Саlculation of heat transfer processes at canlendering of polyethylene sheets

Abstract

Introduction. The technological limitations of the calendering process include the condition of leaving the sheet from the calender in the presence of a middle layer of melt, or a sufficient value of the average temperature of the sheet, which determines the flatness of the sheet with subsequent cooling and glazing in a flat state on the roller conveyor. The process of vitrification of the polymer melt has a wide temperature range, which greatly complicates the calculations.Materials and methods. Processing of high density polyethylene (HDPE) on a calender with three rolls is considered. A series of numerical experiments was performed.Results and discussion. Boundary conditions for the mathematical model of sheet cooling and conditions for numerical integration of the equation of nonstationary thermal conductivity taking into account the heat of crystallization are formulated, the equation is presented in finite differences, using a grid with a step along the sheet length.The letter from HDPE in the physical model is conditionally expanded, the following assumptions are made:1. the thickness of the sheet is much smaller than the diameter of the shafts of the calender, so the orthogonal coordinate system is used;2. the transition of the melt from the initial thickness of the workpiece to the final occurs at the same linear velocity (the melt does not slip on the shaft);3. the thermal conductivity of HDPE is much less than the thermal conductivity of the shaft material, so the temperature of the sheet at the point of contact with the shaft is equal to the temperature of the shaft;4. reduction of sheet thickness in the second gap does not occur;5. energy dissipation in the gaps does not affect the temperature fields in the melt;6. heat transfer along the sheet due to thermal conductivity is absent;7. the width of the sheet is much larger than the thickness, so the model of the cooling process is simplified to one-dimensional, without heat transfer across the sheet.For the surface of the sheet, which is cooled by air by free convection, the method of control volume (heat balance method) was used for the boundary layer with a thickness of half a step of the grid along the thickness of the sheet.Numerical experiments were performed for the following conditions: HDPE performance 500 kg / h; initial melt temperature 235°C; diameter of calender shafts 0,25 m; sheet thickness 1.0; 2.0; 3.0; 5.0 mm. Sheet width 1.0 m. The temperature of the first shaft 125°С, shaft temperatures №2 and №3 were selected under the condition of the average melt temperature at the outlet of the calender 125°С, ambient air temperature 20°С, heat transfer coefficient from the sheet and the shaft to air 25 W / (m2K).An example of the results of numerical integration by the Runge – Kutta method (temperature fields and average melt temperature) is shown in the figures.The theoretical analysis of heat exchange processes during calendering of sheets from high density polyethylene melt is carried out, the technological parameters of calendering and their influence on the main quality parameters are analyzed.For the conditions of the numerical experiment, it was found that when calendering sheets with HDPE with a thickness of 1.0 to 2.0 mm will have to choose a high-temperature coolant, which greatly complicates the system of thermal stabilization of the shafts. A 1 mm thick sheet will not have gloss due to the high temperature of the shafts, and the temperature inhomogeneity of the shaft surface due to the high heat flux density can lead to the formation of a central strip on the surface of the sheet without gloss. Calendering of sheets with HDPE with a thickness of 5 mm or more for the conditions of numerical experiment causes difficulties due to the possible "blasting" of the sheet up (behind the hot shaft).Conclusions. It is established that when calendering sheets of smaller thickness, the heat load on the middle shaft increases, and it may be necessary to use high-temperature coolants. The optimal temperature of the calender shafts is in a narrow range, so when designing new equipment, thermal calculation is important.