drag coefficient of solid recovered fuels (srf)
TRANSCRIPT
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Short communication
Drag coefficient of Solid Recovered Fuels (SRF)
Gregory Dunnu *, Jörg Maier, Uwe Schnell, Günter Scheffknecht
Institute of Combustion and Power Plant Technology – IFK, University of Stuttgart, Pfaffenwaldring 23, 70569 Stuttgart, Germany
a r t i c l e i n f o
Article history:
Received 18 May 2010
Received in revised form 16 June 2010Accepted 24 June 2010
Available online 6 July 2010
Keywords:
Solid Recovered Fuels
Numerical simulation
Drag coefficient
Co-combustion
a b s t r a c t
The numerical simulation of Solid Recovered Fuels (SRF) co-combustion in pulverised coal power plants
requires a flexible particle model, which among other properties should be able to predict the aerody-
namic behaviour of the irregular-shaped particles, especially their trajectories along the boiler axis. Thiswill help to provide vital information on whether the SRF particles are entrained in the combustion gases
or drop to the boiler bottom. One difficulty encountered in the process is the true value of the drag coef-
ficient (C D) of the coarse SRF particles. Most of the numerical simulation codes calculate the particle tra-
jectories by integrating the force balance of the particles in which the C D plays an important role. As a
result, a true C D of SRF will definitely lead to more realistic results.
In this short communication, the authors have taken a practical approach in determining the C D of the
SRF. It was found that within the Newton’s law range the C D of the SRF lies between 0.6 and 2.0 with a
mean value of 1.5. The results were further validated by correlating the calculated lift velocities of SRF
using different C D values and that obtained through experiment.
Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction
The numerical simulation of Solid Recovered Fuels (SRF) co-
combustion in pulverised coal power plants based on numerical
calculations requires a flexible particle model, which should be
able to predict:
1. Species and gas phase reactions,
2. mass transfer, and
3. the aerodynamic behaviour of the irregular-shaped particles,
especially their trajectories along the boiler axis.
The latter will help provide vital information on whether the
SRF, which are generally coarse particles, are entrained in the com-
bustion gases or fall to the boiler bottom. One difficulty encoun-
tered in the process is the true value of the drag coefficient of
such fuel particles. Most of the numerical simulation codes calcu-
late the particle trajectories by integrating the force balance of the
particles in which the C D plays an important role. As a result, a true
C D of SRF will definitely lead to more realistic results.
In comparison to SRF, the particle sizes of coal dust are in the
micron range and their form can be approximated to be spherical.
Hence in numerical calculations their aerodynamic behaviour can
be approximated by that of spheres. Unlike coal dust, SRF derived
from municipal solid waste (MSW) are coarser with particle sizes
in the range of centimetres. They are loose, fluffy and of course
their aerodynamic behaviour cannot be approximated to that of spheres. In this research work the authors have taken practical
steps to determine the aerodynamic properties of SRF, namely
the effective particle diameter and the C D of the particles. The re-
sults of the research work concerning the effective diameter have
been discussed elsewhere [1], therefore this paper will only deal
with the drag coefficient of SRF particles.
SRF is produced in special waste treatment facilities operated
by both private and public companies. Input materials are munici-
pal waste streams and production residues. Also included are pack-
aging materials, paper/cardboard and textiles. The common
process technologies used are:
Mechanical processing in order to separate the high-calorific
fraction and to remove unwanted components (e.g. PVC), and
mechanical–biological treatment plants with process-inte-
grated separation and processing of high-calorific fractions.
Depending on the production line, the SRF products are mainly
produced as bales, fluff, soft or hard pellets. Wastes suitable for the
production of SRF are defined according to the waste catalogue and
the Commission Decision 2000/532/EC1. According to the waste
categories, the input materials can be separated in five main groups:
0016-2361/$ - see front matterÓ 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.fuel.2010.06.039
* Corresponding author. Tel.: +49 71168563750; fax: +49 711 685 63491.
E-mail addresses: [email protected] , [email protected].
de (G. Dunnu).
1 Decision (2000/532/EC) has subsequently been amended by Commission Decision
2001/118/EC of 16 January 2001, Commission Decision 2001/119/EC of 22 January
2001 and Commission Decision 2001/573/EC 23 July 2001.
Fuel 89 (2010) 4053–4057
Contents lists available at ScienceDirect
Fuel
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / f u e l
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1. Wood, paper, cardboard and cardboard boxes,
2. textiles and fibres,
3. plastics and rubber,
4. other materials (e.g. waste ink, used absorbers, spent activated
carbon), and
5. High-Calorific Fractions – HCF from non-hazardous mixed col-
lected wastes.
The SRF used in this study is pictured in Fig. 1 together with its
percentage weight compositions. It is made of high-calorific frac-
tion (HCF) derived from municipal solid waste (MSW). The particle
sizes range between 3 mm and 25 mm with a d50 of 9.8 mm.
2. Experiments
2.1. Determination of aerodynamic lift velocity (ALV) of SRF particles
The ALV depicts a characteristic parameter that is used to de-
scribe the ability of the SRF to be fully suspended in a gas stream.
It is determined at room temperature and later corrected to flue
gas conditions. This parameter gives an estimated value of the
essential gas stream velocity needed to prevent the SRF particles
from falling to the bottom ash hopper before they are completely
burned. The experimental set-up built to determine the ALV of
the SRF particles is shown in Fig. 2. It consists of a 1000 mm fall
column with a wire mesh mounted at 500 mm. SRF particles are
dropped on the mesh one after the other and the air flow rate
needed to just lift it is recorded. With this set-up the ALV of a par-
ticle is measured as the velocity of air in the fall column that is
needed to create the lift force necessary to just suspend a particle
above the mesh. The results obtained under laboratory conditions
are transferred to a real boiler after correlating them to the existing
conditions in the boiler. The formula [2] linking the two conditions
is derived as:
ALVFG ¼ ALVmeasured ffiffiffiffiffiffiffiffiqf
qFGr ð1Þ
where qf is the density of air, and qFG is the density of flue gas (FG).
The theoretical model of the set-up is developed based on Rey-
nolds number calculations. Considering the balance of forces acting
on a suspended particle in a fluid, the forces of buoyancy, drag and
gravity acting on it are summarized as:
gravity À buoyancy À drag ¼ accelerationforce ð2Þ
At equilibrium position, Eq. (2) becomes:
pd3 p
6ðq p À q f Þ g À C DðReÞ
1
2q f
ALV2
f 2w
pd2 p
4¼ 0 ð3Þ
thus leading to the following expression for the drag coefficient:
C DðReÞ ¼4
3f
2w
gdp
ALV2
ðqp À qf Þ
qf
;
Newton’s law region ð500 < Re < 2 Â 105
Þ ð4Þ
Here qf is the air density, qA is the particle density, dP is the
equivalent circle diameter, C D (Re) is the drag coefficient, ALV is
the aerodynamic lift velocity and f w is the wall factor correction,
calculated using Eq. (5).
Munroe f w ¼ 1 Àdp
D
1:5
; 1036 Rep 6 10
4; 0:1 6 dp=D 6 0:8
ð5Þ
The introduction of f w is based on the fact that when the diam-
eter of a settling particle is significant compared to the diameter of
the fall column (D), the settling velocity is reduced. The effect of
boundaries on terminal velocity is corrected using the correlation
preferred by Munroe [3]. This was selected because most of the cal-
culated Re of the SRF particles and the ratio of particle diameter to
diameter of the fall column lies within the limits of this equation.
2.2. Particle size measurements using image analysis method
The dp of the SRF were determined using particle image analysis
method (PIAM), here the maximum projected area of the individ-
ual particles are extracted from digital photographs. Earlier re-
search (1) has shown that particle size measurement using this
method gives data that captures the aerodynamic properties of
the particles. This is supported by the fact that particles fall with
their maximum projection area perpendicular to the direction of
fall, and a size measure representing this maximum projection area
is most likely to relate to behavioural (aerodynamic) properties [4].
An illustration to demonstrate this phenomenon is for e.g. when a
piece of paper is falling, it will almost and always fall with the larg-
est surface facing the direction of fall. In view of this the ability to
describe precisely the largest projected area of a particle will im-
mensely help in any modelling of particle trajectories in boilersand industrial furnaces. Validation work on this method has previ-
ously been published by the authors [1]. The equivalent circle
diameter (dp) is then calculated using Eq. (6). Fig. 3 illustrates
the principle of measurement.
The characteristic parameter (dp) is defined as the diameter of a
circle with the same area as the maximum projection of a particle,
computed as:
dp ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4 Â Maximum Projection Area
p
r ð6Þ
In comparisons, sieve analysis which is the most commonly
used method for particle size analysis has been shown to be
unsuitable for detailed analysis of SRF particles. The reasons are
Fig. 1. SRF derived from HCF of MSW and its compositions in weight percent.
4054 G. Dunnu et al. / Fuel 89 (2010) 4053–4057
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that SRF are characterized by very heterogeneous mixtures, fluffy
materials, and variable particle densities. They entangle each other
and agglomerate during sieving. Particles can wrongly be classified
simply by the orientation of which they approach the sieve aper-
ture, thus slipping through the sieve when the shortest sides of
the particles are correctly aligned to the sieve opening. A funda-
mental difference between the two methods is that, particle sizes
determined by PIAM capture more of the aerodynamic properties
than when sieve analysis is used. In this respect, PIAM was used
to determine the aerodynamic diameters as a function of the max-
imum projected area of the SRF particles.
3. Results and discussions
3.1. The drag coefficient of SRF
The drag coefficients for the individual SRF particles were deter-
mined using Eq. (4). The results show that the C D values for theloose SRF fractions effectively lie between 0.6 and 2.0 with a mean
value of 1.5 in the Newton’s law region. In Fig. 4, a scatter plot of
the results as a function of Reynolds numbers is shown. It is ob-
served that C D is independent of the Reynolds number in this
region.
In comparisons, the data published by Lapple and Shepherd [5]
for cylinders and disc-shaped objects shown in Fig. 5 show that thedrag coefficients of both shapes in the Newton’s law range are also
independent of the Reynolds number, and the magnitude is about
twice as high compared to spheres. In their research, cylinders and
disc-shaped objects were defined as follows;
– cylinder defined as object with infinite length with axis perpen-
dicular to the direction of motion, and
– disc-shaped defined as objects with flat side perpendicular to the
direction of motion.
The fractions found in SRF, namely paper, plastic-foils, and tex-
tiles, can be described as loose, flat, and fluffy objects. Their aero-
dynamic behaviour can be linked to that of disc-shaped
materials, hence the C D of SRF were compared with that of disc-
shaped materials as published in literature. In the Newton’s lawrange, the drag coefficient of cylinders and disc-shaped objects
stays constant. After superimposing the results, the hatched area
indicated in Fig. 5 shows the values of SRF and that of Lapple and
Shepherd Fig. 5. It can be seen that both are found in the same
vicinity. In view of this, the approximation of the aerodynamic
behaviour of SRF to that of disc-shaped objects is a plausible
assumption.
Additional validation is performed by correlating the experi-
mental and theoretical results in two scenarios. First using a C D of
1.5, and secondusinga C D of 0.5to calculatethe ALV. Fig. 6a,b shows
the correlation between ALV of several single particles calculated
using Eq. (4) with drag coefficients of 1.5 and 0.5 and experimental
results. The ideal line is a reference with gradient unity. It repre-
sents the case where the experimental values are the same as thetheoretic values. Comparing the reference line to the other lines
Fig. 2. Set-up to determine the aerodynamic lift velocity (ALV) of SRF particles [2].
L
B
P
A circle with area equal to the
projected area of particle P
dp
Key
L: Major Axis Length P: Maximum projection area of a particle
B: Minor axis length dp: Equivalent circle diameter
Fig. 3. Measurement principle of image analysis method for particle size analysis.
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reveals that the ALV calculated using a C D value of 1.5 provides the
best correlation between theoretic and experimental values. The
gradients of the lines arecloser to the referenceline than those esti-
mated using C D = 0.5. Moreover, the lines with PIAM data2 show a
much better correlation between experimental values and theoreti-
cal values than those with sieve analysis data3. These comparisons
clearly confirm that the C D of SRF estimated to be 1.5 can be used
for calculations with higher accuracy. The correlations also showed
Fig. 4. Drag coefficient of SRF as a function of Reynolds number.
Sieve analysis data used
y = 1,94x
R2 = 0.7
PIAM data usedy = 0,96x
R2 = 0.7
Ideal
y = x
R2
= 1
0
1
2
3
4
5
6
7
0.0 0.5 1.0 1.5 2.0 2.5 3.0
ALV (experiment), m/s ALV (experiment), m/s
Sieve analysis data used
y = 3.53x
R2 = 0.6 PIAM data used
y = 1.35x
R2 = 0.6
Ideal
y = x
R2 = 1
0
1
2
3
4
5
6
7
0.0 0.5 1.0 1.5 2.0 2.5 3.0
A L V
( c a l c u l a t e d ) , m / s
A L V
( c a l c u l a t e d ) , m / s
(a) ALV calculated with C D = 1.5 (b) ALV calculated with C D = 0.5 [1]
Fig. 6. Comparison of ALV using different C D values.
2 PIAM data means particle sizes determined by particle image analysis. 3 Sieve analysis data means particle sizes determined by sieve analysis.
Fig. 5. C D of spheres, disks, cylinders, and SRF. Source: Perry’s Chemical Engineers’ Handbook 7th Ed. (Original: Lapple and Shepherd, Ind. Eng. Chem.,1940, 32, 605 [5]).
4056 G. Dunnu et al. / Fuel 89 (2010) 4053–4057
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significant differences in results between particle size data derived
from sieve analysis method and PIAM.
3.2. Effect of combustion on C D
Three main factors determine the drag of burning solid particles
[6]:
1. The mass transfer due to the combustion process,
2. Temperature gradient between particle and ambient medium,
and
3. Surface and volumetric reactions on the particle and in its
boundary layer.
The influences of the above factors on the particle drag differ
widely. For example, mass transfer leads to thickening of the
boundary layer and reduction of the drag coefficient, whereas tem-
perature difference between particle and medium affects mainly
the variation of the physical properties of the fluid. Irrespective
of this, several researches have shown contrary views.
Experimental investigations of the drag of a burning particle
(coal, charcoal, coke) published by Babii and Kuvaev [7] over a
wide ranges of particle diameters, oxygen concentration and initial
ambient temperatures: 0.1 < d < 15 mm, 0.21 < C < 100%, 300 < T <
1400 K, have shown that the drag coefficient of burning particles
is larger than that of non-burning ones in the Stokes’ law and inter-
mediate region, but unaffected in the Newton’s law region. Con-
trary, the data published by Ogasawara et al. [8] concerning the
drag coefficient of a burning cylindrical and spherical particles
(cylinder, d = 3.52 mm; spheres, d = 9.7 mm) showed significant
differences between burning and non-burning particles, with burn-
ing particles having a reduced drag coefficient of up to 30% and 40%
for cylinders and spheres, respectively.
The drag coefficients of different fractions found in the SRF
might not remained unchanged during combustion. Therefore,
consideration should be given especially to the non-char bear-
ing particles like plastics in numerical calculations. In this case,
their form and drag rapidly changes. As such the appropriate
assumptions and boundary conditions should be outlined con-
cerning individual non-char bearing fractions of the SRF and
how their drag coefficients might vary in the combustion
process.
4. Conclusions
It has been shown in this work that the aerodynamic parame-
ters, namely the drag coefficient and the lift velocity of SRF parti-
cles are essential inputs to the overall aerodynamic behaviour.
The results showed that the drag coefficients of SRF particles with-
in the Newton’s law region have values which range between 0.6
and 2 with a mean of 1.5. The mean value was a very good input
in the estimation of the aerodynamic lift velocity SRF using Rey-
nolds number based calculation.
References
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[2] Dunnu G, Maier J, Hilber T, Scheffknecht G. Characterisation of large solidrecovered fuel particles for direct co-firing in large PF power plants. Fuel, 2009.doi:10.1016/j.fuel.2009.03.004.
[3] Munroe HS. Trans AIMME, 1888–1889, 17. 637–657.[4] Sneed ED, Folk RL. Pebbles in the Lower Colorado river, Texas, a study in particle
morphogenesis. J Geol 1958;66:114–50.[5] Lapple CE, Shepherd CB. Calculation of particle trajectories. Ind Eng Chem
1940;32.[6] Yarin LP, Hetsroni G. Combustion of two-phase reactive media. 2004, ISBN 3-
540-40339-6,1–45.[7] Babii VI, Kuvaev JaF. Combustion of coal dust and coal dust flame calculation (in
Russian). Energoatomizdat, 1986, Moscow.[8] Ogasawara M, Adachi T, Yashiki T. Study of the drag of cylinder and sphere with
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