6 results
The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects
- Peter J. Ireland, Andrew D. Bragg, Lance R. Collins
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- Journal:
- Journal of Fluid Mechanics / Volume 796 / 10 June 2016
- Published online by Cambridge University Press:
- 11 May 2016, pp. 617-658
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In this study, we analyse the statistics of both individual inertial particles and inertial particle pairs in direct numerical simulations of homogeneous isotropic turbulence in the absence of gravity. The effect of the Taylor microscale Reynolds number, $R_{{\it\lambda}}$, on the particle statistics is examined over the largest range to date (from $R_{{\it\lambda}}=88$ to 597), at small, intermediate and large Kolmogorov-scale Stokes numbers $St$. We first explore the effect of preferential sampling on the single-particle statistics and find that low-$St$ inertial particles are ejected from both vortex tubes and vortex sheets (the latter becoming increasingly prevalent at higher Reynolds numbers) and preferentially accumulate in regions of irrotational dissipation. We use this understanding of preferential sampling to provide a physical explanation for many of the trends in the particle velocity gradients, kinetic energies and accelerations at low $St$, which are well represented by the model of Chun et al. (J. Fluid Mech., vol. 536, 2005, pp. 219–251). As $St$ increases, inertial filtering effects become more important, causing the particle kinetic energies and accelerations to decrease. The effect of inertial filtering on the particle kinetic energies and accelerations diminishes with increasing Reynolds number and is well captured by the models of Abrahamson (Chem. Engng Sci., vol. 30, 1975, pp. 1371–1379) and Zaichik & Alipchenkov (Intl J. Multiphase Flow, vol. 34 (9), 2008, pp. 865–868), respectively. We then consider particle-pair statistics, and focus our attention on the relative velocities and radial distribution functions (RDFs) of the particles, with the aim of understanding the underlying physical mechanisms contributing to particle collisions. The relative velocity statistics indicate that preferential sampling effects are important for $St\lesssim 0.1$ and that path-history/non-local effects become increasingly important for $St\gtrsim 0.2$. While higher-order relative velocity statistics are influenced by the increased intermittency of the turbulence at high Reynolds numbers, the lower-order relative velocity statistics are only weakly sensitive to changes in Reynolds number at low $St$. The Reynolds-number trends in these quantities at intermediate and large $St$ are explained based on the influence of the available flow scales on the path-history and inertial filtering effects. We find that the RDFs peak near $St$ of order unity, that they exhibit power-law scaling for low and intermediate $St$ and that they are largely independent of Reynolds number for low and intermediate $St$. We use the model of Zaichik & Alipchenkov (New J. Phys., vol. 11, 2009, 103018) to explain the physical mechanisms responsible for these trends, and find that this model is able to capture the quantitative behaviour of the RDFs extremely well when direct numerical simulation data for the structure functions are specified, in agreement with Bragg & Collins (New J. Phys., vol. 16, 2014a, 055013). We also observe that at large $St$, changes in the RDF are related to changes in the scaling exponents of the relative velocity variances. The particle collision kernel closely matches that computed by Rosa et al. (New J. Phys., vol. 15, 2013, 045032) and is found to be largely insensitive to the flow Reynolds number. This suggests that relatively low-Reynolds-number simulations may be able to capture much of the relevant physics of droplet collisions and growth in the adiabatic cores of atmospheric clouds.
The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects
- Peter J. Ireland, Andrew D. Bragg, Lance R. Collins
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- Journal:
- Journal of Fluid Mechanics / Volume 796 / 10 June 2016
- Published online by Cambridge University Press:
- 11 May 2016, pp. 659-711
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In Part 1 of this study (Ireland et al., J. Fluid Mech., vol. 796, 2016, pp. 617–658), we analysed the motion of inertial particles in isotropic turbulence in the absence of gravity using direct numerical simulation (DNS). Here, in Part 2, we introduce gravity and study its effect on single-particle and particle-pair dynamics over a wide range of flow Reynolds numbers, Froude numbers and particle Stokes numbers. The overall goal of this study is to explore the mechanisms affecting particle collisions, and to thereby improve our understanding of droplet interactions in atmospheric clouds. We find that the dynamics of heavy particles falling under gravity can be artificially influenced by the finite domain size and the periodic boundary conditions, and we therefore perform our simulations on larger domains to reduce these effects. We first study single-particle statistics that influence the relative positions and velocities of inertial particles. We see that gravity causes particles to sample the flow more uniformly and reduces the time particles can spend interacting with the underlying turbulence. We also find that gravity tends to increase inertial particle accelerations, and we introduce a model to explain that effect. We then analyse the particle relative velocities and radial distribution functions (RDFs), which are generally seen to be independent of Reynolds number for low and moderate Kolmogorov-scale Stokes numbers $St$. We see that gravity causes particle relative velocities to decrease by reducing the degree of preferential sampling and the importance of path-history interactions, and that the relative velocities have higher scaling exponents with gravity. We observe that gravity has a non-trivial effect on clustering, acting to decrease clustering at low $St$ and to increase clustering at high $St$. By considering the effect of gravity on the clustering mechanisms described in the theory of Zaichik & Alipchenkov (New J. Phys., vol. 11, 2009, 103018), we provide an explanation for this non-trivial effect of gravity. We also show that when the effects of gravity are accounted for in the theory of Zaichik & Alipchenkov (2009), the results compare favourably with DNS. The relative velocities and RDFs exhibit considerable anisotropy at small separations, and this anisotropy is quantified using spherical harmonic functions. We use the relative velocities and the RDFs to compute the particle collision kernels, and find that the collision kernel remains as it was for the case without gravity, namely nearly independent of Reynolds number for low and moderate $St$. We conclude by discussing practical implications of the results for the cloud physics and turbulence communities and by suggesting possible avenues for future research.
On the relationship between the non-local clustering mechanism and preferential concentration
- Andrew D. Bragg, Peter J. Ireland, Lance R. Collins
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- Journal:
- Journal of Fluid Mechanics / Volume 780 / 10 October 2015
- Published online by Cambridge University Press:
- 03 September 2015, pp. 327-343
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‘Preferential concentration’ (Squires & Eaton, Phys. Fluids, vol. A3, 1991, pp. 1169–1178) refers to the clustering of inertial particles in the high strain, low-rotation regions of turbulence. The ‘centrifuge mechanism’ of Maxey (J. Fluid Mech., vol. 174, 1987, pp. 441–465) appears to explain this phenomenon. In a recent paper, Bragg & Collins (New J. Phys., vol. 16, 2014, 055013) showed that the centrifuge mechanism is dominant only in the regime $St\ll 1$, where $St$ is the Stokes number based on the Kolmogorov time scale. Outside this regime, the centrifuge mechanism gives way to a non-local, path history symmetry breaking mechanism. However, despite the change in the clustering mechanism, the instantaneous particle positions continue to correlate with high strain, low-rotation regions of the turbulence. In this paper, we analyse the exact equation governing the radial distribution function and show how the non-local clustering mechanism is influenced by, but not dependent upon, the preferential sampling of the fluid velocity gradient tensor along the particle path histories in such a way as to generate a bias for clustering in high strain regions of the turbulence. We also show how the non-local mechanism still generates clustering, but without preferential concentration, in the limit where the time scales of the fluid velocity gradient tensor measured along the inertial particle trajectories approaches zero (such as white noise flows or for particles in turbulence settling under strong gravity). Finally, we use data from a direct numerical simulation of inertial particles suspended in Navier–Stokes turbulence to validate the arguments presented in this study.
A comparison of the root and shoot growth of winter barley and winter wheat, and the effect of an early application of chlormequat
- P. L. Bragg, P. Rubino, F. K. G. Henderson, W. J. Fielding, R. Q. Cannell
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- Journal:
- The Journal of Agricultural Science / Volume 103 / Issue 2 / October 1984
- Published online by Cambridge University Press:
- 27 March 2009, pp. 257-264
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In a field experiment where winter wheat and winter barley were sown on the same date, the patterns of root growth of the two species were similar, with a few roots reaching a depth of at least 120 cm. Roots senesced sooner in barley, in association with earlier maturity of the shoots and grain. The number of shoots and leaf area index of the barley were greater than for the wheat, but rates of dry-matter production until anthesis of the barley were similar in both species. The grain yield of wheat was about 10% heavier than for barley. Where chlormequat had been applied in early December at the 3- to 4-leaf stage, when shoot apices of both species were still vegetative, root density of the winter wheat in the following March and April was slightly greater than for untreated plants, but the difference disappeared later. For winter barley there was no effect of chlormequat on root growth until July when root length tended to be greater at depth after the chlormequat treatment. The chlormequat treatment significantly shortened stem length, but did not significantly affect the number of shoots, crop dry weight or grain yield of either species.
A winter wheat crop simulation model without water or nutrient limitations
- A. H. Weir, P. L. Bragg, J. R. Porter, J. H. Rayner
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- Journal:
- The Journal of Agricultural Science / Volume 102 / Issue 2 / April 1984
- Published online by Cambridge University Press:
- 27 March 2009, pp. 371-382
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A whole crop computer simulation model of winter wheat has been written in FORTRAN and used to simulate the growth of September- and October-sown crops of Hustler wheat at Rothamsted for the years 1978–9, 1979–80 and 1980–1. Results of the simulations, which are for crops with adequate water and nutrients, are compared with observations from experiments at Rothamsted. The model uses daily maximum and minimum temperatures and daylength to calculate the dates of emergence, double ridge, anthesis and maturity of the crops and the growth and senescence of tillers and leaves. In the simulations, the canopy intercepts daily radiation and produces dry matter that is partitioned between roots, shoots, leaves, ears and grain. Partial simulations, using observed LAI values, produced dry matter in close agreement with observations of late-sown crops, but consistently overestimated the total dry-matter production of the early-sown crops. Full simulation described satisfactorily the average difference in dry-matter production to be expected with changes in time of sowing, but did not give as close correspondence for individual crops. A grain growth submodel, that linked maximum grain weight to average temperatures during the grain growth period, correctly simulated the observed growth of individual grains in the 1981 crop. The benefits to be obtained by combining whole crop modelling with detailed crop observations are discussed.
More mileage in disclaimers
- R. J. Bragg
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- Journal:
- Legal Studies / Volume 2 / Issue 2 / July 1982
- Published online by Cambridge University Press:
- 02 January 2018, pp. 172-179
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- July 1982
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It is thirteen years since the passing of the Trade Descriptions Act 1968 and case law has now largely determined the effect of the major provisions of the Act. There is little doubt statistically that the Act has had its primary impact upon the motor trade, and that the most prosecuted offence is that of the ‘clocked’ car. There is a lot of additional money to be made if a car is sold with a low mileage rather than with a high one. A high proportion of new cars are supplied to companies who keep these fleet vehicles for about two years and then sell them, often through the large motor auctions, whereby they come into the hands of the motor trade. These fleet cars will invariably have travelled in excess of sixty thousand miles. Too many of these cars are handled by several dealers and then are displayed for sale to the public with a mileage shown in the region of twenty to thirty thousand. All that can be said in such a case is that someone, somewhere along the chain of distributors, has fraudulently turned back the vehicle odometer but it is usually very difficult to prove who did it.