Numerical Analysis of the Non-Stationary Thermal State of the Tool in the Combined Casting and Extrusion of Non-Ferrous Metals

The results of a numerical analysis of unsteady heat transfer in the "metal-mold-environment" system during continuous combined casting and extrusion of an aluminum alloy in an installation with a horizontal carousel mold are presented. The heat engineering zones characterized by different intensity of heat transfer between the melt and the surface of the mold have been determined. A quantitative assessment of the influence of the rate of heating of the crystallizer on the temperature-time characteristics during the period of the transient thermal process is given. It is shown that an increase in the productivity of the installation reduces the duration of the transient thermal process when starting the installation from a cold state until it reaches a stationary thermal regime. The dependence of the time at which the installation reaches the stationary thermal regime on the rotation speed of the crystallizer wheel has been obtained.

1die stopper; 2press product; 3stationary arcuate segment; 4solidified ingot; 5metal melt; 6dispenser; 7crystallizer wheel; 8annular groove A necessary condition for combining continuous casting and extrusion of metal is the observance of such thermal conditions in the "metal-crystallizer-environment" system, which ensures the solidification of the melt and stabilization of its temperature in the section in front of the container [28][29][30]. An analysis of the thermal regimes of continuous casting before extrusion of aluminum alloys carried out on the basis of the method proposed in [31,32] that confirmed this statement.
Further studies of the nature of the dependence of the thermal operation of the "metalcrystallizer-environment" system on the parameters of the technological process showed that in an unstable transient mode the crystallizer wheel gradually warms up with each round from the initial temperature until a stationary thermal state is reached. At the same time on the basis of computer simulation it was found that the degree and rate of heating of the crystallizer in the initial period of operation of the installation have the main effect on the nature of unsteady heat transfer and changes in the enthalpy of the melt [33,34]. As a result, operational and design solutions were proposed that ensure rational temperature-time conditions for the installation at a fixed design rotational speed of the mold (the productivity of the installation in terms of the mass flow rate of the melt poured in) in a long-term stable period of its operation [29,30].
The purpose of this work was to theoretically study unsteady heat transfer to determine the temperature-time conditions of the elements of the system "metal-horizontal crystallizerenvironment" in transient thermal modes of operation of the Conform installation with combined casting-extrusion of an aluminum alloy.

Materials and method of carrying out research
The analysis of the dynamics of heat transfer in the transient operating mode of the installation was carried out in three calculated sections passing through the volume of the metal and the material of the mold solidifying in the groove. The sections are formed by a vertical cutting plane located at a distance from the pouring point of the melt P at angles φ1 = 30°, φ2 = 120° and φ3 = 210° (Fig. 2). As can be seen, the central angles φi of the circular arc of the mold groove with radius Rk = 0.175 m are located between the polar axis OP (segment OP = Rk) and the rays connecting the pole O with the design sections. The φi reading is taken in a clockwise direction.
In accordance with the technological conditions in the control section φ3, located at an angular distance ∆φ = 15° from the beginning of the extruding zone (stationary arcuate segment) a temperature range must be provided over the metal section the maximum value of which is 3-5 °C lower than the solidification temperature aluminum melt [35]. Numerical studies were carried out on a previously developed three-dimensional computer model of heat transfer in a pilot plant implemented on the basis of software [35][36][37] SolidWorks (2017) and Ansys CFX 17.1.
Nonlinear differential equations for the conservation of energy for the processed melt and the elements of the installation were written in the form of a substantial derivative: where ti is the temperature field in the i-th element; ρi, ci and λidensity, volumetric heat capacity and thermal conductivity of the i-th element; wi is the vector of the angular velocity of motion of the i-th element in the body of the mold and the melt; qvi is a function characterizing heat sources (internal heat release during phase transition and metal pressing) in the i-th element [38]: where Sh 'internal heat release during phase transition; Sh "heat release from the forces of contact friction and deformation forces of the metal being processed.
In the mathematical model a cylindrical coordinate system was used (Fig. 2), where the divergence and Laplace operator included in the system of differential equations (1) had the following form: Equation (1) was supplemented by the boundary conditions: Here qifunction characterizing the conditions of radiation-convective heat transfer at the boundary of the surface of the i-th element Гi (qi > 0heat flux is directed inside the element).
In the boundary conditions (5) the angular velocity of movement of the installation elements wi relative to the Z axis of the system will change: the mold wheel with the melt solidifying in its groove, the other elements of the design model are stationary (wi = 0). The enthalpy of the melt poured into the groove of the crystallizer is calculated based on the accepted initial values of its temperature and flow rate which is functionally related to the value of wi.

Results and discussion
A numerical study of the process of continuous combined casting-extrusion was carried out for the eutectic aluminum alloy Al12Si with a melting (solidification) temperature of 580 °C. When analyzing the temperature-time characteristics of the transient thermal process the speed of rotation of the crystallizer wheel wc was taken as the operating parameter, the range of which varied within 1-3 rpm. The temperature tp of the metal melt poured into the groove was taken equal to 750 °C, the ambient temperature was 20 °C.
In accordance with the specified value wk and the dimensions of the section of the mold groove 10×10 mm, the mass flow rate of the melt (unit productivity) Gp took values 0.27-0.81 kg/min. Note that in proportion to the value of Gр in equation (1) the amount of heat supplied with the poured metal to the elements of the installation also changed.
The results of modeling the dynamics of heat transfer in a transient thermal process indicate a significant effect of the rotation speed of the horizontal mold wheel on the rate of its heating and, as a consequence, on the nature of the temperature field in the tool body and solidifying melt. Fig. 3 shows the isotherms t1, t2, and t3 calculated during the transient thermal process corresponding to the temperature value over the cross section of the mold body 700, 650, and 600 ºC, at tp = 750 °C and the rotation speed of the mold wheel wc = 1 and 3 rpm. Fig. 3. The values of the isotherms ti in the body of the mold in the transient thermal process at tр = 750 ºC: 1 -t1 = 700 ºC; 2 -t2 = 650 ºC; 3 -t3 = 600 ºC; a -τex = 320 s, wk = 3 rpm; b -τex = 840 s, wk = 3 rpm; c -τex = 320 s, wk = 1 rpm; d -τex = 840 s, wk = 1 rpm As can be seen, during the transient thermal process τex the location of the considered isotherms changes, associated with a different rate of heating of the mold. So, for example, an isotherm with a temperature of t1 = 700 °C during periods of time τex = 320 and 840 s, at a mold rotation speed wк = 3 rpm, the length of an arc segment ∆φi from the pouring point of the melt Р (Fig. 2) equal to 0.066 and 0.115 m respectively. At wк = 1 rpm the arc distance ∆ φi changes significantly and the length of the arc segments for the considered time periods τex decreases to 0.025 and 0.045 m respectively.
Analysis shows that at the initial moment of time after the start-up of the installation in the "melt -tool" system, the bulk of the heat goes to heating the mold (Fig. 3). In this case, the more heat is supplied with the melt the faster the crystallizer heats up and, accordingly, the time for reaching the stationary thermal mode of operation of the installation as a whole decreases. It has been determined that when the rotation speed of the mold changes from 1 to 3 rpm, the time to reach the stationary thermal regime (τst) decreases almost three times (from 46 to 15 minutes).
It was found that in the transient thermal process, the crystallizer has two temperature-time heating zones the characteristics of which depend on the productivity of the installation.
In the first zone intense heat exchange occurs between the metal melt and the walls of the mold wheel. The analysis shows that at tр = 750 ºC and Gр = 0.81 kg/min (wк = 3 rpm), the time interval from the start of the installation to the passage of this zone ∆τex is 320 s. In this case the rate of change of the average temperature of the mold in the first design section along its rotation (φ1) In the second zone, the rate of heat removal from the melt to the mold decreases, and the length of the arc of solidification of the melt increases. So, in the considered section φ1 at wk = 3 rpm, the values and / k ex t    gradtmold decrease to 4.5 ºC/min and 2.3 ºC/mm respectively. At wk = 1 rpm, these values take the corresponding values of 1.82 ºC/min and 4.2 ºC/mm. Fig. 6 shows the generalized temperature-time dependences obtained during the period of the transient thermal process at different productivity of the installation in the calculated sections φi of the crystallizer body and the solidifying melt.
It can be seen that the nature of the temperature field of the mold and the metal changes both during ∆τex from the start of the installation until it reaches a stationary thermal regime and in the course of their movement from the pouring point to the pressing zone. With an increase in the productivity of the installation the temperature of the mold and the alloy being processed increases in the design sections φi which is associated with an increase in the heat supplied to the castingextrusion process with the poured melt. a -φ1 = 30º; b -φ2 = 120º; c -φ3 = 210º With an increase in the rotational speed of the mold up to 3 rpm during the period of the transient process, the asymmetry of the temperature field in the calculated sections of the metal φ2 and φ3 increases. The region with the maximum temperature is shifted to the surface layers of the metal in contact with the environment. When the speed decreases to 1 rpm the shift of the temperature field with the maximum temperature over the metal cross section is insignificant. In the design sections φ2 and φ3 the region with the maximum temperature shifts towards their central part.
It should be noted that at wk ≤ 1.75 rpm the design of the installation upon reaching a stationary thermal regime provides in the third control section φ3 in front of the extrusion zone the temperature of the solidifying melt below the point of its phase transition due to sufficient heat removal into the environment.

Summary
1. A numerical study of unsteady heat transfer during continuous combined castingextrusion of an aluminum eutectic alloy Al12Si was carried out, on the basis of which two temperature-time zones were determined in transient thermal modes of operation of the Conform installation.
2. The dependence of the time at which the installation reaches a stationary thermal regime on the rotation speed of the crystallizer wheel wk at start-up from a cold state has been obtained.
3. It was found that during the transient thermal process the character of the temperature field in the body of the tool and the solidifying melt is significantly affected by the value of wk. So, with its increase, an increase in the asymmetry of the temperature distribution in the calculated sections of the metal near the extruding zone is observed with a shift of the region of maximum values to its surface layers.
4. It is shown that an increase in the productivity of the installation in terms of the mass flow rate of the poured melt is accompanied by an almost linear reduction in the time of the transient thermal process from the start-up of the installation to its stationary mode of operation.