25 results
Non-continuum tangential lubrication gas flow between two spheres
- Melanie Li Sing How, Donald L. Koch, Lance R. Collins
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- Journal:
- Journal of Fluid Mechanics / Volume 920 / 10 August 2021
- Published online by Cambridge University Press:
- 04 June 2021, A2
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As two particles approach each other, the continuum lubrication force diverges, with decreasing separation preventing contact. However, for separations comparable to the mean free path of the gas, $\lambda$, non-continuum effects cause the lubrication force to diverge more slowly with decreasing separation distance, allowing for contact in finite time. The first study of this phenomenon was done by Sundararajakumar & Koch (J. Fluid Mech., vol. 313, 1996, pp. 238–308) for two particles moving along their line of centres. We extend their normal motion study to include tangential motions. For small Knudsen number $Kn=\lambda / a$, where $a$ is the harmonic mean of the two particle radii, we use a matched asymptotic expansion technique to obtain the non-continuum forces and torques for tangential motions of spheres separated by distances within the lubrication regime that are at or below the mean free path of the gas. The hydrodynamic resistivity functions are fitted to provide a uniformly valid approximation that smoothly transitions between the continuum multipole and non-continuum lubrication expressions for the forces and torques as the minimum gap between the particles $h_0$ varies from values of $O(a)$ to values of $O(\lambda )$. These functions, in combination with the result by Sundararajakumar & Koch (J. Fluid Mech., vol. 313, 1996, pp. 238–308) and the classical work by Jeffrey & Onishi (J. Fluid Mech., vol. 139, 1984, pp. 261–290), yield a complete formulation for the hydrodynamic interactions of two spheres at all separations, from non-interacting spheres in the extreme far field through all the transitions that occur up to contact. We apply the new formulation to the classical case of a particle settling parallel to a vertical wall. The continuum Stokes equation predicts a settling speed that decreases with decreasing gap separation and vanishes at contact, whereas the non-continuum model developed herein predicts a finite settling speed at contact.
Effects of Reynolds number and Stokes number on particle-pair relative velocity in isotropic turbulence: a systematic experimental study
- Zhongwang Dou, Andrew D. Bragg, Adam L. Hammond, Zach Liang, Lance R. Collins, Hui Meng
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- Journal of Fluid Mechanics / Volume 839 / 25 March 2018
- Published online by Cambridge University Press:
- 26 January 2018, pp. 271-292
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The effects of Reynolds number ($R_{\unicode[STIX]{x1D706}}$) and Stokes number ($St$) on particle-pair relative velocity (RV) are investigated systematically using a recently developed planar four-frame particle tracking technique in a novel homogeneous and isotropic turbulence chamber. We compare the measured results with direct numerical simulation (DNS), verifying whether the conclusions of the DNS for simplified conditions and limited $R_{\unicode[STIX]{x1D706}}$ are still valid in reality. Two experiments are performed: varying $R_{\unicode[STIX]{x1D706}}$ between 246 and 357 at six $St$ values, and varying $St$ between 0.02 and 4.63 at five $R_{\unicode[STIX]{x1D706}}$ values. The measured mean inward particle-pair RV $\langle w_{r}^{-}\rangle$ as a function of separation distance $r$ is compared with the DNS under closely matched conditions. At all experimental conditions, an excellent agreement is achieved, except when the particle separation distance $r\lesssim 10\unicode[STIX]{x1D702}$ ($\unicode[STIX]{x1D702}$ is the Kolmogorov length scale), where the experimental $\langle w_{r}^{-}\rangle$ is consistently higher, possibly due to particle polydispersity and finite laser thickness in the experiments (Dou et al., arXiv:1712.07506, 2017). At any fixed $St,\langle w_{r}^{-}\rangle$ is essentially independent of $R_{\unicode[STIX]{x1D706}}$, echoing the DNS finding of Ireland et al. (J. Fluid Mech., vol. 796, 2016, pp. 617–658). At any fixed $R_{\unicode[STIX]{x1D706}}$, $\langle w_{r}^{-}\rangle$ increases with $St$ at small $r$, showing dominance of the path-history effect in the dissipation range when $St\gtrsim O(1)$, but decreases with $St$ at large $r$, indicating dominance of inertial filtering. We further compare the $\langle w_{r}^{-}\rangle$ and RV variance $\langle w_{r}^{2}\rangle$ from experiments with DNS and theoretical predictions by Pan & Padoan (J. Fluid Mech., vol. 661, 2010, pp. 73–107). For $St\lesssim 1$, experimental $\langle w_{r}^{-}\rangle$ and $\langle w_{r}^{2}\rangle$ match these values well at $r\gtrsim 10\unicode[STIX]{x1D702}$, but they are higher than both DNS and theory at $r\lesssim 10\unicode[STIX]{x1D702}$. For $St\gtrsim 1$, $\langle w_{r}^{-}\rangle$ from all three match well, except for $r\lesssim 10\unicode[STIX]{x1D702}$, for which experimental values are higher, while $\langle w_{r}^{2}\rangle$ from experiment and DNS are much higher than theoretical predictions. We discuss potential causes of these discrepancies. What this study shows is the first experimental validation of $R_{\unicode[STIX]{x1D706}}$ and $St$ effect on inertial particle-pair $\langle w_{r}^{-}\rangle$ in homogeneous and isotropic turbulence.
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 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
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- 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.
Investigation of sub-Kolmogorov inertial particle pair dynamics in turbulence using novel satellite particle simulations
- Baidurja Ray, Lance R. Collins
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- Journal:
- Journal of Fluid Mechanics / Volume 720 / 10 April 2013
- Published online by Cambridge University Press:
- 27 February 2013, pp. 192-211
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Clustering (or preferential concentration) of weakly inertial particles suspended in a homogeneous isotropic turbulent flow is driven primarily by the smallest eddies at the so-called Kolmogorov scale. In particle-laden large-eddy simulations (LES), these small scales are not resolved by the grid and hence their effect on both the resolved flow scales and the particle motion have to be modelled. In order to predict clustering in a particle-laden LES, it is crucial that the subgrid model for the particles captures the mechanism by which the subgrid scales affect the particle motion (Ray & Collins, J. Fluid Mech., vol. 680, 2011, pp. 488–510). In this paper, we describe novel satellite particle simulations (SPS), in which we study the clustering and relative velocity statistics of inertial particles at separation distances well below the Kolmogorov length scale. SPS is designed to isolate pairwise interactions of particles, and is therefore well suited for developing two-particle models. We show that the power-law dependence of the radial distribution function (RDF), a statistical measure of clustering, is predicted by the SPS in excellent agreement with direct numerical simulations (DNS) for Stokes numbers up to 3, implying that no explicit information from the inertial range is required to accurately describe particle clustering. This result further explains our successful prediction of the RDF power using the drift-diffusion model of Chun et al. (J. Fluid Mech., vol. 536, 2005, pp. 219–251) for $\mathit{St}\leq 0. 4$. We also consider the second-order longitudinal relative velocity structure function for the particles; we show that the SPS is able to capture its power-law exponent for $\mathit{St}\leq 0. 5$ and attribute the disagreement at larger $\mathit{St}$ to the effect of the larger scales of motion not captured by the SPS. Further, the SPS is able to capture the ‘caustic activation’ of the structure function at zero separation and predict the critical $\mathit{St}$ and rate of activation in agreement with the DNS (Salazar & Collins, J. Fluid. Mech., vol. 696, 2012, pp. 45–66). We show comparisons between filtered DNS and equivalently filtered SPS, and the findings are similar to the unfiltered case. Overall, SPS is an efficient and accurate computational tool for investigating particle pair dynamics at small separations, as well as an interesting platform for developing LES subgrid models designed to accurately reproduce particle clustering.
Direct numerical simulation of inertial particle entrainment in a shearless mixing layer
- Peter J. Ireland, Lance R. Collins
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- Journal:
- Journal of Fluid Mechanics / Volume 704 / 10 August 2012
- Published online by Cambridge University Press:
- 02 July 2012, pp. 301-332
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We present the first computational study of the dynamics of inertial particles in a shearless turbulence mixing layer. We parametrize our direct numerical simulations to isolate the effects of turbulence, Reynolds number, particle inertia, and gravity on the entrainment process. By analysing particle concentrations, particle and fluid velocities, particle size distributions, and higher-order velocity moments, we explore the impact of particle inertia and gravity on the mechanism of turbulent mixing. We neglect thermodynamic processes, including phase changes between the drops and surrounding air, which is equivalent to assuming the air is saturated (i.e. 100 % humidity). Entrainment is found to be governed by the large scales of the flow and is relatively insensitive to the Reynolds number over the range considered. Our results show that both fluid and particle velocities exhibit intermittency and that gravity and turbulent diffusion interact in unexpected ways to dictate particle dynamics. An analysis of the temporal evolution of fluid and particle statistics suggests that particle concentration profiles and velocities are self-similar under certain circumstances. We also observe large fluctuations in particle concentrations resulting from entrainment and introduce a model to estimate the impact these fluctuations have on the radial distribution function, a statistic that is often used to quantify inertial particle clustering. Our study is both a computational counterpart to and an extension of the wind tunnel experiments by Gerashchenko, Good & Warhaft (J. Fluid Mech., vol. 668, 2011, pp. 293–303) and Good, Gerashchenko, & Warhaft (J. Fluid Mech., vol. 694, 2012, pp. 371–398). We find good agreement between these experimental studies and our computational results. We anticipate that a better understanding of the role of gravity and turbulence in inertial particle entrainment will lead to improved cloud evolution predictions.
Inertial particle relative velocity statistics in homogeneous isotropic turbulence
- Juan P. L. C. Salazar, Lance R. Collins
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- Journal:
- Journal of Fluid Mechanics / Volume 696 / 10 April 2012
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- 05 March 2012, pp. 45-66
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In the present study, we investigate the scaling of relative velocity structure functions, of order two and higher, for inertial particles, both in the dissipation range and the inertial subrange using direct numerical simulations (DNS). Within the inertial subrange our findings show that contrary to the well-known attenuation in the tails of the one-point acceleration probability density function (p.d.f.) with increasing inertia (Bec et al., J. Fluid Mech., vol. 550, 2006, pp. 349–358), the opposite occurs with the velocity structure function at sufficiently large Stokes numbers. We observe reduced scaling exponents for the structure function when compared to those of the fluid, and correspondingly broader p.d.f.s, similar to what occurs with a passive scalar. DNS allows us to isolate the two effects of inertia, namely biased sampling of the velocity field, a result of preferential concentration, and filtering, i.e. the tendency for the inertial particle velocity to attenuate the velocity fluctuations in the fluid. By isolating these effects, we show that sampling is playing the dominant role for low-order moments of the structure function, whereas filtering accounts for most of the scaling behaviour observed with the higher-order structure functions in the inertial subrange. In the dissipation range, we see evidence of so-called ‘crossing trajectories’, the ‘sling effect’ or ‘caustics’, and find good agreement with the theory put forth by Wilkinson et al. (Phys. Rev. Lett., vol. 97, 2006, 048501) and Falkovich & Pumir (J. Atmos. Sci., vol. 64, 2007, 4497) for Stokes numbers greater than 0.5. We also look at the scaling exponents within the context of the model proposed by Bec et al. (J. Fluid Mech., vol. 646, 2010, pp. 527–536). Another interesting finding is that inertial particles at low Stokes numbers sample regions of higher kinetic energy than the fluid particle field, the converse occurring at high Stokes numbers. The trend at low Stokes numbers is predicted by the theory of Chun et al. (J. Fluid Mech., vol. 536, 2005, 219–251). This work is relevant to modelling the particle collision rate (Sundaram & Collins, J. Fluid Mech., vol. 335, 1997, pp. 75–109), and highlights the interesting array of phenomena induced by inertia.
Contributors
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- By Aakash Agarwala, Linda S. Aglio, Rae M. Allain, Paul D. Allen, Houman Amirfarzan, Yasodananda Kumar Areti, Amit Asopa, Edwin G. Avery, Patricia R. Bachiller, Angela M. Bader, Rana Badr, Sibinka Bajic, David J. Baker, Sheila R. Barnett, Rena Beckerly, Lorenzo Berra, Walter Bethune, Sascha S. Beutler, Tarun Bhalla, Edward A. Bittner, Jonathan D. Bloom, Alina V. Bodas, Lina M. Bolanos-Diaz, Ruma R. Bose, Jan Boublik, John P. Broadnax, Jason C. Brookman, Meredith R. Brooks, Roland Brusseau, Ethan O. Bryson, Linda A. Bulich, Kenji Butterfield, William R. Camann, Denise M. Chan, Theresa S. Chang, Jonathan E. Charnin, Mark Chrostowski, Fred Cobey, Adam B. Collins, Mercedes A. Concepcion, Christopher W. Connor, Bronwyn Cooper, Jeffrey B. Cooper, Martha Cordoba-Amorocho, Stephen B. Corn, Darin J. Correll, Gregory J. Crosby, Lisa J. Crossley, Deborah J. Culley, Tomas Cvrk, Michael N. D'Ambra, Michael Decker, Daniel F. Dedrick, Mark Dershwitz, Francis X. Dillon, Pradeep Dinakar, Alimorad G. Djalali, D. John Doyle, Lambertus Drop, Ian F. Dunn, Theodore E. Dushane, Sunil Eappen, Thomas Edrich, Jesse M. Ehrenfeld, Jason M. Erlich, Lucinda L. Everett, Elliott S. Farber, Khaldoun Faris, Eddy M. Feliz, Massimo Ferrigno, Richard S. Field, Michael G. Fitzsimons, Hugh L. Flanagan Jr., Vladimir Formanek, Amanda A. Fox, John A. Fox, Gyorgy Frendl, Tanja S. Frey, Samuel M. Galvagno Jr., Edward R. Garcia, Jonathan D. Gates, Cosmin Gauran, Brian J. Gelfand, Simon Gelman, Alexander C. Gerhart, Peter Gerner, Omid Ghalambor, Christopher J. Gilligan, Christian D. Gonzalez, Noah E. Gordon, William B. Gormley, Thomas J. Graetz, Wendy L. Gross, Amit Gupta, James P. Hardy, Seetharaman Hariharan, Miriam Harnett, Philip M. Hartigan, Joaquim M. Havens, Bishr Haydar, Stephen O. Heard, James L. Helstrom, David L. Hepner, McCallum R. Hoyt, Robert N. Jamison, Karinne Jervis, Stephanie B. Jones, Swaminathan Karthik, Richard M. Kaufman, Shubjeet Kaur, Lee A. Kearse Jr., John C. Keel, Scott D. Kelley, Albert H. Kim, Amy L. Kim, Grace Y. Kim, Robert J. Klickovich, Robert M. Knapp, Bhavani S. Kodali, Rahul Koka, Alina Lazar, Laura H. Leduc, Stanley Leeson, Lisa R. Leffert, Scott A. LeGrand, Patricio Leyton, J. Lance Lichtor, John Lin, Alvaro A. Macias, Karan Madan, Sohail K. Mahboobi, Devi Mahendran, Christine Mai, Sayeed Malek, S. Rao Mallampati, Thomas J. Mancuso, Ramon Martin, Matthew C. Martinez, J. A. Jeevendra Martyn, Kai Matthes, Tommaso Mauri, Mary Ellen McCann, Shannon S. McKenna, Dennis J. McNicholl, Abdel-Kader Mehio, Thor C. Milland, Tonya L. K. Miller, John D. Mitchell, K. Annette Mizuguchi, Naila Moghul, David R. Moss, Ross J. Musumeci, Naveen Nathan, Ju-Mei Ng, Liem C. Nguyen, Ervant Nishanian, Martina Nowak, Ala Nozari, Michael Nurok, Arti Ori, Rafael A. Ortega, Amy J. Ortman, David Oxman, Arvind Palanisamy, Carlo Pancaro, Lisbeth Lopez Pappas, Benjamin Parish, Samuel Park, Deborah S. Pederson, Beverly K. Philip, James H. Philip, Silvia Pivi, Stephen D. Pratt, Douglas E. Raines, Stephen L. Ratcliff, James P. Rathmell, J. Taylor Reed, Elizabeth M. Rickerson, Selwyn O. Rogers Jr., Thomas M. Romanelli, William H. Rosenblatt, Carl E. Rosow, Edgar L. Ross, J. Victor Ryckman, Mônica M. Sá Rêgo, Nicholas Sadovnikoff, Warren S. Sandberg, Annette Y. Schure, B. Scott Segal, Navil F. Sethna, Swapneel K. Shah, Shaheen F. Shaikh, Fred E. Shapiro, Torin D. Shear, Prem S. Shekar, Stanton K. Shernan, Naomi Shimizu, Douglas C. Shook, Kamal K. Sikka, Pankaj K. Sikka, David A. Silver, Jeffrey H. Silverstein, Emily A. Singer, Ken Solt, Spiro G. Spanakis, Wolfgang Steudel, Matthias Stopfkuchen-Evans, Michael P. Storey, Gary R. Strichartz, Balachundhar Subramaniam, Wariya Sukhupragarn, John Summers, Shine Sun, Eswar Sundar, Sugantha Sundar, Neelakantan Sunder, Faraz Syed, Usha B. Tedrow, Nelson L. Thaemert, George P. Topulos, Lawrence C. Tsen, Richard D. Urman, Charles A. Vacanti, Francis X. Vacanti, Joshua C. Vacanti, Assia Valovska, Ivan T. Valovski, Mary Ann Vann, Susan Vassallo, Anasuya Vasudevan, Kamen V. Vlassakov, Gian Paolo Volpato, Essi M. Vulli, J. Matthias Walz, Jingping Wang, James F. Watkins, Maxwell Weinmann, Sharon L. Wetherall, Mallory Williams, Sarah H. Wiser, Zhiling Xiong, Warren M. Zapol, Jie Zhou
- Edited by Charles Vacanti, Scott Segal, Pankaj Sikka, Richard Urman
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- Essential Clinical Anesthesia
- Published online:
- 05 January 2012
- Print publication:
- 11 July 2011, pp xv-xxviii
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Preferential concentration and relative velocity statistics of inertial particles in Navier–Stokes turbulence with and without filtering
- BAIDURJA RAY, LANCE R. COLLINS
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- Journal:
- Journal of Fluid Mechanics / Volume 680 / 10 August 2011
- Published online by Cambridge University Press:
- 06 June 2011, pp. 488-510
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The radial distribution function (RDF, a statistical measure of preferential concentration), and the relative velocity measured along the line-of-centres of two particles are the key statistical inputs to the collision kernel for finite-inertia particles suspended in a turbulent flow Sundaram & Collins (J. Fluid Mech., vol. 335, 1997, p. 75). In this paper, we investigate the behaviour of these two-particle statistics using direct numerical simulation (DNS) of homogeneous isotropic turbulence. While it is known that the RDF for particles of any Stokes number (St) decreases with separation distance Sundaram & Collins (J. Fluid Mech., vol. 335, 1997, p. 75), Reade & Collins (Phys. Fluids, vol. 12, 2000, p. 2530), Salazar et al. (J. Fluid Mech., vol. 600, 2008, p. 245), we observe that the peak in the RDF versus St curve shifts to higher St as we increase the separation distance. Here, St is defined as the ratio of the particle's viscous relaxation time to the Kolmogorov time-scale of the flow. Furthermore, as found in a previous study Wang, Wexler, & Zhou (J. Fluid Mech., vol. 415, 2000, p. 117), the variance of the radial relative velocity (wr) is found to increase monotonically with increasing separation distance and increasing Stokes number; however, we show for the first time that the parameteric variation of the skewness of wr with St and r/η is qualitatively similar to that of the RDF, and points to a connection between the two. We then apply low-pass filters (using three different filter scales) on the DNS velocity field in wavenumber space in order to produce ‘perfect’ large-eddy simulation (LES) velocity fields without any errors associated with subgrid-scale modelling. We present visual evidence of the effect of sharp-spectral filtering on the flow structure and the particle field. We calculate the particle statistics in the filtered velocity field and find that the RDF decreases with filtering at low St and increases with filtering at high St, similar to Fede & Simonin (Phys. Fluids, vol. 18, 2006, p. 045103). We also find that the variation of the RDF with St shifts towards higher St with filtering at all separation distances. The variance of wr is found to decrease with filtering for all St and separation distances, but the skewness of wr shows a non-monotonic response to filtering that is qualitatively similar to the RDF. We consider the variation of the RDF and moments of wr with filter scale and find that they are approximately linear in the inertial range. We demonstrate that a simple model consisting of a redefinition of the St based on the time-scale of the filtered velocity field cannot recover the unfiltered statistics. Our findings provide insight on the effect of subgrid-scale eddies on the RDF and wr, and establish the requirements of a LES model for inertial particles that can correctly predict clustering and collisional behaviour.
Effect of the shear parameter on velocity-gradient statistics in homogeneous turbulent shear flow
- JUAN C. ISAZA, LANCE R. COLLINS
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- Journal:
- Journal of Fluid Mechanics / Volume 678 / 10 July 2011
- Published online by Cambridge University Press:
- 18 May 2011, pp. 14-40
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The effect of the shear parameter on the small-scale velocity statistics in an homogeneous turbulent shear flow is investigated using direct numerical simulations (DNSs) of the incompressible Navier–Stokes equations on a 5123 grid. We use a novel pseudo-spectral algorithm that allows us to set the initial value of the shear parameter in the range 3–30 without the shortcomings of previous numerical approaches. We find that the tails of the probability distribution function of components of the vorticity vector and rate-of-strain tensor are progressively distorted with increasing shear parameter. Furthermore, we show that the shear parameter has a direct effect on the structure of the vorticity field, which manifests through changes in its alignment with the eigenvectors of the rate-of-strain tensor. We also find that increasing the shear parameter causes the main contribution to enstrophy production to shift from the nonlinear terms to the rapid terms (terms that are proportional to the mean shear) due to the aforementioned changes in the alignment. We attempt to explain these trends using viscous rapid distortion theory; however, while the theory does capture some effects of the shear parameter, it fails to predict the correct dependence on Reynolds number. Comparisons with recent experiments are also shown. The trends predicted by the DNS and the experiments are in good agreement. Moreover, the prefactors in the Reynolds number scaling laws for the skewness and flatness of the longitudinal velocity derivative are shown to have a statistically significant dependence on the shear parameter.
Polymer-laden homogeneous shear-driven turbulent flow: a model for polymer drag reduction
- ASHISH ROBERT, T. VAITHIANATHAN, LANCE R. COLLINS, JAMES G. BRASSEUR
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- Journal:
- Journal of Fluid Mechanics / Volume 657 / 25 August 2010
- Published online by Cambridge University Press:
- 28 June 2010, pp. 189-226
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Drag reduction (DR) under a turbulent boundary layer implies the suppression of turbulent momentum flux to the wall, a large-eddy phenomenon. Our hypothesis is that the essential mechanisms by which dilute concentrations of long-chain polymer molecules reduce momentum flux involve only the interactions among turbulent velocity fluctuations, polymer molecules and mean shear. Experiments indicate that these interactions dominate in a polymer-active ‘elastic layer’ outside the viscous sublayer and below a Newtonian inertial layer in a polymer-laden turbulent boundary layer. We investigate our hypothesis by modelling the suppression of momentum flux with direct numerical simulation (DNS) of homogeneous turbulent shear flow (HTSF) and the finite extensible nonlinear elastic with Peterlin approximation (FENE-P) model for polymer stress. The polymer conformation tensor equation was solved using a new hyperbolic algorithm with no artificial diffusion. We report here on the equilibrium state with fixed mean shear rate S, where progressive increases in non-dimensional polymer relaxation time WeS (shear Weissenberg number) or concentration parameter 1 − β produced progressive reductions in Reynolds shear stress, turbulence kinetic energy and turbulence dissipation rate, concurrent with increasing polymer stress and elastic potential energy. The changes in statistical variables underlying polymer DR with 1 − β, WeS, %DR and polymer-induced changes to spectra are similar to experiments in channel and pipe flows and show that the experimentally measured increase in normalized streamwise velocity variance is an indirect consequence of DR that is true only at lower DR. Comparison of polymer stretch and elastic potential energy budgets with channel flow DNS showed qualitative correspondence when distance from the wall was correlated to WeS. As WeS increased, the homogeneous shear flow displayed low-DR, high-DR and maximum-DR (MDR) regimes, similar to experiments, with each regime displaying distinctly different polymer–turbulence physics. The suppression of turbulent momentum flux arises from the suppression of vertical velocity fluctuations primarily by polymer-induced suppression of slow pressure–strain rate correlations. In the high-Weissenberg-number MDR-like limit, the polymer nearly completely blocks Newtonian inter-component energy transfer to vertical velocity fluctuations and turbulence is maintained by the polymer contribution to pressure–strain rate. Our analysis from HTSF with the FENE-P representation of polymer stress and its comparisons with experimental and DNS studies of wall-bounded polymer–turbulence supports our central hypothesis that the essential mechanisms underlying polymer DR lie directly in the suppression of momentum flux by polymer–turbulence interactions in the presence of mean shear and indirectly in the presence of the wall as the shear-generating mechanism.
On the asymptotic behaviour of large-scale turbulence in homogeneous shear flow
- JUAN C. ISAZA, LANCE R. COLLINS
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- Journal:
- Journal of Fluid Mechanics / Volume 637 / 25 October 2009
- Published online by Cambridge University Press:
- 17 September 2009, pp. 213-239
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The asymptotic behaviour of large-scale velocity statistics in an homogeneous turbulent shear flow is investigated using direct numerical simulations (DNS) of the incompressible Navier–Stokes equations on a 5123 grid, and with viscous rapid distortion theory (RDT). We use a novel pseudo-spectral algorithm that allows us to set the initial value of the shear parameter in the range 3–30 without the shortcomings of previous numerical approaches. We find there is an explicit dependence of the early-time behaviour on the initial value of the shear parameter. Moreover, the long-time asymptotes of large-scale quantities such as the ratio of the turbulent kinetic energy production rate over dissipation rate, the Reynolds stress anisotropic tensor and the shear parameter itself depend sensitively on the initial value of the shear parameter over the range of Reynolds number we could achieve (26 ≤ Rλ ≤ 63) with the stringent resolution requirements that were satisfied. To gain further insight into the matter, we analyse the full viscous RDT. While inviscid RDT has received a great deal of attention, viscous RDT has not been fully analysed. Our motivation for considering viscous RDT is so that the energy dissipation rate enters the problem, enabling the shear parameter to be defined. We show asymptotic expansions for the short-time behaviour and numerically evaluate the integrals to determine the long-time prediction of viscous RDT. The results are in quantitative agreement with DNS for short times; however, at long times viscous RDT predicts the turbulent energy decays to zero. Through an analysis of the pressure–strain terms, we show that the nonlinear ‘slow’ terms are essential for rearranging turbulent energy from the streamwise direction to the mean shear direction, and this sustains the indefinite growth of the kinetic energy at long times. In effect, the nonlinear pressure–strain correlation maintains the three-dimensionality of the turbulence, countering the tendency of the mean shear to project the turbulence onto the two-dimensional plane of the mean-flow streamlines. We postulate that the predictions of viscous RDT at long times could be improved by introducing a model for the ‘slow’ pressure–strain term, along the lines of the Rotta model.
Experimental and numerical investigation of inertial particle clustering in isotropic turbulence
- JUAN P. L. C. SALAZAR, JEREMY DE JONG, LUJIE CAO, SCOTT H. WOODWARD, HUI MENG, LANCE R. COLLINS
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- Journal:
- Journal of Fluid Mechanics / Volume 600 / 10 April 2008
- Published online by Cambridge University Press:
- 26 March 2008, pp. 245-256
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This paper presents the first detailed comparisons between experiments and direct numerical simulations (DNS) of inertial particle clustering in nearly isotropic ‘box turbulence’. The experimental system consists of a box 38cm in each dimension with fans in the eight corners that sustain nearly isotropic turbulence in the centre of the box. We inject hollow glass spheres with a mean diameter of 6 μm and measure the locations of several hundred particles in a 1 cm3 volume in the centre of the box using three-dimensional digital holographic particle imaging. We observe particle concentration fluctuations that result from inertial clustering (sometimes called ‘preferential concentration’). The radial distribution function (RDF), a statistical measure of clustering, has been calculated from the particle position field. We select this measure because of its relevance to the collision kernel for particles. DNS of the equivalent system, with nearly perfect parameter overlap, have also been performed. We observe good agreement between the RDF predictions of the DNS and the experimental observations, despite some challenges in the interpretation of the experiments. The results provide important guidance on ways to improve the measurement.
Polymer mixing in shear-driven turbulence
- T. VAITHIANATHAN, ASHISH ROBERT, JAMES G. BRASSEUR, LANCE R. COLLINS
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- Journal:
- Journal of Fluid Mechanics / Volume 585 / 25 August 2007
- Published online by Cambridge University Press:
- 07 August 2007, pp. 487-497
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We investigate numerically the influence of polymer mixing on shear-driven turbulence. Of particular interest is the suppression of mixing that accompanies drag reduction with dilute polymer solutions. The simulations use the finite extensible nonlinear elastic model with the Peterlin closure (FENE-P) to describe the polymer stresses in the momentum equation, with polymer concentration allowed to vary in space and time. A thin slab of concentrated polymer was placed in an initially Newtonian homogeneous turbulent shear flow on a plane perpendicular to the mean velocity gradient, and allowed to mix in the gradient direction while actively altering the turbulence. The initially higher concentration of polymer near the centreplane suppressed production of turbulent kinetic energy and Reynolds stress in that region, while turbulence outside the polymer-rich region remained shear-dominated Newtonian turbulence. The rate of mixing in the shear direction was severely damped by the action of the polymer compared to a passive scalar in the corresponding Newtonian turbulent shear flow. This, in part, was a result of the same damping of vertical velocity fluctuations by the polymer that leads to the suppression of momentum flux. However, the cross-correlation between the polymer concentration and vertical velocity fluctuations was also suppressed, indicating that the explanation for the reduction in polymer mixing involves both the suppression of vertical velocity fluctuations and an alteration of turbulence structure by the polymer–turbulence interactions.
Clustering of aerosol particles in isotropic turbulence
- JAEHUN CHUN, DONALD L. KOCH, SARMA L. RANI, ARUJ AHLUWALIA, LANCE R. COLLINS
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- Journal:
- Journal of Fluid Mechanics / Volume 536 / 10 August 2005
- Published online by Cambridge University Press:
- 26 July 2005, pp. 219-251
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It has been recognized that particle inertia throws dense particles out of regions of high vorticity and leads to an accumulation of particles in the straining-flow regions of a turbulent flow field. However, recent direct numerical simulations (DNS) indicate that the tendency to cluster is evident even at particle separations smaller than the size of the smallest eddy. Indeed, the particle radial distribution function (RDF), an important measure of clustering, increases as an inverse power of the interparticle separation for separations much smaller than the Kolmogorov length scale. Motivated by this observation, we have developed an analytical theory to predict the RDF in a turbulent flow for particles with a small, but non-zero Stokes number. Here, the Stokes number ($\hbox{\it St}$) is the ratio of the particle's viscous relaxation time to the Kolmogorov time. The theory approximates the turbulent flow in a reference frame following an aerosol particle as a local linear flow field with a velocity gradient tensor and acceleration that vary stochastically in time. In monodisperse suspensions, the power-law dependence of the pair probability is seen to arise from a balance of an inward drift caused by the particles' inertia that scales linearly with the particle separation distance and a pairwise diffusion owing to the random nature of the flow with a diffusivity that scales quadratically with the particle separation distance. The combined effect leads to a power law behaviour for the RDF with an exponent, $c_1$, that is proportional to $\hbox{\it St}^2$. Predictions of the analytical theory are compared with two types of numerical simulation: (i) particle pairs interacting in a local linear flow whose velocity varies according to a stochastic velocity gradient model; (ii) particles interacting in a flow field obtained from DNS of isotropic turbulence. The agreement with both types of simulation is very good. The theory also predicts the RDF for unlike particle pairs (particle pairs with different Stokes numbers). In this case, a second diffusion process occurs owing to the difference in the response of the pair to local fluid accelerations. The acceleration diffusivity is independent of the pair separation distance; thus, the RDF of particles with even slightly different viscous relaxation times undergoes a transition from the power law behaviour at large separations to a constant value at sufficiently small separations. The radial separation corresponding to the transition between these two behaviours is predicted to be proportional to the difference between the Stokes numbers of the two particles. Once again, the agreement between the theory and simulations is found to be very good. Clustering of particles enhances their rate of coagulation or coalescence. The theory and linear flow simulations are used to obtain predictions for the rate of coagulation of particles in the absence of hydrodynamic and colloidal particle interactions.
Three Surveillance Strategies for Vancomycin-Resistant Enterococci in Hospitalized Patients: Detection of Colonization Efficiency and a Cost-Effectiveness Model
- Todd A. Lee, Donna M. Hacek, Kevin T. Stroupe, Susan M. Collins, Lance R. Peterson
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- Journal:
- Infection Control & Hospital Epidemiology / Volume 26 / Issue 1 / January 2005
- Published online by Cambridge University Press:
- 21 June 2016, pp. 39-46
- Print publication:
- January 2005
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Objective:
To evaluate the cost-effectiveness and detection sensitivity associated with three active surveillance strategies for the identification of patients harboring vancomycin-resistant enterococci (VRE) to determine which is the most medically and economically useful.
Design:Culture for VRE from 200 consecutive stool specimens submitted for Clostridium difficile culture. Following this, risk factors were assessed for patients whose culture yielded VRE, and a cost-effectiveness evaluation was performed using a decision analytic model with a probabilistic analysis.
Setting:A 688-bed, tertiary-care facility in Chicago, Illinois, with approximately 39,000 annual admissions, 7,000 newborn deliveries, 56,000 emergency department visits, and 115,000 home care and 265,000 outpatient visits.
Subjects:All stool specimens submitted to the clinical microbiology laboratory for C. difficile culture from hospital inpatients.
Results:From 200 stool samples submitted for C. difficile testing, we identified 5 patients with VRE in non-high-risk areas not screened as part of our routine patient surveillance. Medical record review revealed that all 5 had been hospitalized within the prior 2 years. Three of 5 had a history of renal impairment. The strategy that would involve screening the greatest number of patients (all those with a history of hospital admission in the prior 2 years) resulted in highest screening cost per patient admitted ($2.48), lower per patient admission costs ($480), and the best survival rates.
Conclusion:An expanded VRE surveillance program that encompassed all patients hospitalized within the prior 2 years was a cost-effective screening strategy compared with a more traditional one focused on high-risk units.
Breakup in stochastic Stokes flows: sub-Kolmogorov drops in isotropic turbulence
- VITTORIO CRISTINI, J. BŁAWZDZIEWICZ, MICHAEL LOEWENBERG, LANCE R. COLLINS
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- Journal:
- Journal of Fluid Mechanics / Volume 492 / 10 October 2003
- Published online by Cambridge University Press:
- 16 September 2003, pp. 231-250
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Deformation and breakup of drops in an isotropic turbulent flow has been studied by numerical simulation. The numerical method involves a pseudospectral representation of the turbulent outer flow field coupled to three-dimensional boundary integral simulations of the local drop dynamics. A statistical analysis based on an ensemble of drop trajectories is presented; results include breakup rates, the distribution of primary daughter drops produced by breakup events, and stationary distributions for drop deformation and orientation. Depending on the local flow history, drops may break at modest length or become highly elongated and relax without breaking. Drop deformation is the dominant mechanism of drop reorientation. The volume of the primary daughter drops, produced by a given fluctuation in flow strength, scales with the volume of the corresponding critical drop size for the fluctuation. A simplified description for the evolution of the drop size distribution, based on this scaling, is presented.
A spectral study of differential diffusion of passive scalars in isotropic turbulence
- MARK ULITSKY, T. VAITHIANATHAN, LANCE R. COLLINS
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- Journal:
- Journal of Fluid Mechanics / Volume 460 / 10 June 2002
- Published online by Cambridge University Press:
- 25 June 2002, pp. 1-38
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In a companion paper, Ulitsky & Collins (2000) applied the eddy-damped quasi-normal Markovian (EDQNM) turbulence theory to the mixing of two inert passive scalars with different diffusivities in stationary isotropic turbulence. Their paper showed that a rigorous application of the EDQNM approximation leads to a scalar covariance spectrum that violates the Cauchy–Schwartz inequality over a range of wavenumbers. The violation results from the improper functionality of the inverse diffusive time scales that arise from the Markovianization of the time evolution of the triple correlations. The modified inverse time scale they proposed eliminates this problem and allows meaningful predictions of the scalar covariance spectrum both with and without a uniform mean gradient.
This study uses the modified EDQNM model to investigate the spectral dynamics of differential diffusion. Consistent with recent DNS results by Yeung (1996), we observe that whereas spectral transfer is predominantly from low to high wavenumbers, spectral incoherence, being of molecular origin, originates at high wavenumbers and is transferred in the opposite direction by the advective terms. Quantitative comparisons between the EDQNM model and the DNS show good agreement. In addition, the model is shown to give excellent estimates for the dissipation coefficient defined by Yeung (1998).
We show that the EDQNM scalar covariance spectrum for two scalars with different molecular diffusivities can be approximated by the EDQNM autocorrelation spectrum for a scalar with molecular diffusivity equal to the arithmetic mean of the first two scalars. The result is exact for the case of an isotropic scalar and is shown to be a very good approximation for the scalar with a uniform mean gradient. We then exploit this relationship to derive a simple formula for the correlation coefficient of two differentially diffusing scalars as a function of their two Schmidt numbers and the turbulent Reynolds number. A comparison of the formula with the EDQNM model shows the model predicts the correct Reynolds number scaling and qualitatively predicts the dependence on the Schmidt numbers.
To investigate the degree of local versus non-local transfer of the scalar covariance spectrum, we divided the energy spectrum into three ranges corresponding to the energy-containing eddies, the inertial range, and the dissipation range. Then, by conditioning the scalar transfer on the energy contained within each of the three ranges, we have determined that the transfer process is dominated first by local interactions (local transfer) followed by non-local interactions leading to local transfer. Non-local interactions leading to non-local transfer are found to be significant at the higher wavenumbers. This result has important implications for defining simpler spectral models that potentially can be applied to more complex engineering flows.
Relationship between the intrinsic radial distribution function for an isotropic field of particles and lower-dimensional measurements
- GRETCHEN L. HOLTZER, LANCE R. COLLINS
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- Journal:
- Journal of Fluid Mechanics / Volume 459 / 25 May 2002
- Published online by Cambridge University Press:
- 17 June 2002, pp. 93-102
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In this paper, we present relationships between the intrinsic radial distribution function (RDF) for a three-dimensional, isotropic system of particles and the lower-dimensional RDFs obtained experimentally from either two-dimensional or one-dimensional sampling of the data. The lower-dimensional RDFs are shown to be equivalent to integrals of the three-dimensional function, and as such contain less information than their three-dimensional counterpart. An important consequence is that the lower-dimensional RDFs are attenuated at separation distances below the characteristic length scale of the measurement. In addition, the inverse problem (calculating the three-dimensional RDF from the lower-dimensional measurements) is not well posed. However, recent results from direct numerical simulations (Reade & Collins 2000) showed that the three-dimensional RDF for aerosol particles in a turbulent flow field obeys a power-law dependence on r for r [Lt ] η, where η is the Kolmogorov scale of the turbulence. In this case, the inverse problem is well posed and it is possible to obtain the prefactor and exponent of the power law from one- or two-dimensional measurements. A procedure for inverting the data is given. All of the relationships derived in this paper have been validated by data derived from direct numerical simulations.