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Computational Fluid Dynamics 1st Edition Guy B. Marin
(Editors) Digital Instant Download
Author(s): Guy B. Marin (Editors)
ISBN(s): 9780120085316
Edition: 1
File Details: PDF, 9.75 MB
Year: 2006
Language: english

CONTRIBUTORS
Numbers in parentheses indicate the pages on which the authors’ contribution begin.
A. T. ANDREWS IV, Department of Chemical Engineering, Princeton University,
Princeton, NJ 08544, USA (65)
A. G. DIXON, Department of Chemical Engineering, Worcester Polytechnic
Institute, Worcester, MA 01609, USA (307)
L.-S. FAN, Department of Chemical and Biomolecular Engineering, The Ohio
State University, 140 West 19th Avenue, Columbus, OH 43210, USA (1)
R. O. Fox, Herbert L. Stiles Professor of Chemical Engineering, Iowa State
University, 3162 Sweeney Hall, Ames, IA 50011-2230, USA (231)
Currently on sabbatical at:
Swiss Federal Institute of Technology Zurich, ETHZ Institut für Chemie-
und Bioingenieurwissenschaften ETH-Hönggerberg/HCI H 109 (Gruppe
Morbidelli), CH-8093 Zurich, Switzerland
Y. GE, Department of Chemical and Biomolecular Engineering, The Ohio State
University, 140 West 19th Avenue, Columbus, OH 43210, USA (1)
J. A. M. KUIPERS, University of Twente, Faculty of Science & Technology, PO
Box 217, NL - 7500 AE Enschede, The Netherlands (65)
M. NIJEMEISLAND, Johnson Matthey Catalysts, Billingham, UK (307)
E. H. STITT, Johnson Matthey Catalysts, Billingham, UK (307)
S. SUNDARESAN, Department of Chemical Engineering, Princeton University,
Princeton, NJ 08544, USA (65)
H. E. A. VAN DEN AKKER, Delft University of Technology, Molenwindsingel 50,
NL 4105 HK Culemborg, The Netherlands (151)
M. A. VAN DER HOEF, Department of Science and Technology, University of
Twente, PO 217, NL - 7500 AE Enschede, The Netherlands (65)
M. VAN SINT ANNALAND, Department of Science and Technology, University of
Twente, PO 217, NL - 7500 AE Enschede, The Netherlands (65)
M. YE, Department of Science and Technology, University of Twente, PO 217,
NL - 7500 AE Enschede, The Netherlands (65)
ix

PREFACE
This issue attempts to give a feeling of the state-of-the-art of the application
of computational fluid dynamics (CFD) in chemical engineering. It is, however,
not limited to a snap-shot but is aimed at providing a perspective: how did we
arrive at the present status and where do we go from here? To do so, contri-
butions from five complementary contributions are brought together. From the
definition of CFD as the ensemble ‘‘of all computational approaches that solve
for the spatial distribution of the velocity, concentration, and temperature
fields’’ recalled by Fox, it is clear that a selection had to be made as to the topics
covered. In the wake of volume 30 on ‘‘Multiscale Analysis’’ the present volume
is organized from ‘‘small’’ to ‘‘large’’: from ‘‘bubbles and droplets’’ in the first
contribution, to a ‘‘fixed catalyst bed’’ in the last one. The application of direct
numerical simulations (DNS) clearly is still limited to the small scale. Today
subgrid-scale (SGS) models are required to cover the full spectrum.
The reader will be confronted with some redundancy but this allows each
contribution to stand on its own. Also, a good balance is maintained between
the style of a tutorial and that of a research paper. Those who will read the
complete volume will realize that opinions can vary from looking at CFD as an
alternative for experimentation to emphasizing the need of experimental val-
idation. Some contributions are entirely limited to velocity and temperature
fields. Others, on the contrary, emphasize the difficulties associated with the
combination of transport and reaction. The latter can introduce stiffness even
for laminar flow. Averaging (e.g. Reynolds-averaged Navier–Stokes, RANS) or
filtering (e.g. large eddy simulations, LES), performed to model velocity fields,
does not alleviate this difficulty. Clearly, this is still quite a challenge.
The contribution from the Ohio State University by Ge and Fan is dealing
with the simulation of gas–liquid bubble columns and gas–liquid–solid fluidized
beds. A scientist of a major engineering company told me a few years ago that
when he wanted to know how serious an academic group was about CFD, he
would ask whether they could simulate bubble columns. He would only engage
into further conversation if the answer was negative. The group from Columbus
is wise enough to focus on a single air bubble rising in water, and bubble
formation from a single nozzle. In a second part the hydrodynamics and heat
transfer phenomena of a liquid droplet in motion and during the impact process
with a hot flat surface, as well as with a particle are studied. The applied
numerical techniques, such as the level set and immersed boundary method, are
outlined and important contributions are highlighted. Next, detailed imple-
mentations for particular problems are presented. Finally, numerous simulation
results are shown and compared with experimental data.
xi

The second contribution addresses the different levels of modeling that are
required in order to cover the full spectrum of length scales that are important
for industrial applications. It is a joint paper from Twente and Princeton Uni-
versity and claims to put ‘‘Emphasis on technical details.’’ The latter is a too
modest description of what is really offered to the reader. The recent devel-
opments in two leading research groups on the modeling of gas-fluidized beds
are presented. The holy grail for those interested in the design of industrial units
being the closure of the model equations in general and SGS modeling in par-
ticular. The latest developments of both the ‘‘filtering’’ approach pursued at
Princeton University by Sundaresan and coworkers and the ‘‘discrete bubble
model’’ developed in Twente by the team of Kuipers are presented. The authors
realize fully that there is still a long way to go, as evidenced by their last
sentence: ‘‘Finally, the adapted model should be augmented with a thermal
energy balance, and associated closures for the thermo-physical properties, to
study heat transport in large scale fluidized beds, such as FCC-regenerators and
PE and PP gas-phase polymerization reactors.’’ This is even more so because
inclusion of reaction kinetics remains beyond the scope of the contribution!
Chemical reactions come into the picture in the context of stirred turbulent
vessels in Chapter 3. Van den Akker from Delft strongly emphasizes the po-
tential of LES and DNS for reproducing not only the hydrodynamics of tur-
bulent stirred vessels but also for providing a basis for simulating a wide variety
of physical and chemical processes in this equipment. The author advocates the
use of the lattice–Boltzmann (LB) technique to this purpose. Van den Akker
certainly belongs to those who believe that one can and should be much more
positive about the merits of CFD so far and about the term at which CFD will
replace and improve existing mixing correlations. To quote him: ‘‘It may be
easier to ‘measure’ the local and transient details of the turbulent flows in stirred
vessels and the spatial distributions in e.g. mixing rates and bubble, drop and
crystal sizes computationally than by means of experimental techniques!’’ When
it comes to the design of chemical reactors the authors admit that CFD is
certainly not a panacea. ‘‘Scale-up of many chemical reactors, in particular the
multi-phase types, is still surrounded by a fame of mystery indeed.’’
The importance of chemical-reaction kinetics and the interaction of the latter
with transport phenomena is the central theme of the contribution of Fox from
Iowa State University. The chapter combines the clarity of a tutorial with the
presentation of very recent results. Starting from simple chemistry and single-
phase flow the reader is lead towards complex chemistry and two-phase flow.
The issue of SGS modeling discussed already in Chapter 2 is now discussed with
respect to the concentration fields. A detailed presentation of the joint Prob-
ability Density Function (PDF) method is given. The latter allows to account
for the interaction between chemistry and physics. Results on impinging jet
reactors are shown. When dealing with particulate systems a particle size dis-
tribution (PSD) and corresponding population balance equations are intro-
PREFACE
xii

duced. The author emphasizes that a balance between the degree of detail or
complexity of the chemistry and that of the physics should be maintained.
The last contribution comes from Dixon (Worcester Polytechnic Institute),
and Nijemeisland and Stitt (Johnson Matthey). The subject is another classic of
reactor engineering: the catalytic fixed-bed reactor. Heat transfer issues on both
reactor scale and catalyst pellet scale are addressed. Steam reforming is used as a
typical example of a strongly endothermic reaction requiring high-heat fluxes
through the reactor walls. The presence of the tube wall causes changes in bed
structure, flow patterns, transport rates and the amount of catalyst per unit
volume, and is usually the location of the limiting heat-transfer resistance.
Special attention is given to the modeling of the ‘‘structure’’ of a packed bed.
The importance of wall functions, to be applied not only at the reactor wall but
also at the external pellet surface, is stressed. The authors show ample results of
their own work without neglecting the contributions of others. At the end of this
chapter the reader will be convinced of the importance of the local nonuni-
formities in the temperature field not only within a catalyst pellet but also from
one pellet to the other.
Let me conclude by thanking the authors for their willingness to contribute,
despite health problems for some of them, and for their flexibility with respect to
timing.
Guy B. Marin
Ghent, Belgium
April 2006
PREFACE xiii

3-D DIRECT NUMERICAL SIMULATION OF GAS–LIQUID
AND GAS–LIQUID–SOLID FLOW SYSTEMS USING THE
LEVEL-SET AND IMMERSED-BOUNDARY METHODS
Yang Ge and Liang-Shih Fan
Department of Chemical and Biomolecular Engineering, The Ohio State University,
Columbus, OH 43210, USA
I. Introduction 2
II. Front-Capturing and Front-Tracking Methods 4
A. Level-Set Method 6
B. Immersed Boundary Method 9
III. System 1: Flow Dynamics of Gas–Liquid–Solid Fluidized
Beds 11
A. Numerical Procedure for Solving the Gas–Liquid
Interface 12
B. Governing Equations for the Gas–Liquid–Solid Flow 13
C. Modeling the Motion and Collision Dynamics of Solid
Particles in Gas–Liquid–Solid Fluidization 14
D. Results and Discussions 16
IV. System 2: Deformation Dynamics of Liquid Droplet in
Collision with a Particle with Film-Boiling Evaporation 27
A. Simulation of Saturated Droplet Impact on Flat Surface
in the Leidenfrost Regime 29
B. Simulation of Subcooled Droplet Impact on Flat
Surface in Leidenfrost Regime 38
C. Simulation of Droplet–Particle Collision in the
Leidenfrost Regime 49
V. Concluding Remarks 58
References 61
Abstract
The recent advances in level-set and Immersed Boundary methods
(IBM) as applied to the simulation of complex multiphase ﬂow systems
are described. Two systems are considered. For system 1, a computa-
tional scheme is conceived to describe the three-dimensional (3-D) bubble
Corresponding author. Tel.: +1-614-688-3262(o). E-mail: fan@chbmeng.ohio-state.edu
1
Advances in Chemical Engineering, vol. 31
ISSN 0065-2377
DOI 10.1016/S0065-2377(06)31001-0
Copyright r 2006 by Elsevier Inc.
All rights reserved

dynamics in gas–liquid bubble columns and gas–liquid–solid fluidized
beds. This scheme is utilized to simulate the motion of the gas, liquid, and
solid phases, respectively, based on the level-set interface tracking
method, the locally averaged time-dependent Navier–Stokes equations
coupled with the Smagorinsky subgrid scale stress model, and the Lag-
rangian particle motion equations. For system 2, the hydrodynamics and
heat-transfer phenomena of a liquid droplet in motion and during the
impact process with a hot flat surface, as well as with a particle, are
illustrated. The 3-D level-set method is used to portray the droplet surface
deformation whilst in motion and during the impact process. The IBM is
employed so that the particle–fluid boundary conditions are satisfied. The
governing equations for the droplet and the surrounding gas phase are
solved utilizing the finite volume method with the Arbitrary Lagrangian
Eulerian (ALE) technique. To account for the multiscale effect due to
lubrication-resistance induced by the vapor layer between the droplet and
solid surface or solid particle formed by the film-boiling evaporation, a
vapor-flow model is developed to calculate the pressure and velocity dis-
tributions along the vapor layer. The temperature fields in all phases and
the local evaporation rate on the droplet surface are illustrated using a
full-field heat-transfer model.
I. Introduction
Gas–liquid–solid (three-phase) flow systems involve a variety of operating
modes of gas, liquid, and solid phases, including those with solid particles and/or
liquid droplets in suspended states. Commercial or large-scale operations using
three-phase flow systems are prevalent in physical, chemical, petrochemical,
electrochemical, and biological processes (Fan, 1989). In the gas–liquid–solid
fluidization systems with liquid as the continuous phase, the systems are char-
acterized by the presence of gas bubbles, which induce significant liquid mixing
and mass transfer. The flow structure in the systems is complex due to intricate
coalescence and breakup phenomena of bubbles. The fundamental dynamics of
solids suspensions in the systems is closely associated with the particle–particle
collision and particle–bubble interactive behavior. For three-phase flows that
occur in the feed nozzle area of a fluid catalytic cracking (FCC) riser in gas oil
cracking, on the other hand, the gas phase is continuous where oil is injected
from the nozzle with the mist droplets formed from the spray in contact with
high-temperature catalyst particles (Fan et al., 2001). The droplets may splash,
rebound, or remain on the catalyst particle surface after the impact, and the oil is
evaporated and cracked into lighter hydrocarbons. Such contact phenomena
are also prevalent in the condensed mode operation of the Unipol process for
YANG GE AND LIANG-SHIH FAN
2

polypropylene or polyethylene production, where droplet–particle collisions in
the feed nozzle are also accompanied by intense liquid evaporation. In this
study, both systems involving three-phase fluidization and evaporative droplet
and particle collisions are simulated using CFD based on the 3-D level-set and
immersed boundary method (IBM).
CFD is a viable means for describing the fluid dynamic and transport
behavior of gas–liquid–solid flow systems. There are three basic approaches
commonly employed in the CFD for study of multiphase flows (Feng and
Michaelides, 2005): the Eulerian–Eulerian (E-E) method, the Eulerian–Lag-
rangian (E-L) method, and direct numerical simulation (DNS) method. In
the E-E method (Anderson and Jackson, 1967; Joseph and Lundgren, 1990;
Sokolichin and Eigenberger, 1994, 1999; Zhang and Prosperetti, 1994, 2003;
Mudde and Simonin, 1999), both the continuous phase and the dispersed phase,
such as particles, bubbles, and droplets, are treated as interpenetrating contin-
uous media, occupying the same space as does the continuous phase with differ-
ent velocities and volume fractions for each phase. In this method, the closure
relationships such as the stress and viscosity of the particle phase need to be
formulated. In the E-L method, or discrete particle method (e.g., Tsuji et al.,
1993; Lapin and Lübbert, 1994; Hoomans et al., 1996; Delnoij et al., 1997), the
continuous fluid phase is formulated in the Eulerian mode, while the position
and the velocity of the dispersed phase, particles, or bubbles, is traced in the
Lagrangian mode by solving Lagrangian motion equations. The grid size used in
the computation for the continuous-phase equations is typically much larger
than the object size of the dispersed phase, and the object in the dispersed phase
is treated as a point source in the computational cell. With this method, the
coupling of the continuous phase and the dispersion phase can be made using the
Particle-Source-In-Cell method (Crowe et al., 1977). The closure relationship for
the interaction forces between phases requires to be provided in the E-L method.
In the DNS (Unverdi and Tryggvason, 1992a,b; Feng et al., 1994a,b; Sethian
and Smereka, 2003), the grid size is commonly much smaller than the object size
of the dispersed phase, and the moving interface can be represented by implicit
or explicit schemes in the computational domain. The velocity fields of the fluid
phase are obtained by solving the Navier–Stokes equation considering the in-
terfacial forces, such as surface tension force or solid–fluid interaction force.
The motion of the object of the dispersed phase is represented in terms of a
time-dependent initial-value problem. With the rapid advances in the speed and
memory capacity of the computer, the DNS approach has became important in
characterizing details of the complex multiphase flow field.
This paper is intended to describe recent progress on the development of
the level-set method and IBM in the context of the advanced front-capturing
and front-tracking methods. The paper is also intended to discuss the appli-
cation of them for the 3-D DNS of two complex three-phase flow systems as
described earlier.
SIMULATION OF GAS– LIQUID AND GAS– LIQUID– SOLID FLOW SYSTEMS 3

II. Front-Capturing and Front-Tracking Methods
In the DNS of multiphase flow problems, there are various methods available
for predicting interface position and movement, such as the moving-grid
method, the grid-free method (Scardovelli and Zeleski, 1999) and the fixed-grid
front-tracking/front-capturing method. In the moving-grid method, which is
also known as the discontinuous-interface method, the interface is a boundary
between two subdomains of the grid (Dandy and Leal, 1989). The grid may be
structured or unstructured and even near-orthogonal, moving with the interface
(Hirt et al., 1974). It treats the system as two distinct flows separated by a
surface. When the interface moves or undergoes deformation, new, geometri-
cally adapted grids need to be generated or remeshed (McHyman, 1984). The
remeshing can be a very complicated, time-consuming process, especially when
it involves a significant topology change, and/or a 3-D flow. Methods in which
grids are not required include the marker particle method (Harlow and Welch,
1965) and the smoothed particle hydrodynamics method (Monaghan, 1994).
The fixed-grid method, which is also known as the continuous-interface
method, employs structured or unstructured grids with the interface cutting
across the fixed grids. It treats the system as a single flow with the density
and viscosity varying smoothly across a finite-thickness of the interface. The
numerical techniques used to solve the moving interface problem with fixed,
regular grids can be categorized by two basic approaches: the front-tracking
method (e.g., Harlow and Welch, 1965; Peskin, 1977; Unverdi and Tryggvason
1992a, b; Fukai et al., 1995) and the front-capturing method (e.g., Osher and
Sethian, 1988; Sussman et al., 1994; Kothe and Rider, 1995; Bussmann et al.,
1999). For a 3-D multiphase flow problem, the fixed-grid method is the most
frequently used due to its efficiency and relative ease in programming.
The front-tracking method explicitly tracks the location of the interface by the
advection of the Lagrangian markers on a fixed, regular grid. The marker-and-
cell (MAC) method developed by Harlow and Welch (1965) was the first front-
tracking technique applied in DNS, e.g., it was used by Harlow and Shannon
(1967) to simulate the droplet impact on a flat surface without considering
the viscosity and the surface-tension forces in the momentum-conservation
equation. Fujimoto and Hatta (1996) simulated the impingement process of a
water droplet on a high-temperature surface by using a single-phase 2-D MAC
type solution method. The no-slip and free-slip boundary conditions are itera-
tively adopted on the liquid–solid interface for the spreading and recoiling
process, respectively. Fukai et al. (1995) developed the adaptive-grid, finite-
element method to track the droplet free surface in collision with a surface while
considering the wettability on the contact line. The front-tracking method
developed by Unverdi and Tryggvason (1992a, b) and Tryggvason et al. (2001)
leads to many applications in the simulation of droplet or bubble flow. In this
method, the location of the interface is expressed by discrete surface-marker
4

particles. High-order interpolation polynomials are employed to ensure a high
degree of accuracy in the representation of the interface. An unstructured sur-
face grid connecting the surface-marker particles is introduced within a volu-
metric grid to track the bubble front within the computational domain. Thus,
discretization of the field equations is carried out on two sets of embedded
meshes: (a) the Eulerian fluid grid, which is 3-D, cubical, staggered structured,
and nonadaptive; and (b) the Largrangian front grid, which is 2-D, triangular,
unstructured, and adaptive (Unverdi and Tryggvason 1992a, b). The infinitely
thin boundary can be approximated by a smooth distribution function of
a finite thickness of about three to four grid spacing. The variable density
Navier–Stokes equations can then be solved by conventional Eulerian tech-
niques (Unverdi and Tryggvason 1992a, b). This method can be numerically
stiff as the density ratio of the two fluids increases, and may pose difficulties
when the appearance, the connection, the detachment, and the disappearance of
the gas–liquid interface are encountered. Such interface behavior occurs in the
coalescence, breakup, or formation of bubbles and droplets in an unsteady flow.
The front-tracking method is therefore computationally intensive. Agresar et al.
(1998) extended the front-tracking method with adaptive refined grids near the
interface to simulate the deformable circulation cell. Sato and Richardson
(1994) developed a finite-element method to simulate the moving free surface of
a polymeric liquid. The IBM proposed by Peskin (1977) in studying the blood
flow through heart valves and the cardiac mechanics also belongs to the class of
front-tracking techniques. In the IBM method, the simulation of the fluid flow
with complex geometry was carried out using a Cartesian grid, and a novel
procedure was formulated to impose the boundary condition at the interface.
Some variants and modifications of this method were proposed in simulating
various multiphase flow problems (Mittal and Iaccarino, 2005). An introduction
to the IBM method is given in Section II.B.
The front-capturing method, on the other hand, is the Eulerian treatment of
the interface, in which the moving interface is implicitly represented by a scalar-
indicator function defined on a fixed, regular mesh point. The movement of the
interface is captured by solving the advection equation of the scalar-indicator
function. At every time step, the interface is generated by piecewise segments
(2-D) or patches (3-D) reconstructed by this scalar function. In this method, the
interfacial force, such as the surface-tension force, is incorporated into the flow-
momentum equation as a source term using the continuum surface force (CSF)
method (Brackbill et al., 1992). This technique includes the volume of fluid
(VOF) method (Hirt and Nichols, 1981; Kothe and Rider, 1995), the marker
density function (MDF) (Kanai and Mtyata, 1998), and the level-set method
(Osher and Sethian, 1988; Sussman et al., 1994).
In the VOF method, an indicator function is defined as: 0 for a cell with pure
gas, 1 for a cell with pure liquid, and 0 to 1 for a cell with a mixture of gas and
liquid. An interface exists in those cells that give a VOF value of neither 0 nor 1.
Since the indicator function is not explicitly associated with a particular front

grid, an algorithm is needed to reconstruct the interface. This is not an easy
task, especially for a complex dynamic interface requiring 3-D calculation.
Pasandideh-Ford et al. (1998) used a modified SOLA-VOF method to solve the
momentum and heat-transfer equations for droplet deposition on a steel sur-
face. Bussmann et al. (1999, 2000) developed a 3-D model to simulate the
droplet collision onto an incline surface and its splash on the surface, utilizing a
volume-tracking methodology. Mehdi-Nejad et al. (2003) also used the VOF
method to simulate the bubble-entrapment behavior in a droplet when it im-
pacts a solid surface. Karl et al. (1996) simulated small droplet (100–200 mm)
impact onto the wall in the Leidenfrost regime using a VOF method. A free-slip
boundary condition and a 1801 contact angle were applied on the solid surface.
Harvie and Fletcher (2001a,b) developed an axisymmetric, 2-D VOF algorithm
to simulate the volatile liquid droplet impacting on a hot solid surface. The
vapor flow between the droplet and solid surface was solved by a 1-D, creeping
flow model, which neglects the inertial force of the flow. This model, despite
being accurate at a lower We, failed to reproduce the droplet dynamics at a
higher Weber number. Other front-capturing methods include the constrained
interpolation profile (CIP) method (Yabe, 1997), and the phase-field method
(Jamet et al., 2001).
In the level-set method, the moving interface is implicitly represented by
a smooth level-set function (Sethian and Smereka, 2003). The level-set method
has proved capable of handling problems in which the interface moving speed
is sensitive to the front curvature and normal direction. A significant advan-
tage of the level-set method is that it is effective in 3-D simulation of the
conditions with large topological changes, such as bubble breaking and merg-
ing, droplet–surface collisions with evaporation. In this study, the level-set
technique (Sussman et al., 1994) is employed to describe the motion of 3-D
gas–liquid interfaces. In the following section a description of this technique
is given.
A. LEVEL-SET METHOD
The level-set method, which was first derived by Osher and Sethian (1988), is
a versatile method for capturing the motion of a free surface in 2-D or 3-D on a
fixed Eulerian grid. While similar to the VOF method, the level-set method also
uses an indicator function to track the gas–liquid interface on the Eulerian
grid. Instead of using the marker particles or points to describe the interface, a
smooth level-set function is defined in the flow field (Sussman et al., 1994).
Consider a nonbody conformal Cartesian grid which is used to simulate the
flow with a deformable interface G, as shown in Fig. 1. The whole computa-
tional domain is separated by the interface into two regions: O and O+. The
value of the level-set function is negative in the O region and positive in the
O+ region, while the interface G is simply described as the zero level set of
6

the level-set function f, i.e.,
G ¼ xjfðx; tÞ ¼ 0

(1)
where x represents the position vector and t the time. Taking fo0 as being
inside the interface G (in O) and f40 as being outside the interface G (in O+),
the level-set function has the form:
fðx; tÞ
o0; x 2 O
¼ 0; x 2 G
40; x 2 Oþ
8

:
(2)
The evolution of f in a flow field is given by the so-called weak-form equation:
@f
@t
þ V rf ¼ 0 (3)
where V is the velocity of fluid, and is given by
V ¼
V; x 2 O
V ¼ Vþ; x 2 G
Vþ; x 2 Oþ
8

:
(4)
For gas–liquid bubble flow, V and V+ are the gas and liquid velocities, respec-
tively, and the zero-level set of f marks the bubble interface, which moves with
time. For gas-droplets flows, on the other hand, V and V+ represent the
+
-
Γ
Ω+
Ω-
FIG. 1. The level sets of distance function for a smooth interface over a Cartesian grid.

velocity of the liquid and gas phases, respectively, and the zero-level set of f
defines the droplet surface (Ge and Fan, 2005).
To compute the motion of two immiscible and incompressible fluids such as a
gas–liquid bubble column and gas-droplets flow, the fluid-velocity distributions
outside and inside the interface can be obtained by solving the incompressible
Navier–Stokes equation using level-set methods as given by Sussman et al.
(1994):
@r
@t
þ r ðrVÞ ¼ 0 (5)
@rV
@t
þ r ðrVVÞ ¼ rp þ r s þ rg þ Fs (6)
where Fs is the surface tension force which is calculated by (Brackbill et al.,
1992):
Fs ¼ skðfÞdðfÞrf (7)
k(f) is the curvature which can be estimated as r (rf/|rf|). A smooth d
function is defined as (Sussman et al., 1998; Sussman and Fatemi, 1999):
dbðfÞ
dHbðfÞ
df
¼
1
2 ð1 þ cosðpf=bÞÞ=b; f

ob
0; otherwise
(
(8)
where Hb(f) follows the Heaviside formulation (Sussman et al., 1998; Sussman
and Fatemi, 1999) given by
HbðfÞ ¼
1 f4b
0 fo b
1
2 ð1 þ f
b þ 1
p sinðpf=bÞÞ otherwise
8

:
(9)
The surface-tension force Fs in Eq. (7) is smoothed and distributed into the
thickness of the interface. In order to circumvent numerical instability, the fluid
properties such as density and viscosity in the interface region are determined
with a continuous transition:
rðfÞ ¼ r þ ðr rþÞHbðfÞ (10)
mðfÞ ¼ m þ ðm mþÞHbðfÞ (11)
Since the values for r(f), m(f), and the surface-tension force could be distorted
if the variation of rf along the interface is very large, the thickness of the
interface needs to be maintained uniformly, i.e. rf

¼ 1 (Sussman et al., 1998).
In the algorithm developed, the general level set function f(x,t) is replaced by a
8

distance function d(x,t), whose value represents the signed normal distance from
x to the interface. d(x,t) would satisfy rd
j j ¼ 1 and d ¼ 0 for xAG (Sussman
et al., 1998).
Even if the initial value of the level-set function f(x,0) is set to be the distance
function, the level set function f may not remain as a distance function at t40
when the advection equation, Eq. (3), is solved for f. Thus, a redistance scheme
is needed to enforce the condition of rf

¼ 1. An iterative procedure was
designed (Sussman et al., 1998) to reinitialize the level-set function at each time
step so that the level-set function remains as a distance function while main-
taining the zero level set of the level-set function. This is achieved by solving for
the steady-state solution of the equation (Sussman et al., 1994, 1998; Sussman
and Fatemi, 1999):
@d
@t
¼ sinðfÞð1 rf

Þ (12)
dðx; 0Þ ¼ fðxÞ (13)
until
rd
j j ¼ 1 þ OðD2
Þ (14)
where the sin function is defined as
sinðfÞ ¼
1; fo0
0; f ¼ 0
1; f40
8

:
(15)
In Eq. (12), t is an artificial time that has the unit of distance. The solutions
for Eq. (12) are signed distances and only those within a thickness of 3–5 grid
sizes from the interface are of interest (Sussman et al., 1994, 1998; Sussman and
Fatemi, 1999). Equation (12) needs to be integrated for 3–5 time steps using a
time step Dt ¼ 0.5D.
B. IMMERSED BOUNDARY METHOD
The IBM was originally proposed by Peskin (1977) to model the blood flow
through heart valves. Since then, this method has been extensively modified and
extended to simulate various fluid flows in a complex geometrical configuration
using a fixed Cartesian mesh (Unverdi and Tryggvason, 1992a,b; Udaykumar,
et al., 1997; Ye et al., 1999; Fadlun et al., 2000; Lai and Peskin, 2000; Kim et al.,
2001). In the IBM, the presence of the solid object in a fluid field is represented
by a virtual-body force field, which is applied on the computational grid in the
vicinity of the solid–flow interface through a Dirac delta function (Lai and

Peskin, 2000). Various schemes have been proposed to calculate the virtual force
density in the literature. Goldstein et al. (1993) developed a virtual boundary
formulation to simulate the startup flow over a cylinder. In their formation, the
virtual force field is calculated in a feedback manner in order to satisfy the
boundary condition at the solid surface. Mohd-Yusof (1997) developed an
alternative direct forcing scheme to evaluate the virtual force based on the N-S
equation at discrete times. Fadlum et al. (2000) extended the direct forcing
scheme of Mohd-Yusof (1997) to a 3-D finite-difference method. Instead of
evaluating and applying the virtual force, the velocity at the first grid point
outside the solid boundary is estimated through a linear interpolation of the
moving velocity of the boundary and the velocity at the second external grid
point. Conceptually, this velocity interpolation scheme is equivalent to applying
the momentum force inside the flow field (Kim et al., 2001). This scheme is more
efficient in 3-D because it has no adjustable constant and has no extra restric-
tion on the scale of the time step, which is required in the feedback-forcing
scheme. Kim et al. (2001) simulated the flow over complex geometry in a finite-
volume approach with staggered meshes. The momentum force and mass source
were applied on the immersed boundary to satisfy the no-slip boundary con-
dition and the flow continuity.
The basic idea of the IBM is that the presence of the solid boundary (fixed or
moving) in a fluid can be represented by a virtual body force field ~
Fp applied on
the computational grid at the vicinity of solid–flow interface. Thus, the Navier–
Stokes equation for this flow system in the Eulerian frame can be given by
@rV
@t
þ r ðrVVÞ ¼ rp þ r s þ rg þ ~
Fp (16)
It is noted that the virtual body force ~
Fp depends not only on the unsteady
fluid velocity, but also on the velocity and location of the particle surface, which
is also a function of time. There are several ways to specify this boundary force,
such as the feedback forcing scheme (Goldstein et al., 1993) and direct forcing
scheme (Fadlun et al., 2000). In 3-D simulation, the direct forcing scheme
can give higher stability and efficiency of calculation. In this scheme, the disc-
retized momentum equation for the computational volume on the boundary is
given as
Vtþ1
¼ Vt
þ DtðRHSt
þ Ft
pÞ (17)
where RHS refers to all the terms in the right-hand side of Eq. (16) except the
virtual body force ~
Fp. The virtual body force Ft
p is used to maintain the fluid
velocity to be equal to the particle velocity at the particle surface (i.e., no-slip
boundary condition), which is
Vtþ1
¼ VpðtÞ (18)
10

where Vp is the particle velocity. Thus, the discrete virtual force can be defined as
Ft
p ¼ ðVp Vt
Þ=Dt RHSt
(19)
Since the computational grids are generally not coincident with the location of
the particle surface, a velocity interpolation procedure needs to be carried out in
order to calculate the boundary force and apply this force to the control volumes
close to the immersed particle surface (Fadlun et al., 2000).
Other than the virtual momentum force ~
Fp, a virtual mass source/sink should
also be applied to the particle surface to satisfy the continuity for the control
volume containing the particle surface or the particle (Kim et al., 2001). The
mass source can be calculated by
qt
¼
1
DV
X
i
ai
~
V
t
i ~
niDsi (20)
where DV is the volume of the computation cell (control volume) and Dsi the
surface area of surface i of this cell. For a 3-D case, i ¼ 1, 2, y, 6. ~
ni is
the normal vector of each face of the cell. ~
V
t
i the fluid velocity at each face of the
cell. ai the flag to indicate whether the virtual body force is applied to face i of
the cell or not. ai ¼ 1 when the force is applied, otherwise it is zero. Therefore,
the continuity equation of the incompressible fluid can be written as (Kim et al.,
2001):
r ~
V ¼ q (21)
III. System 1: Flow Dynamics of Gas–Liquid–Solid Fluidized Beds
The flows in a gas–liquid–solid fluidized bed or a gas–liquid bubble column
are represented by two regimes, the homogeneous and the heterogeneous. In the
homogenous regime, the coalescence of bubbles does not occur and there is little
variation of bubble sizes. However, this is not the case in the heterogeneous
regime. The flow structure in the heterogeneous regime is complex due to sub-
stantial coalescence and breakup of bubbles. Both the E-E and the E-L methods
have proven to be more effective in modeling the homogenous regime than the
heterogeneous regime of gas–liquid flow. In the simulation of the heterogeneous
regime of gas–liquid flows using either the E-E or the E-L method, the challenge
lies in the establishment of an accurate closure relationship for the interphase
momentum exchange. The interphase momentum exchange is induced through
the drag force that liquid exerts on the bubble surface, the virtual mass force due
to the bubble and liquid inertial motion, and the lift force caused by the shear
flows around the bubbles. In gas–liquid bubble columns and gas–liquid–solid

fluidized systems, the interstitial forces under the bubble coalescence and
breakup conditions are not well established. A computational model based on
the level-set methods given below provides some information on the much
needed closure relationship of the interphase momentum exchange noted above.
A. NUMERICAL PROCEDURE FOR SOLVING THE GAS– LIQUID INTERFACE
The level-set technique described in Section II.A is employed to capture the
motion of 3-D gas–liquid interfaces. The numerical procedures for solving the
gas–liquid interface include finding the solution for the time-dependent Eqs. (3),
(5), and (6). Given fnand Vndefined at cell centers at one time instant tn, fn+1,
and Vn+1 can be solved over a time increment at a new time instant
tn+1 ¼ tn+Dt following the procedures given below:
Solve Eqs. (5) and (6) to obtain the velocity distribution in the flow field Vn+1
using the Arbitrary-Lagrangian-Eulerian (ALE) scheme (Kashiwa et al., 1994).
Solve Eq. (3) to obtain fn+1 using the second-order TVD-Runge-Kutta
method presented as follows:
f̄nþ1 ¼ fn þ Dtftn (22)
fnþ1 ¼ fn þ
Dt
2
ðf̄tnþ1 þ ftnÞ (23)
where ftn ¼ VnDfn and the time steps are the same as that used in calculating
Vn+1, which is determined by restrictions due to the Courant–Friedrichs–Levy
(CFL) condition, gravity, viscosity, and surface tension.
Solve Eq. (12) to perform the redistancing.
Although, in principle, Eq. (12) would not alter the location of the zero-level
set of f, in practice, with numerical computation it may not be true. A redis-
tance operation is needed to maintain the volume conservation. Therefore, Eq.
(12) is modified to (Sussman et al., 1998):
@d
@t
¼ sinðfÞð1 rf

Þ þ lijf ðfÞ Lðf; dÞ þ lijf ðfÞ (24)
where
lij ¼
R
Oij
H0
ðfÞLðf; dÞ
R
Oij
H0
ðfÞf ðfÞ
(25)
and
f ðfÞ H0
ðfÞ rf

(26)
12

B. GOVERNING EQUATIONS FOR THE GAS– LIQUID– SOLID FLOW
The gas–liquid–solid flow is characterized by a wide range of physical length
scales, including small to large eddies in the bubble wake, and size in the milli-
meter range for solid particles and in the millimeter/centimeter range for gas
bubbles. The accurate description of the gas bubble surface and bubbling flow
requires the use of fine grids, while the tracking of the motion of solid particles
needs the grid size to be much larger than the particle sizes.
For simulation of a gas–liquid–solid fluidized bed, the locally averaged
Navier–Stokes equations (Anderson and Jackson, 1967) are used to describe the
liquid phase flow outside the gas bubble, and the gas phase flow inside the gas
bubble. Due to the large grid size used, the liquid phase turbulence needs to be
considered. In this study, a modified coefficient that illustrates the effect of the
bubble-induced turbulence for a subgrid scale (SGS) stress model is employed.
The level-set method and the numerical procedures described in Sections II.A
and III. are used to simulate the motion and the topological variation of the gas
bubble. The locally averaged governing equations of Eqs. (5) and (6) for liquid
flow outside the bubble and gas flow inside the bubble are given as:
@r
@t
þ r ðrVÞ ¼ 0 (27)
@rV
@t
þ r ðrVVÞ ¼ rp þ r s r ssg
þ rg þ FD þ Fs (28)
e represents the void fraction of liquid or gas and satisfies:
þ p ¼ 1 (29)
where ep is the void fraction of solid particles. tsg
the SGS stress term. It is
modeled by the Smagorinsky (1963) model written as
ssg
ij ¼ nT
@Vi
@xj
þ
@Vj
@xi

(30)
where nT is defined as
nT ¼ ðCslÞ2
S
j j (31)
for bulk flow, and
nT ¼ Csf ðyÞl2
S
j j (32)
for walls with a wall function f(y). Cs is the Smagorinsky coefficient, l ¼ D, and
S
j j
ffiffiffiffiffiffiffiffiffiffiffiffiffi
2SijSij
p
(33)

The volumetric fluid–particle interaction force FD in Eq. (28) is calculated from
the forces acting on the individual particles in a cell:
FD ¼
P
f k
d
DOij
, (34)
where fd is the fluid–particle interaction force for a single particle and DO the
cell volume.
C. MODELING THE MOTION AND COLLISION DYNAMICS OF SOLID PARTICLES IN
GAS– LIQUID– SOLID FLUIDIZATION
The motion of a particle in the flow field can be described in the Lagrangian
coordinate with the origin placed at the center of the moving particle. There are
two modes of particle motion, translation and rotation. Interparticle collisions
result in both the translational and the rotational movement, while the fluid
hydrodynamic forces cause particle translation. Assuming that the force acting
on a particle can be determined exclusively from its interaction with the sur-
rounding liquid and gas, the motion of a single particle without collision with
another particle can be described by Newton’s second law as
dxp
dt
¼ Vp (35)
mp
dVp
dt
¼ mpg þ
p
6
d3
pðrp þ r s r ssg
Þ þ f d þ f am þ f s (36)
where xp and Vp are the particle position and particle velocity, respectively, and
dp the diameter of the particle. The five terms on the right-hand side of Eq. (36)
represent, respectively, the gravity force, the fluid stress gradient force, the total
drag force, the added mass force and the bubble-surface-tension-induced force.
The Saffman, the Magnus, and the Basset forces are ignored.
Note that the lubrication effect due to particle collisions in liquid is signifi-
cant. The liquid layer dynamics pertaining to the lubrication effect was exami-
ned by Zenit and Hunt (1999). Zhang et al. (1999) used a Lattice-Boltzmann
(LB) simulation to account for a close-range particle collision effect and
developed a correction factor for the drag force for close-range collisions, or the
lubrication effect. Such a term has been incorporated in a 2-D simulation based
on the VOF method (Li et al., 1999). Equation (36) does not consider the
lubrication effect. Clearly, this is a crude assumption. However, in the three-
phase flow simulation, this study is intended to simulate only the dilute solids
suspension condition (ep ¼ 0.42–3.4%) with the bubble flow time of less than 1 s
starting when bubbles are introduced to the solids suspension at a prescribed ep.
14

The particle collision effect under this simulation condition, therefore, would
be small.
Note that depending on the manner in which the drag force and the buoyancy
force are accounted for in the decomposition of the total fluid–particle inter-
active force, different forms of the particle motion equation may result (Jackson,
2000). In Eq. (36), the total fluid–particle interaction force is considered to be
decomposed into two parts: a drag force (fd) and a fluid stress gradient force (see
Eq. (2.29) in Jackson, 2000)). The drag force can be related to that expressed by
the Wen–Yu equation, fWen–Yu, by
f d ¼ f WenYu (37)
The Wen and Yu (1966) equation is given by
f WenYu ¼
1
8
pd2
pCD2
r V Vp

ðV VpÞ (38)
where the effective drag coefficient CD is calculated by
CD ¼ CD04:7
(39)
In Eq. (39), CD0 is a function of the particle Reynolds number, Rep ¼
rdpjV Vpj=m. For rigid spherical particles, the drag coefficient CD0 can be
estimated by the following equations (Rowe and Henwood, 1961):
CD0 ¼
24
Rep
ð1 þ 0:15ðRepÞ0:687
Þ; Repo1000
0:44; Rep 1000
(
(40)
The added mass force accounts for the resistance of the fluid mass that is moving
at the same acceleration as the particle. Neglecting the effect of the particle
concentration on the virtual-mass coefficient, for a spherical particle, the volume
of the added mass is equal to one-half of the particle volume, so that
f am ¼
1
12
pd3
pr
DV
Dt

DVp
Dt

(41)
When particles approach the gas–liquid interface, the surface-tension force acts
on the particles through the liquid film. The bubble-surface-tension induced
force can be described by
f s ¼
p
6
d3
psKðfÞdðfÞrf (42)
When the particle inertia overcomes the surface-tension-induced force, the par-
ticle will penetrate the bubbles. Recognizing that particle penetration may not
lead to bubble breakage, details of bubble instability due to particle collision are
given in Chen and Fan (1989a, b).

To simulate the particle–particle collision, the hard-sphere model, which is
based on the conservation law for linear momentum and angular momentum, is
used. Two empirical parameters, a restitution coefficient of 0.9 and a friction
coefficient of 0.3, are utilized in the simulation. In this study, collisions between
spherical particles are assumed to be binary and quasi-instantaneous. The equa-
tions, which follow those of molecular dynamic simulation, are used to locate
the minimum flight time of particles before any collision. Compared with the
soft-sphere particle–particle collision model, the hard-sphere model accounts for
the rotational particle motion in the collision dynamics calculation; thus, only
the translational motion equation is required to describe the fluid induced par-
ticle motion. In addition, the hard-sphere model also permits larger time steps in
the calculation; therefore, the simulation of a sequence of collisions can be more
computationally effective. The details of this approach can be found in the
literature (Hoomans et al., 1996; Crowe et al., 1998).
D. RESULTS AND DISCUSSIONS
The computation performed in this study is based on the model equations
developed in this study as presented in Sections II.A, III.A, III.B, and III.C
These equations are incorporated into a 3-D hydrodynamic solver, CFDLIB,
developed by the Los Alamos National Laboratory (Kashiwa et al., 1994). In
what follows, simple cases including a single air bubble rising in water, and
bubble formation from a single nozzle in bubble columns are first simulated. To
verify the accuracy of the model, experiments are also conducted for these cases
and the experimental results are compared with the simulation results. Simu-
lations are performed to account for the bubble-rise phenomena in liquid–solid
suspensions with single nozzles. Finally, the interactive behavior between bub-
bles and solid particles is examined. The bubble formation and rise from multi-
ple nozzles is simulated, and the limitation of the applicability of the models is
discussed.
1. Single Air Bubble Rising in Water
The simulation for a single air bubble rising in water (density: 0.998 kg/cm3
;
viscosity: 0.01 Pa s; surface tension: 0.0728 N/m) is performed in a 4 4
8 cm3
3-D column. A uniform grid size of 0.05 cm is used for three dimensions
which generates 80 80 160 ( ¼ 1.024 106
) grid points in the computational
domain. Initially, a spherical air bubble is positioned at rest in this domain with
its center located 0.5 cm above the bottom and the liquid is quiescent. The free-
slip boundary conditions are imposed on all six walls. Note that the dimension
of the computational domain is selected based on numerical experiments. It is
found that, under both free-slip and no-slip wall boundary conditions, when the
distance of the bubble interface to the wall is more than twice as large as the
16

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Title: Memoirs of the life, exile, and conversations of the
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David. Cooper.
NAPOLEON.
Published for Henry Colburn, Nov.r
17, 1835.

MEMOIRS
OF
THE LIFE, EXILE,
AND
CONVERSATIONS,
OF THE
EMPEROR NAPOLEON.
BY
THE COUNT DE LAS CASES.
A NEW EDITION.
WITH PORTRAITS
AND NUMEROUS OTHER EMBELLISHMENTS.
VOL. I.
LONDON:
PUBLISHED FOR HENRY COLBURN,
BY RICHARD BENTLEY; BELL AND BRADFUTE, EDINBURGH; J. CUMMING,
DUBLIN;
AND ALL BOOKSELLERS.
MDCCCXXXVI.

ANDOVER:
STEREOTYPED AND PRINTED BY B BENSLEY.

LIST OF ILLUSTRATIONS.
VOLUME I.
PAGE.
Portrait of the Emperor Napoleon, to face the title.
Napoleon on board the Bellerophon 26
Portrait of Charles Bonaparte 66
Portrait of Letizia Bonaparte 69
Residence of the Emperor at Longwood 264
VOLUME II.
Portrait of the Empress Josephine, to face the title.
Portrait of Marshal Bertrand 33
Map of Saint Helena 39
Portrait of Prince Talleyrand 64
Eugene Beauharnois claiming his Father’s Sword 186
VOLUME III.
Portrait of Sir Hudson Lowe, to face the title.
Ground Plan of Longwood 21
The House in which Napoleon was Born 113

The Burning of Moscow 164
Napoleon’s Return from Elba 302
VOLUME IV.
Portrait of Count De Las Cases, to face the title.
Napoleon at Saint Helena 149
Death of Napoleon 386
Statue of Napoleon on the Place Vendome 388
Tomb of Napoleon 399

PREFACE.
Circumstances the most extraordinary have long kept me near the
most extraordinary man that ever existed. Admiration made me
follow him, without knowing him, and when I did know him, love
alone would have fixed me for ever near his person. The world is full
of his glory, his deeds, and his monuments; but no one knows the
true shades of his character, his private qualities, or the natural
disposition of his soul. This great void I undertake to fill up, and for
such a task I possess advantages unexampled in history.
I collected and recorded, day by day, all that I saw of Napoleon,
all that I heard him say, during the period of eighteen months in
which I was constantly about his person. In these conversations,
which were full of confidence, and which seemed to pass, as it were,
in another world, he could not fail to be portrayed by himself as if in
a mirror, in every point of view, and under every aspect. Henceforth
the world may freely study him: there can be no error in the
materials.
Count Las Cases.

MEMOIRS
OF
THE EMPEROR NAPOLEON.

INTRODUCTION.
It is my intention to record daily all that the Emperor Napoleon did
or said while I was about his person; but, before I begin my diary, I
hope to be excused for offering a few preliminary remarks, which
may not be altogether useless.
I never commenced the perusal of any historical work without first
wishing to know the character of the author, his situation in society,
and his political and domestic relations; in fact, all the important
circumstances of his life; conceiving that nothing but a knowledge of
these matters could furnish a key to his writings, or a safe ground of
confidence in his statements. I therefore proceed to supply in my
turn that which I always sought for in others; and, in presenting this
diary, to relate a few facts respecting my past life.
I was scarcely twenty-one years of age when the Revolution broke
out, and had just been made a Lieutenant de Vaisseau, which
corresponded with the rank of a field officer in the line: my family
was at court, and I had been recently presented there myself. I was
not rich; but my name and rank in life, together with my professional
prospects, were likely, according to the notions and views of the
times, to enable me to marry according to my wishes. It was at such
a moment that our political troubles burst forth.
One of the principal vices in our system of admission to the
service was that of depriving us of the benefits of a solid and
finished education. Withdrawn from school at the early age of
fourteen, abandoned from that instant to ourselves, and launched as
it were on a wide waste, how was it possible to attain the slightest
notion of social organization, public rights, or the duties of civil life?

Thus, prompted by noble prejudice, rather than by a just sense of
duty, above all, led on by a natural fondness for generous resolves, I
was amongst the first to hasten abroad and join our Princes; to
save, as it was said, the monarch from revolutionary fury, and to
defend our hereditary rights, which we could not, it was asserted,
yet abandon without shame. From the mode in which we had been
educated, it required either a very strong head or a very weak mind
to resist the torrent.
The emigration soon became general; this fatal measure is but too
well known to Europe; nor can its folly, as a political blunder and a
social crime, find any excuse in the present day, except in the
unenlightened but upright character of most of those by whom it
was undertaken.
Defeated on our own frontiers, discharged and disbanded by
foreigners, rejected and proscribed by the laws of our country,
numbers of us reached England, whose Ministers lost no time in
landing us on the shore of Quiberon. Being so fortunate as not to
disembark, I had, after my return, time to reflect on the horrible
alternative of fighting against our country under foreign banners;
and, from this moment, my ideas, principles, and projects were
either disconcerted or entirely changed.
Despairing of events, abandoning the world and my natural
sphere, I devoted myself to study; and, under a borrowed name,
went through a second course of education in attempting to assist
that of others.
After a lapse of some years, the treaty of Amiens, and the
amnesty offered by the First Consul, re-opened to us the gates of
France. I had no longer any property there: the laws had disposed of
my patrimony; but can any thing make us forget our native soil, or
destroy the charm of breathing the air of our own country!
I hurried back, and was grateful for a pardon, rendered more
acceptable since I could say with pride that I received it without
having any motives of self-reproach. When monarchy was
proclaimed soon after, my situation and sentiments were of a most
singular kind. I found myself a soldier punished for a cause that had
triumphed. Every day brought us back to our former ideas: all that

had been dear to our principles and prejudices was renewed; and
yet delicacy and honour rendered it a kind of duty in us to keep at a
distance.
It was in vain that the new government loudly proclaimed the
union of all parties; and equally so that its chief had declared he
would no longer recognise any but Frenchmen in France; in vain had
old friends and former companions offered me the advantages of a
new career to be chosen by myself. Unable to subdue the conflicting
feelings which agitated my mind, I obstinately persevered in a
system of self-denial; and, devoting all my time to literature, I
composed under a feigned name, an historical work that re-
established my fortune; after which I passed five or six of the
happiest years of my life.
Meanwhile, unprecedented events succeeded each other with
extraordinary rapidity: they were of such a nature, and bore so
peculiar a character, that it became impossible for any person whose
heart possessed the least predilection for whatever was great or
noble to view them with indifference. The glory of our country was
raised to a pitch unknown in the history of any other people: the
administration of affairs was unexampled, not less by its energy than
the consequences it produced; a simultaneous impulse, which was
suddenly given to every species of industry, excited the emulation of
all at the same moment; the army was unrivalled, striking terror
abroad and creating a just pride at home.
Every day added to the number of our trophies, while numerous
monuments proclaimed our exploits; the victories of Austerlitz, Jena,
and Friedland; the treaties of Presburg and Tilsit had constituted
France the first of nations, and made her the arbitress of Europe. It
was a signal honour to be a Frenchman; and yet all these exploits,
labours and prodigies, were the work of one man. For my own part,
whatever might have been my former prepossessions and
prejudices, I was now filled with admiration; and, as we all know,
there is but one step from admiration to affection. It was precisely at
this period that the Emperor called some of the first families of
France round his throne, and caused it to be circulated, amongst the
rest, that he would consider those who remained aloof as bad

Frenchmen. I did not hesitate for an instant: I have, said I to myself,
fulfilled the obligations of my natural oath, that of my birth and
education, to which I have continued faithful until its extinction. Our
princes too were no longer thought of: we even doubted their
existence. The solemnities of religion, the alliance of kings, the
example of Europe, and the splendour of France, henceforth taught
me that I had a new sovereign. Had those who preceded us made
so long a resistance to such powerful efforts, before rallying round
the first of the Capets? I answered therefore, for myself, that, happy
in being thus enabled to obey a call which removed me with honour
from the delicate situation in which I was placed, I freely,
spontaneously, and without reserve, transferred the zeal, loyalty, and
attachment which I had constantly cherished for my old masters, to
the new sovereign: the result of this step was my immediate
admission at court.
In this state of things, I felt extremely anxious that my recent
protestations should be ratified by deeds. The English had invaded
Flushing, and threatened Antwerp; I therefore hastened to assist in
the defence of the latter place, as a volunteer; and, on the
subsequent evacuation of Flushing, my nomination to the office of
chamberlain called me near the person of the Emperor. Being
desirous of adding some more useful occupation to the duties of this
honourable post, I solicited and obtained a seat in the Council of
State. Hence followed several confidential missions: I was sent to
Holland at the period of its union to the French Empire, in order to
receive whatever related to the naval department; then to Illyria, for
the purpose of liquidating the public debt; and afterwards over half
the Empire, to superintend establishments of public beneficence.
During our late misfortunes, I received some consoling proofs that
the inhabitants of the countries to which I had thus been sent were
not dissatisfied with my conduct.
Providence had however fixed a limit to our prosperity. The
catastrophe of Moscow, the disasters of Leipsic, and the siege of
Paris, are well known. I commanded in that city one of the legions
which acquired honour by its severe losses on the 31st of March.
When the capitulation took place I gave up the command, feeling

that other duties were to be performed near the person of my
sovereign, but could not reach Fontainebleau in time:—the Emperor
had abdicated, and was succeeded by the King.
My situation now became more singular than it had been twelve
years before. The cause for which I had sacrificed my fortune, for
which I remained so long in exile, and six years in a state of self-
denial at home, was at length triumphant; nevertheless, the point of
honour and other considerations were about to prevent my reaping
any benefit from the event! What could be more capricious than my
fate? Two revolutions had been effected in opposition to each other:
—by the first I lost my patrimony; by the second I might have been
deprived of life: neither the one nor the other had been favourable
to my fortune. Vulgar minds will only perceive an unfortunate
tergiversation of opinions in this wayward destiny, while the lovers of
intrigue will assert that I was twice a dupe: only the few will
understand that I have twice honourably fulfilled my duty. Be this as
it may, those early friends, whose esteem was not lessened by the
line of conduct I had pursued, having now become all powerful,
invited me to join them: it was impossible to obey the generous call;
disgusted and disheartened, I resolved that my public life should
terminate. Ought I to have exposed myself to the false judgment of
those who were watching my proceedings? Could every body see
what was passing in my mind?
Having now become a Frenchman even to enthusiasm, and unable
to endure that national degradation of which I was a daily witness
amidst foreign bayonets, I determined to endeavour to divert my
thoughts at a distance from the scene of calamity, and went to pass
a few months in England. How altered did every thing appear there!
On reflection, I found that it was myself who had undergone a great
change.
I had scarcely returned, when Napoleon appeared on our coasts:
he was transported to the capital as it were by magic, and this
without battles, excesses, or effusion of blood. I thought I saw the
stain brought on us by foreign hands effaced, and all our glory
restored. Destiny had ordered otherwise!

No sooner did I hear of the Emperor’s arrival, than I
spontaneously repaired to attend on his person. I was present at the
moment of abdication; and, when the question of his removal was
agitated, I requested permission to participate in his fate. Such had
been till then the disinterestedness and simplicity, some will say folly,
of my conduct, that, notwithstanding my daily intercourse as an
officer of the household and member of his council, Napoleon
scarcely knew me. “Do you know whither your offer may lead you?”
said he, in his astonishment. “I have made no calculation about it,” I
replied. He accepted me, and I am at St. Helena.
I have now made myself known; the reader has my credentials in
his hands: a host of contemporaries are living—it will be seen
whether a single individual amongst them stands up to invalidate
them: I therefore begin my task.
RETURN OF THE EMPEROR TO THE ELYSÉE, AFTER
THE BATTLE OF WATERLOO.
Tuesday, June 20th, 1815.—Heard of the Emperor’s return to the
Elysée Palace: placed myself in immediate attendance there. Found
Messrs. Montalambert and Montholon there, brought by the same
sentiment.
Napoleon had just lost a great battle; so that the safety of the
nation thenceforth depended on the wisdom and zeal of the
Chamber of Representatives. The Emperor, still covered with dust
from the field of Waterloo, was on the point of hurrying into the
midst of them, there to declare our dangers and resources, and to
engage that his personal interests should never be a barrier to the
happiness of France; after which he intended to quit Paris
immediately. It is said that several persons dissuaded him from this
step, by leading him to apprehend an approaching ferment amongst
the deputies.
It is as yet impossible to comprehend every report that circulates
with regard to this fatal battle: some say there is manifest treason;
others, a fatality without example. Thirty thousand men under
Grouchy lost their way and were too late, taking no part in the

engagement; the army, victorious till the evening, was, it is said,
suddenly seized with a panic towards eight o’clock, and became
broken in an instant. It is another Crecy, another Azincourt,———![1]
every one trembles and thinks all is lost!
THE ABDICATION.
21st.—The best intentioned and most influential members of the
national representation have been tampered with all last evening
and all night, by certain persons, who, if their word is to be taken,
produce authentic documents and demi-official papers guaranteeing
the safety of France, on condition of the mere abdication of the
Emperor, as they pretend.
The above opinion had become so strong this morning that it
seemed irresistible: the president of the assembly, the first men in
the state, and the Emperor’s particular friends, come to supplicate
him to save France by abdicating. Though by no means convinced,
yet the Emperor answers with magnanimity:—he abdicates!
This circumstance causes the greatest bustle round the Elysée;
the multitude rushes towards the gate, and testifies the deepest
interest; numbers penetrate within the hall, while some even of the
popular class scale the walls; some in tears, others in a state
approaching to distraction, crowd up to the Emperor, who is walking
tranquilly in the garden, and make offers of every description.
Napoleon alone is calm, constantly replying that they ought in future
to employ this zeal and tenderness for the good of their country.
I presented the deputation of Representatives, in the course of the
day: it came to thank the Emperor for his devotedness to the
national interests.
The documents and state-papers, which have produced such a
powerful sensation, and brought about the grand event of this day,
are said to be official communications of Messrs. Fouché and
Metternich, in which the latter guarantees Napoleon II. and the
regency, in case of the abdication of the Emperor. These
communications must have been long carried on unknown to

Napoleon. M. Fouché must have a furious partiality for clandestine
operations. It is well known that his first disgrace, which took place
several years ago, arose from his having opened some negotiations
with England of his own accord, without the Emperor’s knowledge:
he has in fact always shewn the greatest obliquity in affairs of
moment. God grant that his present mysterious acts do not prove
fatal to our country!
DEPUTATION OF THE CHAMBER OF PEERS.—CAULAINCOURT.—FOUCHÉ.
22nd.—Went home to pass a few hours at my own house: in the
course of this day the deputation of the Peers was presented: a
portion of the Provisional Government was named in the evening.
Caulaincourt and Fouché, who were of the number, happened to be
with us in the ante-chamber: we complimented the first on his
nomination, which was, indeed, only congratulating ourselves on the
public good: his reply was full of alarm. “We applaud the choice
hitherto known,” said we. “It is certain,” observed Fouché, with an
air of levity, “that I am not suspected.”—“If you had been,“ rudely
rejoined the deputy Boulay de la Meurthe, who was also present, “be
assured we should not have named you.”
THE PROVISIONAL GOVERNMENT PRESENTED TO
THE EMPEROR.
23rd—The acclamations and interest without continued at the
Elysée. I presented the members of the Provisional Government to
the Emperor, who, in dismissing them, directed the Duke Decrés to
see them out. The Emperor’s brothers, Joseph, Lucien, and Jerome,
were introduced frequently through the day, and conversed with him
for some time.
As usual, there was a great multitude of people collected round
the palace in the evening: their numbers were constantly increasing.
Their acclamations and the interest shewn for the Emperor created
considerable uneasiness amongst the different factions. The

fermentation of the capital now became so great that Napoleon
determined to depart on the following day.
THE EMPEROR QUITS THE ELYSÉE.
25th.—I accompanied the Emperor to Malmaison, and again
requested permission to follow his future fortunes. My proposal
seemed to create astonishment, for I was still only known to him by
my employments; but he accepted the offer.
26th.—My wife came to see me; she had divined my intentions: it
became a somewhat delicate task to avow them, and still more
difficult to convince her of their propriety. “My dear,” said I, “in
following the dutiful dictates of my heart, it is consoling to reflect
that your interests are not thereby prejudiced. If Napoleon II. is to
govern us, I leave you strong claims on his protection; should
Heaven order it differently, I shall have secured you a glorious
asylum, a name honoured with some esteem. At all events we shall
meet again, at least in a better world.” After tears and even
reproaches, which could not but be gratifying, she consented to my
departure, exacting a promise however, that I would allow her to
join me without loss of time. From this moment she manifested a
courage and strength of mind that would have animated myself in
case of necessity.
THE MINISTER OF MARINE COMES TO MALMAISON.
27th.—I went to Paris for a short time with the minister of Marine,
who came to Malmaison, on business respecting the frigates
destined for the Emperor. He read me the instructions drawn out for
the commanders, said his Majesty depended on my zeal, and
intended taking me with him; adding, that he would take care of my
family during my absence.
Napoleon II. is proclaimed by the Legislature.
Sent for my son from his school, having determined that he should
accompany me. We prepared a small parcel of clothes and linen,

then proceeded to Malmaison, accompanied by my wife, who
returned immediately. The road had now become rather unsafe,
owing to the approach of the enemy.
28th.—Being desirous of making some other arrangements before
our departure, the Duchess de Rovigo took me and my son to Paris
in her carriage. I found Messrs. de Vertillac and de Quitry at my
house; these were the last friends I embraced: they were terrified.
The agitation and uncertainty hourly increased in the capital, for the
enemy was at the gates. On reaching Malmaison, we saw the bridge
of Chatou in flames: guards were posted round the palace, and it
became prudent to remain within the park walls. I went into the
Emperor’s room, and described how Paris had appeared to me;
stating the general opinion that Fouché openly betrayed the National
cause; and that the hopes of all patriots were that his Majesty would
this very night join the army who loudly called for him. The Emperor
listened to me with an air of deep thought, but made no reply, and I
withdrew soon after.
NAPOLEON QUITS MALMAISON, AND DEPARTS FOR
ROCHEFORT.
29th-30th.—A cry of Long live the Emperor! was continually heard
on the great road to Saint Germain; it proceeded from the troops
who passed under the walls of Malmaison.
Towards noon. General Becker came from Paris, sent by the
Provisional government; he told us, with feelings of indignation, that
he had received a commission to guard and watch Napoleon.[3]
A sentiment the most base had dictated this choice: Fouché knew
that General Becker had a private pique against the Emperor, and
therefore did not doubt of finding in the former a man disposed to
vengeance; but he was grossly deceived in his expectations, for
Becker constantly shewed a degree of respect and attachment to the
Emperor highly honourable to his own character.
Meanwhile time pressed. When on the point of setting out, the
Emperor sent a message to the Provisional Government, by General
Becker, offering to place himself at the head of the army, merely as a

private citizen, adding, that, after having repulsed Blucher, he would
continue his route. On the refusal of this offer, we left Malmaison;
the Emperor and a part of his suite taking the road to Rochefort by
Tours; I and my son, with Messieurs Montholon, Planat, and Résigny,
proceeded towards Orleans, as did also two or three other carriages.
We reached this place early on the 30th, and got to Chatellerault at
midnight.
July 1st–2nd. We passed through Limoges on the 1st, at four in
the afternoon; dined at Rochefoucault on the 2nd, and reached
Jarnac about seven. We slept here, owing to the obstinacy of the
postmaster, which forced us to remain till next day.
3rd.—We could not set out before five o’clock. On account of the
misconduct of the postmaster, who, not content with detaining us all
night, had recourse to secret means for keeping us still longer, we
were obliged to proceed at a slow pace to Cognac, where the
postmaster and inhabitants received us very differently. It was easy
to perceive that our journey occasioned a great deal of agitation
amongst all parties. On reaching Saintes, towards eleven o’clock, we
nearly fell victims to the fury of some miscreants, collected by an
officer of the royal guard, a native of that place. This person had
prepared an ambuscade for us, and had even laid a plan for our
assassination. We were arrested by the mob, but a part of the
national guard interfered, and conducted us as prisoners to an
adjoining inn. It was said that we were carrying off the treasures of
the State, and therefore merited death. Some of them, who
pretended to be the most distinguished inhabitants, and above all,
the women, were the most outrageous, and called for our immediate
execution.
We saw these females pass in succession before some windows
that were open near our temporary prison, in order that their insults
should not be lost upon us. It will scarcely be credited that they
went so far as to gnash their teeth in sign of hatred, and from
vexation at seeing the indifference we displayed; yet they formed
the fashionable circle of Saintes! Could Real be in the right, when he
told the Emperor, during the hundred days, that as for Jacobins, he
had reason to know something of them; protesting that the only

difference between the blacks and whites was that the former wore
wooden shoes and the latter silk stockings?
Prince Joseph, who was passing through Saintes unknown to us,
came to increase the interest of our adventure. He was also
arrested, and conducted to the prefecture; but highly respected.
The windows of the inn faced a large square, which continued to
be filled with an agitated and hostile rabble, who were extremely
violent and abusive. I found an old acquaintance in the under-
prefect, who was thus enabled to state who we were. The carriage
in which we travelled was next examined; while we were ourselves
retained in a species of solitary confinement. I obtained leave,
however, to visit the Prince about four o’clock.
While on my way to the prefecture, and though guarded by a non-
commissioned officer, several individuals addressed me: some put
notes secretly into my hands; others whispered something friendly;
while all united in assuring me we might feel perfectly tranquil, for
the patriots and well-intentioned inhabitants would protect us.
Towards the evening we were allowed to depart; and by this time
things had so totally changed that we left the inn amidst the most
lively acclamations: females of the lower classes, in tears, kissed our
hands: many persons offered to accompany us, that we might avoid
the enemies of the Emperor, who, they said, lay in wait to murder
us, at a short distance from the town. This singular transition arose
in some degree from the arrival of numbers of country people and
federates, who gave an immediate turn to public opinion.
4th.—On approaching Rochefort we met a party of gendarmerie,
who, on the report of our reception at Saintes, had been dispatched
to meet us. We arrived at this place about two o’clock in the
morning: the Emperor had reached it on the preceding evening.[4]
Prince Joseph arrived in the afternoon; when I conducted him to the
Emperor.
I profited by the first moment of leisure to inform the President of
the Council of State why I absented myself. “Rapid and important
events,” said I “obliged me to quit Paris without the necessary leave
of absence. The peculiarity and importance of the case led to this
irregularity: being in attendance on the Emperor at the moment of

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