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Andrew D. Bragg

Publications and source records attributed to Andrew D. Bragg.

At least 37 records · Page 2Linked to original sources
arXiv2021

Analysis of scale-dependent kinetic and potential energy in sheared, stably stratified turbulence

Budgets of turbulent kinetic energy (TKE) and turbulent potential energy (TPE) at different scales $\ell$ in sheared, stably stratified turbulence are analyzed using a filtering approach. Competing effects in the flow are considered, along with the physical mechanisms governing the energy fluxes between scales, and the budgets are used to analyze data from direct numerical simulation (DNS) at buoyancy Reynolds number $Re_b=O(100)$. The mean TKE exceeds TPE by an order of magnitude at the large scales, with the difference reducing as $\ell$ is decreased. At larger scales, buoyancy is never observed to be positive, with buoyancy always converting TKE to TPE. As $\ell$ is decreased, the probability of locally convecting regions increases, though it remains small at scales down to the Ozmidov scale. The TKE and TPE fluxes between scales are both downscale on average and their instantaneous values are positively correlated, but not strongly so, and this occurs due to the different physical mechanisms that govern these fluxes. Moreover, the contribution to these fluxes arising from the sub-grid fields are shown to be significant, in addition to the filtered scale contributions associated with the processes of strain-self amplification, vortex stretching, and density gradient amplification. Probability density functions (PDFs) of the $Q,R$ invariants of the filtered velocity gradient are considered. Unlike isotropic turbulence, as $\ell$ increases the sheared-drop shape of the PDF disappears and the PDF becomes symmetric about $R=0$, meaning regions of vortex stretching and compression become equi-probable, as well as regions of strain amplification or suppression.

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arXiv2021

An experimental study on the multiscale properties of turbulence in bubble-laden flows

The properties of bubble-laden turbulent flows at different scales are investigated experimentally, focusing on the flow kinetic energy, energy transfer, and extreme events. The experiments employed particle shadow velocimetry measurements to measure the flow in a column generated by a homogeneous bubble swarm rising in water, for two different bubble diameters ($2.7$ mm $\&$ $3.9$ mm) and moderate gas volume fractions ($0.26\%\sim1.31\%$). The two velocity components were measured at high-resolution, and used to construct structure functions up to twelfth order for separations spanning the small to large scales in the flow. Concerning the flow anisotropy, the velocity structure functions are found to differ for separations in the vertical and horizontal directions of the flow, and the cases with smaller bubbles are the most anisotropic, with a dependence on void fraction. The degree of anisotropy is shown to increase as the order of the structure functions is increased, showing that extreme events in the flow are the most anisotropic. Our results show that the average energy transfer with the horizontal velocity component is downscale, just as for the three-dimensional single-phase turbulence. However, the energy transfer associated with the vertical component of the fluid velocity is upscale. The probability density functions of the velocity increments reveal that extreme values become more probable with decreasing Reynolds number, the opposite of the behaviour in single-phase turbulence. We visualize those extreme events and find that regions of intense small scale velocity increments occur near the turbulent/non-turbulent interface at the boundary of the bubble wake.

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arXiv2021

When is settling important for particle concentrations in wall-bounded turbulent flows?

We explore the role of gravitational settling on inertial particle concentrations in a wall-bounded turbulent flow. While it may be thought that settling can be ignored when the settling parameter $Sv\equiv v_s/u_τ$ is small ($v_s$ - Stokes settling velocity, $u_τ$ - fluid friction velocity), we show that even in this regime the settling may make a leading order contribution to the concentration profiles. This is because the importance of settling is determined, not by the size of $v_s$ compared with $u_τ$ or any other fluid velocity scale, but by the size of $v_s$ relative to the other mechanisms that control the vertical particle velocity and concentration profile. We explain this in the context of the particle mean-momentum equation, and show that in general, there always exists a region in the boundary layer where settling cannot be neglected, no matter how small $Sv$ is (provided it is finite). Direct numerical simulations confirm the arguments, and show that the near-wall concentration is highly dependent on $Sv$ even when $Sv\ll 1$, and can reduce by an order of magnitude when $Sv$ is increased from $O(10^{-4})$ and $O(10^{-2})$. The results also show that the preferential sampling of ejection events in the boundary layer by inertial particles when $Sv=0$ is profoundly altered as $Sv$ is increased, and is replaced by a preferential sampling of sweep events due to the onset of the preferential sweeping mechanism.

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arXiv2021

Dimension Reduced Turbulent Flow Data From Deep Vector Quantizers

Analyzing large-scale data from simulations of turbulent flows is memory intensive, requiring significant resources. This major challenge highlights the need for data compression techniques. In this study, we apply a physics-informed Deep Learning technique based on vector quantization to generate a discrete, low-dimensional representation of data from simulations of three-dimensional turbulent flows. The deep learning framework is composed of convolutional layers and incorporates physical constraints on the flow, such as preserving incompressibility and global statistical characteristics of the velocity gradients. The accuracy of the model is assessed using statistical, comparison-based similarity and physics-based metrics. The training data set is produced from Direct Numerical Simulation of an incompressible, statistically stationary, isotropic turbulent flow. The performance of this lossy data compression scheme is evaluated not only with unseen data from the stationary, isotropic turbulent flow, but also with data from decaying isotropic turbulence, a Taylor-Green vortex flow, and a turbulent channel flow. Defining the compression ratio (CR) as the ratio of original data size to the compressed one, the results show that our model based on vector quantization can offer CR$=85$ with a mean square error (MSE) of $O(10^{-3})$, and predictions that faithfully reproduce the statistics of the flow, except at the very smallest scales where there is some loss. Compared to the recent study of Glaws. et. al. (Physical Review Fluids, 5(11):114602, 2020), which was based on a conventional autoencoder (where compression is performed in a continuous space), our model improves the CR by more than $30$ percent...

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arXiv2021

Hydrodynamic interactions and extreme particle clustering in turbulence

From new detailed experimental data, we found that the Radial Distribution Function (RDF) of inertial particles in turbulence grows explosively with $r^{-6}$ scaling as the collision radius is approached. We corrected a theory by Yavuz et al. (Phys. Rev. Lett. 120, 244504 (2018)) based on hydrodynamic interactions between pairs of weakly inertial particles, and demonstrate that even this corrected theory cannot explain the observed RDF behavior. We explore several alternative mechanisms for the discrepancy that were not included in the theory and show that none of them are likely the explanation, suggesting new, yet to be identified physical mechanisms are at play.

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arXiv2021

Scale-dependent anisotropy, energy transfer and intermittency in bubble-laden turbulent flows

Data from Direct Numerical Simulations of disperse bubbly flows in a vertical channel are used to study the effect of the bubbles on the carrier-phase turbulence. A new method is developed, based on the barycentric map approach, that allows to quantify the anisotropy and componentiality of the flow at any scale. Using this the bubbles are found to significantly enhance flow anisotropy at all scales compared with the unladen case, and for some bubble cases, very strong anisotropy persists down to the smallest flow scales. The strongest anisotropy observed was for the cases involving small bubbles. Concerning the inter-scale energy transfer, our results indicate that for the bubble-laden cases, the energy transfer is from large to small scales, just as for the unladen case. However, there is evidence of an upscale transfer when considering the transfer of energy associated with particular components of the velocity field. Although the direction of the energy transfer is the same with and without the bubbles, the transfer is much stronger for the bubble-laden cases, suggesting that the bubbles play a strong role in enhancing the activity of the nonlinear term in the flow. The normalized forms of the fourth and sixth-order structure functions are also considered, and reveal that the introduction of bubbles into the flow strongly enhances intermittency in the dissipation range, but suppresses it at larger scales. This strong enhancement of the dissipation scale intermittency has significant implications for understanding how the bubbles might modify the mixing properties of turbulent flows.

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arXiv2019

Local analysis of the clustering, velocities and accelerations of particles settling in turbulence

Using 3D Vorono\text{ï} analysis, we explore the local dynamics of small, settling, inertial particles in isotropic turbulence using Direct Numerical Simulations (DNS). We independently vary the Taylor Reynolds number $R_λ\in[90,398]$, Froude number $Fr\equiv a_η/g\in[0.052,\infty]$ (where $a_η$ is the Kolmogorov acceleration, and $g$ is the acceleration due to gravity), and Kolmogorov scale Stokes number $St\equivτ_p/τ_η\in[0,3]$. In agreement with previous results using global measures of particle clustering, such as the Radial Distribution Function (RDF), we find that for small Vorono\text{ï} volumes (corresponding to the most clustered particles), the behavior is strongly dependent upon $St$ and $Fr$, but only weakly dependent upon $R_λ$, unless $St>1$. However, larger Vorono\text{ï} volumes (void regions) exhibit a much stronger dependence on $R_λ$, even when $St\leq 1$, and we show that this, rather than the behavior at small volumes, is the cause of the sensitivity of the standard deviation of the Vorono\text{ï} volumes that has been previously reported. We also show that the largest contribution to the particle settling velocities is associated with increasingly larger Vorono\text{ï} volumes as the settling parameter $Sv\equiv St/Fr$ is increased. Our local analysis of the acceleration statistics of settling inertial particles shows that clustered particles experience a net acceleration in the direction of gravity, while particles in void regions experience the opposite. The particle acceleration variance, however, is a convex function of the Vorono\text{ï} volumes, with or without gravity, which seems to indicate a non-trivial relationship between the Vorono\text{ï} volumes and the sizes of the turbulent flow scales. Results for the variance of the fluid acceleration at the inertial particle "..."

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arXiv2019

Is vortex stretching the main cause of the turbulent energy cascade?

In three dimensional turbulence there is on average a cascade of kinetic energy from the largest to the smallest scales of the flow. While the dominant idea is that the cascade occurs through the physical process of vortex stretching, evidence for this is debated. In the framework of the Karman-Howarth equation for the two point turbulent kinetic energy, we derive a new result for the average flux of kinetic energy between two points in the flow that reveals the role of vortex stretching. However, the result shows that vortex stretching is in fact not the main contributor to the average energy cascade; the main contributor is the self-amplification of the strain-rate field. We emphasize the need to correctly distinguish and not conflate the roles of vortex stretching and strain-self amplification in order to correctly understand the physics of the cascade, and also resolve a paradox regarding the differing role of vortex stretching on the mechanisms of the energy cascade and energy dissipation rate. Direct numerical simulations are used to confirm the results, as well as provide further results and insights on vortex stretching and strain-self amplification at different scales in the flow. Interestingly, the results imply that while vortex stretching plays a sub-leading role in the average cascade, it may play a leading order role during large fluctuations of the energy cascade about its average behavior.

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arXiv2018

Multiscale fluid--particle thermal interaction in isotropic turbulence

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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arXiv2018

Enhanced and suppressed multiscale dispersion of bidisperse inertial particles due to gravity

Using Direct Numerical Simulations (DNS), we investigate how gravity modifies the multiscale dispersion of bidisperse inertial particles in isotropic turbulence. The DNS has a Taylor Reynolds number $R_λ=398$, and we simulate Stokes numbers (based on the Kolmogorov timescale) in the range $St\leq 3$ , and consider Froude numbers $Fr = 0.052$ and $\infty$, corresponding to strong gravity and no gravity, respectively. The degree of bidispersity is quantified by the difference in the Stokes number of the particles $|ΔSt|$. We first consider the mean-square separation of bidisperse particle-pairs and find that without gravity (i.e. $Fr = \infty$), bidispersity leads to an enhancement of the the mean-square separation over a significant range of scales. When $|ΔSt|\geq O(1)$, the relative dispersion is further enhanced by gravity due to the large difference in the settling velocities of the two particles. However, when $|ΔSt|\ll1$, gravity suppresses the relative dispersion as the settling velocity contribution is small, and gravity suppresses the non-local contribution to the particle dynamics. In order to gain further insights, we consider separately the relative dispersion in the vertical (parallel to gravity) and horizontal directions. As expected, the vertical relative dispersion can be strongly enhanced by gravity due to differences in the settling velocities of the two particles. However, a key finding of our study is that gravity can also significantly enhance the horizontal relative dispersion. This non-trivial effect occurs because fast settling particles experience rapid fluctuations in the fluid velocity field along their trajectory, leading to enhanced particle accelerations and relative velocities. For sufficiently large initial particle separations...

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arXiv2018

The influence of Reynolds and Froude number on the motion of settling, bidisperse inertial particles in turbulence

Using Direct Numerical Simulations (DNS), we examine the effects of Taylor Reynolds number, $R_λ$, and Froude number, $Fr$, on the motion of settling, bidisperse inertial particles in isotropic turbulence. Particle accelerations play a key role in the relative motion of bidisperse particles, and we find that reducing $Fr$ leads to an enhancement of the accelerations, but a suppression of their intermittency. For Stokes numbers $St>1$, the effect of $R_λ$ on the accelerations is enhanced by gravity, since settling causes the particle accelerations to be affected by a larger range of flow scales. The results for the Probability Density Function (PDF) of the particle relative velocities show that for bidisperse particles, decreasing $Fr$ leads to an enhancement of their relative velocities in both the vertical (parallel to gravity) and horizontal directions. Importantly, our results show that even when the particles are settling very fast, turbulence continues to play a key role in their vertical relative velocities, and increasingly so as $R_λ$ is increased. This occurs because although the settling velocity may be much larger than typical velocities of the turbulence, due to intermittency, there are significant regions of the flow where the turbulence contribution to the particle motion is of the same order as that from gravitational settling...

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arXiv2017

Particle-Pair Relative Velocity Measurement in High-Reynolds-Number Homogeneous and Isotropic Turbulence Using 4-Frame Particle Tracking Velocimetry

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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arXiv2017

Do fluid particles separate exponentially in the dissipation range?

In this paper we consider how the statistical moments of the separation between two fluid particles grow with time when their separation lies in the dissipation range of turbulence. In this range the fluid velocity field varies smoothly, and the relative velocity of two fluid particles depends linearly upon their separation. While this may suggest that the rate at which fluid particles separate is exponential in time, this is not guaranteed because the strain-rate governing their separation is a strongly fluctuating quantity in turbulence. Indeed, the recent paper by Afik \& Steinberg (Nat. Commun. \textbf{8}: 468, 2017) argues that there is no convincing evidence that the moments of the separation between fluid particles grow exponentially with time in the dissipation range of turbulence. Motivated by this, we use Direct Numerical Simulations (DNS) to compute the moments of the particle separation over very long periods of time to see if we ever see evidence for exponential separation. Our results show that if the initial separation between the particles is infinitesimal, the moments of the particle separation first grow as power laws in time, but we then observe, for the first time, convincing evidence that at sufficiently long times the moments do grow exponentially. However, this exponential growth is only observed after extremely long times $\gtrsim 200τ_η$, where $τ_η$ is the Kolmogorov timescale. This is due to fluctuations in the strain-rate about its mean value measured along the particle trajectories, the effect of which on the moments of the particle separation persists for very long times. We also consider the Backward-in-Time (BIT) moments of the particle separation, and observe that they too grow exponentially in the long-time regime. However, a dramatic consequence of the exponential separation is that at long-times the difference between..

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arXiv2017

Small-scale dynamics of settling, bidisperse particles in turbulence

We use Direct Numerical Simulations (DNS) to investigate the dynamics of settling, bidisperse particles in isotropic turbulence. In agreement with previous studies, we find that without gravity (i.e. $Fr=\infty$, where $Fr$ is the Froude number), bidispersity leads to an enhancement of the relative velocities, and a suppression of their spatial clustering. For $Fr<1$, the relative velocities in the direction of gravity are enhanced by the differential settling velocities of the bidisperse particles, as expected. However, we also find that gravity can strongly enhance the relative velocities in the "horizontal" directions (i.e. in the plane normal to gravity). This non-trivial behavior occurs because fast settling particles experience rapid fluctuations in the fluid velocity field along their trajectory, leading to enhanced particle accelerations and relative velocities. Indeed, the results show that even when $Fr\ll1$, turbulence can still play an important role, not only on the horizontal motion, but also on the vertical motion of the particles, with significant implications for understanding the mixing rates of settling bidisperse particles in turbulence. We also find that gravity drastically reduces the clustering of bidisperse particles. These results are strikingly different to the monodisperse case, for which recent results have shown that when $Fr<1$, gravity strongly suppresses the relative velocities in all directions, and can enhance clustering. We then consider the implications of these results for the collision rates of settling, bidisperse particles in turbulence. We find that for $Fr=0.052$, the collision kernel is almost perfectly predicted by the collision kernel for bidisperse particles settling in quiescent flow, such that the effect of turbulence may be ignored...

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arXiv2017

Analysis of the forward and backward in time pair-separation PDFs 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 $St$. 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 ${St\geq O(1)}$, 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...

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arXiv2016

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

In this paper, we use our recently developed theory for the backward-in-time (BIT) relative dispersion of inertial particles in turbulence (Bragg \emph{et al.}, Phys. Fluids 28, 013305, 2016) to develop the theoretical model by Pan \& Padoan (J. Fluid Mech. 661 73, 2010) for inertial particle relative velocities in isotropic turbulence. We focus on the most difficult regime to model, the dissipation range, and find that the modified Pan \& Padoan model (that uses the BIT dispersion theory) can lead to significantly improved predictions for the relative velocities, when compared with Direct Numerical Simulation (DNS) data. However, when the particle separation distance, $r$, is less than the Kolmogorov length scale, $η$, the modified model overpredicts the DNS data. We explain how these overpredictions arise from two assumptions in the BIT dispersion theory, that are in general not satisfied when the final separation of the BIT dispersing particles is $<η$. We then demonstrate the failure of both the original and modified versions of the Pan \& Padoan model to predict the correct scale-invariant forms for the inertial particle relative velocity structure functions in the dissipation regime. It is shown how this failure, which is also present in other models, is associated with our present inability to correctly predict not only the quantitative, but also the qualitative behavior of the Radial Distribution Function in the dissipation range when $St=\mathcal{O}(1)$

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arXiv2015

Spectral Model of Non-Stationary, Inhomogeneous Turbulence

We compare results from a spectral model for non-stationary, inhomogeneous turbulence (Besnard et al., Theor. Comp. Fluid. Dyn., vol. 8, pp 1-35, 1996) with Direct Numerical Simulation (DNS) data of a shear-free mixing layer (SFML) (Tordella et al., Phys. Rev. E, vol. 77, 016309, 2008). The SFML is used as a test case in which the efficacy of the model closure for the physical-space transport of the fluid velocity field can be tested in a flow with inhomogeneity, without the additional complexity of mean-flow coupling. The model is able to capture certain features of the SFML quite well for intermediate to long-times, including the evolution of the mixing-layer width and turbulent kinetic energy. At short-times, and for more sensitive statistics such as the generation of the velocity field anisotropy, the model is less accurate. We present arguments, supported by the DNS data, that a significant cause of the discrepancies is the local approximation to the intrinsically non-local pressure-transport in physical-space that was made in the model, the effects of which would be particularly strong at short-times when the inhomogeneity of the SFML is strongest.

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