Engineering, 2010, 2, 353-359
doi:10.4236/eng.2010.25046 Published Online May 2010 (http://www.SciRP.org/journal/eng)
353
Structural Analysis and Optimal Design for Water Tube
Panel in an Alkali Recovery Boiler
Zaili Zhao1, Jinsheng Xiao2,3, Ying Wu4, Xiaojun Zhang1, Zhiming Wang4
1School of Energy and Power Engineering, Wuhan University of Technology, Wuhan, China
2School of Automobile Engineering, Wuhan University of Technology, Wuhan, China
3State Key Laboratory of Advanced Technology for Materials Synthesis and Processing,
Wuhan University of Technology, Wuhan, China
4Wuhan Lanxiang Energy & Environment Protection Technology Co. Ltd., Wuhan, China
Received December 7, 2009; revised February 22, 2010; accepted February 26, 2010
Abstract
Alkali recovery aiming at recovering NaOH is the best available technology in China's pulp and paper indus-
try; an alkali recovery boiler is a popular one among all alkali recovery units. For the purpose of designing
the most reasonable tube-panel of an evaporator in a 1500 t/d alkali recovery boiler, a total of 8 kinds of
cases are put forward for finite element analysis. The modeling, meshing and calculation are carried out for
each case. The stress values and their distribution rules are revealed in this paper. The slotting size for the
water tubes panel is analyzed by using the optimum design module of ANSYS. After all cases are compared
with each other, the optimal one is developed and exemplified in conclusion.
Keywords: Alkali Recovery Boiler, Water Tubes Panel, Finite Element, Thermal Stress, Optimum Design
1. Introduction
Alkali recovery is the best available and the most eco-
nomically viable technology for black liquor (BL) from
caustic pulping, the predominant process in China (over
70%). It can remove most of the COD load, and at the
same time recover chemicals and heat to such a great
amount that it makes itself economically feasible [1]. So
the alkali recovery which includes the processes of BL
evaporation, combustion, green-liquid causticizing and
alkali recovery represents an important economic and
ecological factor. There are varieties of alkali recovery
units which have been using in China's pulp and paper
industry at present; the alkali recovery boiler is a most
popular one.
The boiler studied by us is a single drum, natural cir-
culation, low odor type alkali recovery boiler. With
whole steel, full suspension and full-sealed structure, the
gravity of the boiler is withstood by a roof through a
boom. The principle of the alkali recovery boiler is that
waste water (commonly known as BL) which is dis-
charged after making paper is concentrated as fuel,
which is put into the boiler for combustion. Then liquid
slag, which is the burning resultant of BL, is discharged
from the bottom and recovered into alkali after a causti-
cizing process. Alkali recovery boilers are used by paper
mills for not only recovering alkali produced by making
paper but also generating heat and electricity. Conse-
quently, the purposes of recycling, energy conservation
and reducing pollution are achieved. The alkali recovery
boiler was originally designed to deal with waste water
generated by pulp and recycle cooking alkali, but there
are three effect factors for the current alkali recovery
boiler: to generate steam by burning organic matter in
BL; to generate a green solution for causticizing, reduc-
tion of pollutant emission, energy-saving and environ-
mental protection [2].
The difference between model WGZ220/6.8-1 1500
t/d alkali recovery boiler [3] and other similar boilers that
have already come into use is that, compared with the
latter the size of the water tubes panel of alkali recovery
boiler in length is extended to somewhat, and the most
noticeable difference is that the temperature difference
between inlets and outlets of exhaust gas tube rises in a
wide range, causing the thermal stress of the tube panel
to increase [4]. Therefore structural optimal analysis and
safety assessment are quite important for the water tubes
panel of evaporators in the boiler.
In order that the boilers are in good condition during
long time operation, that there is low stress in stress

Z. L. ZHAO ET AL. 354
concentration parts of boilers (in places such as the
welding seam between the tubes and fins), that the boil-
ers consume fewer materials, and that they are produced
and manufactured easily, the structure of the water tubes
panel should receive much more attention in design [5].
Generally, there are lots of analytic methods used to
carry out structural analysis and optimal design, but a
finite element method is a most efficient one [6]. There-
fore the finite element method is used to analyze the first
stage boiler’s evaporator in this paper. Eight kinds of
different three-dimensional models for the water tubes
panel of the evaporator are proposed and calculated with
ANSYS software for getting optimal construction. The
optimizing design for obtaining smallest stress of the
tube panel is made by analyzing and comparing the stress
fields among the 8 kinds of models, and one kind of
models is calculated by using the optimized design mod-
ule of ANSYS software.
2. Analytic Models and Cases
2.1. Geometry Model
The water tubes panels with a vertical structure which
are in membrane type are all hung up to the framework
roof through the suspending plate. Each sheet is made up
of 22 pieces of Ø42 × 5 tubes through a welding method,
and there are fins between the tubes for increasing heat
transfer. The distance between two adjacent tubes is
111.5 mm, and all tubes are connected respectively to the
upper and lower header. Totally 55 pieces of upper
headers together with their water tubes panel are con-
nected to the general header with a bend, as shown in
Figure1.
2.2. Finite Element Model
In order to calculate and analyze the temperature and
stress fields of water tubes panel conveniently, the
three-dimensional models set up in the paper have been
Figure 1. The upper tube panel and headers.
simplified as follows [7]:
1) Only a quarter of the whole evaporator is put into
research due to its structural symmetry;
2) The welding seams between upper headers and
general header are modeled according to their actual di-
mensions. The welding seams between lower headers
and panel tubes have not been taken into account in
modeling because of their small size, and consequently
calculation is easy. Other small welding seams are to be
dealt with similarly;
3) Heat-conducting fins are mounted at the locations
which are between every two adjacent tubes in order to
increase the heat transfer from the exhaust gas to the
water. Only one tube panel is taken into account in mod-
eling because of the same size, material of tubes and fins
in each panel. There are locating pins between the panels
for locating and separating each panels, and it is not con-
sidered for simplifying model;
4) The upper headers are not restricted by the upper
general header due to their flexible link, and it is as-
sumed that the upper headers are in symmetrical struc-
ture.
The model of the tube panel and its meshing illustra-
tion are established as shown in Figure 2 after above
simplification. The three-dimensional and 8 nodal SOLID
70 element type is adopted in modeling when tempera-
ture field are calculated. The total elements and nodal
numbers are 44350 and 70534 respectively in the model
of a tube panel. The element type of SOLID 45 is
adopted for stress field calculation [8].
In Figure 2(a), there are fins between the tubes; their
structural parameters such as thickness of fins, the length
of slotting and round radius of the slotting end needs to
be chosen and decided in the paper. There is a heat-
conducting fin with large width which is located between
the 11th and 12th tubes on the panels, and it is called a
middle plate. The middle plate can be designed in a
whole or several pieces type according to different cases
for stress calculating. The meshing of the tube panel
model near the bottom of the suspending plate is shown
in Figure 2(b).
2.3. The Eight Analytic Cases
In order to find out the distribution rules and try to make
sure that the stress of water tubes panel is minimum, the
designs with different parameters, such as the fin thick-
ness, the slotting size on the fins and the shapes of the
middle plates should be compared with each other and
analyzed. Therefore, a total of 8 kinds of cases for the
water tubes panel of the first stage evaporator in the pa-
per were proposed. The slotting on the fins contributes is
used for reducing the thermal stress in some cases. The
slotting size is decided by optimum design module of
ANSYS. The detail features and description of them are
shown in Table 1.

Z. L. ZHAO ET AL. 355
1 2 3 4 5 6 7 8 9 10 11
fin middle plate
slotting
(a) Upper tube panel (b) Amplified suspending plate
Figure 2. Modeling and meshing.
Table 1. Descriptions for all cases.
Cases Descriptions
A Fins are not slotted, and the middle plate is taken as an entire plate.
B Fins are not slotted, and the middle plate is cut into four pieces. The length of each one is 600 mm.
C Fins are slotted, but slotting is not staggered , and the description of middle plate is the same as case B.
D Only fins between the 9th and 11th tubes are slotted, and the description of middle plate is the same as case B.
E Fins are slotted, slotting is staggered , and the description of middle plate is the same as case B.
F Fins are slotted at the upper and lower part, but slotting is not staggered. Fins are slotted at the middle part, and slotting is
staggered. The middle plate is cut into four pieces. The length of each one is 300 mm.
G Fins are not slotted, and there is no middle plate.
H Fins are slotted, but there is no middle plate.
3. Structural Parameters & Boundary
Conditions
3.1. Structural Parameters
The structural parameters of the tube panel for the first
stage evaporator are shown in Table 2 [9].
3.2. Boundary Conditions
The thermal boundary conditions in the evaporator are
shown in Table 3 [10].
According to Table 3, the inlet temperature of the ex-
haust gas is 548.7 and the outlet temperature is 378 ℃℃.
The water temperature (295.3) inside tubes is r℃egarded
as saturation temperature corresponding to design pres-
sure in the boiler drum. When models established by us
are calculated by ANSYS software, the value of water
pressure is a constant, about 8.15 MPa (it is a design
pressure in the boiler drum according to Table 2). The
heat transfer coefficient of water and exhaust gas are
5180 and 19.13 W/(m2) respectively℃ [6]. Exhaust gas
temperatures at inlet and outlet which are at design val-
ues are used for calculation. When exhaust gas flows
from the top to the bottom of the tube panel, its tempera-
ture will decrease gradually, so the thermal load or tem-
perature applied to the tube panel walls is linear and its
inlet and outlet temperatures are accordant with Table 3.
According to the geometry characteristic of model, the
Cartesian coordinate system is adopted, with Z-axis
standing for the tubes’ axial direction and the positive
direction pointing to the upper headers [11]. The axial
direction of upper headers is taken as the X direction,

Z. L. ZHAO ET AL. 356
Table 2. Structural parameters of a tube panel.
Parameters Value
Rated evaporation capacity 220 t/h
Rated steam temperature 480 ℃
Heat transfer coefficient 19.13W/(m2 ) ℃
Tube-sheets numbers 55
Tube NOS. in each tube panels 22
Length × width (the first row) 22000×2590 mm2
Length × width (the next row) 22300×2590 mm2
Distance between two tube panels 180 mm
Width of middle plate 111.5mm
Rated steam pressure 6.8MPa
Designed steam pressure 8.15MPa
Size of upper headers Ø 108 mm×12 mm
Size of lower headers Ø 76 mm ×8 mm
Size of upper general headers Ø273 mm×25 mm
Tube material 20G/GB5310-1995
Materials of fins Q235- A
Inner diameter of the tubes 16 mm
Table 3. Thermal boundary conditions.
Inlet tem-
peratures
(℃)
Outlet tem-
peratures
(℃)
Heat transfer
coefficients
W/(m2℃)
Exhaust gas 548.7 378 19.13
Water 295.3 295.3 5180.0
and the direction from middle plates to the left sus-
pending plate is taken as the positive direction. Y posi-
tive direction is decided by X and Z axis according to the
right hand rule.
Because the evaporator’s vertical-horizontal length
ratio is too great, only the upper model of the tube panel
is shown in Figure3. The panel model is symmetrical in
positions of C and D as shown in Figure 3, so symmet-
rical constraints are applied to the two positions. The X
direction constraint is applied to section A, i.e. UX in
ANSYS. The displacement boundary condition (s
u

0)u and stress boundary condition (0
C B A
D
Figure3. Constraints on a tube sheet.
4. Structural Analysis and Optimization
4.1. Optimization for Structural Parameters of
the Water Tubes Panel
In order to ascertain whether the slotting parameters on
water tubes panel are correct or not, the optimized calcu-
lation is carried out by using ANSYS software; and the
results calculated to case D are shown in Figure 4.
In Figure 4 (a), the Y-coordinate stands for the maxi-
mum of Von Mises Stress; the X-coordinate stands for
the Set Number of iteration [13]. For each set number,
there is a set of parameters such as B, R and L. B repre-
sents the thickness of the fins, R represents the round
radius of the slotting end, and L represents the slotting
length.
In Figure 4 (a), straight line 1 stands for stress setting
value, and curve 2 stands for stress which is calculated
by using ANSYS software [14]. After careful observa-
tion for curves in Figure 4 (a), the curve 2 is found
higher than line 1 when Set Number is bigger than 7, so
the SET above 7 cannot be regarded as design parame-
ters. In Figure 4 (b), the numbers of curve 3 below SET
5 will cause more volume or weight to be taken. By
comparing the results in Figure 4 (a) and (b), the num-
ber of SET 7 is chosen as the optimum one. Thus we can
get the optimal B, L and R, i. e. B = 3.0814, L = 696.22
and R = 5.0937.
The results show that the slotting sizes B, L and R
adopted in case D are reasonable. As for other cases,
structural optimization is also carried out for checking
the parameters of the water tubes panel.
yz Z



s
w
)
in the Z-direction are apparent. The vertical constraint
is applied to positions of B which is on top of the sus-
pending plate of the upper header, i.e. UZ in ANSYS
[12]. Its displacement boundary condition is

0uand its stress boundary condition is 0X
4.2. Structural Analysis and Optimization for
Different Cases

xy

in the X-direction. The overall weight is withstood by
two suspending plates, so the water tubes panel can
freely expand in any direction except the upward one.
In order to compare the stress in 8 kinds of cases with
each other, the tube stress in different cases is shown in
Figure 5. The Y-coordinate stands for Von Mises Stress
(σe); the X-coordinate stands for pipe number from the

Z. L. ZHAO ET AL. 357
left side to the middle plate; the tube serial number can
be seen in Figure 2(a). Curve A stands for case A, Curve
B stands for case B, and other curves are expressed in the
same way.
The stresses in all cases with the exception of case G
and H, which are not mounted with middle plates, begin
to increase gradually from tube 1 to the middle plate as
shown in Figure 5. From the Figure 5, the stress of the
11th tube in case A is the greatest because the middle
plates prevent the central tubes from expanding at high
temperature. On the contrary, the stress in case F is
minimal because the length of the middle plates has been
reduced and the slotting on fins is staggered. According to
the results calculated, we can conclude that decrease and
control of the length of the middle plates or slotting stag-
gered in fins can reduce the maximum stress of the tubes.
(a) Stress iteration.
(b) Volume iteration
Figure 4. Structure optimization for slotting on a tube sheet.

Z. L. ZHAO ET AL. 358
1234567891011
0
20
40
60
80
100
120
140
160
A
C
E
G

e
/ MPa
1234567891011
0
20
40
60
80
100
120
140
160
B
D
F
H

e
/ MPa
tube numbertube number
Figure 5. The maximum stress curves of all cases
The middle plate has been cancelled in case G and case
H in which stresses from tube 1 to tube 11 are relatively
low because the water tubes panel can expand freely to
both sides in the X-direction. Case G, in which there is
no slotting on the fins, is simpler than case H. Therefore,
case G is the best one among those cases of boiler
evaporators. Comparing with the similar boilers which
are used in industry and mostly slotted on the fins, we
conclude that if case G is adopted we could not only
achieve the same results and simpler manufacture, but
also save more materials.
5. Conclusions
In order to obtain better recovery of NaOH and safe op-
eration, the design of water tubes panel in the 1500 t/d
alkali recovery boiler should be considered as follows.
1) In each case, the place of maximum stress is located
either at the corner of the middle plate, or at the connec-
tion between the tubes and lower header, which is termed
as stress concentration. Transition arcs are applied for
those places of stress concentration in practical design
and manufacture so that the actual stresses are smaller
than the calculated values.
2) Among case A, B, C, D, E and F, after maximal
Von Mises Stresses on the 11th and 12th tubes are com-
pared with each other, the maximum can be found in
case A, the minimum can be found in case F. The stress
value in other cases is between the stress value of case A
and that of case F.
3) After case B, C, D, E and F are compared with each
other, we find that the tube stress in case F is relatively
low. The results calculated show that the smaller the
length of the middle plate, the less stress in the tube
sheet.
4) Among a total of 8 kinds of cases, the manufacture
of a water tubes panel without middle plates described in
case G is the simplest and the stress level in this case is
the lowest. Therefore, case G is the optimal one.
5) The design parameters of the water tubes panel such
as the length of fins and the slotting sizes are considered
into the optimal design model, and especially the ques-
tion of how to choose the staggered slotting should also
be taken into account. The final result shows that the
proper set such as B, L and R adopted in the cases can be
chosen and make it reasonable.
6
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