Three‐dimensional remeshed smoothed particle hydrodynamics for the simulation of isotropic turbulence

We present a remeshed particle‐mesh method for the simulation of three‐dimensional compressible turbulent flow. The method is related to the meshfree smoothed particle hydrodynamics method, but the present method introduces a mesh for efficient calculation of the pressure gradient, and laminar and turbulent diffusion. In addition, the mesh is used to remesh (reorganise uniformly) the particles to ensure a regular particle distribution and convergence of the method. The accuracy of the presented methodology is tested for a number of benchmark problems involving two‐ and three‐dimensional Taylor‐Green flow, thin double shear layer, and three‐dimensional isotropic turbulence. Two models were implemented, direct numerical simulations, and Smagorinsky model. Taking advantage of the Lagrangian advection, and the finite difference efficiency, the method is capable of providing quality simulations while maintaining its robustness and versatility.     

湍流横掠固定颗粒的全尺度直接数值模拟

气固两相流模拟中,当固相尺度接近或大于Kolmogorov尺度时,普通的点源模型将不再适用,固体相的体积效应和表面效应将对流体相产生显著的影响。通过采用直接数值模拟方法,结合内嵌边界方法对湍流中不同湍流强度流体横掠大于Kolmogorov尺度的固相颗粒进行了全尺度模拟,讨论分析了在两种湍流度下方形颗粒对湍流的调制影响以及颗粒的受力情况。     

Direct numerical simulation of decaying two‐dimensional turbulence in a no‐slip square box using smoothed particle hydrodynamics

This paper explores the application of SPH to a DNS of decaying turbulence in a two‐dimensional no‐slip wall‐bounded domain. In this bounded domain, the inverse energy cascade, and a net torque exerted by the boundary, results in a spontaneous spin‐up of the fluid, leading to a typical end state of a large monopole vortex that fills the domain. The SPH simulations were compared against published results using a high‐accuracy pseudo‐spectral code. Ensemble averages of the kinetic energy, enstrophy and average vortex wavenumber compared well against the pseudo‐spectral results, as did the evolution of the total angular momentum of the fluid. However, although the pseudo‐spectral results emphasised the importance of the no‐slip boundaries as generators of long‐lived coherent vortices in the flow, no such generation was seen in the SPH results. Vorticity filaments produced at the boundary were always dissipated by the flow shortly after separating from the boundary layer. The kinetic energy spectrum of the SPH results was calculated using an SPH Fourier transform that operates directly on the disordered particles. The ensemble kinetic energy spectrum showed the expected k^?3 scaling over most of the inertial range. However, the spectrum flattened at smaller length scales (initially less than 7.5 particle spacings and growing in size over time), indicating an excess of small‐scale kinetic energy.Copyright © 2011 John Wiley & Sons, Ltd.     

Acceleration of heavy particles in isotropic turbulence

The paper concerns the effect of particle inertia on acceleration statistics. A simple analytical model for predicting the acceleration of heavy particles suspended in an isotropic homogeneous turbulent flow field is developed. This model is capable of describing the influence of both Stokes and Reynolds numbers on the particle acceleration variance. Comparisons of model predictions with numerical simulations are presented.     

Dispersion and clustering of bidisperse particles in isotropic turbulence

A statistical kinetic model describing the dispersion and clustering of particles with different inertia in homogeneous turbulence is presented. The model developed is used for calculating the relative velocity, the radial distribution function, and the particle collision kernel in a stationary bidisperse suspension. The results obtained are compared with the data of a direct numerical simulation.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 94–107. Original Russian Text Copyright © 2005 by Alipchenkov and Zaichik.     

Direct numerical simulation of preferential particle concentration in decaying turbulence under the influence of magnetic field

This paper presents a direct numerical simulation of an isotropic turbulence at Reynolds number R_λ=71.4. The statistics of heavy particles in such turbulence has been investigated. The numerical results indicate the merit of method in solving the magnetohydrodynamic turbulence. The revision of the paper was made based on the reviewers' comments. The paper was improved significantly. Hence, review suggests accepting the submission in current form. Copyright © 2009 John Wiley & Sons, Ltd.     

Direct numerical simulation of homogeneous stratified rotating turbulence

The effects of the Prandtl number on stratified rotating turbulence have been studied in homogeneous turbulence by using direct numerical simulations and a rapid distortion theory. Fluctuations under strong stable-density stratification can be theoretically divided into the WAVE and the potential vorticity (PV) modes. In low-Prandtl-number fluids, the WAVE mode deteriorates, while the PV mode remains. Imposing rotation on a low-Prandtl-number fluid makes turbulence two-dimensional as well as geostrophic; it is found from the instantaneous turbulent structure that the vortices merge to form a few vertically-elongated vortex columns. During the period toward two-dimensionalization, the vertical vortices become asymmetric in the sense of rotation. Communicated by S. Obi PACS 47.55.Hd     

Computation of strongly swirling confined flows with cubic eddy‐viscosity turbulence models

An investigation on the predictive performance of four cubic eddy‐viscosity turbulence models for two strongly swirling confined flows is presented. Comparisons of the prediction with the experiments show clearly the superiority of cubic models over the linear k–εmodel. The linear k–εmodel does not contain any mechanism to describe the stabilizing effects of swirling motion and as a consequence it performs poorly. Cubic models return a lower level of Reynolds stresses and the combined forced‐free vortex profiles of tangential velocity close to the measurements in response to the interaction between swirl‐induced curvature and stresses. However, a fully developed rotating pipe flow is too simple to contain enough flow physics, so the calibration of cubic terms is still a topic of investigation. It is shown that explicit algebraic stress models require fewer calibrations and contain more flow physics. Copyright © 2003 John Wiley & Sons, Ltd.     

Direct numerical simulation of stationary particles in homogeneous turbulence decay: Application of the k–ε model

This study focuses on understanding how the presence of particles, in homogeneous turbulence decay, affects the dissipation of dissipation coefficient within the volume averaged dissipation transport equation. In developing this equation, the coefficient for dissipation of dissipation was assumed to be the sum of the single phase coefficient and an additional coefficient that is related to the effects of the dispersed phase. Direct numerical simulation was used to isolate the effect of stationary particles in homogeneous turbulent decay at low Reynolds numbers (Re_L = 3.3 and 12.5). The particles were positioned at each grid point and modeled as point forces and a comparison was made between a 64³ and 128³ domain. The results show that the dissipation of dissipation coefficient correlates well with a dimensionless parameter called the momentum coupling factor.     

Direct numerical simulation of turbulent Taylor–Couette flow

The direct numerical simulation (DNS) of the Taylor–Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio and Luchini [M. Quadrio, P. Luchini, Eur. J. Mech. B/Fluids 21 (2002) 413–427], and is based on a parallel computer code which uses mixed spatial discretization (spectral schemes in the homogeneous directions, and fourth-order, compact explicit finite-difference schemes in the radial direction). A DNS is carried out to simulate for the first time the turbulent Taylor–Couette flow in the turbulent regime. Statistical quantities are computed to complement the existing experimental information, with a view to compare it to planar, pressure-driven turbulent flow at the same value of the Reynolds number. The main source for differences in flow statistics between plane and curved-wall flows is attributed to the presence of large-scale rotating structures generated by curvature effects.     

Performance of very‐high‐order upwind schemes for DNS of compressible wall‐turbulence

The purpose of the present paper is to evaluate very‐high‐order upwind schemes for the direct numerical simulation (DNS ) of compressible wall‐turbulence. We study upwind‐biased (UW ) and weighted essentially nonoscillatory (WENO ) schemes of increasingly higher order‐of‐accuracy (J. Comp. Phys. 2000; 160 :405–452), extended up to WENO 17 (AIAA Paper 2009‐1612, 2009). Analysis of the advection–diffusion equation, both as Δx→0 (consistency), and for fixed finite cell‐Reynolds‐number Re_Δx (grid‐resolution), indicates that the very‐high‐order upwind schemes have satisfactory resolution in terms of points‐per‐wavelength (PPW ). Computational results for compressible channel flow (Re∈[180, 230]; M?_CL ∈[0.35, 1.5]) are examined to assess the influence of the spatial order of accuracy and the computational grid‐resolution on predicted turbulence statistics, by comparison with existing compressible and incompressible DNS databases. Despite the use of baseline O(Δt²) time‐integration and O(Δx²) discretization of the viscous terms, comparative studies of various orders‐of‐accuracy for the convective terms demonstrate that very‐high‐order upwind schemes can reproduce all the DNS details obtained by pseudospectral schemes, on computational grids of only slightly higher density. Copyright © 2009 John Wiley & Sons, Ltd.     

Direct numerical simulation of particle behaviour in the wall region of turbulent flows in horizontal channels

The motion of small particles in the wall region of turbulent channel flows has been investigated using direct numerical simulation. It is assumed that the particle concentration is low enough to allow the use of one-way coupling in the calculations, i.e. the fluid moves the particles but there is no feedback from the particles on the fluid motion. The velocity of the fluid is calculated by using a pseudospectral, direct solution of the Navier-Stokes equations. The calculations indicate that particles tend to segregate into the low-speed regions of the fluid motion near the wall. The segregation tendency depends on the time constant of the particle made non-dimensional with the wall shear velocity and kinematic viscosity. For very small and very large time constants, the particles are distributed more uniformly. For intermediate time constants (of the order 3), the segregation into the low-speed fluid regions is the highest. The finding that segregation occurs for a range of particle time constants is supported by experimental results. The findings regarding the more uniform distributions, however, still remain to be verified against experimental data which is not yet available. For horizontal channel flows, it is also found that particles are resuspended by ejections (of portions of the low-speed streaks) from the wall and are, therefore, primarily associated with low-speed fluid. The smaller particles are flung further upwards and, as they fall back towards the wall, they tend to be accelerated close to the fluid velocity. The larger particles have greater inertia and, consequently, accelerate to lower velocities giving higher relative velocities. This velocity difference, as a function of wall-normal distance, follows the same trend as in experiments but is always somewhat smaller in the calculations. This appears to be due to the Reynolds number for the numerical simulation being smaller than that in the experiment. It is concluded that the average particle velocity depends not only on the wall variables for scaling, but also on outer variables associated with the mean fluid velocity and fluid depth in the channel. This is because fluid depth in combination with the wall shear velocity determines how much time a particle, of a given size and density, spends in the outer flow and, hence, how close it gets to the local fluid velocity.     

Coupling the lattice‐Boltzmann and spectrin‐link methods for the direct numerical simulation of cellular blood flow

The implementation of a spectrin‐link (SL) red blood cell (RBC) membrane method coupled with a lattice‐Boltzmann (LB) fluid solver is discussed. Details of the methodology are included along with subtleties associated with its integration into a massively parallel hybrid LB finite element (FE) suspension flow solver. A comparison of the computational performance of the coupled LB–SL method with that of the previously implemented LB–FE is given for an isolated RBC and for a dense suspension in Hagen–Poiseuille flow. Validating results for RBCs isolated in shear and parachuting in microvessel flow are also presented. Copyright © 2011 John Wiley & Sons, Ltd.     

Cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density

An investigation on the predictive performance of cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density is presented. Comparisons of the prediction with the experiments show some improvements of cubic models over the linear k–ε model. The linear k–ε model does not contain any mechanism to represent the interaction of swirl and density variation and as a consequence it performs poorly. With appropriate modelling, two‐equation cubic turbulence models can capture the subcritical nature of the flow, represent the azimuthal velocity profiles of combined forced‐free vortex motion, and predict the combined effects of swirl and density variation fairly well. However, the calibration of model coefficients is still a topic of investigation. Further amendments are also needed for the equations of k and ε to take into account the effects of swirl and density gradients correctly. Copyright © 2004 John Wiley & Sons, Ltd.     

A scalable parallel algorithm for the direct numerical simulation of three-dimensional incompressible particulate flow

Particulate flow is of great importance from both the scientific and engineering points of view. Owing to the complexity of particle-flow interactions, direct numerical simulations (DNS) of inertial particulate flow with finite-size particles have been limited to a very small number of particles, while the industrial applications involve larger numbers with many orders of magnitude. This article presents a parallel implementation of a fictitious domain method for the DNS of particulate flows. The method is thoroughly tested and its parallel performance on distributed memory clusters is evaluated on a large-scale problem. Finally, we present the results for the separation of 21,336 particles of two different densities in a viscous fluid. Although there is still a significant gap between DNS and the industrial applications, the present algorithm allows to simulate significantly large number of particles so that a meaningful statistical analysis can be performed. This will help in the development of new closure relations for the averaged models of multiphase flows.     

A discontinuous Galerkin‐based sharp‐interface method to simulate three‐dimensional compressible two‐phase flow

A numerical method for the simulation of compressible two‐phase flows is presented in this paper. The sharp‐interface approach consists of several components: a discontinuous Galerkin solver for compressible fluid flow, a level‐set tracking algorithm to follow the movement of the interface and a coupling of both by a ghost‐fluid approach with use of a local Riemann solver at the interface. There are several novel techniques used: the discontinuous Galerkin scheme allows locally a subcell resolution to enhance the interface resolution and an interior finite volume Total Variation Diminishing (TVD) approximation at the interface. The level‐set equation is solved by the same discontinuous Galerkin scheme. To obtain a very good approximation of the interface curvature, the accuracy of the level‐set field is improved and smoothed by an additional P_NP_M‐reconstruction. The capabilities of the method for the simulation of compressible two‐phase flow are demonstrated for a droplet at equilibrium, an oscillating ellipsoidal droplet, and a shock‐droplet interaction problem at Mach 3. Copyright © 2015 John Wiley & Sons, Ltd.     

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.     

Direct numerical simulation of confined swirling jets

This study investigates the Lagrangian acceleration and velocity of fluid particles in swirling flows via direct numerical simulation. The intermittency characteristics of acceleration and velocity of fluid particles are investigated at different swirl numbers and Reynolds numbers. The flatness factor and trajectory curvature are used to analyse the effect of Lagrangian intermittency. The joint probability density function of Lagrangian acceleration and turbulence intensity is shown to explain the augmentation effect of Lagrangian intermittency by the strongly swirling levels under the relatively low intensity of turbulence. In addition, the correlation between the Lagrangian acceleration and the turbulence intensity is enhanced as the swirl level increases. It shows the important effect of swirl on the motion behaviour of fluid particles in the strongly swirling flows.     

Gas turbulence modulation in the pneumatic conveying of massive particles in vertical tubes

The present work is concerned with the interaction between large particles and gas phase turbulence. Gas turbulence modulation in these systems is considered to be dominated by a generation mechanism which arises due to the presence of wakes behind particles. Following a recent proposal, a closure for gas turbulence modulation accounting for the effect of wakes is employed within the context of a mathematical model for particle-laden, turbulent flows. The model accounts for particle particle and particle-wall interactions associated with larger particles based on concepts from gas kinetic theory. It is shown that due to the significant flattening of the mean gas velocity profile with the addition of particles, and the corresponding decrease in turbulent energy production, a generation mechanism must be present in order to produce gas velocity fluctuation predictions which are consistent with the experimental measurements, even in the case where the experimental results indicate a net suppression of gas phase turbulence in the presence of particles.