Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session M18: Particle Laden Flows VI: Turbulence |
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Chair: Sarma Rani, University of Alabama in Huntsville Room: 28D |
Tuesday, November 20, 2012 8:00AM - 8:13AM |
M18.00001: On Pair Diffusion and Preferential Concentration of High Stokes Number Particles in Isotropic Turbulence Sarma Rani, Donald Koch In this study, we derived the Fokker-Planck equation governing the PDF of pair separation and relative velocity vectors of high $St$ particles. The PDF equation contains a particle-pair diffusion coefficient in relative velocity space. We developed an analytical theory to predict this relative velocity-space pair diffusion coefficient in the limit of high $St$. Using the diffusion coefficient, Langevin-equation-based stochastic simulations were performed to evolve pair separation and velocity vectors in isotropic turbulence for particle Stokes numbers, $St = 1,~2,~4,~10, \mbox{ and,}~20$ and a Taylor micro-scale Reynolds number, $Re_\lambda = 75$. The most significant finding from the Langevin simulations is that our pair diffusivity theory successfully captures the transition of relative velocity PDF from a Gaussian PDF at separations of the order of integral length scale to a non-Gaussian PDF at smaller separations. The pair radial distribution functions (RDFs) computed using our theory show that as the Stokes number increased, particles preferentially accumulate even at integral length scale separations. Another significant finding of our approach is that the slope of RDF at Kolmogorov length scale separations for higher St particles is not zero. [Preview Abstract] |
Tuesday, November 20, 2012 8:13AM - 8:26AM |
M18.00002: A stochastic model of particle dispersion in turbulent reacting gaseous environments Guangyuan Sun, David Lignell, John Hewson We are performing fundamental studies of dispersive transport and time-temperature histories of Lagrangian particles in turbulent reacting flows. The particle-flow statistics including the full particle temperature PDF are of interest. A challenge in modeling particle motions is the accurate prediction of fine-scale aerosol-fluid interactions. A computationally affordable stochastic modeling approach, one-dimensional turbulence (ODT), is a proven method that captures the full range of length and time scales, and provides detailed statistics of fine-scale turbulent-particle mixing and transport. Limited results of particle transport in ODT have been reported in non-reacting flow. Here, we extend ODT to particle transport in reacting flow. The results of particle transport in three flow configurations are presented: channel flow, homogeneous isotropic turbulence, and jet flames. We investigate the functional dependence of the statistics of particle-flow interactions including (1) parametric study with varying temperatures, Reynolds numbers, and particle Stokes numbers; (2) particle temperature histories and PDFs; (3) time scale and the sensitivity of initial and boundary conditions. Flow statistics are compared to both experimental measurements and DNS data. [Preview Abstract] |
Tuesday, November 20, 2012 8:26AM - 8:39AM |
M18.00003: Eulerian models for particle trajectory crossing in turbulent flows over a large range of Stokes numbers Rodney O. Fox, Aymeric Vie, Frederique Laurent, Christophe Chalons, Marc Massot Numerous applications involve a disperse phase carried by a gaseous flow. To simulate such flows, one can resort to a number density function (NDF) governed a kinetic equation. Traditionally, Lagrangian Monte-Carlo methods are used to solve for the NDF, but are expensive as the number of numerical particles needed must be large to control statistical errors. Moreover, such methods are not well adapted to high-performance computing because of the intrinsic inhomogeneity of the NDF. To overcome these issues, Eulerian methods can be used to solve for the moments of the NDF resulting in an unclosed Eulerian system of hyperbolic conservation laws. To obtain closure, in this work a multivariate bi-Gaussian quadrature is used, which can account for particle trajectory crossing (PTC) over a large range of Stokes numbers. This closure uses up to four quadrature points in 2-D velocity phase space to capture large-scale PTC, and an anisotropic Gaussian distribution around each quadrature point to model small-scale PTC. Simulations of 2-D particle-laden isotropic turbulence at different Stokes numbers are employed to validate the Eulerian models against results from the Lagrangian approach. Good agreement is found for the number density fields over the entire range of Stokes numbers tested. [Preview Abstract] |
Tuesday, November 20, 2012 8:39AM - 8:52AM |
M18.00004: Turbulence effects on particle dispersion in free-surface flow Salvatore Lovecchio, Cristian Marchioli, Alfredo Soldati We study the dispersion of light particles in a two-dimensional (2D) flow on a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. This simplified configuration mimics the motion of active/passive ocean surfactants (e.g. phytoplankton, floaters or drifters) when surface waves and ripples are absent. We perform direct numerical simulation of turbulence coupled with Lagrangian particle tracking, considering different values of the shear Reynolds number (Re=171 and 510) and of the Stokes number (0.06 $<$ St $<$ 1 in viscous units). Simulations show that particles reach the free surface upon entrainment in upwelling motions, then quickly move toward downwelling regions where they are trapped for long residence times and advected by the mean flow. Surface flow is neither compressible nor incompressible but strongly influenced by the 3D flow underneath the surface. Results highlight the fractal nature of particle distribution at the surface, which appears to be driven by flow scales different from those of incompressible 2D/3D homogenous isotropic turbulence. In particular, we observe an asymptotic scaling of particle transport dynamics with the Lagrangian integral time scale of the fluid at the surface. [Preview Abstract] |
Tuesday, November 20, 2012 8:52AM - 9:05AM |
M18.00005: A subgrid model for inertial particle clustering in large-eddy simulations of turbulence Baidurja Ray, Andrew D. Bragg, Lance R. Collins Existing subgrid models for inertial particles in large-eddy simulations (LES) of turbulence do not correctly predict particle clustering. Synthetic turbulence models such as kinematic simulations (KS) have been shown to capture many features of fully developed turbulence, at low computational cost. The presence of small-scale flow structure (with a specified energy spectrum) makes KS an attractive choice for reconstructing the subgrid fluctuations seen by inertial particles in a LES. We apply such a model (referred to as KSSGM) to a filtered isotropic turbulence simulation with particles. Preliminary results show that the KSSGM is able to recover the RDF for moderately large Stokes numbers (for which clustering is still significant) and shows the correct qualitative trend in the RDF for smaller Stokes numbers ($St$). This suggests that the effect of subgrid scales on the high $St$ particles is simpler than for particles having time-scales of the order of the Kolmogorov time-scale or less. Importantly, the KSSGM captures the opposing effect of the subgrid scales on clustering of particles with high and low $St$, which may stem from the fact that the KSSGM is able to describe the spatially correlated nature of the subgrid velocity field experienced by a particle pair. [Preview Abstract] |
Tuesday, November 20, 2012 9:05AM - 9:18AM |
M18.00006: A comparison of theoretical models for the spatial clustering of inertial particles in homogeneous, isotropic turbulence Andrew Bragg, Lance Collins In this talk we will consider two theoretical models for the clustering of inertial particles in turbulence, one by Chun~\emph{et.al.} (J. Fluid Mech. 536:219, 2005) and the other by Zaichik~\emph{et.al.} (Phys. Fluids. 19:113308, 2007). Although their predictions for the RDF (Radial Distribution Function) are similar in the regime $St\ll1$ we will show that the two theories describe the physical origin of clustering in quite different ways. The Chun~\emph{et.al.} theory describes the origin of the clustering in terms of a local drift mechanism which arises because inertial particles sample more strain than rotation, and the Zaichik~\emph{et.al.} theory describes the origin of the clustering in terms of a drift mechanism which is influenced by both the local dynamics of the fluid velocity gradient tensor and also by the particle memory of its interaction with the fluid velocity field in its path history. We will discuss an artificial test case that demonstrates the physical mechanism described in the Chun~\emph{et.al.} theory does not completely describe the mechanism responsible for the clustering. Finally, we explain the discrepancies between the two theories and explain, despite those discrepancies, why their predictions in the regime $St\ll1$ are so similar. [Preview Abstract] |
Tuesday, November 20, 2012 9:18AM - 9:31AM |
M18.00007: A novel state-space based method for direct numerical simulation of particle-laden turbulent flows Reetesh Ranjan, Carlos Pantano We present a novel state-space-based numerical method for transport of the particle density function, which can be used to investigate particle-laden turbulent flows. Here, the problem can be stated purely in a deterministic Eulerian framework. The method is coupled to an incompressible three-dimensional flow solver. We consider a dilute suspension where the volume fraction and mass loading of the particles in the flow are low enough so that the approximation of one-way coupling remains valid. The particle transport equation is derived from the governing equation of the particle dynamics described in a Lagrangian frame, by treating position and velocity of the particle as state-space variables. Application and features of this method will be demonstrated by simulating a particle-laden decaying isotropic turbulent flow. It is well known that even in an isotropic turbulent flow, the distribution of particles is not uniform. For example, heavier-than-fluid particles tend to accumulate in regions of low vorticity and high strain rate. This lead to large regions in the flow where particles remain sparsely distributed. The new approach can capture the statistics of the particle in such sparsely distributed regions in an accurate manner compared to other numerical methods. [Preview Abstract] |
Tuesday, November 20, 2012 9:31AM - 9:44AM |
M18.00008: Spatial effects of flow straining on inertial particles in turbulence Chung-min Lee, Prasad Perlekar, Federico Toschi, Armann Gylfason The effects of axisymmetric expansion on the movement of inertial particles are studied numerically. Turbulence with different strain rates is simulated with Direct Numerical Simulation and Rogallo's algorithm on a deforming domain, and particle movements are computed with the assumption of one-way coupling between the flow and particle fields. We are interested in the influence of the large scale geometric change on particle movements. We will present distribution results on inertial particles such as temporal correlations on particle locations, stagnation tendency, and encounters among particles with different Stokes numbers. [Preview Abstract] |
Tuesday, November 20, 2012 9:44AM - 9:57AM |
M18.00009: Particle tracking in LES flow fields: Lagrangian conditional statistics of filtering error Mario Tesone, Maria Vittoria Salvetti, Cristian Marchioli, Sergio Chibbaro, Alfredo Soldati The Lagrangian PDFs of the fluid velocity filtering error associated to Lagrangian particle tracking in filtered DNS flow fields are examined. To this aim, we perform a-priori tests in which the error purely due to filtering is singled out removing error accumulation effects, which would lead to progressive divergence between DNS and filtered DNS trajectories. PDFs are then obtained for the reference case of turbulent channel flow, conditioning the initial particle distribution within regions where either a sweep or an ejection is taking place. Preliminary results confirm the stochastic and non-Gaussian nature of filtering error in non-homogeneous flows. Compared to Eulerian PDFs, however, Lagrangian conditional PDFs exhibit differences which may offer useful insights for physical modelling. Specifically, for short times upon particle release, PDFs indicate a strong subgrid anisotropic effect of sweeps and ejections along the wall-normal direction. This feature underlines the link between turbulent coherent structures and strain, suggesting the possibility to model coherent structures with a direct link to velocity gradients. Asymptotically, the Lagrangian conditional PDFs recover the Eulerian behavior showing Stokes number effects limited to the PDF tails. [Preview Abstract] |
Tuesday, November 20, 2012 9:57AM - 10:10AM |
M18.00010: A numerical investigation of cluster fall velocity in vertical particle-laden turbulent pipe flow Jesse Capecelatro, Olivier Desjardins Particle clusters are known to play a key role in the multiphase dynamics as well as secondary processes such as heat transfer and catalytic conversion within vertical pipe flows. For example, vertical risers in circulating fluidized bed reactors consists of a dilute suspension of particles that ascend in the core of the flow, then condense into clusters and descend at the walls. In this work, an Euler-Lagrange strategy is used to study particle cluster dynamics in turbulent risers for a range of Archimedes numbers and density ratios. The simulations are conducted in the framework of NGA, a high-order fully conservative code tailored for turbulent flows. The particles are solved in a Lagrangian framework and the two phases are coupled using a two-step filtering process to ensure conservation, as well as convergence during mesh refinement. Normal and tangential collisions are computed via a soft-sphere model. A conservative immersed boundary method is used to represent the 3D cylindrical geometry on a Cartesian mesh. Simulation results are compared with experimental correlations in terms of cluster fall velocity and size. The role of the carrier fluid on the cluster behavior is also studied. [Preview Abstract] |
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