Andrew D. Bragg

New insights from comparing statistical theories for inertial particles in turbulence: I. Spatial distribution of particles

In this paper, we contrast two theoretical models for the spatial clustering of inertial particles in isotropic turbulence, one by Chun et al (2005 J. Fluid Mech. 536 219) and the other by Zaichik et al (2007 Phys. Fluids 19 113308). Although their predictions for the radial distribution function are similar in the regime , they appear to describe the physical mechanism responsible for the clustering in quite different ways. We demonstrate why the theories generate such similar results in the regime by showing that the clustering mechanism in the Chun et al theory captures the leading order effects of the clustering mechanism in the Zaichik et al theory for . However, outside of this regime, the similarity between the predictions of the theories breaks down, and we consider the sources of the differences as well as the physical meaning and implications of the differences. Using DNS data we then show that the clustering mechanism described by the Zaichik et al theory accurately describes the clustering up to , and we identify a possible source of error for some of the slight quantitative discrepancies at larger St. We then compare these theories with others in the literature and attempt to reconcile as many of the physical explanations for clustering as we can. Finally, we consider the relationship between clustering in isotropic turbulence and the near-wall accumulation of inertial particles in a turbulent boundary layer, and how they scale with the Stokes number in the weak inertia limit.

Forward and backward in time dispersion of fluid and inertial particles in isotropic turbulence

In this paper, we investigate both theoretically and numerically the Forward-In-Time (FIT) and Backward-In-Time (BIT) dispersion of fluid and inertial particle-pairs in isotropic turbulence. Fluid particles are known to separate faster BIT than FIT in three-dimensional turbulence, and we find that inertial particles do the same. However, we find that the irreversibility in the inertial particle dispersion is in general much stronger than that for fluid particles. For example, the ratio of the BIT to FIT mean-square separation can be up to an order of magnitude larger for the inertial particles than for the fluid particles. We also find that for both the inertial and fluid particles, the irreversibility becomes stronger as the scale of their separation decreases. Regarding the physical mechanism for the irreversibility, we argue that whereas the irreversibility of fluid particle-pair dispersion can be understood in terms of a directional bias arising from the energy transfer process in turbulence, inertial...

New insights from comparing statistical theories for inertial particles in turbulence: II. Relative velocities

Part I of this two-part series compared two theories for the radial distribution function (RDF), a statistical measure of the clustering of inertial particles in isotropic turbulence. In Part II, we will contrast three theoretical models for the relative velocities of inertial particles in isotropic turbulence, one by Zaichik et al (2009 New. J. Phys. 11 103018), the second by Pan et al (2010 J. Fluid Mech. 661 73) and the third by Gustavsson et al (2011 Phys. Rev. E. 84 045304). We find that in general they describe the relative velocities in qualitatively similar ways, capturing the influence of the non-local dynamics on the formation of caustics and non-smooth scaling behavior in the dissipation range. We then compare the theoretical predictions with direct numerical simulation data and find that although they capture the qualitative behavior of the data consistently, they differ quantitatively, and we discuss the possible sources of error in each of the theories. Finally, we consider how the Zaichik et al theory predicts that the formation of caustics modifies the form of the RDF, and show that the theory describes the behavior of the RDF for particles whose response time scales with the inertial range time scales of the turbulence.

Particle transport in a turbulent boundary layer: Non-local closures for particle dispersion tensors accounting for particle-wall interactions

Continuum equations derived from a probability density function kinetic equation contain dispersion tensors that describe the interaction between inertial particles and the underlying turbulent flow in which they are transported. These tensors require closure treatment and recent work has shown that traditional closure approximations perform poorly when applied to the case of particle dispersion in turbulent boundary layers. The dispersion tensors are intrinsically non-local, being sensitive to both the strong inhomogeneity of wall-bounded turbulence and the influence of particle-wall collisions. A new strategy for constructing non-local closure models is presented to account for such influences. An important feature of the approach is that it utilizes exactly the same input parameters required for the traditional closures. Differences between the two approaches are therefore a reflection of the improved closure strategy, rather than a consequence of improved or additional input data. Predictions from bot...

Developments and difficulties in predicting the relative velocities of inertial particles at the small-scales of turbulence

In this paper, we consider the development of theoretical models to predict the relative velocities of inertial particles in isotropic turbulence. In particular, we use our recently developed theory for the backward-in-time (BIT) relative dispersion of inertial particles in turbulence [Bragg et al., “Forward and backward in time dispersion of fluid and inertial particles in isotropic turbulence,” Phys. Fluids 28, 013305 (2016)] to develop the theoretical model by Pan and Padoan [“Relative velocity of inertial particles in turbulent flows,” J. Fluid Mech. 661, 73 (2010)]. We focus on the most difficult regime to model, the dissipation range, and find that the modified Pan and Padoan model (that uses the BIT dispersion theory) can lead to significantly improved predictions for the relative velocities, when compared with the Direct Numerical Simulation (DNS) data. However, when the particle separation distance, r, is less than the Kolmogorov lengthscale, η, the modified model overpredicts the DNS data. We ex...

Analysis of the forward and backward in time pair-separation probability density functions for inertial particles in isotropic turbulence

In this paper we investigate, using theory and Direct Numerical Simulations (DNS), the Forward In Time (FIT) and Backward In Time (BIT) Probability Density Functions (PDFs) of the separation of inertial particle-pairs in isotropic turbulence. In agreement with our earlier study (Bragg et al., Phys. Fluids 28, 013305 (2016)), where we compared the FIT and BIT mean-square separations, we find that inertial particles separate much faster BIT than FIT, with the strength of the irreversibility depending upon the final/initial separation of the particle-pair and their Stokes number

On the theory of drainage area for regular and non-regular points

St

Is the kinetic equation for turbulent gas-particle flows ill-posed?

. However, we also find that the irreversibility shows up in subtle ways in the behavior of the full PDF that it does not in the mean-square separation. In the theory, we derive new predictions, including a prediction for the BIT/FIT PDF for

Effects of Reynolds Number and Stokes Number on Particle-pair Relative Velocity in Isotropic Turbulence: An Experimental Study

{St\geq O(1)}

Do fluid particles separate exponentially in the dissipation range

, and for final/initial separations in the dissipation regime. The prediction shows how caustics in the particle relative velocities in the dissipation range affect the scaling of the pair-separation PDF, leading to a PDF with an algebraically decaying tail. The predicted functional behavior of the PDFs is universal, in that it does not depend upon the level of intermittency in the underlying turbulence. We also analyze the pair-separation PDFs for fluid particles at short-times, and construct theoretical predictions using the multifractal formalism to describe the fluid relative velocity distributions. The theoretical and numerical results both suggest that the extreme events in the inertial particle-pair dispersion at the small-scales are dominated by their non-local interaction with the turbulent velocity field, rather than due to the strong dissipation range intermittency of the turbulence itself...