Accepted Manuscript Thermal model of the Gas Metal Arc Welding hardfacing process Andrzej Sachajdak, Jacek Słoma, Ireneusz Szczygieł PII: DOI: Reference:
S1359-4311(17)35139-6 https://doi.org/10.1016/j.applthermaleng.2018.05.120 ATE 12259
To appear in:
Applied Thermal Engineering
Received Date: Accepted Date:
1 September 2017 28 May 2018
Please cite this article as: A. Sachajdak, J. Słoma, I. Szczygieł, Thermal model of the Gas Metal Arc Welding hardfacing process, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/j.applthermaleng. 2018.05.120
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Thermal model of the Gas Metal Arc Welding hardfacing process Andrzej Sachajdaka,∗, Jacek Slomab , Ireneusz Szczygiela a
Silesian University of Technology, Intitute of Thermal Technology, Konarskiego 22, 44-100 Gliwice, Poland b Alstom Konstal S.A. Metalowc´ ow 9, 41-500 Chorzow, Poland
Abstract The article presents the application of the CFD FVM model for thermal simulation of the GMAW hardfacing process. The paper focuses on heat transfer aspects of welding process like distribution of temperatures, heat transfer from electric arc, thermal effects of melting and solidifying of metal. Because detailed CFD and thermal analysis of welding process is computationally expensive, the modified, faster approach has been proposed to obtain realizable compromise between accuracy and calculation efforts for engineering heat transfer analysis. It allows getting the thermal simulation closer to engineering practise as a base for structure analysis. The model has been tested and validated against thermography measurements. The procedure of thermography measurements and validation has been presented in the article. Results showed high reliability of proposed approach, particularly for heat transfer around electric arc. The developed model can be applied for various FVM codes and useful as a part of multi physics analysis. Keywords: gas metal arc welding, welding simulation, heat transfer, hardfacing, GMAW 1. Introduction Hardfacing is a technological process where a base metal is covered using another metal to obtain a surface with different properties. Hardfacing is usually applied to improve surface parameters of metal parts e.g. the surface ∗
Corresponding author:
[email protected]
Preprint submitted to Applied Thermal Engineering
May 30, 2018
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with improved level of hardness. Another common application is repairing or renovation of worn machine parts. The surface of the part, which is damaged due to operation, is covered by a layer of fresh material. Hardfacing process commonly bases on welding. A number of welding technologies like GTAW (Gas Tungsten Arc Welding), GMAW (Gas Metal Arc Welding), SMAW (Shielded Metal Arc Welding), PAW (Plasma Arc Welding) and others are used in industrial practice. In welding process, the material is provided to the surface in molten form, the electric arc is usually the main source of heat and driving force. The quality of the hardfacing weld strongly depends on heat condition during process. Generally, the quicker cooling and crystallization leads to higher quality of weld and higher efficiency of overall process. Heat transfer can be controlled mainly by the motion speed of the welding head and the power of electric arc. From the economic point of view, the motion of the head should be as fast as possible. It requires increasing of the electrical power, which however may cause several harmful effects like non-controlled distortion, flooding etc. Identification of heat transfer processes is one of the crucial knowledge for effective technology development. The main aim of the work is the development and validation of fast, industrially usable, numerical model of heat transfer in the hardfacing GMAW technology. In the GMAW process, the deposit is delivered to the base material within the inert gas shield. The melting of the wire and the liquid metal transport are carried by the heat and electromagnetic forces produced by the electric arc which glows between the base material and the deposit wire, without any additional electrodes or plasma sources. The wire is provided by the feeding system through the inert gas nozzle. The inert gas is used to separate electric arc region from the atmospheric gases. The heat transfer in a solidified weld and in a metal plate can be described using well known Fouriers differential equation of heat conductivity. Physical phenomena at the metal delivery region, in the solidification zone and above the weld surface are however much more complicated. They include coupled heat and mass transfer with significant role of radiation as well strong electromagnetic fields. The popularity of welding technology and its economic importance enforced researchers to examine wide aspects of welding process where one of important fields of research is numerical modelling of heat transfer [1, 2, 3]. It can be observed two trends in the modelling of heat transfer of welding process. First bases on the Finite Element Method which technique is widely used for the numerical structural analysis of solids. While FEM can be easily 2
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adopted for the heat transfer analysis in solids, it causes significant problem in adaptation to the fluid flow analysis. In practice, the detailed analysis of heat transfer is usually limited to the solid region and various simplified models are used as a weld heat source. These models are responsible for estimating heat transfer in the electric arc region [2]. That approach is commonly used in welding simulation software available on market e.g. Sysweld, Simufact.welding and others. Latest examples of application that method to GMAW and analysis of various models of heat source can be found in publications by C.Heinze at al [4] or Hatiegan at al [5]. Another trend goes to the detailed modelling of electric arc processes with strong emphasis on the fluid dynamics. Wide range of modelling attempts to the various welding technologies can be found in literature, where however only limited part of them concerns GMAW in contrary to the popularity of GMAW in industry. J. Hu et al in the series of articles [6, 7] presented the detailed simulating models of transfer phenomenon in GMAW. The interactive coupling between arc and plasma, melting of the electrode, droplet formation, droplet detachment and the weld pool dynamics as well as heat transfer in the solid metal was simulated using unified model which bases on continuity and conservation equations (flow, momentum, energy, electric current continuity, Maxwell) and on volume of fluid formulation. A.B Murphy [8, 9, 10] has investigated the impact of metal vapours for heat transfer in simulation of GMAW process. Applied numerical model also bases on finite volume method. The work was continued and Lu at al [11] have published developed approach to analyse energy flow in an aluminium GMAW process. High complexity and reliability leads however to very high computational requirements and those models were applied only to relatively small region around electric arc. Mentioned papers focuses on theoretical considerations and do not include application aspects or broad comparison with measurements. The authors, partially derived from cited publication, developed and published [12] model which covers wider region around electrodes: the fragment of weld, hardfaced material, the welding head with the shield gas nozzle and the layer of atmospheric gases. The model based on continuity, momentum and energy conservation equations was solved using finite volume method with volume of fluid formulation for multiphase metal transport. The results were compared and discussed against fast camera imaging and infrared imaging. The purpose of that approach was implementation of fluid and heat transport analysis to the mechanical calculations as a part of fluid-structure analysis. Implementation of it to the industrial practice constituted however 3
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problem with computation cost. Industrial partners pointed the unacceptable high computation requirements of heat transfer analysis compare to the mechanical simulations. It was decided then to do step backward in model details and make it faster and easier for application in combined thermalmechanical simulations with retained accuracy of thermal effects. 2. Model description
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The model has been developed in Ansys-Fluent environment but it bases on general finite volume method (FVM) which allows to develop simulation of the welding process using various FVM codes, available both, as commercial packages (e.g. Ansys, Comsol) or free software (e.g. OpenFoam). Results, e.g. transient temperature field inside metal parts, can be employed in a number of structure analyses where Ansys and Comsol as advanced multiphysics packages seems to be specially suitable for that kind of solution. The experience has shown that the high computational cost of the detailed simulation models of the welding process arises due to combination of multiphase metal transport and transient, fast changing in time, nature of electric arc. Thus, it was attempted to eliminate the multiphase analysis assuming that the weld shape can be predicted with satisfactory accuracy based on experience or short physical tests collected for certain welding parameters. At the same time, the mass transport inside electric arc was considered as an instantaneous process where the global welding process is keeping as transient. Additionally, the model is based on stationary numerical mesh, which allows for lower computational cost concerned with dynamic mesh evolutions. The heat transfer in solid parts of the model (weld and steel sheet) is analysed using the energy equation in the form: ∂ (ρh) + ∇ · (vρh) = ∇ · (λ∇T ) (1) ∂t The solution for fluid region bases on the continuity equation, the momentum conservation equation and the energy equation: ∂ρ + ∇ · (ρvr ) = 0 ∂t
(2)
∂ (ρv) + ∇ · (ρvr v) + ρ [ω × (v − vr )] = −∇p + ∇τ¯ + ρg ∂t
(3)
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∂ (4) (ρh) + ∇ · (ρvr h + pur ) = ∇ · (λ∇T + τ¯ · v) + Sh + Srad ∂t T where t is time, ρ is the density, h = Tref cp dT is the sensible enthalpy, λ is the thermal conductivity, T is the temperature, g is the gravity vector, p means the pressure, τ¯ is the viscous stress. The velocities, in formulation for transient process in stationary mesh, are defined as follow: vr = v − ur
(5)
ur = vt − ω × r
(6)
where vr is relative velocity vector to the moving frame, v is absolute velocity vector to the stationary mesh, ur is the velocity of moving frame to the stationary mesh, vt is the translational frame velocity, ω is the angular velocity. The standard k − ε model was used [13] for turbulence modelling in the fluid. It can be expressed by the set of equations: - turbulent kinetic energy k ∂ μt (ρk) + ∇ · (ρvk) − ∇ · μ + (7) ∇k = Gk + Gb − ρ ∂t σk - dissipation ε ∂ (ρε) + ∇ · (ρvε) − ∇ · ∂t
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μt μ+ σε
ε ε2 (8) ∇ε = C1 (Gk + C3 Gb ) − C2 ρ k k
where μt stands for the turbulent viscosity (sought for in the model): μt = ρCμ
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k2 ε
(9)
Gk source terms represent the generation of turbulence kinetic energy due to the mean velocity gradients, Gb is the generation of turbulence kinetic energy due to buoyancy. C1 , C2 , Cμ , σk and σε are constants [13]. Separate approach was developed for the electric arc volume. It was assumed that the whole electric energy is transformed into heat in the electric arc. Electric energy was calculated based on averaged amperage and voltage
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[14]. It was assumed instantaneous mass transfer through the arc from electrode to the weld where the temperature of input wire is equal to ambient temperature and temperature of output liquid metal is close to the boiling temperature of iron. The volume around electric arc was simulated as a mixture of argon and metal vapours. It was assumed the constant production rate of metal vapours proposed by Schnick at al. [15]. The electric arc volume was sectioned from the rest of calculation domain and the energy source therm for equation (4) was calculated in this region using formula: Sh =
Hwire + IU − Hweld − Hvapour V T ˙ wire cp dT Hwire = m
(10) (11)
Tref
Hweld = (m ˙ wire − m ˙ vapour )(
T
cp dT + L)
(12)
Tref
T
˙ vapour ( Hvapour = m
cp dT + L + Lv )
(13)
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where I is averaged amperage, U is averaged voltage, Hwire is enthalpy of wire delivered through welding head, Hweld is enthalpy of liquid metal delivered to the weld, Hvapour is enthalpy of metal vapours generated in electric arc, V is volume of sectioned electric arc region, m ˙ wire is mass rate of wire, m ˙ vapour is mass rate of metal vapour generation, L is specific latent heat of fusion, Lv is specific latent heat of vaporisation. Enthalpy of liquid metal is transferred directly to the welding pool through boundary between electric arc and welding pool, enthalpy of metal vapours is assign to the mass source of metal vapours inside electric arc. Until full multiphase analysis was not applied in the model, the special treatment is also applied for the liquid weld pool and mushy zone. Mushy zone requires consideration of latent heat release during solidification, which was regarded as uniform heat source between liquidus and solidus temperature. Intensive convention inside welding pool causes more intensive heat transfer in the volume of liquid metal than simply heat conduction in stationary material. Modification of heat conduction coefficient due to natural convection in small spaces can be evaluated using relation:
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λef f (14) = 0.18 · (Gr · P r)0.25 λ where Gr (Grashof number) and P r (Prandtl number) are calculated for liquid metal at given temperature. Radiative heat transfer for complete calculation domain included electric arc were calculated using finite volume scheme of discrete ordinate radiation model (DO) adopted for unstructured meshes by Murthy and Mathur [16]. The discrete ordinates radiation model solves the radiative transfer equation for a finite number of discrete solid angles (15), each associated with a vector direction s fixed in the global Cartesian system. σT 4 (15) π where I is the radiation intensity, s is the direction vector, a is absorption coefficient, σ is the Stefan-Boltzmann constant, scattering terms are omitted in analysis. For each direction the radiative transfer equation is integrated over control volume to obtain radiative source term in energy equation (4). Radiative heat fluxes on the surfaces of solid walls were calculated as for grey, diffuse walls: q˙ = (1 − ) Iin s dΩ + σTw4 (16) ∇ · (I(r, s)s) + aI(r, s) = a
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where is the emissivity of surface. DO is a popular and flexible model, available in the most of FVM software. Theory of DO method is discussed in details in [17]. The model was chosen with regards to its ability to spanning the wide range of optical thickness, from surface-to-surface radiation to participating radiation in radiative dense gases. That requirements are observed in welding process. There is a small region of electric arc with very intensive radiative heat transfer filled up with dense optical metal vapours at plasma temperature where thermal properties of metal vapours were discussed in details in [8]. Radiative activity of the rest of calculation domain is very low, it is filled up with atmospheric gases and argon at moderate temperature. The radiation absorption coefficient at these condition can be omitted, however, the radiative heat transfer still plays significant role in overall heat transfer between weld surfaces and environment. Emissivity of solidified weld and plate surfaces was
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assumed at 0.79 up to 1300o C based on thermography imaging test, the emissivity of welding pool surface was assumed at 0.01 based on literature where spectroscopic methods were used [18]. The linear approximation correlated with temperature between these values was assumed to evaluate emissivity of metal surface in the range between 1300oC and liquids temperature. Until the DO method is highly sensitive for a ray effect, the application of it for spot sources of radiation like electric arc requires appropriate number of discrete solid angles with reasonable balance between accuracy and computational cost. Based on multi-case analysis, the angle division 6x6 with 1x1 pixilation was used to avoid ray effect and keep reasonable computation time. Parameters of welding process were matched according to the manuals and technology delivered by industrial partner of research to obtain 2 mm thick padding weld. The diameter of the wire was 1.2 mm. Welding head moved parallel to the surface with speed of 0.008 m/s. At the same time the electrode wire at the speed of 0.11 m/s was provided. Average electric current was 230 A at voltage 26 V. Argon came through the nozzles of shield gas at the volume rate of 12 liters/min. These values reflect the standard values of hardfacing. Construction steel S500MC was used as the base material [19]. The steel is covered using OK Autrod 13.91 low-alloyed solid GMAW wire used for hardfacing and building up highly wear-resistant layers on tools and machinery parts [20]. The specific heat and the heat conductivity for both materials were defined as piecewise-linear functions Figure1 [21]. The geometrical model of described system is shown in the Figure 2. The dimensions of the steel sheet are 100mmx40mmx6mm. Calculation domain is limited to the lower surface of metal sheet at bottom and 40mm layer of atmosphere above plate and weld surface. The atmospheric part of the model covers also welding head. It is filled with mixture of air and shield gas released from welding head nozzle. The volume of geometrical model is divided into 0.6 million cells using symmetric system for reducing the number of cells. A stationary polyhedral non-structural mesh is used for calculations, as shown in the Figure 3. That type of mesh allows to simplify process of mesh creation compared to structural mesh with reasonable packing of volume with limited number of cells. Because it is expected significant gradient differences of temperature and velocities in the calculation domain, the proper mesh adaptation was required. Available CFD solver does not allow for automatic adaptation of polyhedral mesh during calculation therefore the mesh had to be prepared based on preliminary calculation and external iterative mesh correction. In each step the 8
Figure 1: Thermal conductivity and specific heat of steel
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density of mesh was doubled until temperature distribution along the weld was stabilized between iterations. It is expected that the prepared mesh can be used for wider range of cases at similar thermal conditions. For models with significant differences in mesh density, in relatively big volumes, if is possible to perform mesh pre-adaptation outside calculations,the benefit of using that type of mesh seems to be predominant, specially from calculation cost site. Boundary conditions are assumed as follows: • velocity of inert gas at nozzle inlet 0.5 m/s, normal to inlet, uniform distribution, ambient temperature equal to 25o C
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• ambient temperature tam =25o C and ambient gauge pressure pam =0 Pa assumed as pressure outlet boundary condition at the boundary of calculation region, • the convective heat transfer coefficient 15 W/m2 K and free stream temperature 25oC were assumed at the bottom of welding plate, 9
hardfacing weld welding head (gas nozzle)
plate (base metal) wire arc
Figure 2: Geometrical model.
• ambient temperature tam =25o C at the inlet of welding plate 3. Experiment 235
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Measuring thermal effects of welding process constitutes one of more serious problems in thermal technique. Extremely high temperature at electric arc region practically excluded direct thermal measurements inside welding pool. Spectroscopic analysis is only possible technique that allows direct measurements of electric arc and surface of weld pool, but it is difficult to use in engineering practise. More often encountered are indirect methods, where thermography can be listed as the most popular non-invasive method and metallography microscopy is the most common experimental invasive technique. Both of them were used in the paper. Application of the infrared imaging including thermography to the diagnostics of welding processes was presented many times, as well the usefulness of it was proved. Examples of using this technique for GMAW can be found in [22], [23]. The research was proceeded by calibration of the measurements stand. Although thermography is an effective, non-invasive technique, it is highly sensitive for emissivity of a tested surface. The emissivity of metal plate is then an essential parameter that affects the precision of thermography measurement. This parameter depends on a number of conditions and can vary during temperature changes 10
ambient ambient
inlet of the inert gas
weld inlet of the welding plate
welding plate bottom of the welding plate
Figure 3: Cross section of the mesh.
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due to oxidation reactions on metal surface. Most common method to verify the expected emissivity of a metal plate surface is just the comparison between the thermography and thermocouples measurements results in several selected spots of the measured area. Performed test showed that the emissivity at value of 0.79 is valid in the range from 400oC to 1300oC. That range was then assumed as valid range of temperature measurements of presented equipment. The conditions in which the experiment was carried out were the same as those used in the numerical model and reflect the standard conditions of hardfacing. The Flir Therma CAM SC2000 device was used in the work. Range of available temperature measurements extends from -40oC to 2000oC where the high temperature equipment limits the range from 200o C to 2000oC. Sensitivity of the matrix is 0.08 K at 30o C where the measurements accuracy is kept at 2% up to 2000oC, wave length range: 7.5 μm to 13 μm, resolution of matrix is 320x240pixels. The Figure 4 presents thermography image of tested welding process. A sequence of raster images corresponded to the infrared intensity, registered at 2s regular intervals, was the base for analysis. The last image of the sequence, in form of temperature distribution, was placed in the Figure 4. The analysis required to establish certain geometrical elements (points, lines, areas) which 11
Figure 4: Thermogram: measured temperature field
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can be connected and compared to the numerical model. It was decided to use line conducted on the ridge of weld (Li1) as a specific geometrical location which can be outlined with relatively small position error, even on thermographs with limited resolution. A number of 2mm circles were marked on the line as distinguish points where the model and measurements can be compared quantitatively. Presented analysis showed that only part of infrared image can be directly used to temperature comparison between models and measurements. The most serious limitation concerns infrared imaging of electric arc region. Until the electric arc is not a solid body with established surface, the temperature registered with infrared camera cannot be trusted as real temperature. Temperature distribution obtained from thermography is just a calculated value based on infrared radiation intensity with assumed constant emissivity and diffuse surface. From these reasons the electric arc region had to be excluded from the measurements. Another uncertainty was observed at the fragment of weld between electric arc and point where the temperature of weld is established at level of 1350oC. That temperature corresponds to the solidus temperature of steel. Expected real temperature of this region is much higher than registered in infrared 12
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image. Additional observation with fast camera in visible range (Figure 5), shows that the emissivity of not-solidified surface is much lower than solid steel surface. The infrared measurements are highly uncertain in that condition, even with known emissivity. The image can be however suitable for estimation of solidification boundary at surface of weld.
Figure 5: Welding pool in infrared and visible light.
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4. Analysis of the results Figure 6 presents the comparison of a temperature field on metal surface with thermography in area of computation domain. Colour maps of both images were synchronised. There are highlighted equivalent regions on model and on thermogram where the direct comparison of temperature field can be done. It contains the fragment of weld with temperature in range 4001300oC for which the emissivity was verified. Observations prove qualitative agreement between temperature fields obtained from infrared imaging and calculations. Quantitative analysis was presented in form of chart in Figure 7. The chart function (called numerical model) shows temperature distribution along line formed at crossing of symmetry plane and the ridge of weld. Measurement temperatures were derived as average values from 2mm diameter spots marked in figure 6. Vertical error bars correspond to minimum and maximum of temperature registered in each spot, horizontal error bars correspond to diameter of spots. Measurement point at x=0.01m corresponds to boundary between liquid and solidification region and its value was derived from liquidus temperature of welding wire steel. 13
Figure 6: Calculated temperature field (lower) and thermography. Colour scale is the same. The lowest range of colour means temperature equal and lower than 400oC.
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Figure 7: Temperature distribution along central line of weld surface. Comparison between model calculations and measurements.
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Third way of validation was based on comparison between predicted weld shape, calculated temperature distribution at cross section of weld and metallography analysis (Figure 8). As it was described in section 2, the geometrical shape of weld is assumed in the model based on experimental test and parameters specific for welding method. To ensure that the weld shape is conformable with real welding process, it is checked using standard metallography test. It is invasive procedure where the weld is cut and analysed optically. Observation of number of cross sections confirmed that the weld shape is repeatable for specific welding method at certain welding parameters. Cross section shape is also rough symmetrical in horizontal and vertical directions which allows to predict it using limited number of parameters, for example thickness, width and surface radius. Thermal conditions calculated by the model should be then appropriate to assure predicted weld shape. Particularly the boundary of solidus temperature should reproduce the shape of weld. Metallography test can also show range of allotropic transformations due to thermal impact inside base metal. Time dependent and 3D analysis of the model proved satisfactory agreement between simulation
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Figure 8: The weld cross section at certain location. Red dot points represent range of liquidus temperature, green dot points represent range of solidus temperature, both obtained from simulation. Photo presents metallography cross section of experimental weld at the same scale.
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and metallography results. Computational performance of the model was compared to the configuration with identical heat transfer settings but based on full time dependent sliding mesh solution and volume of fluid multiphase flows method with solidification and melting mechanism. Mentioned extensions to the model require enlargement of the mesh from 0.6 million to 3 million volumetric cells to keeping precisely interphase boundary. Sliding mesh solution regime of fast changing in time flow in electric arc requires also time steps established at level of 0.0005s. In result, the solution time of the full developed model on average equipped workstation (Intel Xeon 2.5GHz, 8 cores, 64 GB RAM) can takes about 2 weeks compared to about 30 minutes using presented model.
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Figure 9: Comparative model based on volume of fluid method and sliding mesh calculation technique.
5. Conclusions
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The CFD FVM model for thermal simulation of the GMAW hardfacing process has been developed. It supports wide range of heat transfer aspects of welding process like distribution of temperatures inside weld and base metal, heat transfer and energy efficiency of electric arc, thermal effects of melting and solidifying of metal. Because detailed CFD and thermal analysis of welding process is computationally expensive, the modified, faster approach has been proposed to obtain realizable compromise between accuracy and calculation efforts for engineering heat transfer analysis. A non-structural, polyhedral mesh has been used which allows automation of mesh creation and reasonable volume packing with limited number of volume elements. Multiphase flows problem has been substituted by thermal effects of liquid metal transport, melting, solidifying and allotropic changes. Separate approach has been developed for the electric arc region with regards to heat generation from electric current, radiation from plasma and metal vapours, heat transfer to the liquid weld. The model is calculated employing moving reference frame approach which means usage of stationary mesh for transient problem. All these modifications can shorten required calculation time sev17
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eral times and gets the thermal simulation closer to engineering practise as a base for structural analysis. The model has been tested and validated against thermography measurements. The procedure of thermography measurements and validation has been presented in the article. Results showed high reliability of proposed approach, particularly for heat transfer around electric arc. The developed model is universal and can be applied for various FVM codes and applied as a part of multi physics analysis, particularly it can play supplementary role for MES models for cases with complicated or extreme heat transfer conditions. Acknowledgements
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The work has been done in the frame of statutory activity of the Institute of Thermal Technology. [1] Z. Feng, et al, Processes and Mechanism of Welding Residual Stress and Distortion, Woodhead Publishing Limited, 2005.
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• • • •
The CFD FVM model for thermal simulation of the GMAW hardfacing process Fast approach has been proposed for engineering multiphysics analysis The model has been tested and validated against thermography measurements The developed model can be applied for various FVM codes