Anthony Wachs

A fictitious domain method for particulate flows with heat transfer

The distributed-Lagrange-multiplier/fictitious-domain (DLM/FD) method of Glowinski et al. [R. Glowinski, T.-W. Pan, T.I. Hesla, D.D. Joseph, A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow 25 (1999) 755-794] is extended to deal with heat transfer in particulate flows in two dimensions. The Boussinesq approximation is employed for the coupling between the flow and temperature fields. The fluid-flow equations are solved with the finite-difference projection method on a half-staggered grid. In our operator splitting scheme. the Lagrange multipliers at the previous time level are kept in the fluid equations, and the new Lagrange multipliers for the rigid-body motion constraint and the Dirichlet temperature boundary condition are determined from the reduced saddle-point problem, whereas a very simple scheme based on the fully explicit computation of the Lagrange multiplier is proposed for the problem in which the solid heat conduction inside the particle boundary is also considered. Our code for the case of fixed temperature on the immersed boundary is verified by comparing favorably our results on the natural convection driven by a hot cylinder eccentrically placed in a square box and on the sedimentation of a cold circular particle in a vertical channel to the data in the literature. The code for the case of freely varying temperature on the boundaries of freely moving particles is applied to analyze the motion of a catalyst particle in a box and in particular the heat conductivities of nanofluids and sheared non-colloidal suspensions, respectively. Our preliminary computational results support the argument that the micro-heat-convection in the fluids is primarily responsible for the unusually high heat conductivity of nanofluids. It is shown that the Peclet number plays a negative role in the diffusion-related heat conductivity of a sheared non-colloidal suspension, whereas the Reynolds number does the opposite.

On the Numerical Simulation of Viscoplastic Fluid Flow

Publisher Summary This chapter provides an overview of the main mathematical and computational aspects of viscoplasticity. It discusses Bingham flow in cylinders and cavities; the numerical simulation of nonisothermal, compressible, and thixotropic viscoplastic flow, which is an augmented Lagrangian finite-volume approach; the application of fictitious domain; and methods for the numerical simulation of viscoplastic flow. Among the various classes of non-Newtonian materials, those exhibiting viscoplastic properties are particularly interesting in accordance with their ability to strain only if the stress intensity exceeds a minimum value. Many industrial processes involve viscoplastic fluids. The chapter mentions only a few of them—namely, mud, cement slurries, food, waxy crude oils, suspensions, emulsions, foams, etc. In a viscoplastic fluid flow, the flow pattern highlights two kinds of regions: the regions where the stress intensity exceeds the yield stress and the regions where it does not. The former and latter regions are usually called the “yielded” and “unyielded” regions, respectively. The most commonly encountered viscoplastic model is the Bingham fluid.

Rising of 3D catalyst particles in a natural convection dominated flow by a parallel DNS method

Abstract We investigate the problem of particulate flows with heat transfer by parallel direct numerical simulation (DNS). Among other heat transfer problems, we examine in detail the case of a 3D spherical catalyst rising in an enclosure due to natural convection though it is heavier than the suspending fluid. Natural convection is created by heat transferred from the warmer particle to the fluid. Heat is assumed to be produced at a constant rate in the particle bulk. As expected, there exists a critical production rate that leads to the rising of the catalyst. Compared to the 2D circular cylinder counterpart, momentum and heat transfers are slower in 3D and the spherical catalyst rises for a lower production rate. At the numerical level, we employ a Distributed Lagrange Multiplier/Fictitious Domain formulation together with an operator-splitting algorithm to solve the coupled problem. Two families of Lagrange multiplier are introduced to relax the velocity and temperature constraints respectively. As suggested in Wachs (2009) , particle collisions are handled by an efficient Discrete Element Method granular solver. As it is, the model is restricted to the case of homogeneous temperature over the particles. From a computational viewpoint, this work might be regarded as an extension of the method proposed in our previous contributions Dan and Wachs, 2010 , Yu et al., 2006 to distributed computing with our new parallel code PeliGRIFF. 1 This opens up new possibilities to study a broad range of applications in 3D and to get more insight in the comprehension of particulate flows with heat transfer. In particular, we examine how a bed of spherical catalysts can be self-fluidized as a result of the heat produced in the particles bulk, mimicking an exothermic catalyst reaction in a chemical engineering reactor.

Non-isothermal viscoelastic flow computations in an axisymmetric contraction at high Weissenberg numbers by a finite volume method

Abstract This paper presents a numerical study of non-isothermal viscoelastic flows in a 4:1 axisymmetric abrupt contraction. The model retained for the simulations is an upper convected Maxwell (UCM) constitutive equation whose temperature dependence is described by a WLF equation. General thermodynamical framework leads to introduce the complex energy conversion mechanism from elastic to thermal energy occurring in viscoelastic fluid flow. The mass, momentum, constitutive and energy equations are discretized using a finite volume method on a staggered grid with upwind scheme for the convective-type terms. A decoupled algorithm stabilized by a pseudo-transient stress term and an elastic viscous stress splitting (EVSS) formulation are employed. Convergence is reached by a fixed-point iteration. The Stokes problem is solved by a fast augmented Lagrangian method and convective-type equations by a bi-conjugate gradient stabilized iterative procedure. Elastic effects are investigated in both isothermal and non-isothermal flow situations. Thermodynamical behaviour related to pure energy elasticity and pure entropy elasticity is considered. Various temperature boundary conditions corresponding to an external cooling of the flow are prescribed at the wall in order to investigate the temperature dependence in flows with large temperature gradients. Without encountering any upper limit for convergence, the present method provides solutions up to Weissenberg number We=10.00 and is able to take into account great temperature changes. General difficulties involved in thermal control processing are underlined.

Progress in numerical simulation of yield stress fluid flows

Numerical simulations of viscoplastic fluid flows have provided a better understanding of fundamental properties of yield stress fluids in many applications relevant to natural and engineering sciences. In the first part of this paper, we review the classical numerical methods for the solution of the non-smooth viscoplastic mathematical models, highlight their advantages and drawbacks, and discuss more recent numerical methods that show promises for fast algorithms and accurate solutions. In the second part, we present and analyze a variety of applications and extensions involving viscoplastic flow simulations: yield slip at the wall, heat transfer, thixotropy, granular materials, and combining elasticity, with multiple phases and shallow flow approximations. We illustrate from a physical viewpoint how fascinating the corresponding rich phenomena pointed out by these simulations are.

Free falling and rising of spherical and angular particles

Direct numerical simulations of freely falling and rising particles in an infinitely long domain, with periodic lateral boundary conditions, are performed. The focus is on characterizing the free motion of cubical and tetrahedral particles for different Reynolds numbers, as an extension to the well-studied behaviour of freely falling and rising spherical bodies. The vortical structure of the wake, dynamics of particle movement, and the interaction of the particle with its wake are studied. The results reveal mechanisms of path instabilities for angular particles, which are different from those for spherical ones. The rotation of the particle plays a more significant role in the transition to chaos for angular particles. Following a framework similar to that of Mougin and Magnaudet [“Wake-induced forces and torques on a zigzagging/spiralling bubble,” J. Fluid Mech. 567, 185–194 (2006)], the balance of forces and torques acting on particles is discussed to gain more insight into the path instabilities of an...

Computations of non‐isothermal viscous and viscoelastic flows in abrupt contractions using a finite volume method

A finite volume method is applied to numerical simulations of steady isothermal and non‐isothermal flows of fluids obeying different constitutive equations: Newtonian, purely viscous with shear‐thinning properties (Carreau law) and viscoelastic Upper Convected Maxwell differential model whose temperature dependence is described by a William‐Landel‐Ferry equation. The flow situations concern various abrupt axisymmetric contractions from 2:1 to 16:1. Such flow geometries are involved in polymer processing operations. The governing equations are discretized on a staggered grid with an upwind scheme for the convective‐type terms and are solved by a decoupled algorithm, stabilized by a pseudo‐transient stress term and an elastic viscous stress splitting technique. The numerical results highlight the influence of temperature on the flow situations, and also the complex behaviour of the materials under non‐isothermal conditions.

Particle resolved simulations of liquid/solid and gas/solid fluidized beds

The present work studies particle resolved simulations of liquid/solid and gas/solid fluidization in a cuboid domain with periodic lateral boundary conditions. The focus is on investigating particles’ dynamics, while a particular care is devoted to the spatial grid resolution and statistical time convergence of the results. A statistical analysis of particles’ motion and fluid fluctuations asserts the intrinsic differences in the flow characteristics and mixing properties of these two configurations. Results reveal anisotropic mechanisms driving particles’ motion and highlight the dominance of diffusive and convective mechanisms in liquid/solid and gas/solid regimes, respectively. Following a framework similar to that of Nicolai et al. [“Particle velocity fluctuations and hydrodynamic self-diffusion of sedimenting non-Brownian spheres,” Phys. Fluids 7(1), 12–23 (1995)], we estimate the correlation time and the fluctuation length of particles’ motion. A force budget analysis is discussed to gain more insight into the role of collision in isotropization of the system. Owing to the wide range of employed grid resolutions and accurate error analysis, the present dataset is also deemed to be useful in calibrating the grid resolution for a desired accuracy of the solution in a fluidization configuration.

A fictitious domain method for particulate flows

Abstract The distributed Lagrange multiplier based fictitious domain (DLM/FD) method was proposed by Glowinski and his coworkers for the simulation of particulate flows. We have recently extended the DLM/FD method to deal with the particle motion in a Bingham fluid and the particulate flow with heat transfer. The progresses are reported in this paper.

Inline motion and hydrodynamic interaction of 2D particles in a viscoplastic fluid

In Stokes flow of a particle settling within a bath of viscoplastic fluid, a critical resistive force must be overcome in order for the particle to move. This leads to a critical ratio of the buoyancy stress to the yield stress: the critical yield number. This translates geometrically to an envelope around the particle in the limit of zero flow that contains both the particle and encapsulated unyielded fluid. Such unyielded envelopes and critical yield numbers are becoming well understood in our previous studies for single (2D) particles as well as the means of calculating. Here we address the case of having multiple particles, which introduces interesting new phenomena. First, plug regions can appear between the particles and connect them together, depending on the proximity and yield number. This can change the yielding behaviour since the combination forms a larger (and heavier) “particle.” Moreover, small particles (that cannot move alone) can be pulled/pushed by larger particles or assembly of partic...