Multiphysics Modelling of Fluid-Particulate Systems

365 Pages·2020·14.164 MB·English

by  Dr. Hassan Khawaja (editor), Mojtaba Moatamedi (editor)

Multiphysics Modelling
of Fluid-Particulate
Systems
Edited by
Hassan Khawaja
Mojtaba Moatamedi
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Contributors
Hassan Abbas Khawaja
UiT—The Arctic University of Norway, Tromsø, Norway
Gernot Boiger
ICP Institute of Computational Physics, ZHAW Zurich University of Applied
Sciences, Winterthur, Switzerland
Ramzi Messahel
ISAE-SUPAERO, Université de Toulouse, France; Al Ghurair University, Dubai,
United Arab Emirates
Mojtaba Moatamedi
Oslo Metropolitan University, Norway, Oslo, Norway
Iason Zisis
TU Eindhoven, The Netherlands
Introduction
Multiphysics modeling of fluid-particulate systems
The book focuses on Multiphysics Modeling of Fluid-Particulate Systems. The most
commonly used models are combinations of Eulerian and Lagrangian methods. Eulerian
models are usually less computationally intensive in comparison to Lagrangian. The book
will present the models with respect to required computational resources and discuss the
merits and their applications. In order to simulate multiphysics processes, all necessary
phenomena need to be modeled. In addition, it is also essential to model the interactions
between the phases. In most cases, the fluid is modeled using the Eulerian method. The
solid particles can be modeled using the Eulerian or the Lagrangian method. To simulate
the fluid behavior using the Eulerian method, the interaction with the particles is volume
averaged, and the fluid motion is represented by a set of differential equations. The motion
of the particles can be solved using the Lagrangian method by stepping the accelerations,
velocities, and displacements of each individual particle forward in time using Newton’s
second law of motion. The net force on each particle is computed by summing the forces
due to contact with other particles drag and buoyancy forces from the fluid as well as the
force due to gravity. There are a number of techniques based on the combination of Eule-
rian and Lagrangian methods available to simulate solid-gas flow. The book will include
the following sections:
1. Unresolved Eulerian-Lagrangian;
2. Resolved Eulerian-Lagrangian;
3. Lagrangian-Lagrangian.
Multiphysics fluid-particulate modeling has become a key area of research in re-
cent times. It is because of the availability of computational resources capable of mod-
eling such complex phenomenon. The book intends to provide detailed understanding
of the above discussed methods for fluid-particulate modeling in conjunction with
their real life/industrial applications.
Unresolved Eulerian-Lagrangian: CFD-DEM modeling of
fluidized beds
The first part is an introduction into fluidization and fluidized beds and discusses their
applications and basic fluidization science. An overview is given of the various meth-
odologies from literature which can be employed to simulate a two-phase medium
such as that found in a fluidized bed. In this part, CFD-DEM, that is, discrete element
modeling coupled with computation fluid dynamics is employed to study various as-
pects of fluidization. A description of the method and discussion of its applicability
is the subject of Chapter Two, where governing equations of CFD are introduced. In
xiv Introduction
order to use CFD governing equation with DEM, they must first be volume averaged.
The resulting volume averaged equations, which now require some experimental clo-
sures, are discretized and solved numerically, alongside the DEM simulation. The
DEM simulation uses Newtonian Mechanics to describe the motion of every particle
in the system. This requires sub-models for the particle contact forces, and the drag
(i.e., the fluid particle interaction). Two different methods of solution namely pres-
sure driven method and density driven method for CFD are described, and their ap-
plications to DEM simulations are discussed. In Chapters Three and Four, provided
CFD-DEM methodology is validated. In Chapter Three, the phenomenon of bubbling
in gas-solid fluidized beds is investigated in detail via the CFD-DEM method, and
some comparisons are made with experiment. A compressible fluid code is used in
preference to the more usual pressure-driven methods employed in CFD-DEM. This
method has some advantages, especially as one aspect studied here is the propagation
of information via pressure waves, which limits the time step to an acoustic time-
scale. For the particles simulated (i.e., relatively large, Geldart D particles), it appears
that as if there are no low speed waves propagating through the medium, as has been
suggested for smaller particles. The simulated pressure and voidage fluctuations are
comparable to those measured experimentally. In the Fourth Chapter, the speed of
sound waves is investigated in more details using CFD-DEM numerical simulations.
The idea of establishing standing waves in a two-phase medium as reported by Roy
et al. (1990) was employed. Appropriate initial and boundary conditions were applied
in the CFD-DEM simulation to capture the phenomenon. The effect of varying the
height of the bed was also investigated. The results of the simulations matched those
from literature, giving a speed of sound in the two-phase medium very close to that of
the expression of Roy et al. (1990). The simulations allowed details of the fluctuations
in the pressure, gas velocity, and particle velocity to be studied. Functions (based on
a damped standing wave) were fitted to these fluctuations, which allowed their evolu-
tion in time and space to be described. These fitted functions were substituted to the
linearized governing equations for two-phase flow. Using these assumed solutions al-
lowed a new relationship for speed of sound and damping in the system to be derived.
It was concluded that the damping in the system is due to the effective bulk viscosity
of the solid phase, which arises from the particle contacts.
Resolved Eulerian-Lagrangian: large (non-) spherical
particle modeling in the context of fluid filtration
applications
The second part focuses on introducing a resolved Eulerian-Lagrangian modeling
scheme. It tackles settings of fluid flows being laden with solid particles where high-
density-information concerning individual particle movement is required. Demon-
strating an example for a method used to describe Lagrangian particle motion in an
exceptionally high level of detail, the second chapter introduces a six-degrees-of-free-
dom (DOF), large Lagrangian particle model for (non-) spherical dirt particles within
highly viscous fluids. The whole demonstration is thereby based on the application
Introduction xv
example of: “Modelling dirt particle filtration processes in oil lubrication circuits of
the automotive industry.”
In this context, two main subjects are being highlighted:
• Laying out the details behind the development of a highly resolved, dirt particle- and deposi-
tion model, capable of simulating spherical and non-spherical dirt particle behavior in- and
outside of any micro scale filter fiber vicinity.
• Describing validation efforts as well as the devise of an appropriate, experimental set up
to verify solver functionality and to provide additional insight into filter fiber behavior and
characteristics.
In the following a short review on the individual sub-chapters of the second book-
chapter is provided:
Chapter 6 describes the applied methodology, where sub-chapter 6.1 presents some
basic fundamentals behind the work. Initially the prevailing physical conditions as
well as resulting model simplifications are discussed. In a next step a fluid structure
interaction (FSI) tool and a digital fiber reconstruction (DFR) utility are laid out in
short.
Furthermore sub-chapter 6.1 presents three important reasons as to why the consid-
eration of particle shape effects in filtration simulation is imperative:
• The particle-inertia-to-fluid force ratio, represented by the particle relaxation time, is strong-
ly shape dependent.
• Particles with small, angular particle relaxation times experience the non-spherical particle
slip effect
.
• Particles with large, angular particle relaxation times experience the non-spherical particle
bulk effect
.
Three fundamental concepts, which form the roots of the presented particle model,
are discussed in sub-chapter 6.2: the Lagrangian simulation approach, the force-to-
motion concept and the large particle model.
Sub-chapter 6.3 is the core part of this book and is about the intrinsic of the (non-)
spherical dirt particle and deposition solvers. Basic, non-spherical modeling con-
cepts, as well as force-interaction implementations and drag-to-lift force calculation
schemes are discussed. Benchmark examples of solver functionality are given as well.
The decisive problem of numerical instability due to Explicit Euler temporal par-
ticle movement discretization is addressed and amended in sub-chapter 6.4. A possible
solution, based on the development of an adaptive time stepping scheme is given.
Sub-chapter 6.5 provides insight into the workflow behind the code and into the
C++ software design pattern of the relevant particle solver classes as well as into their
embedding within the OpenFOAM® program structure. A complete description of all
particle-solver specific, user-definable input parameters is given too.
Chapter 7 deals with the entire issue of solver validation, pointing out several sig-
nificant developments in the field of dirt particle distribution-detection. A macroscop-
ic method for 3D digitalization and visualization of test particle distributions in filter
fiber samples is presented and a MatLab® based reconstruction algorithm is described
and validated.
Chapter 8 brings concrete examples of solver application and demonstrates how
filter fibre engineering might look like in the near future.
xvi Introduction
Concluding Chapter 9 sums up the main development achievements and gives an
outlook toward potential, future extensions of the solver.
Lagrangian-Lagrangian: modeling shocks through
inhomogeneous media with Smoothed Particle
Hydrodynamics
The third part of the book discusses the Smoothed Particle Hydrodynamics (SPH)
computational method, and how is SPH applied to the analysis of multiphase phe-
nomena. SPH algorithms exist for both, Eulerian and Lagrangian, descriptions of the
flow field. Nevertheless, in multiphase applications, a Lagrangian-Lagrangian model
is typically preferred. This is because Lagrangian SPH algorithms inherently treat
interfaces between different phases, thus making redundant any interface tracking
routines. The latter significantly decreases the complexity of the solution strategy and
improves computational times. In the same context, SPH exhibits remarkable ease in
solving problems with free, rapidly evolving, boundaries, making it a strong candi-
date for problems involving violent, momentum-driven flows. In a large class of these
problems, shock propagation is the main characteristic. To this end, a particular type
of SPH solvers is of special interest: fully compressible solvers.
The part starts with a discussion regarding the basics of SPH, current trends in
SPH research as well as current challenges, as they are defined by SPHERIC, the SPH
research and engineering international community, in chapter 10.
In chapter 11, we present with an introduction to traditional SPH schemes from
Newtonian mechanics. Algorithmic details are explained and necessary ingredients
for the simulation of shock propagation are discussed along with the limitations of
the approach. Furthermore, in this part of the book delineates the extension of weakly
compressible SPH schemes to fully compressible schemes and indicates how multiple
phases are correctly incorporated. Furthermore, it discusses how the robustness of
SPH schemes is improved when they are consistent with the principles of Lagrangian
mechanics. The study focuses on the effect of artificial dissipation, which is typically
used as an efficient means to counterweight instabilities around shock regions and
interfaces. Additionally, the computational efficiency of the method is outlined, focus-
ing on the computationally most expensive procedure involved: the particle neighbor
search. This procedure is a common drawback of Lagrangian-Lagrangian approaches
that have no predefined topology.
In chapter 12, we finally exhibit the fidelity of SPH solutions via a broad spectrum
of test cases:
• One dimensional:
• Shock tubes with gases of different equations of state;
• Impacts into multi-material solids.
• Two dimensional:
• Shock chambers;
• Underwater explosion near a planar wall;
• Hypervelocity impacts into targets consisting of large scale as well as small scale inho-
mogeneities.

Introduction: discrete element 1
modeling-computational fluid
dynamics of fluidized beds
Hassan Abbas Khawajaa, Mojtaba Moatamedib
aUiT—The Arctic University of Norway, Tromsø, Norway; bOslo Metropolitan University,
Norway, Oslo, Norway
1.1 Fluidization and fluidized beds
Fluidization is a process in which granular material behaves like a liquid through sus-
pension in a fluid, either gas or liquid. Fluidization occurs when a fluid (liquid or gas)
is pushed upward through a bed of solid granular material. As shown in Fig. 1.1A, at
a low superficial gas velocity, the drag force on the particles is low (i.e., insufficient to
balance the weight of the particles), and thus, the bed remains in a packed state. At the
critical value of the superficial gas velocity, known as the minimum fluidization veloc-
ity, the upward drag force balances the downward gravitational force on the particles;
the particles become suspended within the fluid, and the bed of material is said to be
fluidized, as shown in Fig. 1.1B. After fluidization, the pressure drop across the bed
balances the net weight of the particles, that is
M g
∆P= s (1.1) ∆P=MsgAc
A
c
where ∆P is the pressure drop across the bed, M is the mass of the solid particle in
s
the bed, A is the cross-sectional area of the bed, and g is the gravitational constant.
c
The behavior of a material when fluidized depends on the superficial gas velocity,
particle size, particle density, and fluid properties. As shown in Fig. 1.1C, the fluid-
ized bed expands uniformly once the liquid is passed through the granular particles.
This state is known as uniform fluidization. Uniform fluidization usually occurs with
very small particles fluidized by gas at relatively low superficial velocities or with
granular materials fluidized by a liquid. Granular material composed of larger par-
ticles (e.g., sand with a particle diameter > 250 µm) will bubble without first passing
through the uniform fluidization regime when the gas velocity exceeds the minimum
fluidizing velocity, as shown in Fig. 1.1D. The bubble sizes and frequency of forma-
tion of the bubbles depend on particle size, particle density, gas physical properties,
and the size of the bed. With the increase of fluid velocity through the bed, the bub-
bling frequency increases; hence, there can be multiple bubbles in the bed at any given
time. These bubbles start to coalesce to form bigger bubbles. When the size of the
bubbles reaches the size of the cross-sectional area of the bed, a phenomenon called
Multiphysics Modelling of Fluid-Particulate Systems. http://dx.doi.org/10.1016/B978-0-12-818345-8.00001-9
Copyright © 2020 Elsevier Inc. All rights reserved.