## Abstract

The purpose of this research is to understand the formation of double fillet welds using finite element modeling. This computational study is intended to be an advanced way to predict heat transfer mechanisms in the melt pool prior to empirical testing. AISI 304 austenitic stainless steels are used in this study, and a simplified model of fin-tubes is introduced to simulate submerged arc welding (SAW) on a water wall panel structure. The welding process is numerically implemented by a moving heat source, and the heat distribution is determined by thermo-physical phenomena, e.g., recoil pressure and surface tension due to the welding. Double fillet welding refers to two separate welds which have to be made one by one. A new coordinate system is thus introduced at every starting point of the welding process to overcome geometrical complexities. The computational results are discussed to compare the weld bead estimation with the experimental findings. The melting and evaporation of the metal appear appropriate to explain the formation of weld beads in submerged arc welding since the modeling is in good agreement with the experiments.

## 1 Introduction

Tube membrane panels serve to cool a boiler in modern power plants. The panels, often called water walls, are a simple but effective structure for conveying coolant in many applications. AISI 304 stainless steels are the most common materials used in the stainless steel fabrication industry. Type 304 stainless steels have a face-centered cubic crystal structure that provides high ductility and excellent workability. AISI 304 is, moreover, widely used to manufacture membrane wall panels because the chromium content enhances the resistivity to water corrosion. Although 304 L, which has a lower carbon content, helps to minimize carbide precipitation during welding, 304 stainless steels are used in many of the same applications because of lower material costs. The use of 304 and 304 L stainless steels is not significantly different. AISI 304 is therefore suitable for pipe welding due to excellent corrosion resistance, good machinability, and weldability. Viswanathan et al. noted that SAW is considered the most practical method to produce heat exchangers in power plants due to its high productivity [1].

Welding relied heavily on experimental approaches for a comprehensive understanding of weld formation in early studies. The development of computer technologies has influenced computer-based simulation and motivated the search for a precise understanding of welding for several decades. Many researchers had developed numerical welding techniques to evaluate temperature and stress distribution. Rosenthal introduced a point heat source model traveling along an extremely long weld to simulate weld surface melting [2]. By further developing Rosenthal's equation, Swift-Hook and Gick offered thermal welding power for melting [3]. Hibbitt and Marcal proposed a two-dimensional (2D) static finite element (FE) code to predict the stress distribution during welding [4]. Muraki et al. have developed an FE code related to the elastoplastic behavior of weld metal [5]. Friedman used an FE analysis to predict temperature, stress, and deformation in welding [6]. Advances in computing equipment have made three-dimensional (3D) analysis more accessible since the 1990s. A transient welding simulation has also become easier to complete. For many years, Brown and Song have been involved in introducing time-dependent 3D welding simulations using commercial software packages [7]. The use of FE modeling has become more and more popular in welding simulation. Several finite element analysis (FEA) tools, e.g., ABAQUS, ANSYS, and SYSWELD, have been used in welding research.

Nart and Celik performed an FE-based calculation to understand the formation of an irregular weld pool during the SAW [8]. Podder et al. compared experimental results with FEA results to understand the relationship between welding geometry and heat source parameters [9]. Zargar's research was focused on understanding how the SAW sequence affects the residual distortion of the fillet welded plates [10]. Ansaripour et al. tried to find a solution to minimize the residual stresses and distortion induced by the SAW process [11]. However, simulation of multiple welds has rarely been performed due to the geometric complexity of the numerical application. Many prior welding studies have used single-pass welding on a global coordinate system using a predefined heat source model, e.g., Goldak double ellipsoidal model. In the study, two welds were numerically simulated to account for the time-differential thermal effect during the sequential welding procedure. Fluid flow and heat transfer in different states of matter should be involved simultaneously; therefore, ANSYS-Flotran, a former commercial version of ANSYS, was utilized to simulate the melt flow behavior. A new melt flow solution has been proposed to describe the spontaneous generation of weld pool, as well as a new Gaussian heat source model. A support algorithm has been subcoded in the FEA program to explain the thermal effect of liquid melt flow during welding. A simplified quasi-2D technique, which applied volumetric load to plane models, has been newly proposed for fast computation. A numerical approach to understanding melt dynamics was the primary objective of this research, and experimental observations were compared to verify the suitability of proposed methods.

## 2 Modeling and Characteristic Properties

Tube membrane panels are made up of circular tubes and rectangular fins placed between them. The panels are generally over 10 meters long and are composed of multiple tubes and fins. The outer diameter (OD) of a tube is 44.45 mm (1.75 inches) and 7.62 mm (0.3 inches) thick. A 1.6-mm-diameter electrode wire was supplied to produce a weld bead, and it was assumed that the filler wire was completely melted during welding. Assuming continuous feed of the filler wire, the weld bead would have a stable melting area during the SAW process. An experimental observation was carried out to determine the size of the weld deposit. Although the melting zone could be much deeper and wider, the deposition zone was approximately 10 mm^{2} of triangular shape. Figure 1 illustrates the size of the weld deposit during double fillet fin-tube welding.

Large-scale FEA might require enormous computing resources. A suitable model should be selected to achieve a reliable outcome within a reasonable time frame. Goldak et al. proposed a useful technique splitting a geometric symmetry of a repetitive pattern due to limited computer resources [12]. The smallest repeating unit was modeled to save computation time, and its geometries are detailed in Fig. 2. A symmetrical boundary condition was imposed on the vertical symmetry planes of the half fin-tube model to remove repeated geometric patterns. An expected melting zone within the fusion line was finely meshed to have a 0.2 mm long quadrilateral element by specifying the divisions and the spacing ratio on the lines.

No forced convection was applied inside the tube because there was no air blowing through it. The hollow path was also considered too long and narrow to allow significant natural convection. The inner wall of the tube has therefore been treated as adiabatic. The $k$ and $h$ values had to be determined to complete the $L\u221e$ approximation. The length $L\u221e$ was calculated to be about 595 mm based on the convection heat transfer coefficient of 5 W/(m^{2}·K). The 10-metre panel was therefore long enough to meet the demands of infinity; thus, a 2D approach could be possible for thermal analysis.

Equation (3) proposed by Goldak used a constant emissivity of 90% for a SAW simulation on carbon steel. Liu et al., however, stated that the emissivity of stainless steels depends on temperature. They provided an expression of emissivity for AISI 304 stainless steels as of $\epsilon =0.171,37+0.103,53ln(T\u2212744.092,88)$ in the temperature range of 477–877 °C [17]. Shurtz's experiments showed that the emissivity was strongly temperature-dependent in the temperature range of 25–1100 °C. [18]. Hence, a new combined $h\xaf$ was developed as of Eq. (4) by using temperature-dependent emissivity data of Liu and Shurtz instead of using the Goldak equation for an accurate calculation. $\sigma $ is the stefan-Boltzmann constant, $\epsilon $ is the emissivity of AISI 304 stainless steels, and $T\u221e$ is room temperature. The newly proposed $h\xaf$ was compared to the conventional $h\xaf$ of Goldak, as shown in Fig. 4. The new $h\xaf$ rapidly increased from 5 to 290 W/(m^{2}·K) in the temperature range of ambient to 1400 °C. The new heat transfer coefficient that combined convection and radiation was slightly different, but it was well in agreement with Goldak's findings.

## 3 Welding Procedures

A welding speed of 14 mm/s was used for the welding simulation, and the welding speed was referenced to actual SAW practices. Figure 5 shows the manufacturing process of SAW. Welding was conducted on the upper side and then sequentially on the lower side in the SAW simulation. The welding was completed within seconds, but the overall process required more time for sufficient solidification and air cooling.

Three different coordinate systems were defined in the simulation: one for the entire field and the others for the moving heat source. An automatic welding gun is normally held at a 45 deg angle to the vertical in the SAW process. A coordinate system known as global (0 deg) was used for a 2D plane system composed of the Cartesian *x*-axis and *y*-axis. Two different local coordinate systems were designed for 45 deg (upper) and 135 deg (lower) inclined areas where the heat source was expected to move. The actual welding was first done by creating upper welds, and the whole structure was rotated backward for the opposite welding procedure. However, the simulation handled the turn by sequentially applying the welding heat to the two separate local coordinates.

## 4 Mathematical Approaches

### 4.1 Welding Heat.

The total heat rate of the arc welding gun is simply expressed in $q=\eta VI/v$, where $\eta $ is the arc welding efficiency, $v$ is the welding speed, And $V$ and $I$ are voltage and ampere, which define the electrical power of the welding. No loss in welding efficiency was assumed as Jeffus described 99% arc efficiency for the SAW [19]. Molten electrode droplets were believed to have been deposited at the fin–tube junction. The heat source was given as a form of droplets to exclude the preset geometry as shown in Fig. 6. The droplet size was about the same as the deposit, which was approximately 10 mm^{2} in size and triangular in shape.

The heat source was a function of time and velocity moving perpendicular to the cross section as shown in Fig. 7. $t0$ and $t1$ indicate the time steps for the former and the latter respectively because the heat source was a function of the time that passed along the weld line. Heat dissipation was assumed to occur through heat conduction when the heat was leaving the point of interest. The heat source did not depend on the predetermined heat dissipation along the weld line, although the universal Goldak's heat source model included a half-ellipsoid for its progressive disappearance. The welding parameters used in the FE computation are listed in Table 1.

Parameters (Unit) | Welding speed (mm/s) | Voltage (V) | Current (A) |
---|---|---|---|

Values | 14 | 24 | 300 |

Parameters (Unit) | Welding speed (mm/s) | Voltage (V) | Current (A) |
---|---|---|---|

Values | 14 | 24 | 300 |

where $q\u02d9$ is the heat intensity obtained by a nominal heat density $q0$. $r$ is the expected radius of the molten electrode droplet. $m$ is a heat distribution factor that contributes to the heat density in the center [16]. $x$ is any position in radius $r$ and $v$ is a welding speed. Heat intensity was maximized at the center of the moving heat source, and the heat had the lowest value (near zero) at the border edges. The heat input was given in terms of coordinates and time. The heat was distributed to a target area as the heat source moved along the weld line.

where $\rho $ and $cp$ are density and specific heat. In the medium, heat generation $q\u02d9$ was associated with the volumetric heat source or power density $q\u02d9$. A solid–liquid transition requires considerable thermal energy to transform a substance, and specific heat is one of the important characteristics indicating phase transformation. The specific heat during the transition has been correctly changed to include all possible thermal reactions in the discrete time-based calculation. A commercial software JMatPro was used to verify the thermal conductivity ($cp,\u2009JMatPro$) in advance and has been modified as $cp,\u2009modified$ appropriate for numerical calculation. Figure 8 shows the adjusted specific heat of AISI 304 stainless steels at high temperatures. The governing equation Eq. (7) was numerically computed using the finite element method.

### 4.2 Viscous Flow.

Matsumoto et al. measured surface tension in molten stainless steels. The surface tension of 304 stainless steels was obtained at temperatures of 1550 °C–1800 °C (1823–2073 K), and the equation was given as $\gamma =\u22120.12\xd7T+1980$ (mN/m) with respect to temperature in Kelvin [25]. Zacharia and David found that the use of a constant surface tension gradient was appropriate for high current welding experiments [26]. Therefore, the surface tension gradient of −0.12 was applied to the weld pool surface when the material heated above the melting point.

## 5 Results

### 5.1 Suitability Validation.

Heat dissipates and spreads in all three directions during welding (*x*, *y*, and *z* axes). 3D heat transfer is thermally more conductive than 2D due to the significant effect of through-plane heat conduction. Wahab et al. measured melt penetration using 2D and 3D models and described that the heat in the plane dissipated more quickly in the 2D domain [28]. However, the thermal analysis result of the 2D and 3D models is expected to be approximately the same if the heat input from welding exceeds the dissipation. The SAW method is highly productive because it effectively avoids heat loss, and the arc can penetrate thicker materials deeply [29]. Heat intensity or heating time would have an effect on the penetration of melt. A simplified 2D welding simulation was therefore considered appropriate for the thermal analysis of the SAW process if the heating time was long enough.

A numerical calculation has been added to verify the adequacy of the 2D simulation for heat conduction. The general design of the study was to apply a 3D heat source model on a 2D cross section plane model. The validity of the quasi-2D approach was therefore verified by comparing heat conduction of the 2D results with a conventional 3D process using a preset volumetric heat source. The preset model had a double ellipsoid shape of heat distribution, with the highest heat intensity at the center and a decrease away from the center. The adequacy of the quasi-2D simulation was verified by measuring the depth of melt penetration in the 2D and 3D models while applying the same predefined heat. The thermal analysis results for the quasi-2D and 3D models are shown in Fig. 9. The simple analytical model was assumed to be suitable for certain welding speeds, as long as there is enough heating time.

The purpose of the verification was to determine whether a 3D model could be replaced by a quasi 2D model for fast computation. The moving heat source was set in the same manner in 2D and 3D to assess the effect of the welding speed only. The welding speed was tested as 7 mm/s, 14 mm/s, and 28 mm/s to observe the difference in melt penetration. Figure 10 shows the change in penetration ratio between 2D and 3D according to the welding speed. The 2D and 3D results were similar if the ratio was close to 1, but the 2D melt pool became much bigger than 3D if the ratio approached 0. The result showed little difference between 2D and 3D at a welding speed of 14 mm/s, as the calculated ratio of 0.98 was close to 1. The simulation study was therefore conducted using a quasi 2D simplified model.

### 5.2 Distribution of Temperature.

A heat source was simulated to travel across the section of the fin-tube structure at a speed of 14 mm/s. The heat source was modeled by dispersion over the target surface, and the melt penetration was related to melting and evaporation dynamics. The evolution of the melt pool over time is described in Fig. 11. A red-colored region represented a melting zone (MZ) that was above the liquidus temperature (1450 °C) of AISI 304 stainless steels. The melt pool began to grow with the heat input at the beginning of welding. Surface tension on the melt surface was activated over the melting point due to the temperature gradient created by the welding heat. The melts were drawn by surface tension to a base metal from the center of the heat source due to the elevated temperature gradient. Evaporation of the melt led to an increase in pressure when the melting temperature exceeded the boiling point due to the continuous heat supply. The melt front was pushed away by the overpressure, and the pressure equilibrium process would raise the pool's depth by exerting undue pressure on the melt front. As a result, the recoil pressure caused the melt to penetrate deep into the base metal.

Air cooling started simultaneously when the welding heat was withdrawn. The melt stopped penetrating due to a reduced evaporation rate, and the melt would have begun to widen the pool horizontally by the surface tension of the melt. The melt surface was expected to have increased during the air cooling cycle, but this was not the case. The surface tension might seem less effective for widening because the area of recoil pressure applied was much larger than the surface tension. Because arc welding distributed heat extensively compared to a particular type of welding, e.g., laser welding, which was used to achieve deep and narrow penetration. Recoil pressure was therefore thought to dominate the melt dynamics in SAW more than any other thermophysical phenomenon.

The bottom was welded after the upper weld, as shown in Fig. 12. An air cooling of 1 h was performed to cool the welded structure to ambient temperature, similar to the actual SAW procedure. The shape of the second weld appeared to be the same as the first weld because there was no residual heat left from the first process. The fusion boundary was assumed to be between 1400 (solidus temperature of 304 stainless steels) and 1450 °C. A heat-affected zone (HAZ) has been initiated from the boundary of the MZ. Sheng and Joshi indicated that the lowest temperature limit for HAZ in AISI 304 stainless steels would be 400 °C [30]. Therefore, the HAZ was considered to be between 400 and 1400 °C. The estimation of MZ and HAZ is described in Fig. 12. The size of the MZ was determined by measuring the region above the liquidus point. The computed maximum melt depth was approximately 6.4 mm, and the measured experimental depth was 6 mm as of Fig. 1. The calculated weld size was therefore well agreed with the estimation made at the modeling stage without a predetermined heat source model.

### 5.3 Effect of Melt Dynamics.

The main objective of the study was to use a nonpredefined heat source model. Precisely, a designated welding heat source model, which was primarily from experimental observations, was restricted in order to understand the effect of melt dynamics. The factors determining the growth of the weld pool were thought to be the fluidity of the molten metal and the force to agitate it. Two different cases with and without recoil pressure were compared to measure the effect of the molten fluid flow on the evolution of the melt pool. Figure 13 provides estimates of a simulation with or without recoil pressure.

Melting could occur before the center of the heat source approaches the point of interest due to the application of Gaussian distribution. This study therefore required a minuscule time interval to measure any change in the melt which depended on the welding rate. A millisecond interval was used to monitor the melt fluidity until the recoil pressure was triggered. Once the recoil was activated, the evolution of the melt pool was measured every 10 milliseconds. The time-step effect was assumed to be negligible after the maximum welding pool, and the interval was gradually increased from 1 to 100 s for quick calculation.

The thermal energy from the welding heat continued to influence the vaporization of the molten liquid so that rapid evaporation increased the pressure in the melting pool. The melt would have significantly penetrated due to the overpressure, which continued for a short period of time. Since the red color indicated a temperature above the melting point, the red area was expected to be a final weld after cooling to room temperature. All solids were expressed as blue and other bright colors: cyan and green. During the first penetration phase, the melt penetrated toward the bottom left corner (225 deg) because of a sudden increase in the pressure on the melt front. The penetration increased further as the pressure in the melt continued to rise above the initial penetration. It was therefore apparent that the presence of recoil pressure had a significant effect on the growth of the melting pool.

On the other hand, there was no significant change in melt depth without recoil pressure. There was only a small expansion of the melting pool due to the heat approaching the point of interest over time. As seen in the velocity profile, the melt appeared stagnant with no impact for deep drilling. The SAW simulation clearly demonstrated that recoil pressure was the driving force in expanding the melting pool. The use of melt dynamics was useful in estimating the size of the weld pool without a predefined heat source.

## 6 Conclusions

New models have been employed to understand the evolution of the melt pool. The Goldak double ellipsoid model, which was commonly employed, has been replaced by a newly proposed disc-shaped heat source model with no predefined heat penetration. Multipass welding was proposed although the most of studies was based on a single-pass welding simulation in the past. Melt dynamics, e.g., recoil pressure and surface tension have been subcoded in the numerical computation to theoretically reproduce melt penetration. A new quasi-2D simulation, 3D Thermal load on 2D model, was adopted for fast computation and tested for its adequacy. The new approaches mentioned above were validated by measuring the actual welding results. The result of the weld depth calculation was very much in agreement with the empirical findings. This computational study was effective to describe the formation of melt pool by incorporating numerical modeling of fillet welding and understanding of thermophysical phenomena. According to the double fillet welding mode studies, the results lead to the following conclusions:

The proposed quasi-2D approach was considered appropriate for a rapid simulation of SAW.

According to the final weld geometries, the recoil pressure is a key attribute in the development of the deep melting pool.

Melting behavior can be foreseen using numerical calculation techniques, and coupled thermo-fluid analysis can provide a better understanding of melting behavior in welding.

## Author Contribution Statement

The author confirms sole responsibility for the following: study conception and design, data collection, analysis, and interpretation of results, and manuscript preparation.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

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