1
CHAOS in FLUIDIZED BED COMBUSTOR
D.E. Ventzas
1
, and
P. Tsiakaras
Dpt of Mechanical & Industrial Eng, University of Thessaly,
Pedion Areos, 38334, Volos, GREECE, Email: tsiak@uth.gr
ABSTRACT:
KEYWORDS:
INTRODUCTION:
Combustion in fl
uidized bed combustors includes
mixing, reaction kinetics and bed particle motions, i.e. it is highly nonlinear dynamic
process. The paper statistically correlates flow, acoustic, ultrasonic, pressure data
series, i.e. these parameters with bed fluid dynam
ics. The data are used for statistical
analysis (stationarity), state classification and combustor diagnostics. Nostationary
processes behave as transport phenomena, i.e. present similar statistical properties, but
in space, not in time.
exhaust
bed
microcomputer
DPT
solenoid
HPF
LPF
grid
PT
0.1

40 Hz
supply air
nozzle for
slugging
fluidizing air
control
Fig. . Fluidized bed instrumentation
Four distinct fluidization regimes are possible that follow each other, by
increasing the gas flow, i.e. the vibrating particles, bubbling, slugging and transition
to turbulence regimes, where:
U
mf
=
minimum fluidization flow
1
Visiting Professor, Electronics Dpt, TEI Lamia, E

mail: dventzas@uth.gr
2
U
mss
=
maximum stable sluggi
ng flow
2 v p
b
standard
i a
u
deviation
b r
b
of
ΔΡ
r t
b
transition
a i
l
to
1 t c
i
turbulence
i l
n
n e
g
g s
slugging
0
U
mf
U
mss
gas flow
Fig. . Standard deviation of
ΔΡ
in fluidized
bed v.s. the fluidizing gas flow
Further gas flow increase results in decreased coherency and increased complexity of
macroscopic bed behavior, giving stutters in oscillation that manifest an intermittent
transition to chaos (stutters increase in freque
ncy with increasing flow).
Fig. . Differential pressure signal of a fluidized bed under slugging
conditions
(non periodicities and signal interruption corresponds to stutter,
while cycle magnitude corresponds to the
slug size)
As flow is increased from U
mss
, the slugging patterns become less regular, forming
stutters that collapse and the amplitude of oscillation increases through several cycles
(passage of large bubbles) until it reaches the amplitude of the regula
r slugging
pattern.
Flow stabilization control results in distinct and narrow harmonics, while flow
destabilization distributes power content across many frequencies.
TIME SERIES:
The time series measured from any system, here the
fluidized bed combusto
r, are presented in time domain {x(t), t}, phase

space trajectory
{x(t), y(t)}, delay return map {x(t), x(t+k)}, or mutual information map { R
xy
(
τ), τ
}or
{ R
xy
(
τ), x(t)
}. The measurements are tested by correlation integral tests,
3
In a circulating fluidi
zed bed, flow increase varies rarefication in solid fuels
and pressure frequency changes in a pipe; gradual changes (drifts) and step changes
are recorded and classified (i.e. related to bed states).
High speed measurements of pressure drop and particle
motion
COMBUSTION and CHAOS:
Flame signals produce what is called
deterministic chaos (i.e. non random chaos) from which we can extract a wide range
of useful information, in order to increase reliability.
CHAOTIC CONTROL of FLUIDIZED BEDS:
Hydrody
namics of
fluidized beds are chaotic. They determine the performance of the fluidized bed
reactor (mass transfe / reaction); for instance the average bubble size of gas bubbles in
the bed could be reduced, the bypass of the solids reduces, resulting in a h
igher
conversion.
Since FB are chaotic systems, they have the general characteristics of chaotic
systems, i.e. they are deterministic nonlinear systems, showing irregular (almost
random) behavio; it is impossible to make long term predictions of the syste
m
development because these are extremely sensitive to initial conditions or external
perurbations. However, short term predictions are possible and the sensitivity to
control actions can be exploited by a chaos controller. Such a controller can change
the
system behavior completely at the cost of only very small control actions. This
chaos control idea (1990) has not been applied to complex systems yet. To obtain
experience with chaos control algorithms, a simple experimental chaotic pendulum
(forced by a
n electromotor periodically) is studied. After a transient time, e.g. 100 s,
the control suppresses the chaotic behavior. The contol algorithms developed for the
pendulum are tried in a small (4 cm diameter x 20 cm height) fluidized bed to prevent
slugging
(a very undesired flow regime). Slugging can be reduced when a small
fraction of the gasfeed is injected above the gas distributor.
CHAOS IMPROVES CHEMICAL PERFORMANCE:
Chaotic features and
dynamic performance in small and large reactors, with bubbles g
iving poor mass transfer in a
catalytic reaction, high reactant gas transfer resistance, high rise velocity of the bubbles and
lower reaction results (i.e. reactant gas bypass) than other conventional reactors with the same
contact time. We control bubble
size and reaction system selectivity, including the hydro

dynamics, i.e. chaos control, leading to smaller bubbles, i.e. less reactant gas bypass.
conversion
1
0.8
0.6
0.4
0.2
0.0
0
2
4
6
8
10
bubblesize (cm)
4
Fig. . Calculated conversion as function of bubble size for a model reaction
PRESSURE FLUCTUATIONS:
Hydrodynamic conditions in a hot bubbling
fluidized bed (BFB) combustor and a cold BFB model, i.e. the effect of the loaded solids above
the L

valve o
n the flow rate, the origin of pressure fluctuations in both laboratory and industrial
scale boilers. The hydrodymanic similitude in bubbl
ing fluidized beds (600 μ round sand, fired
with natural gas to 725
o
C, with 150 μ diameter round copper particles) is matched by
dimensionless parameter D/d
p
, or a dimensionless . solids loading to the riser. The height of
solids above the L

valve (under
conditions of varied particle diameter, density and L

valve
aeration rates) affects the flow rate of solids through the L

valve and into the circulating
fluidized bed.
CHAOTIC FLOW:
The simplest chaot
ic flow is defined by:
dx
dt
y
dy
dt
z
dz
dt
x
y
A
z
where
A
x
A
x
x
x
2
2
2
0168
2
0577
0
.
.
.
.
Air

fuel mixing occurs in all combustion phenomena and industrial processes. The
quantitative modeling of mixing efficiency is a fundamental prerequisite for the
correct design and scale

up of chemical reacto
rs. Chaotic nature of mixing induced by
stretching and folding dynamics supported by the local mechanisms (micro

mixing),
results in the existence of KAM surfaces, intrinsic local instability, topological
transitivity within an invariant manifold u (the ch
aotic manifold), local exponential
divergence of nearby trajectories within u, which are analogous to those of non

integrable area preserving (Hamiltonian) systems; these phenomena have been
observed in many different systems (stirred tank reactors at low
Reynolds number
(Re<500), periodically excited closed flows such as cavity flow, or the flow within
two eccentric cylinders, static industrial mixers, open flow systems (the vortex

pair
flow) and can be simulated quantitatively by means of much simpler mo
del flow.
By quantitative description of mixing performances at low Reynolds numbers,
we define an infinitesimal vector l, evolved by:
dx
dt
v
dl
dt
l
v
l
l
t
t
,
.
,
0
0
5
where x is the position vector of the passive particle and v the velocity
,
the
l
l
0
stretching, giving the kinematic analysis of mixing. For real systems, the velocity field
v is not known (and should be calculated). For simple two dimensional systems (e.g.
cavity flow, the fluid dynamic reduces to the solution of the vorticity
ω
stream
function
ψ
equations,
2
2
0
,
while for more complex flows (e.g. in
the case of real static mixers) CFD is needed. A simpler discrete model given by the
sine flow corresponding to a veloocity field described by:
v
v
v
x
L
n
T
t
n
T
v
v
y
L
v
n
T
t
n
T
x
y
x
y
0
2
2
2
1
2
0
2
1
2
2
0
0
.sin
.
(
)
(
)
.sin
.
(
)
(
)
which is a periodic flow with periodic boundary conditions, and T is its half period.
The corresponding Poincare section, in dimensionless coordinates, (stroboscopic map
at t = 2.n.T) is given by:
x
x
T
f
y
T
f
x
y
y
T
f
x
n
n
n
n
n
n
n
1
1
.
.
(
.
(
)
)
where
f(x) = sin(2
π
x)
. The c
haotic nature of the flow induces loss of information in
the analysis of reaction/diffusion/advection equations, especially to local approximate
models (lamellar models associated with a quenched distribution of lamellae), which
may be disappear as a conse
quence of infinitely fast reaction, giving an iterated multi

fractal model; we want to deal with the practical case of high Peclet numbers Pe
>10
4
.
Experimentally tracer gas measurements (He) and mass spectrometer He
concentration measurements, for veloc
ities 1.2

4.3 m/s and silica sand (0.32 mm) as
bed material were carried out.
FLUIDIZED BED GASIFIER CONTROL:
Generating simple linear
models from simple data and using the model for impoved control results in improved
operation of the gasifier, leadin
g to multivariable control strategy.
In the
servo mode
, the control system must adjust the reactor input variables so
that the reactor output meets operational objectives, such as no clinkering, high carbon
conversion, meet targeted gas make and bed densi
ty, high gas heating value, meet
targeted fuel/non

combustible mole ratio and mean bed temperature and maintain
HOC balances inventories.
In the
regulatory mode,
all these objectives and more are considered by
operators during gasifier operation. All inl
et gas flow rates are flow controlled with
simple PID type controllers, gasifier backpressure is controlled via a split range
controller, and MGCR pressure is controlled via a PID controller. The backpressure
control is critical to steady operation of the
gasifier, as fluctuations in backpressure
impact inlet gas flowrates and bed density.
FRACTALS:
In the attempt to study and simulate (by virtual reality) the
fluidized bed, fractals are produced by using a initiating signal (shape) and a fractal
generato
r (signal). In fluidized bed case the initiating shape is the bed’s conditions
(shape, loading, fuel, etc) and the fractal generator is the agitating air/gas stream
and/or the released heat. This is in close conformity with the universal speculation,
6
that
the morphology of systems and organisms have a fractal

like appearance and their
shape (or operation) is encoded according to fractal generators. Fractals allow the
storage of large number of data as mathematical formulae, achieving very high
compression r
atios (over 100:1).
The bed dynamics is a noisy but low

dimensional nonlinear (periodic and
regular) oscillator that undergoes transitions (including slugging), involving a fixed
point, i.e. two limit cycles and chaotic motion. Plots of sequential windows
of signals
(T
i
, T
i+1
, T
i+2
) reveal dynamic structure in slugging sequences, by progressing from
disordered oscillations to noisy limit cycles, see fig. . The stable state corresponds
to:
1
16
1
55
.
.
U
U
mf
T
i
T
i+1
T
i+1
T
i+1
Fig. . Chaotic curves in 2D phase domain (3D projections)
Fractal is a set which is self

similar under magnification; they can be magnified
infi
nitely and expressed mathematically with small sets of data; they are structures
possessing similar

looking forms of many different sizes, extensions of classical
Euclidean shapes. Fluidized bed turbulence under certain conditions could be
considered a fra
ctal image. By the periodic

doubling route to chaos, we access chaotic
7
behavior by doubling the velocity profile peaks, i.e. by flow pulsation, or by
momentary perturbations (short burst) to achieve large scale changes in slugging
patterns in order to enha
nce or disrupt slug formation. 15 % duty cycle pulse, just after
the rising crossing of the pressure variation, drives the solenoid, see fig. , injecting
5% of total bed gas flow. Optimal parameters for bed operating conditions is acquired
by a an expert
monitoring, or manually. Fractal transform expresses mathematically
any real world image, i.e. the fluidized bed condition and substitutes the limited
resolution (detail) pixel

by

pixel (color intensity) photography; this is the so

called
Fractal Image For
mat (FIF) that is resolution independent and consists of domain and
range blocks.
Fig. . Slugging in fluidized bed
CONCLUSIONS:
All the above signals characteristic parameters correspond to
chaotic indices in fluidized b
ed combustor characterization, that assist us in
characterizing states and conditions of the fluidized bed, control it more efficiently in
combustion or heat treatment (circulating) applications. The bed is sensitive to small
perturbations in air flow that
alter the bed behavior, leading to sophisticated control
algorithms that achieve better control results, more economically (in terms of bed
operation and combustion efficiency).
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