A dynamic subgrid-scale model for the large eddy simulation of stratified flow

A new dynamic subgrid-scale (SGS) model, including subgrid turbulent stress and heat flux models for stratified shear flow is proposed by using Yoshizawa’s eddy viscosity model as a base model. Based on our calculated results, the dynamic subgrid-scale model developed here is effective for the large eddy simulation (LES) of stratified turbulent channel flows. The new SGS model is then applied to the large eddy simulation of stratified turbulent channel flow under gravity to investigate the coupled shear and buoyancy effects on the near-wall turbulent statistics and the turbulent heat transfer at different Richardson numbers. The critical Richardson number predicted by the present calculation is in good agreement with the value of theoretical analysis     

Dynamical states of bubbling in vertically vibrated granular materials. Part I: Collective processes

Granular materials deform plastically like a solid under weak shear and they flow like a fluid under high shear. These materials exhibit other unusual kinds of behavior, including pattern formation in shaking of granular materials for which the onset characteristics of the various patterns are not well understood. Vertically shaken granular materials undergo a transition to a convective motion which can result in the formation of bubbles. In Part I, a detailed overview is presented of collective processes in gas-particle flows useful for developing a simplified model for molecular dynamic type simulations of dense gas-particle flows. The large eddy simulation method (LES) has been employed for simulating fluid flows through irregular array of particles. The results obtained may lead to scale-dependent closures for quantities such as the drag, stresses and effective dispersion. These are of use for developing a continuum approach for describing the deformation and flow of dense gas-particle mixtures described in Part II.     

Improving shock-free compressible RANS solvers for LES on unstructured meshes

Standard numerical methods used to solve the Reynolds averaged Navier–Stokes equations are known to be too dissipative to carry out large eddy simulations since the artificial dissipation they introduce to stabilize the discretization of the convection term usually interacts strongly with the subgrid scale model. A possible solution is to resort to non-dissipative central schemes. Unfortunately, these schemes are in general unstable. A way to reach stability is to select a central scheme that conserves the discrete kinetic energy. To that purpose, a family of kinetic energy conserving schemes is developed to perform simulations of compressible shock-free flows on unstructured grids. A direct numerical simulation of the flow past a sphere at a Reynolds number of 300 and a large eddy simulation at a Reynolds number of 10,000 are performed to validate the methodology.     

Discrete large eddy simulation

IntroductionIn previous worksll,2], we discussed several issues associated with the standard version oflarge eddy simulation (LES) such as filtering and averaging. By the standard version, we meanthe traditional practice of first constructing a set of field equations of motions for turbulentmotion and then discretizing the equations to suit computational simulations.In this paper, we revisit the issue of large eddy simulation with a view towards improvingthe filtering procedure that is used i…     

An improved dynamic subgrid-scale model and its application to large eddy simulation of stratified channel flows

In the present paper, a new dynamic subgrid-scale (SGS) model of turbulent stress and heat flux for stratified shear flow is proposed. Based on our calculated results of stratified channel flow, the dynamic subgrid-scale model developed in this paper is shown to be effective for large eddy simulation (LES) of stratified turbulent shear flows. The new SGS model is then applied to the LES of the stratified turbulent channel flow to investigate the coupled shear and buoyancy effects on the behavior of turbulent statistics, turbulent heat transfer and flow structures at different Richardson numbers.     

Large Eddy Simulation of a Compressible Boundary Layer

A large eddy simulation of a compressible boundary layer is performed. To generate an appropriate inflow distribution the rescaling technique for compressible flows is discribed. In this method Morkovin's hypothesis in which the total temperature fluctuations are neglected compared with the static temperature fluctuations is applied to rescale and generate the temperature profile at inlet. This new technique is used for various large eddy simulations of subsonic and supersonic three‐dimensional boundary layers of a flat plate. Simulation results for the time‐averaged mean flow and Reynolds stresses are compared with numerical and analytical data to demonstrate the high quality of the method.     

Artificial viscosity proper orthogonal decomposition

We introduce improved reduced-order models for turbulent flows. These models are inspired from successful methodologies used in large eddy simulation, such as artificial viscosity, applied to standard models created by proper orthogonal decomposition of flows coupled with Galerkin projection. As a first step in the analysis and testing of our new methodology, we use the Burgers equation with a small diffusion parameter. We present a thorough numerical analysis for the time discretization of the new models. We then test these models in two problems displaying shock-like phenomena. Of course, since the Burgers equation does not model turbulence, we next need to test our new models in realistic turbulent flow settings. This is the subject of a forthcoming report.     

The effect of modeling of velocity fluctuations on prediction of collection efficiency of cyclone separators

The effect of modeling of velocity fluctuations on the prediction of collection efficiency of cyclone separators has been numerically investigated using the Reynolds stress turbulence model (RSTM) and large eddy simulation (LES). The Eulerian–Lagrangian modeling approach of CFD code Fluent 6.3.26 has been employed to simulate the three dimensional, unsteady turbulent gas–solid flows in a Stairmand high efficiency cyclone. The simulated results have been compared with experimental observations available in the literature. The analysis of results shows that the RSTM and the LES have adequately predicted the mean flow field. Results of the present study demonstrate that the LES has good performance on prediction of fluctuating flow field and collection efficiency for each and every particle size. However, the performance of the RSTM is found poor in terms of prediction of velocity fluctuations and collection efficiency, especially for small particles. This relates to the precessing of the vortex core phenomenon, which is resolved more accurately by LES as compared to the RSTM simulation. The results suggest that the prediction of collection efficiency, especially for small particles is greatly influenced by the simulation of velocity fluctuations in cyclones.     

Steady state numerical simulation of the particle collection efficiency of a new urban sustainable gravity settler using design of experiments by FVM

The aim of this work is to analyze the efficiency of a new sustainable urban gravity settler to avoid the solid particle transport, to improve the water waste quality and to prevent pollution problems due to rain water harvesting in areas with no drainage pavement. In order to get this objective, it is necessary to solve particle transport equations along with the turbulent fluid flow equations since there are two phases: solid phase (sand particles) and fluid phase (water). In the first place, the turbulent flow is modelled by solving the Reynolds-averaged Navier-Stokes (RANS) equations for incompressible viscous flows through the finite volume method (FVM) and then, once the flow velocity field has been determined, representative particles are tracked using the Lagrangian approach. Within the particle transport models, a particle transport model termed as Lagrangian particle tracking model is used, where particulates are tracked through the flow in a Lagrangian way. The full particulate phase is modelled by just a sample of about 2,000 individual particles. The tracking is carried out by forming a set of ordinary differential equations in time for each particle, consisting of equations for position and velocity. These equations are then integrated using a simple integration method to calculate the behaviour of the particles as they traverse the flow domain. The entire FVM model is built and the design of experiments (DOE) method was used to limit the number of simulations required, saving on the computational time significantly needed to arrive at the optimum configuration of the settler. Finally, conclusions of this work are exposed.     

Numerical simulation of the filling behavior of a Non-Newtonian Fluid

A numerical model for free surface flows of non-newtonian liquids which are injected into a cavity is presented. These flows are regarded as a basic model of injection molding. Model experiments of the injection process are performed with a water-based gel. The flow equations are integrated according to the finite-volume-method. The volume of fluid method (VoF) is employed in order to describe the free surface flow of two incompressible phases, the phase interface is resolved by the method of geometric reconstruction. The Herschel-Bulkley model is used in order to describe shear-thinning behavior of the molding material and the effects of a yielding point. Different patterns of the filling flow depending on the injection parameters are evident in the experiment and the simulation. They are characterized and arranged with respect to the similarity parameters of the flow. Again, the results of the simulation are found to agree well with the experimental observations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vortex breakdown in turbulent pipe flows

In many technical applications turbulent flows with embedded slender vortices exist. Depending on the boundary conditions vortex breakdown can occur. The purpose of this work is to develop and implement a solution scheme for large‐eddy simulations of vortex breakdown in turbulent pipe flows. One of the main problems in this simulation is the formulation of the inflow boundary condition for a fully developed turbulent flow with an embedded vortex. For that purpose a rescaling technique is developed in which a solution at a downstream location is inserted at the inflow boundary after an appropriate rescaling. To determine rescaling laws for pipe flows with an embedded vortex, analytical velocity profiles of swirling flows are first prescribed in a laminar flow. From the spatial development of the vortex a scaling law is deduced. In a next step this procedure is to be transferred to turbulent flows.     

Dispersion of solid particles in turbulant flow through pipe expansions

Studies of the effects upon gas-liquid two-phase flows of pipefittings such as expansions, contractions, bends, and valveshave usually concentrated upon pressuredrop correlations andhave not attempted to determine changes in the distributionsof the gas and liquid phases caused by the fitting. However,it is known that such information is important if, for example,flow separators, which divide the gas and liquid phases in avariety of industrial processes, are to function efficiently.It is therefore important to gain an understanding of the influenceupon phase distributions of the common pipe fittings mentionedabove, which will be found in almost any industrial pipeworksystem. As a first step, the dispersion of solid particles carriedby turbulent gas flows through a pipe expansion has been modellednumerically. The commercial fluid-flow code CFDS-FLOW{smalltilde}hDas been used to model the gas flow, together with aneddy interaction model for determination of the motion of thesolid particles. Mean particle velocities and root-mean-squarevalues of the particle velocity fluctuations, as well as particleconcentrations, are evaluated and compared with recent experimentalresults. The influence of different eddy-length and eddy-lifetimespecifications upon the dispersion of particles of various sizesis investigated. It is found that the different eddy characteristicshave little effect on predicted mean particle velocities, whereasfluctuations in particle velocities and particle concentrationare sensitive to the changes made. By comparing the resultswith experimental data, it is possible to draw conclusions aboutthe relative merits of the different eddy specifications.     

Eulerian and Lagrangian predictions of particulate two-phase flows: a numerical study

To predict particulate two-phase flows, two approaches are possible. One treats the fluid phase as a continuum and the particulate second phase as single particles. This approach, which predicts the particle trajectories in the fluid phase as a result of forces acting on particles, is called the Lagrangian approach. Treating the solid as some kind of continuum, and solving the appropriate continuum equations for the fluid and particle phases, is referred to as the Eulerian approach.Both approaches are discussed and their basic equations for the particle and fluid phases as well as their numerical treatment are presented. Particular attention is given to the interactions between both phases and their mathematical formulations. The resulting computer codes are discussed.The following cases are presented in detail: vertical pipe flow with various particle concentrations; and sudden expansion in a vertical pipe flow. The results show good agreement between both types of approach.The Lagrangian approach has some advantages for predicting those particulate flows in which large particle accelerations occur. It can also handle particulate two-phase flows consisting of polydispersed particle size distributions. The Eulerian approach seems to have advantages in all flow cases where high particle concentrations occur and where the high void fraction of the flow becomes a dominating flow controlling parameter.     

直管束流固耦合振动的数值模拟

为了研究反应堆结构中的诸如燃料棒、蒸汽发生器和其它换热器传热管束等的流体-结构交互作用问题,利用有限体积法离散大涡模拟(large eddy simulation, LES)的流体控制方程,用有限元方法求解结构动力学方程,并结合动网格技术,建立三维流体诱发振动的数值模型,模拟直管束中流体的流动及结构振动,实现计算结构动力学(computational structure dynamics, CSD)与计算流体力学(computational fluid dynamics, CFD)之间的联合仿真．首先,基于流固耦合方法对单管的流致振动特性进行了详细分析,得到了其动力学响应与流场特性;其次基于建立的传热管束流致振动计算模型,研究了两并列管、两串列管以及3×3正方形排列管束的流致振动行为．     

Finite element analysis of laminar and turbulent flows using LES and subgrid-scale models

Numerical simulations of laminar and turbulent flows in a lid driven cavity and over a backward-facing step are presented in this work. The main objectives of this research are to know more about the structure of turbulent flows, to identify their three-dimensional characteristic and to study physical effects due to heat transfer. The filtered Navier–Stokes equations are used to simulate large scales, however they are supplemented by subgrid-scale (SGS) models to simulate the energy transfer from large scales toward subgrid-scales, where this energy will be dissipated by molecular viscosity. Two SGS models are applied: the classical Smagorinsky’s model and the Dynamic model for large eddy simulation (LES). Both models are implemented in a three-dimensional finite element code using linear tetrahedral elements. Qualitative and quantitative aspects of two and three-dimensional flows in a lid-driven cavity and over a backward-facing step, using LES, are analyzed comparing numerical and experimental results obtained by other authors.     

Approximate deconvolution boundary conditions for large eddy simulation

We introduce new boundary conditions for large eddy simulation. These boundary conditions are based on an approximate deconvolution approach. They are computationally efficient and general, which makes them appropriate for the numerical simulation of turbulent flows with time-dependent boundary conditions. Numerical results are presented to demonstrate the new boundary conditions in a simplified linear setting.     

Eddy cascade of instabilities and transition to turbulence

Numerical simulation is used to investigate a shear layer influenced by a constant external forcing in the theory of turbulence (Kolmogorov’s problem). The dynamics of flows developing in the case of various initial streamwise velocity profiles are studied. The transition from a two-dimensional laminar flow to a three-dimensional turbulent flow is considered. It is shown that developing hydrodynamic instabilities give rise to an eddy cascade, which, in the transition of the flow to a turbulent stage, corresponds to an eddy cascade developing in the energy and, then, inertial ranges.     

Superstrings,Cantorian-fractal Spacetime and Quantum-like Chaos in Atmospheric Flows

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with the inverse power law form for spectra of temporal fluctuations. Such non-local connections are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. A recently developed cell dynamical system model for atmospheric flows predicts the observed self-organized criticality as a natural consequence of quantum-like mechanics governing flow dynamics. The model is based on the concept that spatial integration of enclosed small scale fluctuations results in the formation of large eddy circulations. The model predicts the following: (a) The flow structure consists of an overall logarithmic spiral trajectory with the quasiperiodic Penrose tiling pattern for the internal structure. (b) Conventional power spectrum analysis will resolve such spiral trajectories as a continuum of eddies with progressive increase in phase. (c) Increments in phase are concomitant with increases in period length and also represent the variance, a characteristic of quantum systems identified as Berrys phase. (d) The universal algorithm for self-organized criticality is expressed in terms of the universal Feigenbaum constants, a and d, as 2a²=πd, where the fractional volume intermittency of occurrence πd contributes to the total variance 2a² of fractal structures. (e) The Feigenbaum constants are expressed as functions of the golden mean. ( f) The quantum mechanical constants fine structure constant and ratio of proton mass to electron mass, which are pure numbers and are obtained by experimental observations only, are now derived in terms of the Feigenbaum constant, a. (g) Atmospheric flow structure follows Keplers third law of planetary motion. Therefore, Newtons inverse square law for gravitation also applies to eddy masses. The centripetal acceleration representing the inertial masses (of eddies) are equivalent to gravitational masses. The fractal-Cantorian structure of spacetime can also be visualized as a nested continuum of vortex (eddy) circulations, whose inertial masses obey Newtons inverse square law of gravitation. The model concept resembles a superstring model for subatomic dynamics which incorporates gravitational forces.     

Eulerian Simulation of Gas‐Solid Particle Flow by BDIM

The numerical scheme based on the boundary domain integral method (BDIM) for the numerical simulation of twophase two‐component flows is presented. A program is being developed to model the hydrodynamics of fluidized bed systems by using the Eulerian approach in terms of velocity‐vorticity variables formulation. With the vorticity vector both phases motion computation scheme is partitioned into its kinematic and kinetic aspect. Influence of the drag coefficient on the two‐phase two‐component flow field is studied on the two‐phase gas‐solid particles vertical channel flow.     

Asymptotic behaviour of commutation errors and the divergence of the Reynolds stress tensor near the wall in the turbulent channel flow

The derivation of the space averaged Navier–Stokes equations for the large eddy simulation (LES) of turbulent incompressible flows introduces two groups of terms which do not depend only on the space averaged flow field variables: the divergence of the Reynolds stress tensor and commutation errors. Whereas the former is studied intensively in the literature, the latter terms are usually neglected. This note studies the asymptotic behaviour of these terms for the turbulent channel flow at a wall in the case that the commutation errors arise from the application of a non‐uniform box filter. To perform analytical calculations, the unknown flow field is modelled by a wall law (Reichardt law and 1/αth power law) for the mean velocity profile and highly oscillating functions model the turbulent fluctuations. The asymptotics show that near the wall, the commutation errors are at least as important as the divergence of the Reynolds stress tensor. Copyright © 2006 John Wiley & Sons, Ltd.