Heat transfer modeling during thermite welding of rails

. Thermite welding of rails is the only technology that allows connecting rails in hard-to-reach places such as turnouts and bridges. Experience in operating thermite welded joints shows that this type of welding is characterized mainly by casting defects. It is known that casting defects depend on the thermal processes occurring during rail welding. This article presents the results of modeling the heat transfer process of thermite welding of rails. The simulation was carried out using the LVMFlow software product. 3D heat transfer models of the “casting mold – weld – rail” system have been developed, considering phase transitions. Based on the proposed models, thermograms of the distribution of temperature fields are presented both over the cross section of the welded joint and along the length of the welded joint.


Introduction
Thermite welding of rails has been used on the railway network to create continuous welding tracks for many years, but there are still a number of problems associated with both the production technology of this welding and the quality of the welded joints.Thermite rail welding technology consists of three stages: the preparatory stage, the welding process and the post-welding stage.The preparatory stage consists of installing a crucible and filling it with thermite mixture, forming a welding gap between the rails and installing a casting mold, heating the ends of the rails.The welding process is carried out by igniting a thermite mixture, which melts into an exothermic reaction releasing a large amount of heat.After the reaction is completed, the liquid melt flows from the crucible into the mold, filling the welding gap between the rails.Upon completion of the crystallization process of the weld pool, postwelding operations begin: dismantling the welding equipment, removing burrs from the rail head and gates, grinding the rolling surface of the rail head in the area of the welded joint [1][2][3][4][5][6].
The description of the technological process of thermite welding of rails shows that this type of welding is more related to the metallurgical process of casting metal into a mold.Therefore, in welded joints of rails obtained by thermite welding, defects that are inherent in castings are more often observed: cavities, slag inclusions, bubbles, hot cracks in the cast metal (Fig. 1).The formation of casting defects during thermite welding of rails depends on the nature of crystallization of the melt in the casting mold, which in turn is determined by the thermal processes occurring in the "casting mold -weld -rail" system.However, studying the heat transfer of the "casting mold -weld -rail" system is a difficult task, since it is not possible to install temperature measurement sensors in the casting mold and in the weld, since the metal being poured has a high temperature (2300...2800 °C) and can damage the sensors [7].Therefore, it is advisable to study the heat transfer process of thermite welding using software products.Currently, various software packages are used to simulate the rail welding process [8][9][10].This article presents a model developed in the LVMFlow environment, which considers the heat transfer processes of the "casting mold -weld -rail" system, and it allows one to determine the temperature during the crystallization process of the welded joint.

Materials and methods
The dominant influence on temperature change in thermite welds is thermal conductivity.Thus, the energy balance inside the thermite welded joint under study is given as: where Due to the complex nature of thermite welding, it is difficult to include all physical phenomena in one model.Therefore, other thermally significant physical processes of heat exchange during welding: solidification, thermal convection and radiation are represented in the model through the properties of the material, boundary, and initial conditions.
In the process of thermite welding of rails, melting and crystallization processes are carried out, which are accompanied by phase transitions, so it is necessary to consider latent heat.There are several ways to account for the latent heat released (or absorbed) during these phase changes.In our case, latent heat was included through specific heat capacity: (2) where  � � � � �  � � � � � -enthalpy change, Т -temperature.
Numerical modeling was carried out in the LVMFlow environment.In the simulation, the process of thermite welding of rails was divided into two stages.The first stage is the time from the moment the metal is poured into the mold until the mold and excess metal are removed.The second stage is the time from removing the casting mold to the complete cooling of the weld.Two models were built for the two stages (Fig. 2).Model No. 1, consisting of two connecting rails, a weld, a mold, sprues and a profit part.Model No. 2, consisting of two rails and a weld, is necessary in order to evaluate the change in metal temperature in the weld zone.The design of the models was carried out using CAD "KOMPAS-3D".The profile dimensions of the welded rail models corresponded to the values specified in the regulatory documentation [6].The objects obtained because of the design were converted into a format supported by the LVMFlow software package.When converting, the cell size of the difference grid was set to 1 mm, which made it possible to ensure high accuracy of calculations in the process of modeling the cooling of thermite welded joints of rails due to the correspondence of the shape and size of the models to real objects.During the simulation, the initial conditions given in Table 1 were accepted.The duration of the cooling process of the model with a casting mold during modeling (model No. 1) was the same as when welding rails under track conditions according to technological instructions [6] and amounted to 660 seconds.This is exactly how long it takes for the metal of the rail head to crystallize in the weld zone.Premature removal of the mold results in leakage of uncrystallized metal and damage to the rail.A longer wait increases the overall duration of the rail welding process.The initial temperatures for model No. 2 were determined experimentally, based on the results of the first stage of modeling with a casting mold (model No. 1).During dismantling of the casting mold, the temperature of the weld is about 1500 °C, and the temperature of the ends of the welded rails is on average 1200 °C.Temperature readings when modeling thermite welded joints were obtained from sensors (Fig. 3) installed along the cross section of the weld and along the length of the rail welded joint.

Conclusion
Figure 4 shows the results of modeling the heat transfer of the "casting mold -weld -rail" system.Models 1 -4 display the temperature change from the moment the liquid metal is poured into the mold until it is dismantled.The greatest heat dissipation occurs in the welded rails.In this case, the base of the rail and the neck of the rail are cooled faster than the head.This is explained by the fact that there is a profitable part above the rail head, in which the alloy crystallizes last.Models 5 -8 show the temperature distribution after removal of the mold.It should be noted that during thermite welding, crystallization of a large mass of metal occurs, this leads to the fact that the crystallization process in different volumes occurs at different times, which is confirmed by data on models 5 -8.Different cooling rates contribute to the formation of different structures, respectively, properties of the material.
The simulation results were confirmed experimentally.Using a Mastech MS6550A digital pyrometer, the surface temperature of the rail head in the weld zone was measured after removal of the casting mold.Figure 5 shows graphs reflecting changes in the temperature of welds during the modeling process and during the experiment.The experimental values are 15...20 °C lower than the modeling results.Consequently, the temperature values obtained from the simulation and from the experiment differ by less than 5%.Thus, the experiment showed that the developed model of thermite welded joints of rails has a fairly high accuracy and can be used in the technological process of welding rails using the thermite method to determine the temperature of the rolling surface of welds.

Fig. 1 .
Fig. 1.Defects in welded joints of rails obtained by thermite welding: a) cavities in the rail head, b) cavities in the base of the rail.

Fig. 2 .
Fig. 2. Three-dimensional models of thermite welded joints of rails: No. 1 -model of a welded joint with a casting mold, No. 2 -model of a welded joint without a casting mold.

Fig. 3 .
Fig. 3. Placement of temperature sensors during modeling: a) along the length of the rail; b) along the cross section of the rail.

Fig. 4 .
Fig. 4. Heat distribution along the thermite welded joint of rails: 1 -moment of pouring the liquid alloy into the casting mold; 2 -180 s after pouring the alloy into the mold; 3 -360 s after pouring the alloy into the mold; 4 -540 s after pouring the alloy into the mold; 5 -720 s after pouring the alloy into the mold; 6 -900 s after pouring the alloy into the mold; 7 -1080 s after pouring the alloy into the mold; 8 -1260 s after pouring the alloy into the mold.

Fig. 5 .
Fig. 5. Temperature of the rail head rolling surface in the weld zone after removal of the casting mold.

Table 1 .
Initial conditions for modeling the thermite welding process.