arXiv subjects

Ewe-Wei Saw

Publications and source records attributed to Ewe-Wei Saw.

7 recordsLinked to original sources

arXiv2026

Correlated collisions and history filtering: unraveling and reproducing the statistics of coalescing particles in turbulence from the ghost-particle framework

This is the first in a series of papers aimed at understanding the statistics of coalescing particles in turbulent flow and their relation to collisionless ghost particles. We perform three families of Direct Numerical Simulations (DNS) under identical flow conditions: ghost particles without mutual interactions; particles that coalesce upon collision with lost monomers replenished at random positions (CR); and particles with the same collision-coalescence kinetics without replenishment (CN). All analyses are monodisperse and concern only monomers. Across $St=0.01\text{-}3.0$, the ghost-particle system has higher collision kernels ($K$) and radial distribution functions (RDFs, $g(r)$) near contact than the coalescing systems. A velocity-filtered RDF, $g_{\mathrm{G}}^{(-)}(r)$, provides a reasonable estimate of the CR contact RDF, $g_{\mathrm{CR}}(d)$. We show that the residual discrepancy between $g_{\mathrm{G}}^{(-)}(d)$ and $g_{\mathrm{CR}}(d)$, and between the corresponding kernels, arises from correlations among successive collisions in the ghost-particle system. A history-filtered ghost-particle kernel, excluding such correlations, reproduces the coalescing-system kernel. We introduce a collision-correlation time $τ_{\mathrm{cc}}$ that quantifies how long current collisions influence future events and find that it has a finite, narrow range across the studied $St$. Filtering particles with collisions within a period comparable to $τ_{\mathrm{cc}}$ yields a history-filtered RDF that reproduces those of both coalescing systems. Finally, the fraction of repeated collisions involving identical particles decays exponentially with $St$. These results unify the coalescing and ghost-particle systems as a history-filtered framework.

physics.flu-dyn↗

arXiv2024

The effect of collision-coagulation on the mean relative velocity of particles in turbulent flow: systematic results and validation of model

The mean radial component of relative velocity (MRV) between pairs of inertial particles is studied, where the particles are advected by turbulent flow and undergo collision-and-coagulation. A previously proposed phenomenological model of MRV for low-inertia particles \citep{saw2022intricate} is corrected (improved) and shown to produce better predictions of the MRV as a function of particle separation distance $r$. Using direct numerical simulation (DNS), the relationship between the MRV and particle/turbulent parameters is studied. For particles with near-zero Stokes numbers ($St$), the MRV is roughly independent of $St$. At larger $St$, the magnitude of MRV increases with $St$, particularly when $St>0.2$. Assuming that the relative particle velocities are derived from fluid velocity differences associated with a nominal resonant length scale, an empirical relation between $St$ is obtained: $d+αSt^β$, where $β\approx1.86$. Coupled with this empirical result, the aforementioned MRV model could be extended to predict MRV for any finite $St$, and we show that the predictions are accurate against the DNS results. Our results also suggest that the extended model could also accurately account for possible Reynolds number ($Re_λ$) effect by simply allowing $α$ and $β$ to be functions of $Re_λ$. Additionally, when the particle diameter is smaller than the Kolmogorov length scale, the MRV for particles with the same St is independent of the particle diameter. The analysis under different Reynolds numbers ($Re_λ=84,124,189$) reveals that for particles with $St\ll1$, the MRV is $Re_λ$-independent. For larger $St$, $Re_λ$ dependence is observed such that the coefficients $α$ and $β$ decrease with $Re_λ.

physics.flu-dyn↗

arXiv2023

Sharp depletion of radial distribution function of particles due to collision and coagulation inside turbulent flow

We perform direct numerical simulation (DNS) to study the clustering of small, heavy, monodisperse particles subject to collision-coagulation in turbulent flow (i.e., colliding particles always coagulate (coalesce) into large ones). We find that collision-coagulation causes the radial distribution function (RDF) of the particles to decrease strongly at particle separation distances $r$ close to the particle diameter $d$. However, the RDF do not decrease indefinitely but approach a finite value in the limit of $r\to d$. We study how the characteristics of this "depletion zone" relate to the particle Stokes number (St), particle diameter, and the Reynolds number of the turbulent flow. A collision-induced modulation factor $γ_{c}$ is defined to represent the degree of RDF depletion due to collisions-coagulation. In the region where $γ_c(r)$ is a quasi-power-law, the corresponding power-law exponent $\tilde{c}_1$ only depends weakly on $St$. The overall trend of $\tilde{c}_1$ with respect to $St$ is similar to that of the classical power-law exponent $c_{1}$ appearing in the RDF of non-colliding particles, i.e., the exponent increase at small $St$, peak around $St \approx 0.7$, and decrease thereafter. The same qualitative trend is also observed for the limiting values of $γ_c$ at $r\to d$. A complementary investigation on the Stokes number trend of the full RDF in the depletion zone is conducted. The slope of RDF appears constant for $St\ll1$ but is changing when $St$ is getting large. The position where the RDF starts to decrease is found to be $St$-dependent. The depletion zone is insensitive to the flow Reynolds number and $γ_c$ of different $Re_λ$ overlap. With changing particle diameter $d$, the reduction of RDF occurs at scales that shift accordingly and always starts at around $2.4d-3d$. The shape of $γ_c(r)$ is independent of changes in $d$.

physics.flu-dyn↗

arXiv2022

Intricate Relations Among Particle Collision, Relative Motion and Clustering in Turbulent Clouds: Computational Observation and Theory

Considering turbulent clouds containing small inertial particles, we investigate the effect of particle collision, in particular collision-coagulation, on particle clustering and particle relative motion. We perform direct numerical simulation (DNS) of coagulating particles in isotropic turbulent flow in the regime of small Stokes number ($St=0.001-0.54$) and find that, due to collision-coagulation, the radial distribution functions (RDFs) fall-off dramatically at scales $r \sim d\,\,$ (where $d$ is the particle diameter) to small but finite values, while the mean radial-component of particle relative velocities (MRV) increase sharply in magnitudes. Based on a previously proposed Fokker-Planck (drift-diffusion) framework, we derive a theoretical account of the relationship among particle collision-coagulation rate, RDF and MRV. The theory includes contributions from turbulent-fluctuations absent in earlier mean-field theories. We show numerically that the theory accurately accounts for the DNS results (i.e., given an accurate RDF, the theory could produce an accurate MRV). Separately, we also propose a phenomenological model that could directly predict MRV and find that it is accurate when calibrated using fourth moments of the fluid velocities. We use the model to derive a general solution of RDF. We uncover a paradox: the past empirical success of the differential version of the theory is theoretically unjustified. We see a further shape-preserving reduction of the RDF (and MRV) when the gravitational settling parameter ($S_g$) is of order $O(1)$. Our results demonstrate strong coupling between RDF and MRV and imply that earlier isolated studies on either RDF or MRV have limited relevance for predicting particle collision rate.

physics.flu-dyn↗

arXiv2019

Universality and Thermodynamics of Turbulence

We investigate universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and the direct numerical simulations (DNS) of the Navier-Stokes equations. We show that the numerical and experimental velocity structure functions up to order 9 follow a log-universality; we find that they collapse on a universal curve, if we use units that include logarithmic dependence on the Reynolds number. We then investigate the meaning and consequences of such log-universality, and show that it is connected with the properties of a "multifractal free energy", based on an analogy between multifractal and themodynamics. We show that in such a framework, the existence of a fluctuating dissipation scale is associated with a phase transition describing the relaminarisation of rough velocity fields with different Holder exponents. Such a phase transition has been already observed using the Lagrangian velocity structure functions, but was so far believed to be out of reach for the Eulerian data.

physics.flu-dyn↗

arXiv2016

Extreme fluctuations of the relative velocities between droplets in turbulent airflow

We compare experiments and direct numerical simulations to evaluate the accuracy of the Stokes-drag model, which is used widely in studies of inertial particles in turbulence. We focus on statistics at the dissipation scale and on extreme values of relative particle velocities for moderately inertial particles (St < 1). The probability distributions of relative velocities in the simulations were qualitatively similar to those in the experiments. The agreement improved with increasing Stokes number and decreasing relative velocity. Simulations underestimated the probability of extreme events, which suggests that the Stokes drag model misses important dynamics. Nevertheless, the scaling behavior of the extreme events in both the experiments and the simulations can be captured by the same multi-fractal model.

physics.flu-dyn↗

arXiv2016

New criteria to detect singularities in experimental incompressible flows

We introduce two new singularity detection criteria based on the work of Duchon-Robert (DR) [J. Duchon and R. Robert, Nonlinearity, 13, 249 (2000)], and Eyink [G.L. Eyink, Phys. Rev. E, 74 (2006)] which allow for the local detection of singularities with scaling exponent $h\leqslant1/2$ in experimental flows, using PIV measurements. We show that in order to detect such singularities, one does not need to have access to the whole velocity field inside a volume but can instead look for them from stereoscopic particle image velocimetry (SPIV) data on a plane. We discuss the link with the Beale-Kato-Majda (BKM) [J.T. Beale, T. Kato, A. Majda, Commun. Math. Phys., 94, 61 (1984)] criterion, based on the blowup of vorticity, which applies to singularities of Navier-Stokes equations. We illustrate our discussion using tomographic PIV data obtained inside a high Reynolds number flow generated inside the boundary layer of a wind tunnel. In such a case, BKM and DR criteria are well correlated with each other.

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