scholarly journals Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence

2012 ◽  
Vol 693 ◽  
pp. 201-215 ◽  
Author(s):  
Yoshiyuki Tagawa ◽  
Julián Martínez Mercado ◽  
Vivek N. Prakash ◽  
Enrico Calzavarini ◽  
Chao Sun ◽  
...  
Keyword(s):  
Experimental Data ◽  
Isotropic Turbulence ◽  
Response Times ◽  
Three Dimensional ◽  
Voronoi Cell ◽  
Reynolds Numbers ◽  
Point Particle ◽  
Heavy Particles ◽  
Data Set ◽  
Light Particles

AbstractThree-dimensional Voronoï analysis is used to quantify the clustering of inertial particles in homogeneous isotropic turbulence using data sets from numerics in the point particle limit and one experimental data set. We study the clustering behaviour at different density ratios, particle response times (i.e. Stokes numbers $\mathit{St}$) and two Taylor–Reynolds numbers (${\mathit{Re}}_{\lambda } = 75$ and 180). The probability density functions (p.d.f.s) of the Voronoï cell volumes of light and heavy particles show different behaviour from that of randomly distributed particles, i.e. fluid tracers, implying that clustering is present. The standard deviation of the p.d.f. normalized by that of randomly distributed particles is used to quantify the clustering. The clustering for both light and heavy particles is stronger for higher ${\mathit{Re}}_{\lambda } $. Light particles show maximum clustering for $\mathit{St}$ around 1–2 for both Taylor–Reynolds numbers. The experimental data set shows reasonable agreement with the numerical results. The results are consistent with previous investigations employing other approaches to quantify the clustering. We also present the joint p.d.f.s of enstrophy and Voronoï volumes and their Lagrangian autocorrelations. The small Voronoï volumes of light particles correspond to regions of higher enstrophy than those of heavy particles, indicating that light particles cluster in higher vorticity regions. The Lagrangian temporal autocorrelation function of Voronoï volumes shows that the clustering of light particles lasts much longer than that of heavy or neutrally buoyant particles. Due to inertial effects arising from the density contrast with the surrounding liquid, light and heavy particles remain clustered for much longer times than the flow structures which cause the clustering.

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

Recirculation within a fluid sphere at moderate Reynolds numbers

2002 ◽  
Vol 465 ◽  
pp. 293-300 ◽  
Author(s):  
D. A. BARRY ◽  
J.-Y. PARLANGE
Keyword(s):  
Experimental Data ◽  
Vertical Velocity ◽  
Laboratory Data ◽  
Major Axis ◽  
Reynolds Numbers ◽  
Fluid Sphere ◽  
Stagnation Region ◽  
Data Set ◽  
Different Levels

Motion of a single fluid sphere is described by two theories, each characterized by different levels of Hill's vortex circulation within the sphere. An existing experimental data set giving measurements of vertical velocity along the major axis of the sphere is re-examined. Contrary to published discussions of that experiment, we find that the theory of Parlange agrees better with the laboratory data than that of Harper & Moore. This agreement supports the key difference between the two theories, i.e. that the fluid within the sphere is unlikely to have a singular (infinite) velocity as it moves upwards towards the stagnation region at the top of the sphere.

A three-dimensional model of fine particle retention during percolation through a fiber mat

TAPPI Journal ◽  
2015 ◽  
Vol 14 (8) ◽  
pp. 546-554
Author(s):  
TERRY BLISS ◽  
MARTIN OSTOJA-STARZEWSKI ◽  
JAIME CASTRO
Keyword(s):  
Experimental Data ◽  
Fine Particles ◽  
Fiber Diameter ◽  
Three Dimensional ◽  
Particle Diameter ◽  
Three Dimensional Model ◽  
Retention Model ◽  
Data Set ◽  
Fiber Mats ◽  
Rayon Fiber

Fine particles are usually retained in fiber mats by sieving. To date, no theory has combined fiber and mat characteristics into a predictive retention model. A multilayer analytical retention model developed during this study predicts retention within a thick fiber mat by modeling retention as particles pass through a series of very thin fiber mats. A suspension of 5-75 μm toner particles was percolated through rayon fiber mats. The model’s prediction approached the experimental data only when the ratio of particle diameter to fiber diameter increased toward 2.0, the upper limit within the rayon fiber mat data set. Retention was also experimentally determined on the macroscale with simulated fiber mats, through which 4-20 mm beads were dropped. The particle diameter was at least 2.2 times the fiber diameter for all of the macroscale experimental data, explaining the much better fit of the data from those experiments to the model’s predictions.

Expanding theQ–Rspace to three dimensions

2009 ◽  
Vol 641 ◽  
pp. 497-507 ◽  
Author(s):  
BEAT LÜTHI ◽  
MARKUS HOLZNER ◽  
ARKADY TSINOBER
Keyword(s):  
Velocity Gradient ◽  
Isotropic Turbulence ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Data ◽  
Three Dimensions ◽  
Data Set ◽  
Viscous Term ◽  
Johns Hopkins University ◽  
Three Dimensional Representation

The two-dimensional space spanned by the velocity gradient invariantsQandRis expanded to three dimensions by the decomposition ofRinto its strain production −1/3sijsjkskiand enstrophy production 1/4ωiωjsijterms. The {Q;R} space is a planar projection of the new three-dimensional representation. In the {Q; −sss; ωωs} space the Lagrangian evolution of the velocity gradient tensorAijis studied via conditional mean trajectories (CMTs) as introduced by Martínet al. (Phys. Fluids, vol. 10, 1998, p. 2012). From an analysis of a numerical data set for isotropic turbulence ofReλ~ 434, taken from the Johns Hopkins University (JHU) turbulence database, we observe a pronounced cyclic evolution that is almost perpendicular to theQ–Rplane. The relatively weak cyclic evolution in theQ–Rspace is thus only a projection of a much stronger cycle in the {Q; −sss; ωωs} space. Further, we find that the restricted Euler (RE) dynamics are primarily counteracted by the deviatoric non-local part of the pressure Hessian and not by the viscous term. The contribution of the Laplacian ofAij, on the other hand, seems the main responsible for intermittently alternating between low and high intensityAijstates.

Transitional and Turbulent Flow Modeling in a Tesla Valve

2013 ◽  
Author(s):  
Scott M. Thompson ◽  
Tausif Jamal ◽  
Basil J. Paudel ◽  
D. Keith Walters
Keyword(s):  
Experimental Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Flow Speed ◽  
Flow Modeling ◽  
Ansys Fluent ◽  
Local Flow ◽  
Turbulent Characteristics ◽  
Minor Losses ◽  
Tesla Valve

A Tesla valve is a fluidic dioide that may be used in a variety of mini/micro channel applications for passive flow rectification and/or control. The valve’s effectiveness is quantified by the diodicity, which is primarily governed by the incoming flow speed, its design and direction-dependent minor losses throughout its structure during forward and reverse flows. It has been previously shown that the Reynolds number at the valve inlet is not representative of the entire flow regime throughout the Tesla structure. Therefore, pure-laminar solving methods are not necessarily accurate. Local flow instabilities exist and exhibit both transitional and turbulent characteristics. Therefore, the current investigation seeks to identify a suitable RANS-based flow modeling approach to predict Tesla valve diodicity via three-dimensional (3D) computational fluid dynamics (CFD) for inlet Reynolds numbers up to Re = 2,000. Using ANSYS FLUENT (v. 14), a variety of models were employed, including: the Realizable k-ε, k-kL-ω and SST k-ω models. All numerical simulations were validated against available experimental data obtained from an identically-shaped Tesla valve structure. It was found that the k-ε model drastically under-predicts experimental data for the entire range of Reynolds numbers investigated and cannot accurately model the Tesla valve flow. The k-kL-ω and SST k-ω models approach the experimentally-measured diodicity better than regular 2D CFD. The k-kL-ω demonstrates exceptional agreement with experimental data for Reynolds numbers up to approximately 1,500. However, both the k-kL-ω and k-ω SST models over-predict experimental data for Re = 2,000.

The modified cuinulant expansion for two-dimensional isotropic turbulence

1981 ◽  
Vol 110 ◽  
pp. 475-496 ◽  
Author(s):  
Tomomasa Tatsumi ◽  
Shinichiro Yanase
Keyword(s):  
Numerical Solutions ◽  
Isotropic Turbulence ◽  
Initial Period ◽  
Three Dimensional ◽  
Critical Time ◽  
Reynolds Numbers ◽  
Inviscid Limit ◽  
Inertial Subrange ◽  
Quasi Equilibrium ◽  
Two Dimensional

The two-dimensional isotropic turbulence in an incompressible fluid is investigated using the modified zero fourth-order cumulant approximation. The dynamical equation for the energy spectrum obtained under this approximation is solved numerically and the similarity laws governing the solution in the energy-containing and enstrophy-dissipation ranges are derived analytically. At large Reynolds numbers the numerical solutions yield the k−3 inertial subrange spectrum which was predicted by Kraichnan (1967), Leith (1968) and Batchelor (1969) assuming a finite enstrophy dissipation in the inviscid limit. The energy-containing range is found to satisfy an inviscid similarity while the enstrophy-dissipation range is governed by the quasi-equilibrium similarity with respect to the enstrophy dissipation as proposed by Batchelor (1969). There exists a critical time tc which separates the initial period (t < tc) and the similarity period (t > tc) in which the enstrophy dissipation vanishes and remains non-zero respectively in the inviscid limit. Unlike the case of three-dimensional turbulence, tc is not fixed but increases indefinitely as the viscosity tends to zero.

Effects of 3-D Local Unsteadiness on Heat Transfer Prediction in Turbulated Passages

2003 ◽  
Author(s):  
Pamela A. McDowell ◽  
William D. York ◽  
D. Keith Walters ◽  
James H. Leylek
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Turbulence Model ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Successful Outcome ◽  
Small Scale ◽  
Cross Sectional ◽  
Fully Implicit

A newly developed unsteady turbulence model was used to predict heat transfer in a turbulated passage typical of turbine airfoil cooling applications. Comparison of fullyconverged computational solutions to experimental measurements reveal that accurate prediction of heat transfer coefficient requires the effects of local small-scale unsteadiness to be captured. Validation was accomplished through comparison of the time- and area-averaged Nusselt number on the passage wall between adjacent ribs with experimental data from the open literature. The straight channel had a square cross-sectional area with multiple rows of staggered and rounded-edge ribs on opposite walls that were orthogonal to the flow. Simulations were run for Reynolds numbers of 5500, 16500, and 25000. Computational solutions were obtained on a multi-block, multi-topology, unstructured, and adaptive grid, using a pressure-correction based, fully-implicit Navier-Stokes solver. The computational results include two-dimensional (2-D) and three-dimensional (3-D) steady and unsteady simulations with viscous sublayers resolved (y+ ≤ 1) on all the walls in every case. Turbulence closure was obtained using a new turbulence model developed in-house for the unsteady simulations, and a realizable k-ε turbulence model was used for the steady simulations. The results obtained from the unsteady simulations show greatly improved agreement with the experimental data, especially at realistically high Reynolds numbers. The key 3-D physics mechanisms responsible for the successful outcome include: (1) shear layer roll-up over the turbulators; (2) recirculation zones both upstream and downstream of the rib faces; and (3) reattachment regions between each rib pair. Results from the unsteady case are superior to those of the steady because they capture the aforementioned mechanisms, and therefore more accurately predict the heat transfer.

scholarly journals Design and Validation of a Probe for Spatially and Temporally Resolved Measurements of Vorticity and Strain Rates in Compressible Turbulence Interactions

10.14311/994 ◽  
2007 ◽  
Vol 47 (6) ◽  
Author(s):  
S. Xanthos ◽  
M. Gong ◽  
Y. Andreopoulos
Keyword(s):  
Isotropic Turbulence ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Compressible Turbulence ◽  
Expansion Waves ◽  
Custom Made ◽  
Homogeneous And Isotropic Turbulence ◽  
Total Temperature ◽  
Kinetic Energy Term

A custom-made hot-wire vorticity probe was designed and developed capable of measuring the time-dependent highly fluctuating three dimensional velocity and vorticity vectors, and associated total temperature, in non-isothermal and inhomogeneous flows with reasonable spatial and temporal resolution. These measurements allowed computation of the vorticity stretching/tilting terms, vorticity generation through dilatation terms, full dissipation rate of the kinetic energy term and full rate-of-strain tensor. The probe has been validated experimentally in low-speed boundary layers and used in the CCNY Shock Tube Research Facility, where interactions of planar expansion waves or shock waves with homogeneous and isotropic turbulence have been investigated at several Reynolds numbers. 

scholarly journals Intermittency in the relative separations of tracers and of heavy particles in turbulent flows

2014 ◽  
Vol 757 ◽  
pp. 550-572 ◽  
Author(s):  
L. Biferale ◽  
A. S. Lanotte ◽  
R. Scatamacchia ◽  
F. Toschi
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Exit Time ◽  
Three Dimensional ◽  
Stokes Number ◽  
Inertial Range ◽  
Relative Dispersion ◽  
Heavy Particles ◽  
Self Similar

AbstractResults from direct numerical simulations (DNS) of particle relative dispersion in three-dimensional homogeneous and isotropic turbulence at Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathit{Re}}_{\lambda } \sim 300$ are presented. We study point-like passive tracers and heavy particles, at Stokes number $\mathit{St}=0.6,1$ and 5. Particles are emitted from localised sources, in bunches of thousands, periodically in time, allowing an unprecedented statistical accuracy to be reached, with a total number of events for two-point observables of the order of ${10^{11}}$. The right tail of the probability density function (PDF) for tracers develops a clear deviation from Richardson’s self-similar prediction, pointing to the intermittent nature of the dispersion process. In our numerical experiment, such deviations are manifest once the probability to measure an event becomes of the order of – or rarer than – one part over one million, hence the crucial importance of a large dataset. The role of finite-Reynolds-number effects and the related fluctuations when pair separations cross the boundary between viscous and inertial range scales are discussed. An asymptotic prediction based on the multifractal theory for inertial range intermittency and valid for large Reynolds numbers is found to agree with the data better than the Richardson theory. The agreement is improved when considering heavy particles, whose inertia filters out viscous scale fluctuations. By using the exit-time statistics we also show that events associated with pairs experiencing unusually slow inertial range separations have a non-self-similar PDF.

Viscous Flow Computations on a Smooth Cylinders: A Detailed Numerical Study With Validation

2007 ◽  
Author(s):  
Guilherme Vaz ◽  
Christophe Mabilat ◽  
Remmelt van der Wal ◽  
Paul Gallagher
Keyword(s):  
Experimental Data ◽  
Viscous Flow ◽  
Numerical Study ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Detached Eddy Simulation ◽  
Time Step ◽  
Drag Forces

The objective of this paper is to investigate several numerical and modelling features that the CFD community is currently using to compute the flow around a fixed smooth circular cylinder. Two high Reynolds numbers, 9 × 104 and 5 × 105, are chosen which are in the so called drag-crisis region. Using a viscous flow solver, these features are assessed in terms of quality by comparing the numerical results with experimental data. The study involves grid sensitivity, time step sensitivity, the use of different turbulence models, three-dimensional effects, and a RANS/DES (Reynolds Averaged Navier Stokes, Detached Eddy Simulation) comparison. The resulting drag forces and Strouhal numbers are compared with experimental data of different sources. Major flow features such as velocity and vorticity fields are presented. One of the main conclusions of the present study is that all models predict forces which are far from the experimental values, particularly for the higher Reynolds numbers in the drag-crisis region. Three-dimensional and unsteadiness effects are present, but are only fully captured by sophisticated turbulence models or by DES. DES seems to be the key to better solve the flow problem and obtain better agreement with experimental data. However, its considerable computational demands still do not allow to use it for engineering design purposes.

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