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Turbulent molten pool analysis of tandem GMA automotive steel sheet welding
International Journal of Heat and Mass Transfer 129 (2019) 1–6
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Turbulent molten pool analysis of tandem GMA automotive steel sheet welding Kyungbae Park a, Hunchul Jeong a, Sungjin Baek a, Dong-Yoon Kim b, Moon-Jin Kang b, Jungho Cho a,⇑ a b
School of Mechanical Engineering, Chungbuk National University, Cheongju 28644, Republic of Korea Joining R&D Group, Korea Institute of Industrial Technology, Incheon 21999, Republic of Korea
a r t i c l e
i n f o
Article history: Received 10 April 2018 Received in revised form 3 August 2018 Accepted 10 September 2018
Keywords: CFD k–e turbulent model Laminar flow Lap joint fillet Molten pool Tandem GMAW
a b s t r a c t In this research, a three-dimensional turbulent weld pool simulation technique of tandem gas tungsten arc welding (GMAW) in a lap joint fillet is described and compared to a conventional laminar flow simulation. Basically, four governing equations are adopted for continuity, namely, continuity, Navier-Stokes, energy, and the popular volume of fluid equations. According to the basic theory of an arc weld pool, all known characteristics such as the arc heat input, arc pressure, electromagnetic force, and Marangoni flow are applied to the analysis model as a body force term or boundary conditions. A conventional arc weld pool analysis usually adopts a laminar flow; however, its results have shown a weld bead shape that is quite different from an experiment of a tandem GMA lap joint fillet welding of an automotive steel sheet. Therefore, the authors suggest the use of a k-eturbulent analysis model and show that its results coincide with the experiment results. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Tandem gas metal arc welding (GMAW) is a welding technique that uses two welding wires at the same time in parallel for higher productivity through an increase in the deposition rate. Although this technique is often used in shipbuilding and heavy industry, there have been trials in applying the method to the automotive industry. Although zinc-coated steel sheets are widely used by OEM makers to improve the corrosion resistance of body in white (BIW), zinc pores in the beads remain a significant problem. At this point, a tandem arc scheme may be a solution. Between two parallel arcs, the leading one plays a role in removing the zinc coating before joining, and the other trailing arc practically welds the joint. The mechanism sounds simple; however, a difficulty remains in setting up a power balance of the two arcs because their arc pressures and electromagnetic forces affect the molten pool flow behavior. In addition, it is preferable for the leading arc to play a role in removing the zinc coating at the gap and not melt the base metal. A numerical analysis of a molten pool is required in this aspect because experiments and observations using a high-speed camera require an extra budget in addition to the limit of temperature field profiling. It is possible to expect a molten pool flow pattern and temperature distribution through a numerical simulation. ⇑ Corresponding author. E-mail address: [email protected] (J. Cho). https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.046 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
Tsao and Wu [12] and Kim and Basu [10] developed numerical analysis models of GMAW during the early period, which artificially add latent heat and momentum energy to express a droplet transfer without a free surface consideration. Kim et al. [9] dealt with the droplet transfer as a virtual volumetric heat source. Hirt and Nichols [6] developed the popular volume of fluid (VOF) method, which made it possible to successfully express the free surface of a fluid. Wang and Tsai [13] first simulated a two two-dimensional molten pool from arc welding and a droplet transfer problem using the VOF technique. Cao et al. [1] expanded a VOF-based molten pool simulation to a threedimensional model. Cho and Na [2] made advancements in the VOF molten pool model in a laser keyhole simulation when considering real-time multiple reflections. Cho and Na [3] suggested more concrete molten pool analysis model of laser keyhole welding considering polarized beam absorption. Cho and Na [4] added GMA analysis model to the old one then reported molten pool flow characteristics of laser-GMA hybrid welding. Kiran et al. [11] extended the model to a tandem arc welding simulation and created a foundation. Although a molten pool actually shows a turbulent behavior, all previous works above assume it as laminar. Other cases have followed. Choo and Szekely [5] first developed a turbulent molten pool simulation model of gas tungsten arc welding (GTAW), and showed higher accuracy in the model compared to a laminar case. Jaidi et al. [7] expanded the turbulent model to a GMAW simulation. However, both of the
2
K. Park et al. / International Journal of Heat and Mass Transfer 129 (2019) 1–6
Nomenclature CA Cp F ! F fd rA h hA I K Lf n P PA qA rA T Tl Ts
T1 t Ui
concentration coefficient of arc specific heat volume fraction occupied by fluid electromagnetic force per unit volume droplet transfer frequency effective radius of arc enthalpy convection coefficient welding current thermal conductivity latent heat of fusion normal component pressure arc pressure arc heat flux effective radius of arc temperature liquidus temperature solidus temperature
Greek symbols c surface tension es emissivity ga heat input efficiency gd droplet heat efficiency l viscosity l0 magnetic permeagility in vacuum lm magnetic permeability of metal lt turbulent viscosity p circular constant q density r normal stress rs Stefan-Boltzmann constant s tangent direction
previous turbulent models were two-dimensional and did not consider the effects of a free surface. In this research, a numerical analysis model of a threedimensional transient molten pool was newly developed for a tandem GMA of lap joint fillet welding using the commercial package, Flow-3D. The base metal widely used in the automotive industry is 2.3-mm thick zinc-coated steel. Owing to the diameter of each torch, two torches are inclined to satisfy the distance between arcs, which means the arc surface heat flux and electromagnetic body force are also inclined. Therefore, the authors’ previous model has been newly improved to simulate the complex torch setup of tandem GMAW. Development of the simulation was first achieved using a previous laminar flow model, but did not coincide with the experiment, and therefore the model was improved to a turbulent k-e flow. The numerical analysis model is basically composed of four governing equations: continuity, Navier-Stokes, energy, and VOF equations. Two more equations are required in a turbulent model, namely, a turbulent kinetic energy equation and its dissipation rate. Arc heat input is applied as the surface heat flux with a Gaussian distribution. Electromagnetic force and buoyancy are adopted as the body force term in a Navier-Stokes equation. Radiation, convection heat loss, Marangoni shear force, arc pressure, and surface tension pressure are applied as the boundary conditions. 2. Governing equations and boundary conditions In a turbulent weld pool analysis, a total of six governing equations are required: VOF, continuity, momentum, energy, turbulent kinetic energy, and its dissipation rate equations. The first, a VOF equation, makes it possible to track the free surface of a flow. A VOF equation is a kind of continuity equation. In other words, it expresses a conservation of value F, which is between zero and 1. If the value is 1, it means the control volume is full of the flow, whereas a value of zero indicates that the volume is empty. Connecting the cells with values between zero and 1 is the principle of free surface tracking. The governing equation is as follows.
DF @F @FU i ¼ þ ¼0 Dt @t @xi
ambient temperature time velocity tensor
ð1Þ
The continuity equation of mass conservation for an incompressible and Newtonian fluid is as follows.
@U i ¼0 @xi
ð2Þ
The conservation equation of momentum for an eddy viscosity model is induced as follows.
@U i @U i 1 @P @ ¼ þ þ Uj @t @xj q @xi @xj
l þ lt @U i þ Bi q @xj
ð3Þ
The source terms Bi in momentum Eq. (3) include the electromagnetic and buoyancy forces, where lt is the eddy viscosity coefficient. By considering the latent heat of fusion, the energy equation, assuming that the kinetic and potential energies are negligible, is expressed as follows.
@h @h @ þ Uj ¼ @t @xj @xj
C p lt @T Kþ Prt @xj
ð4Þ
h ¼ C p T þ f ðT Þ Lf
f ðT Þ ¼
8 > < > :
ð5Þ
0; ðT T s Þ TT l T l T s
; ðT s < T < T l Þ
ð6Þ
1; ðT T l Þ
where Pr t is turbulent Prandtl number in the second term of right side of Eq. (5).
lt ¼ C l q
2
k
ð7Þ
e
The eddy viscosity coefficient in Eq. (7) is expressed through a multiplication of the velocity and length scales. Because the velocity and length scales in the standard k-e model are determined based on the turbulent kinetic energy and dissipation rate, transport equations of turbulent kinetic energy and dissipation rate are required, respectively. Transport equations are defined as follows.
@ ðqkÞ @ ðqkÞ @ ¼ þ Uj @t @xj @xj
lþ
lt @k @U i qui uj qe rk @xj @xj
ð8Þ
3
K. Park et al. / International Journal of Heat and Mass Transfer 129 (2019) 1–6
@ ðqeÞ @ ðqeÞ @ ¼ þ Uj @t @xj @xj
lþ
lt re
@e e @U i e2 þ C 1e qui uj C 2e q @xj k @xj k ð9Þ
ui uj
where q is called the Reynolds stress and the various turbulent constants are set up according to standard values which can be found in textbooks in easy. As boundary conditions, the top surface of base metal is exposed to two GMA heat sources and heat loss of convection and radiation. Mathematical expression of surface heat flux is as follow.
K
@T ¼ qtrailing þ qleading hA ðT T 1 Þ re es ðT T 1 Þ @n
2 VI x þ y2 qA ¼ gA exp C A r 2A C A pr 2A
ð11Þ
1 r A ¼ z þ 0:3 3
ð12Þ
where gA is the heat input efficiency of GMAW, which has a representative value of 0.8. In addition, assuming the droplet transfer is in spray mode, a droplet has heat capacity qd . The heat of the droplet is directly transferred to a molten pool with frequency f d as the actual volume heat source following the VOF technique.
fd ¼
3r 2w V WFR 4r 3d
ð13Þ
qd ¼
4 3 pr C p T d f d 3 d
ð14Þ
The molten pool surface is subjected to stresses of arc pressure and surface tension, and thus the mathematical expression of this pressure boundary condition on the top surface is as follows.
@V n c ¼ PA þ @n Rc
PA ¼
l0 I2 x2 þ y 2 exp 4p2 r2A 2r 2A
! F ¼
! I2 lm r2 r2 z 2 x b i 1 exp 1 2 2 exp c r 4p rr A 2r A 2 2r A 2
! I 2 lm r2 r2 z 2 y b þ 2 2 exp 1 exp 1 j c r 4p rr A 2r A 2 2r A 2
ð10Þ
where the third and fourth terms on the right side are convectional and radiational heat losses, respectively. The first and second terms on the right side are arc heat inputs. In this study, the arc heat source model for a welding simulation adopts a Gaussian distribution [8], the value of which for an effective radius is linearly proportional to the arc center, namely, from 0.2 to 0.3 cm.
P þ 2l
current flow direction. With this reason, the molten pool simulations used a simplified electromagnetic force model, such as the follow.
ð15Þ ð16Þ
! 2 I2 lm r2 z b k 1 1 exp þ c 4p 2 r 2 c 2r A 2
To consider the travel and working angles, the coordinate transformation based on a welding torch was applied to the analysis.
2 3
^ A 32 3 2 32 x 1 0 0 cos/ 0 sin/ 6x7 6 A^ 7 6 6 76 7 6 y 7 ¼ 4 0 cosh sinh 7 y 0 1 0 4 5 4 5 5 6 7 4^5 z 0 sinh cosh sin/ 0 cos/ A z
@V s @ c @T ¼ @n @T @ s
ð17Þ
The electromagnetic force applied by an interaction between the current flow and the magnetic field induced is expressed as
! ! ! F ¼ I B
ð18Þ
The free surface of a molten pool continuously changes. Therefore, it takes a significant amount of time to compute the electromagnetic force for each cell with respect to a mutually different
ð20Þ
where h and / represent the travel and working angles, respectively. Fig. 1 shows a schematic of the welding joint and torch positions. The numerical analysis domain has a 70 mm length in the x-direction, and 30 mm and 10 mm lengths in the y- and zdirections, respectively. Each axis is divided into a 0.4 mm length, and therefore the analytic domain has a total of 328,125 control volume cells. As shown in Fig. 1, in the VOF method, part of the domain is set to have an F value of 1 to be assigned as a base metal, and the rest of the domain is set to zero. Fig. 2 shows the actual experimental setup. As the figure indicates, there are leading and trailing arcs in tandem GMAW. Both GMAs use a pulsed current, and their setups are as demonstrated in Fig. 3. The leading arc has a fixed wire feeding speed (WFS), whereas the trailing arc has various speeds. Various variables exist, such as the current and voltage, but they are already fixed through a pre-experiment for a synergic line. Widely used 590 MPa grade zinc-coated steel sheets of 2.3-mm thickness were used in the experiment, the thermophysical properties of which are shown in Table 1. The welding process variables applied are listed in Table 2.
The second term on the left side of Eq. (15) denotes Newton’s viscosity law on a weld pool surface in the normal direction. In addition, the first term on the right side expresses the arc pressure, and the other indicates the surface tension pressure from the curved surface. During the welding process, shear stress, which creates a tangential flow, is generated by a change in the surface tension gradient depending on the temperature. This phenomenon, called a Marangoni flow, is defined as follows.
l
ð19Þ
Fig. 1. Schematic diagram of tandem GMAW in lap joint fillet.
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K. Park et al. / International Journal of Heat and Mass Transfer 129 (2019) 1–6 Table 1 Thermophysical properties of SGAFH 590FB(2.3 mm). Property
Value
Symbol 3
Density Thermal conductivity Specific heat Solidus temp Liquidus temp Surface tension gradient
S: 6900/L: 7800 kg=m S: 32.3/L: 26.9 W/m K S: 726/L: 26.9 J/kg K 1723 K 1773 K 0.2e3 N=m K
Magnetic permeability Ambient temp Latent heat of fusion Emissivity Surface tension Convection Coefficient Viscosity
1.26e6 H=m 273 K 277 KJ=Kg 0.8 1.8 N=m 80 W=m2 K 0.0059 N=cm s
q K Cp Ts Tl @c @T
lm T1 Lf
er c
hA
l
Table 2 Tandem GMAW parameters and related constants.
Fig. 2. Experimental apparatus.
Current type Wire feeding speed Wire diameter Travel speed Working angle Travel angle CA rA
Leading arc
Trailing arc
DC pulse 3 mpm 1.2 mm 80 cpm 45 Backward 70 2 0.2–0.3 cm
DC Pulse 3–6 mpm 1.2 mm 80 cpm 45 Forward 70 2 0.2–0.3 cm
3. Results and discussion
WFS 3mpm
Imax 180A
Imin 92A
Vmax 20V
Vmin 2V
Duty ratio 0.85
Freq. 30Hz
Vmin 21V 22V 22V 22V
Duty ratio 0.15 0.22 0.27 0.35
Freq. 70Hz 105Hz 120Hz 150Hz
(a)
WFS 3mpm 4mpm 5mpm 6mpm
Imax 450A 452A 453A 453A
Imin 41A 47A 51A 53A
Vmax 30V 30V 31V 32V
(b) Fig. 3. Welding voltage-current wave form: (a) leading and (b) trailing GMAW.
In this research, a three-dimensional transient numerical analysis model of tandem GMAW is achieved. The simulations were completed in two ways: one using conventional laminar flow assumptions, and the other a k-e turbulent model. Fig. 4 shows the results for various trailing GAMW conditions in the time sequence. The images were prepared in color to show the temperature distribution from room temperature to the melting temperature of steel. They are arranged in order of WFS in the columns and time in the rows. As the figure indicates, the simulation results of the laminar flow under a low current and voltage shows a humping bead, which is not observed in the experimental result. In contrast, the turbulent model of the same welding condition shows a smooth bead formation, which is much more realistic. A humping bead formation is usually due to the cooling of the base metal with an insufficient molten pool. The results of the laminar flow model in this simulation show an additional reason for the low diffusion coefficient value compared to the turbulent model. For a higher heat input, i.e., higher WFS, the difference between laminar and turbulent models becomes more dramatic. Laminar flow models still show a rough weld bead surface, and even full penetration and burn-through for a 6 mpm WFS case, which was also not observed in the experiment. On the contrary, the turbulent model shows a smooth bead and partial penetration, which coincides with the experiment. Verification of the simulation to experiment is accomplished through a cross-sectional bead comparison, as shown in Fig. 5. Locations of the cross-sectional planes were selected from a region in a fully developed quasi-steady state. The boundary of the fusion zone has a liquidus temperature of 1773 K, but is 1100 K for the heat-affected zone. As mentioned above, while the turbulent model shows a comparatively similar fusion zone area and shape under all conditions, the laminar flow model
K. Park et al. / International Journal of Heat and Mass Transfer 129 (2019) 1–6
5
Fig. 5. Cross-sections of tandem GMAW in lap joint fillet.
the weld pool reaches the bottom, finally resulting in full penetration and burn-through. On the other hand, the same downward stream is not conserved, but dissipates as vorticities according to the turbulence theory, which is why the turbulent model shows a more realistic weld pool flow pattern and bead formation coinciding with the experiment under various conditions. 4. Conclusions In this research, a three-dimensional turbulent weld pool simulation technique for a tandem GMAW in a lap joint fillet was developed and compared to a conventional laminar flow simulation. Basically, four governing equations were adopted: continuity, Navier-Stokes, energy, and the popular VOF equations. The turbulent model requires two additional governing equations of the turbulent kinetic energy and its dissipation rate equations. Both simulation results were compared to the tandem GAMW results of the 590 MPa grade lap joint fillet of automotive steel sheets. The results from the simulation can be summarized as follows. Fig. 4. Three dimensional simulation results: (a) laminar flow and (b) k e turbulent models.
shows coincident results only for the 5 mpm case. Therefore, the turbulent model is more suitable than the laminar flow to simulate at least the weld pool of the steel sheets, as the results indicate. Fig. 6 shows the temperature profile and fluid flow of the laminar and turbulent models for 6 mpm WFS trailing GMAW. Streamlines at the moment were generated to directly compare the flow pattern through a post processing. Whereas the maximum velocity of the laminar flow is 33.1 cm/s, it is 2.52 cm/s in the turbulent model. This is because of the strong –z directional stream caused by a droplet transfer and arc pressure. This downward flow is conserved in the laminar flow, and therefore
(1) The working and travel angles of the torches were considered through a coordinate transform, and the current–voltage wave forms with different welding characteristics were applied during the simulation. (2) The k-e turbulent model was verified by comparing it to a laminar flow model and experimental results. (3) The laminar flow model generated a burn-through and humping bead owing to the relatively low diffusion coefficient compared to the turbulent model. (4) In the k-e turbulent model, the Reynolds stress, which is expressed through the turbulent viscosity, increases along the turbulent kinetic energy, and the increased Reynolds stress in the molten pool showed similar results as the experiment thanks to the increasing diffusion coefficient. (5) The simulation model for a turbulent molten pool is more suitable for the tandem GMAW of steel sheets.
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K. Park et al. / International Journal of Heat and Mass Transfer 129 (2019) 1–6
Fig. 6. Molten pool behavior of 6mpm WFS trailing GMAW at 1.7 s. (a) laminar flow and (b) k-e turbulent models.
Conflict of interest Authors declare that there is no conflict of interest. Acknowledgment This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning, Korea (Grant No. 2016R1D1A1B03935036) and Technology Innovation Industrial Program funded by the Ministry of Trade, Industry & Energy, Korea (Grant No. 10052793 and Grant No. 10077517). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.046. References [1] Z. Cao, Z. Yang, X.L. Chen, Three-dimensional simulation of transient GMA weld pool with free surface, Weld. J. 85 (2004) 169s–176s.
[2] J. Cho, S.J. Na, Implementation of real-time multiple reflection and Fresnel absorption of laser beam in keyhole, J. Phys. D: Appl. Phys. 39 (2006) 5372– 5378. [3] J. Cho, S.J. Na, Theoretical analysis of keyhole dynamics in polarized laser drilling, J. Phys. D: Appl. Phys. 40 (2007) 7638–7647. [4] J. Cho, S.J. Na, Three-dimensional analysis of molten pool in GMA-Laser Hybrid welding, Weld. J. 88 (2009) 35s–43s. [5] R.T.C. Choo, J. Szekely, The possible role of turbulence in GTA weld pool behavior, Weld. J. 73 (1994) 25s–31s. [6] C.W. Hirt, B.D. Nichols, Volume of fluid method for dynamics of free boundaries, J. Comp. Phys. 39 (1981) 201s–225s. [7] J. Jaidi, K.S.S. Murthy, P. Dutta, A k-e model for turbulent weld pool convection in gas metal arc welding process, in: Proceedings of 6th International Conference on Trend in Welding Research, 2002, pp. 147–152. [8] H. Jeong, K. Park, Y. Kim, D.Y. Kim, M.J. Kang, J. Cho, Numerical analysis of weld pool for galvanized steel with lap joint in GTAW, J. Mech. Sci. Technol. 31 (6) (2017) 2975–2983. [9] C.H. Kim, W. Zhang, T. Debroy, Modeling of temperature field and solidified surface profile during gas-metal arc fillet welding, J. Appl. Phys. 94 (2003) 2667–2679. [10] L.S. Kim, A. Basu, A mathematical model of heat transfer and fluid flow in the gas metal welding process, J. Mater. Process. Technol. 77 (1998) 17–24. [11] D.V. Kiran, D. Cho, W. Song, S. Na, Arc interaction and molten pool behavior in the three wire submerged arc welding process, Int. J. Heat Mass Transfer 87 (2015) 327–340. [12] K.C. Taso, C.S. Wu, Fluid flow and heat transfer in GMA weld pools, Weld. J. 67 (1988) 70s–75s. [13] Y. Wang, H.L. Tsai, Impingement of filler droplets and weld pool dynamics during metal arc welding process, Int. J. Heat Mass Transf. 44 (2001) 2067– 2080.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Turbulent molten pool analysis of tandem GMA automotive steel sheet welding Kyungbae Park a, Hunchul Jeong a, Sungjin Baek a, Dong-Yoon Kim b, Moon-Jin Kang b, Jungho Cho a,⇑ a b
School of Mechanical Engineering, Chungbuk National University, Cheongju 28644, Republic of Korea Joining R&D Group, Korea Institute of Industrial Technology, Incheon 21999, Republic of Korea
a r t i c l e
i n f o
Article history: Received 10 April 2018 Received in revised form 3 August 2018 Accepted 10 September 2018
Keywords: CFD k–e turbulent model Laminar flow Lap joint fillet Molten pool Tandem GMAW
a b s t r a c t In this research, a three-dimensional turbulent weld pool simulation technique of tandem gas tungsten arc welding (GMAW) in a lap joint fillet is described and compared to a conventional laminar flow simulation. Basically, four governing equations are adopted for continuity, namely, continuity, Navier-Stokes, energy, and the popular volume of fluid equations. According to the basic theory of an arc weld pool, all known characteristics such as the arc heat input, arc pressure, electromagnetic force, and Marangoni flow are applied to the analysis model as a body force term or boundary conditions. A conventional arc weld pool analysis usually adopts a laminar flow; however, its results have shown a weld bead shape that is quite different from an experiment of a tandem GMA lap joint fillet welding of an automotive steel sheet. Therefore, the authors suggest the use of a k-eturbulent analysis model and show that its results coincide with the experiment results. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Tandem gas metal arc welding (GMAW) is a welding technique that uses two welding wires at the same time in parallel for higher productivity through an increase in the deposition rate. Although this technique is often used in shipbuilding and heavy industry, there have been trials in applying the method to the automotive industry. Although zinc-coated steel sheets are widely used by OEM makers to improve the corrosion resistance of body in white (BIW), zinc pores in the beads remain a significant problem. At this point, a tandem arc scheme may be a solution. Between two parallel arcs, the leading one plays a role in removing the zinc coating before joining, and the other trailing arc practically welds the joint. The mechanism sounds simple; however, a difficulty remains in setting up a power balance of the two arcs because their arc pressures and electromagnetic forces affect the molten pool flow behavior. In addition, it is preferable for the leading arc to play a role in removing the zinc coating at the gap and not melt the base metal. A numerical analysis of a molten pool is required in this aspect because experiments and observations using a high-speed camera require an extra budget in addition to the limit of temperature field profiling. It is possible to expect a molten pool flow pattern and temperature distribution through a numerical simulation. ⇑ Corresponding author. E-mail address: [email protected] (J. Cho). https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.046 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
Tsao and Wu [12] and Kim and Basu [10] developed numerical analysis models of GMAW during the early period, which artificially add latent heat and momentum energy to express a droplet transfer without a free surface consideration. Kim et al. [9] dealt with the droplet transfer as a virtual volumetric heat source. Hirt and Nichols [6] developed the popular volume of fluid (VOF) method, which made it possible to successfully express the free surface of a fluid. Wang and Tsai [13] first simulated a two two-dimensional molten pool from arc welding and a droplet transfer problem using the VOF technique. Cao et al. [1] expanded a VOF-based molten pool simulation to a threedimensional model. Cho and Na [2] made advancements in the VOF molten pool model in a laser keyhole simulation when considering real-time multiple reflections. Cho and Na [3] suggested more concrete molten pool analysis model of laser keyhole welding considering polarized beam absorption. Cho and Na [4] added GMA analysis model to the old one then reported molten pool flow characteristics of laser-GMA hybrid welding. Kiran et al. [11] extended the model to a tandem arc welding simulation and created a foundation. Although a molten pool actually shows a turbulent behavior, all previous works above assume it as laminar. Other cases have followed. Choo and Szekely [5] first developed a turbulent molten pool simulation model of gas tungsten arc welding (GTAW), and showed higher accuracy in the model compared to a laminar case. Jaidi et al. [7] expanded the turbulent model to a GMAW simulation. However, both of the
2
K. Park et al. / International Journal of Heat and Mass Transfer 129 (2019) 1–6
Nomenclature CA Cp F ! F fd rA h hA I K Lf n P PA qA rA T Tl Ts
T1 t Ui
concentration coefficient of arc specific heat volume fraction occupied by fluid electromagnetic force per unit volume droplet transfer frequency effective radius of arc enthalpy convection coefficient welding current thermal conductivity latent heat of fusion normal component pressure arc pressure arc heat flux effective radius of arc temperature liquidus temperature solidus temperature
Greek symbols c surface tension es emissivity ga heat input efficiency gd droplet heat efficiency l viscosity l0 magnetic permeagility in vacuum lm magnetic permeability of metal lt turbulent viscosity p circular constant q density r normal stress rs Stefan-Boltzmann constant s tangent direction
previous turbulent models were two-dimensional and did not consider the effects of a free surface. In this research, a numerical analysis model of a threedimensional transient molten pool was newly developed for a tandem GMA of lap joint fillet welding using the commercial package, Flow-3D. The base metal widely used in the automotive industry is 2.3-mm thick zinc-coated steel. Owing to the diameter of each torch, two torches are inclined to satisfy the distance between arcs, which means the arc surface heat flux and electromagnetic body force are also inclined. Therefore, the authors’ previous model has been newly improved to simulate the complex torch setup of tandem GMAW. Development of the simulation was first achieved using a previous laminar flow model, but did not coincide with the experiment, and therefore the model was improved to a turbulent k-e flow. The numerical analysis model is basically composed of four governing equations: continuity, Navier-Stokes, energy, and VOF equations. Two more equations are required in a turbulent model, namely, a turbulent kinetic energy equation and its dissipation rate. Arc heat input is applied as the surface heat flux with a Gaussian distribution. Electromagnetic force and buoyancy are adopted as the body force term in a Navier-Stokes equation. Radiation, convection heat loss, Marangoni shear force, arc pressure, and surface tension pressure are applied as the boundary conditions. 2. Governing equations and boundary conditions In a turbulent weld pool analysis, a total of six governing equations are required: VOF, continuity, momentum, energy, turbulent kinetic energy, and its dissipation rate equations. The first, a VOF equation, makes it possible to track the free surface of a flow. A VOF equation is a kind of continuity equation. In other words, it expresses a conservation of value F, which is between zero and 1. If the value is 1, it means the control volume is full of the flow, whereas a value of zero indicates that the volume is empty. Connecting the cells with values between zero and 1 is the principle of free surface tracking. The governing equation is as follows.
DF @F @FU i ¼ þ ¼0 Dt @t @xi
ambient temperature time velocity tensor
ð1Þ
The continuity equation of mass conservation for an incompressible and Newtonian fluid is as follows.
@U i ¼0 @xi
ð2Þ
The conservation equation of momentum for an eddy viscosity model is induced as follows.
@U i @U i 1 @P @ ¼ þ þ Uj @t @xj q @xi @xj
l þ lt @U i þ Bi q @xj
ð3Þ
The source terms Bi in momentum Eq. (3) include the electromagnetic and buoyancy forces, where lt is the eddy viscosity coefficient. By considering the latent heat of fusion, the energy equation, assuming that the kinetic and potential energies are negligible, is expressed as follows.
@h @h @ þ Uj ¼ @t @xj @xj
C p lt @T Kþ Prt @xj
ð4Þ
h ¼ C p T þ f ðT Þ Lf
f ðT Þ ¼
8 > < > :
ð5Þ
0; ðT T s Þ TT l T l T s
; ðT s < T < T l Þ
ð6Þ
1; ðT T l Þ
where Pr t is turbulent Prandtl number in the second term of right side of Eq. (5).
lt ¼ C l q
2
k
ð7Þ
e
The eddy viscosity coefficient in Eq. (7) is expressed through a multiplication of the velocity and length scales. Because the velocity and length scales in the standard k-e model are determined based on the turbulent kinetic energy and dissipation rate, transport equations of turbulent kinetic energy and dissipation rate are required, respectively. Transport equations are defined as follows.
@ ðqkÞ @ ðqkÞ @ ¼ þ Uj @t @xj @xj
lþ
lt @k @U i qui uj qe rk @xj @xj
ð8Þ
3
K. Park et al. / International Journal of Heat and Mass Transfer 129 (2019) 1–6
@ ðqeÞ @ ðqeÞ @ ¼ þ Uj @t @xj @xj
lþ
lt re
@e e @U i e2 þ C 1e qui uj C 2e q @xj k @xj k ð9Þ
ui uj
where q is called the Reynolds stress and the various turbulent constants are set up according to standard values which can be found in textbooks in easy. As boundary conditions, the top surface of base metal is exposed to two GMA heat sources and heat loss of convection and radiation. Mathematical expression of surface heat flux is as follow.
K
@T ¼ qtrailing þ qleading hA ðT T 1 Þ re es ðT T 1 Þ @n
2 VI x þ y2 qA ¼ gA exp C A r 2A C A pr 2A
ð11Þ
1 r A ¼ z þ 0:3 3
ð12Þ
where gA is the heat input efficiency of GMAW, which has a representative value of 0.8. In addition, assuming the droplet transfer is in spray mode, a droplet has heat capacity qd . The heat of the droplet is directly transferred to a molten pool with frequency f d as the actual volume heat source following the VOF technique.
fd ¼
3r 2w V WFR 4r 3d
ð13Þ
qd ¼
4 3 pr C p T d f d 3 d
ð14Þ
The molten pool surface is subjected to stresses of arc pressure and surface tension, and thus the mathematical expression of this pressure boundary condition on the top surface is as follows.
@V n c ¼ PA þ @n Rc
PA ¼
l0 I2 x2 þ y 2 exp 4p2 r2A 2r 2A
! F ¼
! I2 lm r2 r2 z 2 x b i 1 exp 1 2 2 exp c r 4p rr A 2r A 2 2r A 2
! I 2 lm r2 r2 z 2 y b þ 2 2 exp 1 exp 1 j c r 4p rr A 2r A 2 2r A 2
ð10Þ
where the third and fourth terms on the right side are convectional and radiational heat losses, respectively. The first and second terms on the right side are arc heat inputs. In this study, the arc heat source model for a welding simulation adopts a Gaussian distribution [8], the value of which for an effective radius is linearly proportional to the arc center, namely, from 0.2 to 0.3 cm.
P þ 2l
current flow direction. With this reason, the molten pool simulations used a simplified electromagnetic force model, such as the follow.
ð15Þ ð16Þ
! 2 I2 lm r2 z b k 1 1 exp þ c 4p 2 r 2 c 2r A 2
To consider the travel and working angles, the coordinate transformation based on a welding torch was applied to the analysis.
2 3
^ A 32 3 2 32 x 1 0 0 cos/ 0 sin/ 6x7 6 A^ 7 6 6 76 7 6 y 7 ¼ 4 0 cosh sinh 7 y 0 1 0 4 5 4 5 5 6 7 4^5 z 0 sinh cosh sin/ 0 cos/ A z
@V s @ c @T ¼ @n @T @ s
ð17Þ
The electromagnetic force applied by an interaction between the current flow and the magnetic field induced is expressed as
! ! ! F ¼ I B
ð18Þ
The free surface of a molten pool continuously changes. Therefore, it takes a significant amount of time to compute the electromagnetic force for each cell with respect to a mutually different
ð20Þ
where h and / represent the travel and working angles, respectively. Fig. 1 shows a schematic of the welding joint and torch positions. The numerical analysis domain has a 70 mm length in the x-direction, and 30 mm and 10 mm lengths in the y- and zdirections, respectively. Each axis is divided into a 0.4 mm length, and therefore the analytic domain has a total of 328,125 control volume cells. As shown in Fig. 1, in the VOF method, part of the domain is set to have an F value of 1 to be assigned as a base metal, and the rest of the domain is set to zero. Fig. 2 shows the actual experimental setup. As the figure indicates, there are leading and trailing arcs in tandem GMAW. Both GMAs use a pulsed current, and their setups are as demonstrated in Fig. 3. The leading arc has a fixed wire feeding speed (WFS), whereas the trailing arc has various speeds. Various variables exist, such as the current and voltage, but they are already fixed through a pre-experiment for a synergic line. Widely used 590 MPa grade zinc-coated steel sheets of 2.3-mm thickness were used in the experiment, the thermophysical properties of which are shown in Table 1. The welding process variables applied are listed in Table 2.
The second term on the left side of Eq. (15) denotes Newton’s viscosity law on a weld pool surface in the normal direction. In addition, the first term on the right side expresses the arc pressure, and the other indicates the surface tension pressure from the curved surface. During the welding process, shear stress, which creates a tangential flow, is generated by a change in the surface tension gradient depending on the temperature. This phenomenon, called a Marangoni flow, is defined as follows.
l
ð19Þ
Fig. 1. Schematic diagram of tandem GMAW in lap joint fillet.
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K. Park et al. / International Journal of Heat and Mass Transfer 129 (2019) 1–6 Table 1 Thermophysical properties of SGAFH 590FB(2.3 mm). Property
Value
Symbol 3
Density Thermal conductivity Specific heat Solidus temp Liquidus temp Surface tension gradient
S: 6900/L: 7800 kg=m S: 32.3/L: 26.9 W/m K S: 726/L: 26.9 J/kg K 1723 K 1773 K 0.2e3 N=m K
Magnetic permeability Ambient temp Latent heat of fusion Emissivity Surface tension Convection Coefficient Viscosity
1.26e6 H=m 273 K 277 KJ=Kg 0.8 1.8 N=m 80 W=m2 K 0.0059 N=cm s
q K Cp Ts Tl @c @T
lm T1 Lf
er c
hA
l
Table 2 Tandem GMAW parameters and related constants.
Fig. 2. Experimental apparatus.
Current type Wire feeding speed Wire diameter Travel speed Working angle Travel angle CA rA
Leading arc
Trailing arc
DC pulse 3 mpm 1.2 mm 80 cpm 45 Backward 70 2 0.2–0.3 cm
DC Pulse 3–6 mpm 1.2 mm 80 cpm 45 Forward 70 2 0.2–0.3 cm
3. Results and discussion
WFS 3mpm
Imax 180A
Imin 92A
Vmax 20V
Vmin 2V
Duty ratio 0.85
Freq. 30Hz
Vmin 21V 22V 22V 22V
Duty ratio 0.15 0.22 0.27 0.35
Freq. 70Hz 105Hz 120Hz 150Hz
(a)
WFS 3mpm 4mpm 5mpm 6mpm
Imax 450A 452A 453A 453A
Imin 41A 47A 51A 53A
Vmax 30V 30V 31V 32V
(b) Fig. 3. Welding voltage-current wave form: (a) leading and (b) trailing GMAW.
In this research, a three-dimensional transient numerical analysis model of tandem GMAW is achieved. The simulations were completed in two ways: one using conventional laminar flow assumptions, and the other a k-e turbulent model. Fig. 4 shows the results for various trailing GAMW conditions in the time sequence. The images were prepared in color to show the temperature distribution from room temperature to the melting temperature of steel. They are arranged in order of WFS in the columns and time in the rows. As the figure indicates, the simulation results of the laminar flow under a low current and voltage shows a humping bead, which is not observed in the experimental result. In contrast, the turbulent model of the same welding condition shows a smooth bead formation, which is much more realistic. A humping bead formation is usually due to the cooling of the base metal with an insufficient molten pool. The results of the laminar flow model in this simulation show an additional reason for the low diffusion coefficient value compared to the turbulent model. For a higher heat input, i.e., higher WFS, the difference between laminar and turbulent models becomes more dramatic. Laminar flow models still show a rough weld bead surface, and even full penetration and burn-through for a 6 mpm WFS case, which was also not observed in the experiment. On the contrary, the turbulent model shows a smooth bead and partial penetration, which coincides with the experiment. Verification of the simulation to experiment is accomplished through a cross-sectional bead comparison, as shown in Fig. 5. Locations of the cross-sectional planes were selected from a region in a fully developed quasi-steady state. The boundary of the fusion zone has a liquidus temperature of 1773 K, but is 1100 K for the heat-affected zone. As mentioned above, while the turbulent model shows a comparatively similar fusion zone area and shape under all conditions, the laminar flow model
K. Park et al. / International Journal of Heat and Mass Transfer 129 (2019) 1–6
5
Fig. 5. Cross-sections of tandem GMAW in lap joint fillet.
the weld pool reaches the bottom, finally resulting in full penetration and burn-through. On the other hand, the same downward stream is not conserved, but dissipates as vorticities according to the turbulence theory, which is why the turbulent model shows a more realistic weld pool flow pattern and bead formation coinciding with the experiment under various conditions. 4. Conclusions In this research, a three-dimensional turbulent weld pool simulation technique for a tandem GMAW in a lap joint fillet was developed and compared to a conventional laminar flow simulation. Basically, four governing equations were adopted: continuity, Navier-Stokes, energy, and the popular VOF equations. The turbulent model requires two additional governing equations of the turbulent kinetic energy and its dissipation rate equations. Both simulation results were compared to the tandem GAMW results of the 590 MPa grade lap joint fillet of automotive steel sheets. The results from the simulation can be summarized as follows. Fig. 4. Three dimensional simulation results: (a) laminar flow and (b) k e turbulent models.
shows coincident results only for the 5 mpm case. Therefore, the turbulent model is more suitable than the laminar flow to simulate at least the weld pool of the steel sheets, as the results indicate. Fig. 6 shows the temperature profile and fluid flow of the laminar and turbulent models for 6 mpm WFS trailing GMAW. Streamlines at the moment were generated to directly compare the flow pattern through a post processing. Whereas the maximum velocity of the laminar flow is 33.1 cm/s, it is 2.52 cm/s in the turbulent model. This is because of the strong –z directional stream caused by a droplet transfer and arc pressure. This downward flow is conserved in the laminar flow, and therefore
(1) The working and travel angles of the torches were considered through a coordinate transform, and the current–voltage wave forms with different welding characteristics were applied during the simulation. (2) The k-e turbulent model was verified by comparing it to a laminar flow model and experimental results. (3) The laminar flow model generated a burn-through and humping bead owing to the relatively low diffusion coefficient compared to the turbulent model. (4) In the k-e turbulent model, the Reynolds stress, which is expressed through the turbulent viscosity, increases along the turbulent kinetic energy, and the increased Reynolds stress in the molten pool showed similar results as the experiment thanks to the increasing diffusion coefficient. (5) The simulation model for a turbulent molten pool is more suitable for the tandem GMAW of steel sheets.
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K. Park et al. / International Journal of Heat and Mass Transfer 129 (2019) 1–6
Fig. 6. Molten pool behavior of 6mpm WFS trailing GMAW at 1.7 s. (a) laminar flow and (b) k-e turbulent models.
Conflict of interest Authors declare that there is no conflict of interest. Acknowledgment This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning, Korea (Grant No. 2016R1D1A1B03935036) and Technology Innovation Industrial Program funded by the Ministry of Trade, Industry & Energy, Korea (Grant No. 10052793 and Grant No. 10077517). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.046. References [1] Z. Cao, Z. Yang, X.L. Chen, Three-dimensional simulation of transient GMA weld pool with free surface, Weld. J. 85 (2004) 169s–176s.
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