Dispersion of Gas Bubbles in Large-Scale Homogeneous Isotropic Turbulence

An approximate analysis is given of the dispersion of gas bubbles that rise at large Reynolds number through large-scale homogeneous, isotropic turbulence, characterized by the Kraichnan energy-spectrum function. A fairly well-established equation of motion of the bubbles, originally proposed by Thomas et al. [16], is used to derive a closed set of equations for the components of the dispersion tensor of the bubbles in a manner analogous to that used by Saffman [12] for fluid particles and by Pismen and Nir [10, 11] for solid particles. The equations are then solved to obtain the diffusivities and the intensities of bubble velocity fluctuations. Analytical solutions are compared with results from simulations of the bubble motion in a Gaussian random velocity field.     

Effects of the Similarity Model in Finite-Difference LES of Isotropic Turbulence Using a Lagrangian Dynamic Mixed Model

A Lagrangian dynamic formulation of the mixed similarity subgrid (SGS) model for large-eddy simulation (LES) of turbulence is proposed. In this model, averaging is performed over fluid trajectories, which makes the model applicable to complex flows without directions of statistical homogeneity. An alternative version based on a Taylor series expansion (nonlinear mixed model) is also examined. The Lagrangian models are implemented in a finite difference code and tested in forced and decaying isotropic turbulence. As comparison, the dynamic Smagorinsky model and volume-averaged formulations of the mixed models are also tested. Good results are obtained, except in the case of low-resolution LES (32³) of decaying turbulence, where the similarity coefficient becomes negative due to the fact that the test-filter scale exceeds the integral scale of turbulence. At a higher resolution (64³), the dynamic similarity coefficient is positive and good agreement is found between predicted and measured kinetic energy evolution. Compared to the eddy viscosity term, the similarity or the nonlinear terms contribute significantly to both SGS dissipation of kinetic energy and SGS force. In order to dynamically test the accuracy of the modeling, the error incurred in satisfying the Germano identity is evaluated. It is found that the dynamic Smagorinksy model generates a very large error, only 3% lower than the worst-case scenario without model. Addition of the similarity or nonlinear term decreases the error by up to about 50%, confirming that it represents a more realistic parameterization than the Smagorinsky model alone.     

Non-Equilibrium Mixing of Turbulence Scales Using a Continuous Hybrid RANS/LES Approach: Application to the Shearless Mixing Layer

A new subgrid-scale (SGS) model based on partially integrated transport method (PITM) is applied to the case of a turbulent spectral non-equilibrium flow created by the mixing of two turbulence fields of differing scales: the shearless mixing layer. The method can be viewed as a continuous hybrid RANS/LES approach. In this model the SGS length scale is no longer given by the size of the discretization step, but is dynamically estimated using an additional transport equation for the dissipation rate. The results are compared to those corresponding to the classical model of Smagorinsky and to the experimental data of Veeravalli and Warhaft. A method for creating an anisotropic analytical pseudo-random field for inflow conditions is also proposed. This approach based on subgrid-scale transport modelling combined with anisotropic inlet conditions gives better results for the prediction of the shearless mixing layer.     

Assessment of Turbulence Models for Predicting the Interaction Region in a Wall Jet by Reference to LES Solution and Budgets

Highly-resolved LES and experimental data for a plane wall jet are used to study the characteristics of turbulence-closure proposals, mainly within the framework of second-moment-transport modelling. The study is motivated by the observed importance of diffusive Reynolds-stress transport in the interaction region between the outer shear layer and the near-wall layer of the wall jet, which gives the near-wall flow characteristics that are very different from those of a conventional boundary layer. Comparisons are presented for mean-flow quantities, second moments and budgets. Also included are a priori studies of approximations for the pressure-velocity interaction, pressure-fluctuation-driven transport and turbulent transport of the Reynolds stresses by triple correlations, the last observed to contribute significantly to the stress budgets. The study reveals major defects in the closure approximations for the pressure-velocity interaction terms, especially in the near-wall region. These defects result in a poor representation by the particular second-moment closures investigated of even the integral and mean-flow characteristics of the wall jet.     

Axisymmetric Deformation of a Transversely Isotropic Cylindrical Body: A Hamiltonian State-Space Approach

A state-space approach for exact analysis of axisymmetric deformation and stress distribution in a circular cylindrical body of transversely isotropic material is developed. By means of Hamiltonian variational formulation via Legendre’s transformation, the basic equations in cylindrical coordinates are formulated into a state-space framework in which the unknown state vector comprises the displacements and associated stress components as the dual variables and the system matrix possesses the symplectic characteristics of a Hamiltonian system. Upon delineating the symplecticity of the formulation, a viable solution approach using eigenfunction expansion is developed. For illustration, an exact analysis of a finite thick-walled circular cylinder under internal and external pressures is presented, with emphasis on the end effects.     

Effect of Particle Clusters on Carrier Flow Turbulence: A Direct Numerical Simulation Study

Experiments indicate that particle clusters that form in fluidized–bed risers can enhance gas-phase velocity fluctuations. Direct numerical simulations (DNS) of turbulent flow past uniform and clustered configurations of fixed particle assemblies at the same solid volume fraction are performed to gain insight into particle clustering effects on gas-phase turbulence, and to guide model development. The DNS approach is based on a discrete-time, direct-forcing immersed boundary method (IBM) that imposes no-slip and no-penetration boundary conditions on each particle’s surface. Results are reported for mean flow Reynolds number Re _p ?=?50 and the ratio of the particle diameter d _p to Kolmogorov scale is 5.5. The DNS confirm experimental observations that the clustered configurations enhance the level of fluid-phase turbulent kinetic energy (TKE) more than the uniform configurations, and this increase is found to arise from a lower dissipation rate in the clustered particle configuration. The simulations also reveal that the particle-fluid interaction results in significantly anisotropic fluid-phase turbulence, the source of which is traced to the anisotropic nature of the interphase TKE transfer and dissipation tensors. This study indicates that when particles are larger than the Kolmogorov scale (d _p ?>?η), modeling the fluid-phase TKE alone may not be adequate to capture the underlying physics in multiphase turbulence because the Reynolds stress is anisotropic. It also shows that multiphase turbulence models should consider the effect of particle clustering in the dissipation model.     

Dynamic Analysis of Spatial Linkages: A Recursive Approach

In this paper, recursive equations of motion of spatial linkages are presented. The method uses the concepts of linear and angular momentums to generate the rigid body equations of motion in terms of the Cartesian coordinates of a dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotational transformation matrix. For the open-chain system, the equations of motion are generated recursively along the serial chains. Closed-chain system is transformed to open-chain by cutting suitable kinematic joints and introducing cut–joint constraints. An example is chosen to demonstrate the generality and simplicity of the developed formulation.     

Dynamic Analysis of Planar Linkages: A Recursive Approach

In the present study, the equations of motion for generalized planar linkages that consist of a system of rigid bodies with all common types of kinematic joints are derived using a recursive approach. The system of rigid bodies is replaced by a dynamically equivalent constrained system of particles. Then for the resulting equivalent system of particles, the concepts of linear and angular momentums are used to generate the equations of motion without either introducing any rotational coordinates or distributing the external forces and force couples over the particles. For the open loop case, the equations of motion are generated recursively along the open chains. For the closed loop case, the system is transformed to open loops by cutting suitable kinematic joints and introducing cut-joints kinematic constraints. An example of a multi-branch closed-loop system is chosen to demonstrate the generality and simplicity of the proposed method.     

Stability of Homogeneous States with Gradient Damage Models: Size Effects and Shape Effects in the Three-Dimensional Setting

Considering a family of gradient-enhanced damage models and taking advantage of its variational formulation, we study the stability of homogeneous states in a full three-dimensional context. We show that gradient terms have a stabilizing effect, but also how those terms induce structural effects. We emphasize the great importance of the type of boundary conditions, the size and the shape of the body on the stability properties of such states.     

Models of Elastic Shells in Contact with a Rigid Foundation: An Asymptotic Approach

We consider a family of linearly elastic shells with thickness \(2\varepsilon\) (where \(\varepsilon\) is a small parameter). The shells are clamped along a portion of their lateral face, all having the same middle surface \(S\), and may enter in contact with a rigid foundation along the bottom face.We are interested in studying the limit behavior of both the three-dimensional problems, given in curvilinear coordinates, and their solutions (displacements \(\boldsymbol{u}^{\varepsilon}\) of covariant components \(u_{i}^{\varepsilon}\)) when \(\varepsilon\) tends to zero. To do that, we use asymptotic analysis methods. On one hand, we find that if the applied body force density is \(O(1)\) with respect to \(\varepsilon\) and surface tractions density is \(O(\varepsilon)\), a suitable approximation of the variational formulation of the contact problem is a two-dimensional variational inequality which can be identified as the variational formulation of the obstacle problem for an elastic membrane. On the other hand, if the applied body force density is \(O(\varepsilon^{2})\) and surface tractions density is \(O(\varepsilon^{3})\), the corresponding approximation is a different two-dimensional inequality which can be identified as the variational formulation of the obstacle problem for an elastic flexural shell. We finally discuss the existence and uniqueness of solution for the limit two-dimensional variational problems found.     

Stochastic Analysis of Reactive Solute Transport in Heterogeneous,Fractured Porous Media: A Dual-Permeability Approach

A nonlocal, first-order, Eulerian stochastic theory is developed for reactive chemical transport in a heterogeneous, fractured porous medium. A dual-permeability model is adopted to describe the flow and transport in the medium, where the solute convection and dispersion in the matrix are considered. The chemical is under linear nonequilibrium sorption and first-order degradation. The hydraulic conductivities, sorption coefficients, degradation rates in both fracture and matrix regions, and interregional mass transfer coefficient are all assumed to be random variables. The resultant theory for mean concentrations in both regions is nonlocal in space and time. Under spatial Fourier and temporal Laplace transforms, the mean concentrations are explicitly expressed. The transformed results are then numerically inverted to the real space via Fast Fourier Transform method. The theory developed in this study generalizes the stochastic studies for a reactive chemical transport in a one-domain flow field (Hu et al., 1997a) and in a mobile/immobile flow field (Huang and Hu, 2001). In comparison with one-domain transport, the dual-permeability model predicts a larger second moment in the longitudinal direction, but smaller one in the transverse direction. In addition, various simplification assumptions have been made based on the general solution. The validity of these assumptions has been tested via the spatial moments of the mean concentration in both fracture and matrix regions.     

A Computational Approach to Controllability Issues for Flow-Related Models. (I): Pointwise Control of the Viscous Burgers Equation

We discuss the numerical solution of some controllability problems for time-dependent flow models. The emphasis is on algorithmic aspects, discretization issues, and memory-saving devices. In the first part of the article, we investigate the controllability of the viscous Burgers equation. In part two, we shall discuss the boundary controllability of a linear advection-diffusion equation and then the distributed controllability of the unsteady Stokes equations.     

Two-Phase Inertial Flow in Homogeneous Porous Media: A Theoretical Derivation of a Macroscopic Model

The purpose of this article is to derive a macroscopic model for a certain class of inertial two-phase, incompressible, Newtonian fluid flow through homogenous porous media. Starting from the continuity and Navier–Stokes equations in each phase β and γ, the method of volume averaging is employed subjected to constraints that are explicitly provided to obtain the macroscopic mass and momentum balance equations. These constraints are on the length- and time-scales, as well as, on some quantities involving capillary, Weber and Reynolds numbers that define the class of two-phase flow under consideration. The resulting macroscopic momentum equation relates the phase-averaged pressure gradient to the filtration or Darcy velocity in a coupled nonlinear form explicitly given by

Particle Deposition in Porous Media: Analysis of Hydrodynamic and Weak Inertial Effects

We have studied the transport and capture of non-Brownian particles in porous media, when the particles are mainly submitted to hydrodynamic and weak inertial effects. Visualization experiments have been performed using several models of porous media which consist of transparent etched networks of interconnected channels. Typical particle deposits have been observed at the corners of the grains of the porous medium. Their shape and their orientation were dependent on flow rate and on the anisotropy of the flow field. A trajectory analysis model has been applied to a porous medium made of a doubly periodic array of rectangular grains very close to the experimental model. This numerical model has been used to localize particle deposits and to determine particle capture efficiency on the grains over a range of low Stokes numbers, grain aspect ratios and flow-field anisotropy ratios. The results have been interpreted in terms of shape of particle deposits and compared successfully to experimental observations.     

Effects of Turbulence on Self-sustained Combustion in Premixed Flame Kernels: A Direct Numerical Simulation (DNS) Study

The effects of mean flame radius and turbulence on self-sustained combustion of turbulent premixed spherical flames in decaying turbulence have been investigated using three-dimensional direct numerical simulations (DNS) with single step Arrhenius chemistry. Several flame kernels with different initial radius or initial turbulent field have been studied for identical conditions of thermo-chemistry. It has been found that for very small kernel radius the mean displacement speed may become negative leading ultimately to extinction of the flame kernel. A mean negative displacement speed is shown to signify a physical situation where heat transfer from the kernel overcomes the heat release due to combustion. This mechanism is further enhanced by turbulent transport and, based on simulations with different initial turbulent velocity fields, it has been found that self-sustained combustion is adversely affected by higher turbulent velocity fluctuation magnitude and integral length scale. A scaling analysis is performed to estimate the critical radius for self-sustained combustion in premixed flame kernels in a turbulent environment. The scaling analysis is found to be in good agreement with the results of the simulations.     

Exact Analysis of Curved Beams and Arches with Arbitrary End Conditions: A Hamiltonian State Space Approach

An exact analysis of stress and displacement fields in curved beams and arches subjected to inplane loads is conducted, with emphasis on the end effects. The material considered is cylindrically orthotropic, including transverse isotropy and isotropy as special cases. On the basis of the Hamiltonian state space approach, exact solutions that satisfy any combination of the fixed, free, and sliding-contact end conditions in a pointwise fashion are determined through symplectic eigenfunction expansion. The study allows us to evaluate the conventional solutions based on the elementary theory of curved beams and plane elasticity under simplifying assumptions, thereby, to assess the St. Venant principle as applied to this class of problems.