title: Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ²Ð¾Ð±Ð¾Ð´Ð½Ð¾Ð¹ ÐºÐ¾Ð½Ð²ÐµÐºÑÐ¸Ð¸ ÑÐ°ÑÐ¿Ð»Ð°Ð²Ð»ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÑÐµÐºÐ»Ð° Ð² Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐ¸Ð³Ð»Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Numerical simulation of free convection of molten glass in a two-dimensional crucible model
Creators: name: ÐÑÑÐ¸ÐµÐ², ÐÐµÐ½Ð¸Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
OpenFOAM
COMSOL Multuphysics
ÐµÑÑÐµÑÑÐ²ÐµÐ½Ð½Ð°Ñ ÐºÐ¾Ð½Ð²ÐµÐºÑÐ¸Ñ
Ð¸Ð½Ð´ÑÐºÑÐ¸Ð¾Ð½Ð½ÑÐ¹ Ð¿Ð»Ð°Ð²Ð¸ÑÐµÐ»Ñ ÑÐ¸Ð¿Ð° "Ñ Ð¾Ð»Ð¾Ð´Ð½ÑÐ¹ ÑÐ¸Ð³ÐµÐ»Ñ"
numerical modeling
COMSOL Multiphysics
natural convection
induction melting of the "cold crucible" type

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð¼Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÐµÑÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ð¹ ÐºÐ¾Ð½Ð²ÐµÐºÑÐ¸Ð¸ ÑÐ°ÑÐ¿Ð»Ð°Ð²Ð° Ð¶Ð¸Ð´ÐºÐ¾Ð³Ð¾ ÑÑÐµÐºÐ»Ð° Ð² ÑÐ¿ÑÐ¾ÑÐµÐ½Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»ÑÐ½Ð¾Ð¹ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¸ ÑÐ¸Ð³Ð»Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð¿ÐµÑÐ¸ Ð¿ÑÑÐ¼Ð¾Ð³Ð¾ Ð½Ð°Ð³ÑÐµÐ²Ð°, Ð²ÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ¾Ð¿ÑÑÐ¶ÐµÐ½Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ ÑÐµÐ¿Ð»Ð¾Ð¼Ð°ÑÑÐ¾Ð±Ð¼ÐµÐ½Ð° Ð¸ ÑÐ»ÐµÐºÑÑÐ¾ÑÑÐ°ÑÐ¸ÐºÐ¸ Ñ ÑÑÐµÑÐ¾Ð¼ Ð¿ÐµÑÐµÐ¼ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÑÐ²Ð¾Ð¹ÑÑÐ² ÑÑÐµÐ´Ñ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. Ð£Ð¿ÑÐ¾ÑÐµÐ½Ð¸Ðµ ÑÑÐµÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸Ð¸ Ð¸ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐ¸ Ð·Ð°Ð´Ð°ÑÐ¸. Ð¡Ð¾Ð·Ð´Ð°Ð½Ð¸Ðµ ÑÐ°ÑÑÐµÑÐ½Ð¾Ð¹ ÑÐµÑÐºÐ¸ Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐµÑÐ¾ÑÐ½Ð¾Ð¹ ÑÑÐ¾Ð´Ð¸Ð¼Ð¾ÑÑÐ¸. 2. ÐÐ°Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐµÑÐ°ÑÐµÐ»Ñ Ð´Ð»Ñ OpenFOAM Ð´Ð»Ñ ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ¾Ð¿ÑÑÐ¶ÐµÐ½Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸. 3. ÐÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½Ð¾Ð³Ð¾ ÑÐµÑÐ°ÑÐµÐ»Ñ OpenFOAM Ð¿ÑÑÑÐ¼ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ ÑÐ°ÑÑÑÑÐ°Ð¼Ð¸, Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¼Ð¸ Ð¿ÑÐ¸ Ð¿Ð¾Ð¼Ð¾ÑÐ¸ COMSOL Multiphysics. 4. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð¿ÑÐ¸ÐºÐ»Ð°Ð´ÑÐ²Ð°ÐµÐ¼Ð¾Ð³Ð¾ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ñ Ð¸ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ ÑÐ»ÐµÐºÑÑÐ¾Ð´Ð¾Ð² Ð½Ð° ÑÐµÑÐµÐ½Ð¸Ðµ Ð² ÑÐ¸Ð³Ð»Ðµ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð½ÐµÐºÐ¾ÑÐ¾ÑÑÑ Ð´ÑÑÐ³Ð¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð² Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐµ Ð·Ð°Ð´Ð°ÑÐ¸, Ð²ÐºÐ»ÑÑÐ°Ñ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ Ð½Ð° ÑÑÐµÐ½ÐºÐ°Ñ ÑÐ¸Ð³Ð»Ñ. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ ÑÐ°Ð±Ð¾ÑÑ Ð²ÑÐµ Ð²ÑÑÐµÐ¿ÐµÑÐµÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð±ÑÐ»Ð¸ ÑÑÐ¿ÐµÑÐ½Ð¾ ÑÐµÑÐµÐ½Ñ, Ð° Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¹ Ð¾ÑÐ¸Ð³Ð¸Ð½Ð°Ð»ÑÐ½ÑÐ¹ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð» Ð¸ Ð¾Ð¿ÑÑ Ð¼Ð¾Ð³ÑÑ Ð±ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ Ð² Ð±ÑÐ´ÑÑÐ¸Ñ ÑÐ°Ð±Ð¾ÑÐ°Ñ Ð¿Ð¾ ÑÐµÐ¼Ð°ÑÐ¸ÐºÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ð², Ð¿ÑÐ¾Ð¸ÑÑÐ¾Ð´ÑÑÐ¸Ñ Ð²Ð½ÑÑÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¸Ð½Ð´ÑÐºÑÐ¸Ð¾Ð½Ð½ÑÑ Ð¿ÐµÑÐµÐ¹.
description: This work is devoted to the numerical simulation of the natural convection of molten liquid glass in a simplified crucible design of a direct-heating electric furnace, verification of the numerical solution of the conjugate problem of heat and mass transfer and electrostatics, taking into account the variability of the properties of the medium. Tasks that were solved during the research: 1. Simplification of three-dimensional geometry and definition of the mathematical formulation of the problem. Creation of a computational grid and investigation of grid convergence. 2. Writing your own solver for OpenFOAM so that it is possible to solve the associated problem. 3. Verification and validation of the trial calculation between OpenFOAM and COMSOL Multiphysics. 4. Investigation of the effect of the applied voltage and temperature of the electrodes on the flow in the crucible. Also, the effects of the problem statement and temperature on the walls of the crucible. As a result of the work, all of the above tasks were successfully solved, and the original material and experience obtained can be used in future work on the topic of modeling processes occurring inside various induction furnaces.