a self-similar way. The modification of the fluid temperature field due to the particles is examined by computing the particle concentration and particle heat fluxes conditioned on the magnitude of the local fluid temperature gradient. These statistics highlight that the particles cluster on the fluid temperature fronts, and the important role played by the alignments of the particle velocity and the local fluid temperature gradient. The temperature structure functions, which characterize the temperature fluctuations across the scales of the flow, clearly show that the fluctuations of the fluid temperature increments are monotonically suppressed in the two-way coupled regime as the particle thermal response time is increased. Thermal caustics dominate the particle temperature increments at small scales, that is, particles that come into contact are likely to have very large differences in their temperature. This is caused by the nonlocal thermal dynamics of the particles...
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