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Title: Mathematical Modelling of Gas–Liquid, Two-Phase Flows in a Ladle Shroud

Abstract

Differential and macroscopic models of argon–steel flows in ladle shroud have been developed. In this, argon–steel, two-phase flow phenomena have been formulated via a transient, three dimensional, turbulent flow model, based on the volume of fluid (VOF) calculation procedure. While realizable k–ε turbulence model has been applied to map turbulence, commercial, CFD software ANSYS-Fluent™ (Version 18), has been applied to carry out numerical calculations. Predictions from the model have been directly assessed against experimental measurements across the range of shroud dimensions and volumetric flow rates typically practiced in the industry. It is demonstrated that the two-phase turbulent flow model captures the general features of gas–liquid flows in ladle shroud providing estimates of free jet length and threshold gas flow rates (required to halt air ingression) which are in agreement with corresponding experimental measurements. In the absence of differential solutions, a macroscopic model has been worked out through dimensional analysis embodying multiple non-linear regression. It is shown that dimensionless free jet length in bloom and slab casting shrouds can be estimated reasonably accurately from the following correlation (in SI unit), viz., ((L{sub jet})/(D{sub CN}))=2.8×10{sup −2}(((Q{sub G})/(Q{sub L}))){sup 1.14}(((gD{sub CN}{sup 5})/(Q{sub L}{sup 2}))){sup 0.8}(((σD{sub CN}{sup 3})/(ρ{sub L}Q{sub L}{sup 2}))){sup −0.9}(((D{sub sh})/(D{sub CN}))){supmore » 2.0}(((ρ{sub G})/(ρ{sub L}))){sup −0.30}in which, L{sub jet} is the free liquid jet length (m), Q{sub G} is the gas flow rate (m{sup 3}/s), Q{sub L} is the liquid flow rate (m{sup 3}/s), D{sub sh} is shroud diameter (m), D{sub CN} is the collector nozzle diameter (m), σ is the interfacial tension (N/m), and ρ{sub G} as well as ρ{sub L} are respectively density of gas and liquid (kg/m{sup 3}). It is demonstrated that the proposed correlation is consistent with the laws of physical modeling and leads to estimates that are in good agreement with predictions from the differential models, for both air-water as well as argon–steel systems. Numerical simulations as well as macroscopic modeling have indicated that thermo-physical properties of the gas–liquid system are important and exert some influences on the gas–liquid, two-phase, flow in ladle shrouds, albeit not to a large extent. Despite dissimilar thermo-physical properties, full scale water modeling appears to be sufficiently predictive and provides reasonable macroscopic descriptions of the two-phase flow phenomena in industrial ladle shroud systems.« less

Authors:
 [1]
  1. Indian Institute of Technology, Department of Materials Science and Engineering (India)
Publication Date:
OSTI Identifier:
22933636
Resource Type:
Journal Article
Journal Name:
Metallurgical and Materials Transactions. B, Process Metallurgy and Materials Processing Science
Additional Journal Information:
Journal Volume: 50; Journal Issue: 2; Other Information: Copyright (c) 2019 The Minerals, Metals & Materials Society and ASM International; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1073-5615
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; AIR; ARGON; CASTING; COMPUTER CODES; COMPUTERIZED SIMULATION; DENSITY; FLOW MODELS; FLOW RATE; FLUID MECHANICS; GAS FLOW; LIQUID FLOW; NONLINEAR PROBLEMS; SHROUDS; STEELS; SURFACE TENSION; TURBULENT FLOW; TWO-PHASE FLOW; WATER

Citation Formats

Singh, Prince K., E-mail: princeks@iitk.ac.in, and Mazumdar, Dipak. Mathematical Modelling of Gas–Liquid, Two-Phase Flows in a Ladle Shroud. United States: N. p., 2019. Web. doi:10.1007/S11663-019-01526-Y.
Singh, Prince K., E-mail: princeks@iitk.ac.in, & Mazumdar, Dipak. Mathematical Modelling of Gas–Liquid, Two-Phase Flows in a Ladle Shroud. United States. https://doi.org/10.1007/S11663-019-01526-Y
Singh, Prince K., E-mail: princeks@iitk.ac.in, and Mazumdar, Dipak. 2019. "Mathematical Modelling of Gas–Liquid, Two-Phase Flows in a Ladle Shroud". United States. https://doi.org/10.1007/S11663-019-01526-Y.
@article{osti_22933636,
title = {Mathematical Modelling of Gas–Liquid, Two-Phase Flows in a Ladle Shroud},
author = {Singh, Prince K., E-mail: princeks@iitk.ac.in and Mazumdar, Dipak},
abstractNote = {Differential and macroscopic models of argon–steel flows in ladle shroud have been developed. In this, argon–steel, two-phase flow phenomena have been formulated via a transient, three dimensional, turbulent flow model, based on the volume of fluid (VOF) calculation procedure. While realizable k–ε turbulence model has been applied to map turbulence, commercial, CFD software ANSYS-Fluent™ (Version 18), has been applied to carry out numerical calculations. Predictions from the model have been directly assessed against experimental measurements across the range of shroud dimensions and volumetric flow rates typically practiced in the industry. It is demonstrated that the two-phase turbulent flow model captures the general features of gas–liquid flows in ladle shroud providing estimates of free jet length and threshold gas flow rates (required to halt air ingression) which are in agreement with corresponding experimental measurements. In the absence of differential solutions, a macroscopic model has been worked out through dimensional analysis embodying multiple non-linear regression. It is shown that dimensionless free jet length in bloom and slab casting shrouds can be estimated reasonably accurately from the following correlation (in SI unit), viz., ((L{sub jet})/(D{sub CN}))=2.8×10{sup −2}(((Q{sub G})/(Q{sub L}))){sup 1.14}(((gD{sub CN}{sup 5})/(Q{sub L}{sup 2}))){sup 0.8}(((σD{sub CN}{sup 3})/(ρ{sub L}Q{sub L}{sup 2}))){sup −0.9}(((D{sub sh})/(D{sub CN}))){sup 2.0}(((ρ{sub G})/(ρ{sub L}))){sup −0.30}in which, L{sub jet} is the free liquid jet length (m), Q{sub G} is the gas flow rate (m{sup 3}/s), Q{sub L} is the liquid flow rate (m{sup 3}/s), D{sub sh} is shroud diameter (m), D{sub CN} is the collector nozzle diameter (m), σ is the interfacial tension (N/m), and ρ{sub G} as well as ρ{sub L} are respectively density of gas and liquid (kg/m{sup 3}). It is demonstrated that the proposed correlation is consistent with the laws of physical modeling and leads to estimates that are in good agreement with predictions from the differential models, for both air-water as well as argon–steel systems. Numerical simulations as well as macroscopic modeling have indicated that thermo-physical properties of the gas–liquid system are important and exert some influences on the gas–liquid, two-phase, flow in ladle shrouds, albeit not to a large extent. Despite dissimilar thermo-physical properties, full scale water modeling appears to be sufficiently predictive and provides reasonable macroscopic descriptions of the two-phase flow phenomena in industrial ladle shroud systems.},
doi = {10.1007/S11663-019-01526-Y},
url = {https://www.osti.gov/biblio/22933636}, journal = {Metallurgical and Materials Transactions. B, Process Metallurgy and Materials Processing Science},
issn = {1073-5615},
number = 2,
volume = 50,
place = {United States},
year = {Mon Apr 15 00:00:00 EDT 2019},
month = {Mon Apr 15 00:00:00 EDT 2019}
}