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Effect of structural parameters on the thermal stress of a NiFe2O4-based cermet inert anode in aluminum electrolysis
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ScienceDirect Acta Metall. Sin. (Engl. Lett.) Vol. 20 No.2 pp 139-147 Apr. 2007
ACTA METALLURGICA SINICA (ENGLISH LETTERS) www.ams.0rg.cn
EFFECT OF STRUCTURAL PARAMETERS ON THE THERMAL STRESS OF A NiFezOrBASED CERMET INERT ANODE IN ALUMINUM ELECTROLYSIS J. Li, Z.G. Wang*, Y.Q. h i , Y.Y. Wu, and S.L. Ye School of Metallurgy Science and Engineering, Central South University, Changsha 410083, China Manuscript received 13 August 2006
Inert anode has been a hot issue in the aluminum industty for many decades. With the help of FEA finite element analysis) sojiware ANSYS, a model was developed to simulate the thermal stress dism'bution working condition of an inert anode. To reduce its thermal stress, the effect of some parameters on the thermal stress distribution was investigated, including the anode height, the anode radius, the hole depth, the hole radius, and the radius of inner chamfer and outer chamfer. The results showed that in the actual working condition of an inert anode, there existed a large axial tensile stress near the tangent interface between the anode and bath, which was the major cause of anode breaking. Increasing the anode height and reducing the hole depth properly seemed to be beneficial for the stress distribution. With the increase of anode radius, the stress distribution became better first and then deteriorated, the reasonable value was between 0.04.5to 0.06m. f i e hole radius had a significant effect on the stress and a smaller radius would reduce the thermal stress. The effect of the radius of the inner chamfer and the outer cham$er was less than other parameters. KEY WORDS inert anode; thermal stress; structural parameter; aluminum electrolysis
1. Introduction As the Hall-HCroult process was invented in 1886, the techniques and equipment and many other aspects have greatly improved in the process of aluminum electrolysis. The daily output has increased fiom 24-28kg to 2030-2 170kg.The current efficiency has enhanced fkom less than 80% to 95%['1, and the current intensity has increased to 500kA.Though many kinds of attempts have been made to improve the Hall-HBroult process, it still is the only method to produce aluminum for practical use. Nowadays, there are many problems with the carbon anode, which is still widely used in the industrial reduction cells: (1) Huge consumption of high quality carbon asks for a single carbon anode factory, 'Corresponding author. Tel.: +86 731 8830474. E-mail address: [email protected] (Z.G.Wang)
. 140 which involves a huge investment and production, and meanwhile the anodes need to be replaced continually, which increases the intensity of labour. (2) The ACD (anode cathode distance) is unstable because of the continuous consumption of carbon anode, so a very complicated equipment is required to adjust the ACD, which will increase the complexity of the technique unavoidably. (3) The electrolytic reaction produces a lot of greenhouse gas COz (1.7lUt-Al) and a small quantity of CO and plenty of CF., which can cause cancer. The environment is greatly polluted. Inert anode and its new techniques, which can solve the above problems and reduce the production cost by 30%, have become the research focus of international aluminum and material The advantages of inert anode in the process of aluminum electrolysis are as follows: (1) The anode is not consumptive so a carbon factory is not necessary, which can reduce the cost remarkably. (2) The ACD is stable and can be easily controlled, so an equipment for adjusting the ACD is not required. The number of anodes changing can be decreased consumedly, in the meantime the intensity of labour could be reduced to some extent. (3) A higher anode current density can be adopted, which will improve the output of reduction cells. (4)The product of anode is oxygen, so the environment pollution can be avoided. Additionally, oxygen is the byproduct of electrolysis, its value is about 3% of the value of aluminum produced, according to some researchedq. At present, most researches are carried out on three types of inert anodes, that is, a metal oxide ceramic anode, a metal or alloy anode, and a cermet anode. The research object of this article is NiFe204-basedcermet inert anode and the composition is 17wt% Ni, 83wt% (10Ni0-90NiFe204). Because the inert anode is immersed in the high-temperature electrolyte, a great thermal stress will be produced. To reduce its thermal stress and optimize the stress distribution, a finite element model is developed to simulate the working condition of the inert anode. The effect of some structural parameters is investigated including the anode height, the anode radius, the whole depth, the whole radius, and the radius of inner chamfer and outer chamfer.
2. Model and Calculation Method 2.1 Solid model A half-anode solid model was developed according to the actual dimension (see Fig.1). The model comprised of six parts, i.e. anode, anode rod, filling stuff, alumina powder, bath, and crust. Only a lcm thick bath and crust was taken into consideration to simplify the calculation. The value of anode immersion depth was set to 6cm that is, half of the initial anode height. Taking the heat balance Crust into consideration, the value of ACD was set to \ rod / 7.5cm. The initial value and variation range of the structural parameters, which will be studied, Anode Filling stuff / are listed in Table 1, and Fig.2 shows the anode structure briefly.
Yde
1
2.2 Finite element model The solid model is meshed with hexahedrons to gain a finite element model (see Fig.3).
Bath
\
Fig. 1 Half-anode solid model.
Table 1 The initial value and variation range of structural parameters Structural
Anode height
Anode radius
Hole depth
Hole radius
Radius of
Radius of outer
parameter
m
m
m
m
inner chamfer
chamfer
m
m
0.01
0.025
Initial value
0.12
Variation range
0.09--0.18
0.05 0.035-4.08
0.08
0.024
0.054.10
0.024.04
0-0.02
0.01-4.05
Yl I 0
/R
0.025
Fig.2 The structure of anode (unit: m).
Fig.3 Finite element model.
The SOLID69 element, which has two DOF (degree of freedom, volt and temperature), is used to indicate the electric part of the model and SOLID70 element, which has only one DOF (temperature) is used to indicate the non-electric part of the model. After the thermoelectric analysis, the distribution of temperature and voltage can be gained. After saving the result of node temperature, the volume and mesh of bath would be deleted because the stress result is not affected by the liquid bath. Then transform the whole model to the structural analysis. After reading the saved node temperature result, the stress distribution can be calculated using SOLID45 element.
2.3 Material properties Material properties are very important for the veracity of simulation analysis. The model comprises of six kinds of materials, in which the composition of anode rod is Cr,,MoV and its material properties can be obtained from the material handbook. The composition of anode is 17wt%Ni, 83wt% ( 10Ni0-90NiFeZO4), the form of volume fraction is 10.8%Ni, 89.2%(10Ni0-90NiFez0,) and the resistivity of anode is fiom the experiment data. Because of the similarity of properties between 10Ni0-90 NiFeZO4and 5324 (5324 is a kind of ceramic with 5 1.7wt%NiO and 48.3wt%FeZ0Jq),the other parameters of the anode can be calculated using the linear mixing rule based on Voight's presumption[l p
= p If
+ P zf
(1) where P represents the material property; f is the volume content. The subscripts 1 and 2 represent the relevant materials respectively. The material properties of the anode filling stuff were also calculated from the above mixing rule. Parameters of other materials including alumina powder, bath, and crust can be achieved from the material handbook. Among these parameters, the thermal expansion coefficient, the heat transfer coefficient, and the resistivity of anode and filling stuff are very significant which are listed in Table 2. I
z
. 142
*
Table 2 Material properties at different temperatures Material
Anode Filling stuff
Thermal expansion Coefficient, 1 0 9 ~
Heat transfer coefficient W/(m*"C)
Resistivity D *m-2
500%
1000'C
11OO'C
200'C 350% 500'C
800°C 950°C 200'C 400°C 600°C 8OOC ' 960'C
11.37
11.98
12.00
14.49 11.31 10.52
10.66
12.66
13.03
13.05
98.51 92.80 90.72
88.01 86.85 0.0796 0.0463 0.0343 0.0237 0.0208
10.80 0.1300 0.0756 0.0560 0.0388 0.0340
2.4 Boundary conditions There are three kinds of boundary conditions, which are electrical, thermal and structural boundary conditions. Among the electrical boundary conditions, current was applied to the upper face of the anode rod and the lower surface of bath was applied with zero voltage. Among thermal boundary conditions, the node temperature of bath was set to 960'C, convection and radiation boundary conditions were applied on the surface between the anode and the surrounding air, the effect of radiation was converted to the convection coefficient. The value of convection coefficient and the surrounding temperature were set to 120W/(mZ "C) and 80°C respectively. As for the structural boundary conditions, the plane of Z = 0 was set as symmetrical plane and the center lines on it were restricted by X=O and Z=O, which means the lines cannot be moved in the X direction and Z direction.
3. ResultsandDiscussion 3.1 The distribution characteristics of thermal stress Figs.4a -d showed the thermal stress distribution of the anode of initial structural parameters showed in Table 1. FigAa is the X-direction (radial direction) thermal stress whereas Fig.4b is the Y-direction thermal stress (axial direction) and Fig.4~is the 2-direction (hoop direction) thermal stress. Fig.4d represents the distribution of first principal stress. It is obvious from these figures that there exists a compressive stress on most of the surface of the anode, anode rod, and filling surface (positive value means tensile stress whereas negative value means compressive stress), but it is not harmhl for the anode. The anode is a kind of cermet, which belongs to the fragile material category, and the fragile materials often have a higher intensity, which can resist a relatively large compressive stress. But from these figures it can also be seen that there exists a common characteristic, that is a large tensile stress exists at the contacting surface of the anode and bath (three-phase interface), which is very disadvantageous for the anode and is the major cause for the crack of the anode. If the temperature is changed too rapidly, minor crackles will be produced, then the crackles can expand and cause the breaking up of the anode eventually. To optimize the stress distribution, the idea of gradient inert anode was put forward and Li et $.[*I calculated the stress distribution of gradient inert anode considering the effect of composition distribution exponent, convection heat coefficient, the height, and radius of the anode. The results showed that the composition distribution exponent had a significant influence on the stress distribution and the stress distribution with that structure was not satisfactory. So in this article the structure of anode was simplified and that a complicated anode structure was not adopted. According to the intensity theory and the cracking type, and taking the maximal and minimal value of stress from all directions, and the first principal stress as the optimized goals, the effect of some structural parameters on the stress distribution was investigated.
143 .
Fig.4 Thermal stress distribution of the node: (a) X-direction; (b) Y-direction; (c) 2-direction; (d) first principal stress distribution (unit: Pa).
3.2 The effect of anode heigh The anode height was changed from 0.09 to 0.18m. Figs.5a and b show the relevant change in thermal stress with the increase of anode height. From these figures it can be seen that with the increase of anode height, the total trend of stress distibution is that the maximal value and the absolute minimal value decrease, which means the stress distibution becomes better. In the tensile stresses, the Y-direction stress is much bigger than in other directions (see FigSa), and its value is reduced by 21.4% (fiom 650 to 51 1MPa). The maximal value of first principal stress is reduced by 21.3% (fkom 675 to 531MPa). The absolute minimal value Y-direction stress is reduced by 27.6% (fkom 562 to 407MPa) and the absolute minimal value of first principal stress is reduced by 42.1% (fkom 404 to 234MPa). The developing trend of X-direction and 2-direction stress is similar. Increasing the anode height will reduce the thermal stress but will increase the whole voltage and the cost of anode, so the anode height should be properly increased taking other factors into consideration.
144
-300 m -400
n
5 4-
Y-direction
g
-500
T3
-600
-=-
X-direction Ydirection -o-Z-direction -e-First principal
4-
200
1-
0.08
-800 0.10
0.12 0.14 Anode height, rn
0.16
-900 0.08
0.18
0.10
0.12 0.14 Anode height, rn
0.16
0.18
Fig.5 Maximal value (a) and minimal value (b) of stress us. anode height.
3.3 The effect of anode radius The anode radius is changed from 0.035 to 0.08m. Figs.6a and b show a relevant change in thermal stress with the increase of anode radius. From Fig.6a it is evident that with the increase of anode radius, the maximal value of stress reduces first and then increases a little. This phenomenon is also observed in Fig.6b. The Y-direction tensile stress is still the biggest tensile stress among all directions. The developing trends of X and Z-direction stress are analogous. When the anode radius was increased from 0.035 to 0.055m, the Y-direction tensile stress was reduced by 19.4% (from 754 to 608Mpa), and the first principal stress was reduced by 19.3% (from 786 to 634MPa). When the anode radius was changed from 0.055 to 0.08m, both the Y-direction tensile stress and the first principal stress were increased a little. In Fig.6b, the absolute values of the first principal stress and Y-direction stress got the minimal point at the anode radius of 0.04 and 0.06m respectively. So the reasonable value of anode radius was thought to be between 0.045 to 0.06m.
3.4 The effect of hole depth The hole depth was changed from 0.05 to 0.10m,the relevant change of stress was as shown in Figs.7a and b. Fig.7a shows the biggest tensile stress is from Y-direction, and the X and Z-direction have similar stress distribution. The Y-direction and first principal stresses were increased initially, and then reduced
\ c
800
-300-
700 -I-X-direction
pm
H
!.i
2 '8
500-
-B-
-*400-
-0-
-e-
E
X-direction Y-direction 2-direction First principal
-0-
-25 -500 2 .5
-600 -
-700 200'
0.03
Y-direction ,?-direction -*-First principal
4-
800
0.04
0.05 0.06 Anode radius, rn
0.07
-
0.06
Fig.6 Maximal value (a) and minimal value (b) of stress us. anode radius.
(b)
145
-.-
; !2
X-direction Y-direction -0- Z-direction -+-First principal
400-
._
i
~
p l
4-
300 -
-.-
-*-0-
-8-
X-direction Y-direction 2-direction First principal
~
-600
200
005 0.05
006 0.06
007 008 0.07 0.08 Hole depth, in
009 0.09
010 0.10
005 0.05
006 0.06
007
008 0.08
Hole depth, m
009 0.09
010 0 10
Fig.7 Maximal value (a) and minimal value (b)of stress us. hole depth.
a little. The Y-direction and first principal stresses were increased by 10.8% (from 557 to 617MPa) and 10.7% (from 588 to 651MPa) respectively when the hole depth was changed from 0.05 to 0.08m, and then they were reduced a little when the hole depth was more than 0.08m. From Fig.7b it can be seen that the absolute minimal value decreased with the increase of hole depth which means the stress distribution became better. The absolute minimal values of Y-direction and first principal stresses were reduced by 10.5% (from 582 to 521MPa) and 11.0% (from 327 to 291MPa) respectively. Because the tensile stress is the main reason for anode breaking, reducing the hole depth properly will be beneficial for the inert anode.
3.5 The eflect of hole radius The hole radius was changed from 0.02 to 0.04m, whereas, other parameters were kept constant, the relevant change of stress was as shown in Figs.8a and b. From Fig.8aYthe total trend is that with the increase of hole radius, the maximal value of stress has increased remarkably, which indicates that the stress distribution has become worse. The Y-direction tensile stress is the most important tensile stress among all directions, and its value has increased by 41.5% (from 533 to 754MPa). The maximal value of the first principal stress has increased by 44.4% (from 559 to 807MPa). From Fig.8b, the absolute value of the Y-direction and first principal stress have decreased a little and then increased a little with the increase of hole radius, but the effect is less than its effect on the maximal value of stress. To optimize the stress distribution, a smaller hole radius will be better.
m 'O0-
a I @ -
a
1 g
600
-.-
-
-*-
500-
-0-
-B-
X-direction %direction ,&direction First principal
a"
I
-400 -
-s-9 -500.-
c
Y-direction Z-direction -8-First principal 4-0-
-700 Hole radius, m
Fig.8 Maximal value (a) and minimal value (b) of stress us. hole radius.
'
146 .
3.6 The efSect of the radius of inner chamfer and outer chamfer The radius of inner chamfer is changed from 0 to 0.02m, the relevant change of stress is as shown in Figs.9a and b. It can be seen from the figures that the effect of the radius of inner chamfer is not significant compared with other parameters, both the Y-direction and first principal stress get the minimal value at the radius of 0.005 and 0.015m. The absolute minimal value of stress has been almost kept constant with the increase of the radius of inner chamfer. Considering the simplicity of producing the anode, the radius of 0.005m may be better. The radius of outer chamfer was changed from 0.01 to 0.05m. Figs.lOa and b showed the change of stress. From Fig.lOa, the effect of the radius of outer chamfer is very complicated, the X-direction and 2-direction stress have a similar developing trend, and Y-direction stress still plays a more important role. Both the Y-direction and first principal stress have got the minimal value at the radius of outer chamfer of 0.05m, which is an extreme case that there is a half sphere at the bottom of the anode without no flat part. But Fig.lOb shows that the absolute minimal value of stress has changed a little. Compared with other parameters, the effect of the radius of outer chamfer is not remarkable, the reasonable value of it can be decided taking the flow field into consideration.
-300
a
-350
I
2 I g -400
9m-
B '8E 400 -
X-direction Y-direction -o-Z-dire&n -e- First principal -a-
4-
I
T-
--.-X-direction 4- Y-direction -0- Z-direction +-First principal
.-2 -450
.-c
z
-500
300 -
m 0.m
0.005 0.010 0.015 Radius of inner chamfer, rn
0.000
0.020
0.005 0.010 0.015 Radius of inner chamfer. rn
0.020
-
Fig.9 Maximal value (a) and minimal value (b) of stress US. the radius of inner chamfer. 800
t
-300 (b) 700
n m
I
-G -F
z
600
500
--.-
.-
-a-
i 400
-0-
I
-e-
300 200
A 0.01
0.04 Radius of outer chamfer, rn
0.02
0.03
-=- X-direction 4- %direction --o-Z-directbn -e-First principal
X-direction Y-direction Z-direction First principal
-500 2
0.05
Fig.10 Maximal value (a) and minimal value (b) of stress us. the radius of outer chamfer.
..
. 147 .
4. Conclusions (1) Compressive stress exists on most surface of anode, a large tensile stress exists at the solid-liquid-air three-phase contact line, which is the major cause of the crack of the anode. In the tensile stresses, the Y-direction (axial direction) stress is much bigger than that of X and Z-direction. The stress distributions of X-direction and Z-direction are very similar. (2) With the increase of anode height, the stress distribution becomes better. But the anode height is associated with the energy consumption, increasing the anode height properly will be beneficial for the anode stress distribution. (3) With the increase of anode radius, the stress distribution becomes better first and then becomes worse a little, the reasonable value of it is between 0.045 to 0.06m. (4) The total stress distribution becomes worse when the hole depth is increased, so reducing the hole depth properly will reduce the thermal stress. ( 5 ) The effect of hole radius on the stress distribution is very significant, a smaller hole radius will be advantageous for the anode. (6) The effect of the radius of the inner chamfer and outer chamfer is not significant compared with the other parameters, whereas, the effect of outer chamfer is complicated, the reasonable value of it can be decided taking the flow field into consideration.
Acknowledgements-This work was supported by the National Key Basic Research and Development Programme of China (No. 2005CB623703) and the National Natural Science Foundation of China (No. 50474051 and No. 50374081).
REFERENCES 1 2 3 4 5 6
J.H. Zhang, J.H. Xi, Y.H. Liu, and G.C. Yao, Non-Ferrous Mining and Metallurgy 2q1) (2004) 20 (in Chinese). R.P. Pawlek, Light Metah, ed. W. Schneider (TMS, Warrendale, PA, 2002) p.449. H. Kvande and W. Haupin, JOM 53(5) (2001) 29. V. Nora, Aluminium 76(12) (2000) 998. W.M. Zhou and Z.C. Guo, Metallurgical Collections 1 (2004) 1 (in Chinese). J.D. Weyand, D.H. Deyoung, S.P. Ray, and T.R. Beck, Inert Anodes for Aluminum Smelting DOE/CY40158-20 (Washington D C, Aluminum Company of America, 1986) p.24. 7 B.L. Wang, J.C. Han, and X.H. Zhang, Uneven Moterial Mechanics (Science Press, Beijing, 2003) p.27 (in Chinese). 8 J. Li, Q.S. Zhang, Y.Q.hi,S.L. Ye, and Y.X. Liu, Actu Metall. Sin. (En&. Lett.) 18 (2005) 635.
ScienceDirect Acta Metall. Sin. (Engl. Lett.) Vol. 20 No.2 pp 139-147 Apr. 2007
ACTA METALLURGICA SINICA (ENGLISH LETTERS) www.ams.0rg.cn
EFFECT OF STRUCTURAL PARAMETERS ON THE THERMAL STRESS OF A NiFezOrBASED CERMET INERT ANODE IN ALUMINUM ELECTROLYSIS J. Li, Z.G. Wang*, Y.Q. h i , Y.Y. Wu, and S.L. Ye School of Metallurgy Science and Engineering, Central South University, Changsha 410083, China Manuscript received 13 August 2006
Inert anode has been a hot issue in the aluminum industty for many decades. With the help of FEA finite element analysis) sojiware ANSYS, a model was developed to simulate the thermal stress dism'bution working condition of an inert anode. To reduce its thermal stress, the effect of some parameters on the thermal stress distribution was investigated, including the anode height, the anode radius, the hole depth, the hole radius, and the radius of inner chamfer and outer chamfer. The results showed that in the actual working condition of an inert anode, there existed a large axial tensile stress near the tangent interface between the anode and bath, which was the major cause of anode breaking. Increasing the anode height and reducing the hole depth properly seemed to be beneficial for the stress distribution. With the increase of anode radius, the stress distribution became better first and then deteriorated, the reasonable value was between 0.04.5to 0.06m. f i e hole radius had a significant effect on the stress and a smaller radius would reduce the thermal stress. The effect of the radius of the inner chamfer and the outer cham$er was less than other parameters. KEY WORDS inert anode; thermal stress; structural parameter; aluminum electrolysis
1. Introduction As the Hall-HCroult process was invented in 1886, the techniques and equipment and many other aspects have greatly improved in the process of aluminum electrolysis. The daily output has increased fiom 24-28kg to 2030-2 170kg.The current efficiency has enhanced fkom less than 80% to 95%['1, and the current intensity has increased to 500kA.Though many kinds of attempts have been made to improve the Hall-HBroult process, it still is the only method to produce aluminum for practical use. Nowadays, there are many problems with the carbon anode, which is still widely used in the industrial reduction cells: (1) Huge consumption of high quality carbon asks for a single carbon anode factory, 'Corresponding author. Tel.: +86 731 8830474. E-mail address: [email protected] (Z.G.Wang)
. 140 which involves a huge investment and production, and meanwhile the anodes need to be replaced continually, which increases the intensity of labour. (2) The ACD (anode cathode distance) is unstable because of the continuous consumption of carbon anode, so a very complicated equipment is required to adjust the ACD, which will increase the complexity of the technique unavoidably. (3) The electrolytic reaction produces a lot of greenhouse gas COz (1.7lUt-Al) and a small quantity of CO and plenty of CF., which can cause cancer. The environment is greatly polluted. Inert anode and its new techniques, which can solve the above problems and reduce the production cost by 30%, have become the research focus of international aluminum and material The advantages of inert anode in the process of aluminum electrolysis are as follows: (1) The anode is not consumptive so a carbon factory is not necessary, which can reduce the cost remarkably. (2) The ACD is stable and can be easily controlled, so an equipment for adjusting the ACD is not required. The number of anodes changing can be decreased consumedly, in the meantime the intensity of labour could be reduced to some extent. (3) A higher anode current density can be adopted, which will improve the output of reduction cells. (4)The product of anode is oxygen, so the environment pollution can be avoided. Additionally, oxygen is the byproduct of electrolysis, its value is about 3% of the value of aluminum produced, according to some researchedq. At present, most researches are carried out on three types of inert anodes, that is, a metal oxide ceramic anode, a metal or alloy anode, and a cermet anode. The research object of this article is NiFe204-basedcermet inert anode and the composition is 17wt% Ni, 83wt% (10Ni0-90NiFe204). Because the inert anode is immersed in the high-temperature electrolyte, a great thermal stress will be produced. To reduce its thermal stress and optimize the stress distribution, a finite element model is developed to simulate the working condition of the inert anode. The effect of some structural parameters is investigated including the anode height, the anode radius, the whole depth, the whole radius, and the radius of inner chamfer and outer chamfer.
2. Model and Calculation Method 2.1 Solid model A half-anode solid model was developed according to the actual dimension (see Fig.1). The model comprised of six parts, i.e. anode, anode rod, filling stuff, alumina powder, bath, and crust. Only a lcm thick bath and crust was taken into consideration to simplify the calculation. The value of anode immersion depth was set to 6cm that is, half of the initial anode height. Taking the heat balance Crust into consideration, the value of ACD was set to \ rod / 7.5cm. The initial value and variation range of the structural parameters, which will be studied, Anode Filling stuff / are listed in Table 1, and Fig.2 shows the anode structure briefly.
Yde
1
2.2 Finite element model The solid model is meshed with hexahedrons to gain a finite element model (see Fig.3).
Bath
\
Fig. 1 Half-anode solid model.
Table 1 The initial value and variation range of structural parameters Structural
Anode height
Anode radius
Hole depth
Hole radius
Radius of
Radius of outer
parameter
m
m
m
m
inner chamfer
chamfer
m
m
0.01
0.025
Initial value
0.12
Variation range
0.09--0.18
0.05 0.035-4.08
0.08
0.024
0.054.10
0.024.04
0-0.02
0.01-4.05
Yl I 0
/R
0.025
Fig.2 The structure of anode (unit: m).
Fig.3 Finite element model.
The SOLID69 element, which has two DOF (degree of freedom, volt and temperature), is used to indicate the electric part of the model and SOLID70 element, which has only one DOF (temperature) is used to indicate the non-electric part of the model. After the thermoelectric analysis, the distribution of temperature and voltage can be gained. After saving the result of node temperature, the volume and mesh of bath would be deleted because the stress result is not affected by the liquid bath. Then transform the whole model to the structural analysis. After reading the saved node temperature result, the stress distribution can be calculated using SOLID45 element.
2.3 Material properties Material properties are very important for the veracity of simulation analysis. The model comprises of six kinds of materials, in which the composition of anode rod is Cr,,MoV and its material properties can be obtained from the material handbook. The composition of anode is 17wt%Ni, 83wt% ( 10Ni0-90NiFeZO4), the form of volume fraction is 10.8%Ni, 89.2%(10Ni0-90NiFez0,) and the resistivity of anode is fiom the experiment data. Because of the similarity of properties between 10Ni0-90 NiFeZO4and 5324 (5324 is a kind of ceramic with 5 1.7wt%NiO and 48.3wt%FeZ0Jq),the other parameters of the anode can be calculated using the linear mixing rule based on Voight's presumption[l p
= p If
+ P zf
(1) where P represents the material property; f is the volume content. The subscripts 1 and 2 represent the relevant materials respectively. The material properties of the anode filling stuff were also calculated from the above mixing rule. Parameters of other materials including alumina powder, bath, and crust can be achieved from the material handbook. Among these parameters, the thermal expansion coefficient, the heat transfer coefficient, and the resistivity of anode and filling stuff are very significant which are listed in Table 2. I
z
. 142
*
Table 2 Material properties at different temperatures Material
Anode Filling stuff
Thermal expansion Coefficient, 1 0 9 ~
Heat transfer coefficient W/(m*"C)
Resistivity D *m-2
500%
1000'C
11OO'C
200'C 350% 500'C
800°C 950°C 200'C 400°C 600°C 8OOC ' 960'C
11.37
11.98
12.00
14.49 11.31 10.52
10.66
12.66
13.03
13.05
98.51 92.80 90.72
88.01 86.85 0.0796 0.0463 0.0343 0.0237 0.0208
10.80 0.1300 0.0756 0.0560 0.0388 0.0340
2.4 Boundary conditions There are three kinds of boundary conditions, which are electrical, thermal and structural boundary conditions. Among the electrical boundary conditions, current was applied to the upper face of the anode rod and the lower surface of bath was applied with zero voltage. Among thermal boundary conditions, the node temperature of bath was set to 960'C, convection and radiation boundary conditions were applied on the surface between the anode and the surrounding air, the effect of radiation was converted to the convection coefficient. The value of convection coefficient and the surrounding temperature were set to 120W/(mZ "C) and 80°C respectively. As for the structural boundary conditions, the plane of Z = 0 was set as symmetrical plane and the center lines on it were restricted by X=O and Z=O, which means the lines cannot be moved in the X direction and Z direction.
3. ResultsandDiscussion 3.1 The distribution characteristics of thermal stress Figs.4a -d showed the thermal stress distribution of the anode of initial structural parameters showed in Table 1. FigAa is the X-direction (radial direction) thermal stress whereas Fig.4b is the Y-direction thermal stress (axial direction) and Fig.4~is the 2-direction (hoop direction) thermal stress. Fig.4d represents the distribution of first principal stress. It is obvious from these figures that there exists a compressive stress on most of the surface of the anode, anode rod, and filling surface (positive value means tensile stress whereas negative value means compressive stress), but it is not harmhl for the anode. The anode is a kind of cermet, which belongs to the fragile material category, and the fragile materials often have a higher intensity, which can resist a relatively large compressive stress. But from these figures it can also be seen that there exists a common characteristic, that is a large tensile stress exists at the contacting surface of the anode and bath (three-phase interface), which is very disadvantageous for the anode and is the major cause for the crack of the anode. If the temperature is changed too rapidly, minor crackles will be produced, then the crackles can expand and cause the breaking up of the anode eventually. To optimize the stress distribution, the idea of gradient inert anode was put forward and Li et $.[*I calculated the stress distribution of gradient inert anode considering the effect of composition distribution exponent, convection heat coefficient, the height, and radius of the anode. The results showed that the composition distribution exponent had a significant influence on the stress distribution and the stress distribution with that structure was not satisfactory. So in this article the structure of anode was simplified and that a complicated anode structure was not adopted. According to the intensity theory and the cracking type, and taking the maximal and minimal value of stress from all directions, and the first principal stress as the optimized goals, the effect of some structural parameters on the stress distribution was investigated.
143 .
Fig.4 Thermal stress distribution of the node: (a) X-direction; (b) Y-direction; (c) 2-direction; (d) first principal stress distribution (unit: Pa).
3.2 The effect of anode heigh The anode height was changed from 0.09 to 0.18m. Figs.5a and b show the relevant change in thermal stress with the increase of anode height. From these figures it can be seen that with the increase of anode height, the total trend of stress distibution is that the maximal value and the absolute minimal value decrease, which means the stress distibution becomes better. In the tensile stresses, the Y-direction stress is much bigger than in other directions (see FigSa), and its value is reduced by 21.4% (fiom 650 to 51 1MPa). The maximal value of first principal stress is reduced by 21.3% (fkom 675 to 531MPa). The absolute minimal value Y-direction stress is reduced by 27.6% (fkom 562 to 407MPa) and the absolute minimal value of first principal stress is reduced by 42.1% (fkom 404 to 234MPa). The developing trend of X-direction and 2-direction stress is similar. Increasing the anode height will reduce the thermal stress but will increase the whole voltage and the cost of anode, so the anode height should be properly increased taking other factors into consideration.
144
-300 m -400
n
5 4-
Y-direction
g
-500
T3
-600
-=-
X-direction Ydirection -o-Z-direction -e-First principal
4-
200
1-
0.08
-800 0.10
0.12 0.14 Anode height, rn
0.16
-900 0.08
0.18
0.10
0.12 0.14 Anode height, rn
0.16
0.18
Fig.5 Maximal value (a) and minimal value (b) of stress us. anode height.
3.3 The effect of anode radius The anode radius is changed from 0.035 to 0.08m. Figs.6a and b show a relevant change in thermal stress with the increase of anode radius. From Fig.6a it is evident that with the increase of anode radius, the maximal value of stress reduces first and then increases a little. This phenomenon is also observed in Fig.6b. The Y-direction tensile stress is still the biggest tensile stress among all directions. The developing trends of X and Z-direction stress are analogous. When the anode radius was increased from 0.035 to 0.055m, the Y-direction tensile stress was reduced by 19.4% (from 754 to 608Mpa), and the first principal stress was reduced by 19.3% (from 786 to 634MPa). When the anode radius was changed from 0.055 to 0.08m, both the Y-direction tensile stress and the first principal stress were increased a little. In Fig.6b, the absolute values of the first principal stress and Y-direction stress got the minimal point at the anode radius of 0.04 and 0.06m respectively. So the reasonable value of anode radius was thought to be between 0.045 to 0.06m.
3.4 The effect of hole depth The hole depth was changed from 0.05 to 0.10m,the relevant change of stress was as shown in Figs.7a and b. Fig.7a shows the biggest tensile stress is from Y-direction, and the X and Z-direction have similar stress distribution. The Y-direction and first principal stresses were increased initially, and then reduced
\ c
800
-300-
700 -I-X-direction
pm
H
!.i
2 '8
500-
-B-
-*400-
-0-
-e-
E
X-direction Y-direction 2-direction First principal
-0-
-25 -500 2 .5
-600 -
-700 200'
0.03
Y-direction ,?-direction -*-First principal
4-
800
0.04
0.05 0.06 Anode radius, rn
0.07
-
0.06
Fig.6 Maximal value (a) and minimal value (b) of stress us. anode radius.
(b)
145
-.-
; !2
X-direction Y-direction -0- Z-direction -+-First principal
400-
._
i
~
p l
4-
300 -
-.-
-*-0-
-8-
X-direction Y-direction 2-direction First principal
~
-600
200
005 0.05
006 0.06
007 008 0.07 0.08 Hole depth, in
009 0.09
010 0.10
005 0.05
006 0.06
007
008 0.08
Hole depth, m
009 0.09
010 0 10
Fig.7 Maximal value (a) and minimal value (b)of stress us. hole depth.
a little. The Y-direction and first principal stresses were increased by 10.8% (from 557 to 617MPa) and 10.7% (from 588 to 651MPa) respectively when the hole depth was changed from 0.05 to 0.08m, and then they were reduced a little when the hole depth was more than 0.08m. From Fig.7b it can be seen that the absolute minimal value decreased with the increase of hole depth which means the stress distribution became better. The absolute minimal values of Y-direction and first principal stresses were reduced by 10.5% (from 582 to 521MPa) and 11.0% (from 327 to 291MPa) respectively. Because the tensile stress is the main reason for anode breaking, reducing the hole depth properly will be beneficial for the inert anode.
3.5 The eflect of hole radius The hole radius was changed from 0.02 to 0.04m, whereas, other parameters were kept constant, the relevant change of stress was as shown in Figs.8a and b. From Fig.8aYthe total trend is that with the increase of hole radius, the maximal value of stress has increased remarkably, which indicates that the stress distribution has become worse. The Y-direction tensile stress is the most important tensile stress among all directions, and its value has increased by 41.5% (from 533 to 754MPa). The maximal value of the first principal stress has increased by 44.4% (from 559 to 807MPa). From Fig.8b, the absolute value of the Y-direction and first principal stress have decreased a little and then increased a little with the increase of hole radius, but the effect is less than its effect on the maximal value of stress. To optimize the stress distribution, a smaller hole radius will be better.
m 'O0-
a I @ -
a
1 g
600
-.-
-
-*-
500-
-0-
-B-
X-direction %direction ,&direction First principal
a"
I
-400 -
-s-9 -500.-
c
Y-direction Z-direction -8-First principal 4-0-
-700 Hole radius, m
Fig.8 Maximal value (a) and minimal value (b) of stress us. hole radius.
'
146 .
3.6 The efSect of the radius of inner chamfer and outer chamfer The radius of inner chamfer is changed from 0 to 0.02m, the relevant change of stress is as shown in Figs.9a and b. It can be seen from the figures that the effect of the radius of inner chamfer is not significant compared with other parameters, both the Y-direction and first principal stress get the minimal value at the radius of 0.005 and 0.015m. The absolute minimal value of stress has been almost kept constant with the increase of the radius of inner chamfer. Considering the simplicity of producing the anode, the radius of 0.005m may be better. The radius of outer chamfer was changed from 0.01 to 0.05m. Figs.lOa and b showed the change of stress. From Fig.lOa, the effect of the radius of outer chamfer is very complicated, the X-direction and 2-direction stress have a similar developing trend, and Y-direction stress still plays a more important role. Both the Y-direction and first principal stress have got the minimal value at the radius of outer chamfer of 0.05m, which is an extreme case that there is a half sphere at the bottom of the anode without no flat part. But Fig.lOb shows that the absolute minimal value of stress has changed a little. Compared with other parameters, the effect of the radius of outer chamfer is not remarkable, the reasonable value of it can be decided taking the flow field into consideration.
-300
a
-350
I
2 I g -400
9m-
B '8E 400 -
X-direction Y-direction -o-Z-dire&n -e- First principal -a-
4-
I
T-
--.-X-direction 4- Y-direction -0- Z-direction +-First principal
.-2 -450
.-c
z
-500
300 -
m 0.m
0.005 0.010 0.015 Radius of inner chamfer, rn
0.000
0.020
0.005 0.010 0.015 Radius of inner chamfer. rn
0.020
-
Fig.9 Maximal value (a) and minimal value (b) of stress US. the radius of inner chamfer. 800
t
-300 (b) 700
n m
I
-G -F
z
600
500
--.-
.-
-a-
i 400
-0-
I
-e-
300 200
A 0.01
0.04 Radius of outer chamfer, rn
0.02
0.03
-=- X-direction 4- %direction --o-Z-directbn -e-First principal
X-direction Y-direction Z-direction First principal
-500 2
0.05
Fig.10 Maximal value (a) and minimal value (b) of stress us. the radius of outer chamfer.
..
. 147 .
4. Conclusions (1) Compressive stress exists on most surface of anode, a large tensile stress exists at the solid-liquid-air three-phase contact line, which is the major cause of the crack of the anode. In the tensile stresses, the Y-direction (axial direction) stress is much bigger than that of X and Z-direction. The stress distributions of X-direction and Z-direction are very similar. (2) With the increase of anode height, the stress distribution becomes better. But the anode height is associated with the energy consumption, increasing the anode height properly will be beneficial for the anode stress distribution. (3) With the increase of anode radius, the stress distribution becomes better first and then becomes worse a little, the reasonable value of it is between 0.045 to 0.06m. (4) The total stress distribution becomes worse when the hole depth is increased, so reducing the hole depth properly will reduce the thermal stress. ( 5 ) The effect of hole radius on the stress distribution is very significant, a smaller hole radius will be advantageous for the anode. (6) The effect of the radius of the inner chamfer and outer chamfer is not significant compared with the other parameters, whereas, the effect of outer chamfer is complicated, the reasonable value of it can be decided taking the flow field into consideration.
Acknowledgements-This work was supported by the National Key Basic Research and Development Programme of China (No. 2005CB623703) and the National Natural Science Foundation of China (No. 50474051 and No. 50374081).
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J.H. Zhang, J.H. Xi, Y.H. Liu, and G.C. Yao, Non-Ferrous Mining and Metallurgy 2q1) (2004) 20 (in Chinese). R.P. Pawlek, Light Metah, ed. W. Schneider (TMS, Warrendale, PA, 2002) p.449. H. Kvande and W. Haupin, JOM 53(5) (2001) 29. V. Nora, Aluminium 76(12) (2000) 998. W.M. Zhou and Z.C. Guo, Metallurgical Collections 1 (2004) 1 (in Chinese). J.D. Weyand, D.H. Deyoung, S.P. Ray, and T.R. Beck, Inert Anodes for Aluminum Smelting DOE/CY40158-20 (Washington D C, Aluminum Company of America, 1986) p.24. 7 B.L. Wang, J.C. Han, and X.H. Zhang, Uneven Moterial Mechanics (Science Press, Beijing, 2003) p.27 (in Chinese). 8 J. Li, Q.S. Zhang, Y.Q.hi,S.L. Ye, and Y.X. Liu, Actu Metall. Sin. (En&. Lett.) 18 (2005) 635.