Effect of cold-cap-bottom shear stress on primary foam stability

Hrma, Pavel; Ferkl, Pavel; Pokorný, Richard; Kruger, Albert A.

doi:10.1016/j.jnoncrysol.2024.123262

Effect of cold-cap-bottom shear stress on primary foam stability

Journal Article · Wed Oct 16 00:00:00 EDT 2024 · Journal of Non-Crystalline Solids

DOI:https://doi.org/10.1016/j.jnoncrysol.2024.123262· OSTI ID:2513902

Hrma, Pavel ^[1]; ^[2]; Pokorný, Richard ^[3]; Kruger, Albert A. ^[4]

U.S. Department of Energy, AttainX, Support Services Contractor to the Office of River Protection, Richland, WA (United States)
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
University of Chemistry and Technology Prague (Czech Republic); Institute of Rock Structure and Mechanics of the Czech Academy of Sciences, Prague (Czech Republic)
U.S. Department of Energy, Office of River Protection, Richland, WA (United States)

Here, we analyze the heat transfer between the melt pool and the layer of reacting materials called cold cap, which is the determining factor for the glass production rate in Joule-heated air-bubbled nuclear waste glass melters. We consider the effects of bubbling rate, melt viscosity, melt thermal conductivity, conversion kinetics, and shear rate at the cold-cap bottom, and develop simple relationships for the cold-cap bottom temperature and glass production rate. We show that the melt convection enhances the heat transfer to the cold cap by suppressing the thermal boundary layer and primary foam, while the conversion kinetics opposes these effects. Additionally, we mention how dissolving silica particles affects the primary foam stability and discuss the limitations of the presented approach for vigorously foaming feeds.

View Accepted Manuscript (DOE)

Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 2513902

Report Number(s):: PNNL-SA--202423

Journal Information:: Journal of Non-Crystalline Solids, Journal Name: Journal of Non-Crystalline Solids Vol. 646; ISSN 0022-3093

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (69)

Problems of spectrophotometry of glass-forming melts: II. A technique for measuring the absorption spectra of glasses and melts in the red and near-infrared ranges at temperatures from 20 to 1500°C Prokhorenko, O. A.; Mazurin, O. V.; Chistokolova, M. V. Glass Physics and Chemistry, Vol. 26, Issue 1 https://doi.org/10.1007/BF02735964	journal	January 2000
Šesták–Berggren equation: now questioned but formerly celebrated—what is right: Commentary on the Burnham paper on logistic equations in kinetics Šesták, Jaroslav Journal of Thermal Analysis and Calorimetry, Vol. 127, Issue 1 https://doi.org/10.1007/s10973-015-4998-x	journal	September 2015
Model for a steady state foam blanket Hrma, Pavel Journal of Colloid and Interface Science, Vol. 134, Issue 1 https://doi.org/10.1016/0021-9797(90)90262-M	journal	January 1990
Electric melting of nuclear waste glasses State of the art Chapman, Chris C.; Pope, James M.; Barnes, Steve M. Journal of Non-Crystalline Solids, Vol. 84, Issue 1-3 https://doi.org/10.1016/0022-3093(86)90781-7	journal	July 1986
Study of the kinetics of the mechanism of solid-state reactions at increasing temperatures Šesták, Jaroslav; Berggren, Gunnar Thermochimica Acta, Vol. 3, Issue 1 https://doi.org/10.1016/0040-6031(71)85051-7	journal	October 1971
Glass foams: formation, transport properties, and heat, mass, and radiation transfer Fedorov, Andrei G.; Pilon, Laurent Journal of Non-Crystalline Solids, Vol. 311, Issue 2 https://doi.org/10.1016/S0022-3093(02)01376-5	journal	November 2002
Minimum superficial gas velocity for onset of foaming Pilon, Laurent; Viskanta, Raymond Chemical Engineering and Processing: Process Intensification, Vol. 43, Issue 2 https://doi.org/10.1016/S0255-2701(03)00012-6	journal	February 2004
Eulerian approach for multiphase flow simulation in a glass melter Chang, S. L.; Zhou, C. Q.; Golchert, B. Applied Thermal Engineering, Vol. 25, Issue 17-18 https://doi.org/10.1016/j.applthermaleng.2005.03.014	journal	December 2005
Numerical simulation and experimental analysis of an industrial glass melting furnace Abbassi, A.; Khoshmanesh, Kh. Applied Thermal Engineering, Vol. 28, Issue 5-6 https://doi.org/10.1016/j.applthermaleng.2007.05.011	journal	April 2008
Validation of a coupled 3D CFD simulation model for an oxy-fuel cross-fired glass melting furnace with electric boosting Raič, Juraj; Gaber, Christian; Wachter, Philipp Applied Thermal Engineering, Vol. 195 https://doi.org/10.1016/j.applthermaleng.2021.117166	journal	August 2021
In situ characterization of foam morphology during melting of simulated waste glass using x-ray computed tomography Luksic, Steven A.; Pokorny, Richard; George, Jaime Ceramics International, Vol. 46, Issue 11 https://doi.org/10.1016/j.ceramint.2020.02.215	journal	August 2020
Through a glass darkly: In-situ x-ray computed tomography imaging of feed melting in continuously fed laboratory-scale glass melter Luksic, Steven A.; Pokorny, Richard; Hrma, Pavel Ceramics International, Vol. 47, Issue 11 https://doi.org/10.1016/j.ceramint.2021.02.153	journal	June 2021
CFD model for pneumatic mixing with bubble chains: Application to glass melts Simcik, Miroslav; Ruzicka, Marek C. Chemical Engineering Science, Vol. 127 https://doi.org/10.1016/j.ces.2015.01.052	journal	May 2015
Comprehensive and numerically efficient CFD model for bubbling in an industrial glass tank Daurer, Georg; Raič, Juraj; Demuth, Martin Chemical Engineering Research and Design, Vol. 186 https://doi.org/10.1016/j.cherd.2022.07.044	journal	October 2022
Physicochemical control of foam properties Denkov, Nikolai; Tcholakova, Slavka; Politova-Brinkova, Nadya Current Opinion in Colloid & Interface Science, Vol. 50 https://doi.org/10.1016/j.cocis.2020.08.001	journal	December 2020
Time and surfactant types dependent model of foams based on the Herschel–Bulkley model Gao, Hong; Zhang, Meng; Xia, Jian-Jun Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 509 https://doi.org/10.1016/j.colsurfa.2016.09.010	journal	November 2016
A methodology to reduce the computational cost of transient multiphysics simulations for waste vitrification Abboud, Alexander W.; Guillen, Donna Post Computers & Chemical Engineering, Vol. 115 https://doi.org/10.1016/j.compchemeng.2018.03.027	journal	July 2018
Models for viscosity and shear localization in bubble-rich magmas Vona, Alessandro; Ryan, Amy G.; Russell, James K. Earth and Planetary Science Letters, Vol. 449 https://doi.org/10.1016/j.epsl.2016.05.029	journal	September 2016
Shear thinning and brittle failure in crystal-bearing magmas arise from local non-Newtonian effects in the melt Vasseur, Jérémie; Wadsworth, Fabian B.; Dingwell, Donald B. Earth and Planetary Science Letters, Vol. 603 https://doi.org/10.1016/j.epsl.2023.117988	journal	February 2023
Glass viscosity as a function of temperature and composition: A model based on Adam–Gibbs equation Hrma, P. Journal of Non-Crystalline Solids, Vol. 354, Issue 29 https://doi.org/10.1016/j.jnoncrysol.2008.02.019	journal	July 2008
Cluster formation of silica particles in glass batches during melting Schweiger, Michael J.; Hrma, Pavel; Humrickhouse, Carissa J. Journal of Non-Crystalline Solids, Vol. 356, Issue 25-27 https://doi.org/10.1016/j.jnoncrysol.2010.04.009	journal	June 2010
Conversion kinetics during melting of simulated nuclear waste glass feeds measured by dissolution of silica Ferkl, Pavel; Hrma, Pavel; Abboud, Alexander Journal of Non-Crystalline Solids, Vol. 579 https://doi.org/10.1016/j.jnoncrysol.2021.121363	journal	March 2022
Augmented Adam-Gibbs model for glass melt viscosity and configuration entropy as functions of temperature and composition Ferkl, Pavel; Hrma, Pavel; Kruger, Albert A. Journal of Non-Crystalline Solids, Vol. 595 https://doi.org/10.1016/j.jnoncrysol.2022.121832	journal	November 2022
Mathematical modeling of cold cap Pokorny, Richard; Hrma, Pavel Journal of Nuclear Materials, Vol. 429, Issue 1-3 https://doi.org/10.1016/j.jnucmat.2012.06.013	journal	October 2012
Effect of melter feed foaming on heat flux to the cold cap Lee, SeungMin; Hrma, Pavel; Pokorny, Richard Journal of Nuclear Materials, Vol. 496 https://doi.org/10.1016/j.jnucmat.2017.09.016	journal	December 2017
The rheology of two-phase magmas: A review and analysis Mader, H. M.; Llewellin, E. W.; Mueller, S. P. Journal of Volcanology and Geothermal Research, Vol. 257 https://doi.org/10.1016/j.jvolgeores.2013.02.014	journal	May 2013
Viscosity of transient glass-forming melt and its relation to foaming during batch-to-glass conversion Kunc, Jan; Kloužek, Jaroslav; Vernerová, Miroslava Materials Letters, Vol. 363 https://doi.org/10.1016/j.matlet.2024.136284	journal	May 2024
Glass production rate in an electric melter: Melting rate correlation and primary foam stability Hrma, Pavel; Ferkl, Pavel; Pokorný, Richard Materials Letters, Vol. 369 https://doi.org/10.1016/j.matlet.2024.136689	journal	August 2024
Compositional Models of Glass/Melt Properties and their Use for Glass Formulation Vienna, John D. Procedia Materials Science, Vol. 7 https://doi.org/10.1016/j.mspro.2014.10.020	journal	January 2014
Impacts of constraints and uncertainties on projected amount of Hanford low-activity waste glasses Lu, Xiaonan; Kim, Dong-Sang; Vienna, John D. Nuclear Engineering and Design, Vol. 385 https://doi.org/10.1016/j.nucengdes.2021.111543	journal	December 2021
Temperature Distribution within a Cold Cap during Nuclear Waste Vitrification Dixon, Derek R.; Schweiger, Michael J.; Riley, Brian J. Environmental Science & Technology, Vol. 49, Issue 14 https://doi.org/10.1021/acs.est.5b00931	journal	June 2015
Compositional Dependence of Solubility/Retention of Molybdenum Oxides in Aluminoborosilicate-Based Model Nuclear Waste Glasses Brehault, Antoine; Patil, Deepak; Kamat, Hrishikesh The Journal of Physical Chemistry B, Vol. 122, Issue 5 https://doi.org/10.1021/acs.jpcb.7b09158	journal	January 2018
Effect of Bubbles and Silica Dissolution on Melter Feed Rheology during Conversion to Glass Marcial, José; Chun, Jaehun; Hrma, Pavel Environmental Science & Technology, Vol. 48, Issue 20 https://doi.org/10.1021/es5018625	journal	October 2014
Strain‐Dependent Rheology of Silicate Melt Foams: Importance for Outgassing of Silicic Lavas Ryan, A. G.; Russell, J. K.; Heap, M. J. Journal of Geophysical Research: Solid Earth, Vol. 124, Issue 8 https://doi.org/10.1029/2019JB018099	journal	August 2019
On the Temperature Dependence of Cooperative Relaxation Properties in Glass‐Forming Liquids Adam, Gerold; Gibbs, Julian H. The Journal of Chemical Physics, Vol. 43, Issue 1 https://doi.org/10.1063/1.1696442	journal	July 1965
Thermal conductivity of heat-absorbed soda-lime-silicate glasses at high temperatures Kiyohashi, Hiroshi; Hayakawa, Naoya; Aratani, Shin'ichi High Temperatures-High Pressures, Vol. 34, Issue 2 https://doi.org/10.1068/htwu353	journal	January 2002
Parsimonious viscosity–composition relationships for high-temperature multicomponent glass melts Ferkl, Pavel; Hrma, Pavel; Kruger, Albert Journal of Asian Ceramic Societies, Vol. 10, Issue 1 https://doi.org/10.1080/21870764.2021.2012903	journal	January 2022
Rheology of Basalt in the Melting Range Shaw, H. R. Journal of Petrology, Vol. 10, Issue 3 https://doi.org/10.1093/petrology/10.3.510	journal	October 1969
Radiative heat transfer in processing of glass-forming melts Choudhary, Manoj K.; Purnode, Bruno; Lankhorst, Adriaan Marinus International Journal of Applied Glass Science, Vol. 9, Issue 2 https://doi.org/10.1111/ijag.12286	journal	August 2017
Effects of particle size and briquetting of soda-lime-silicate glass batch on viscosity during batch-to-melt conversion Doi, Yoji; Yano, Tetsuji; McCarthy, Benjamin P. International Journal of Applied Glass Science, Vol. 10, Issue 1 https://doi.org/10.1111/ijag.12665	journal	September 2018
Heat transfer from glass melt to cold cap: Melting rate correlation equation Hrma, Pavel; Pokorny, Richard; Lee, SeungMin International Journal of Applied Glass Science, Vol. 10, Issue 2 https://doi.org/10.1111/ijag.12666	journal	September 2018
Heat transfer from glass melt to cold cap: Effect of heating rate Lee, Seung Min; Hrma, Pavel; Pokorny, Richard International Journal of Applied Glass Science, Vol. 10, Issue 3 https://doi.org/10.1111/ijag.13104	journal	February 2019
Simulation of glass furnace with increased production by increasing fuel supply and introducing electric boosting Li, Luyao; Han, Jianjun; Lin, Huey‐Jiuan International Journal of Applied Glass Science, Vol. 11, Issue 1 https://doi.org/10.1111/ijag.13907	journal	September 2019
Characterization of high temperature optical spectra of glass melts and modeling of thermal radiation conductivity Faber, Anne‐Jans; Rongen, Mathi; Lankhorst, Adriaan International Journal of Applied Glass Science, Vol. 11, Issue 3 https://doi.org/10.1111/ijag.15111	journal	March 2020
Heat transfer from glass melt to cold cap: Computational fluid dynamics study of cavities beneath cold cap Abboud, Alexander W.; Guillen, Donna P.; Hrma, Pavel International Journal of Applied Glass Science, Vol. 12, Issue 2 https://doi.org/10.1111/ijag.15863	journal	January 2021
Melting rate correlation with batch properties and melter operating conditions during conversion of nuclear waste melter feeds to glasses Lee, SeungMin; Cutforth, Derek A.; Mar, Derek International Journal of Applied Glass Science, Vol. 12, Issue 3 https://doi.org/10.1111/ijag.15911	journal	April 2021
Geometric optics based analysis of radiation heat transfer in glass melting furnace foams Choudhary, Manoj K. International Journal of Applied Glass Science, Vol. 12, Issue 3 https://doi.org/10.1111/ijag.15921	journal	April 2021
High‐temperature near‐IR spectral properties and thermal radiation conductivity of (un)colored silicate glass melts Faber, Anne Jans; Rongen, Mathi; De Sousa Meneses, Domingos International Journal of Applied Glass Science, Vol. 14, Issue 2 https://doi.org/10.1111/ijag.16603	journal	August 2022
Conversion degree and heat transfer in the cold cap and their effect on glass production rate in an electric melter Ferkl, Pavel; Hrma, Pavel; Abboud, Alexander International Journal of Applied Glass Science, Vol. 14, Issue 2 https://doi.org/10.1111/ijag.16615	journal	September 2022
High temperature near IR spectral absorption of clear SiO₂‐based glasses Faber, A. J.; Meneses, Domingos de Sousa; van Nijnatten, Peter A. International Journal of Applied Glass Science, Vol. 14, Issue 3 https://doi.org/10.1111/ijag.16636	journal	May 2023
Cold‐cap structure in a slurry‐fed electric melter Ferkl, Pavel; Hrma, Pavel; Kloužek, Jaroslav International Journal of Applied Glass Science, Vol. 15, Issue 1 https://doi.org/10.1111/ijag.16645	journal	October 2023
A Review of Radiant Heat Transfer in Glass Gardon, Robert Journal of the American Ceramic Society, Vol. 44, Issue 7 https://doi.org/10.1111/j.1151-2916.1961.tb15914.x	journal	July 1961
Spectral Transmission of Glass at High Temperatures and Its Application to Heat‐Transfer Problems Grove, F. J. Journal of the American Ceramic Society, Vol. 44, Issue 7 https://doi.org/10.1111/j.1151-2916.1961.tb15916.x	journal	July 1961
Effect of Air Bubbling on Circulation and Heat Transfer in a Glass‐Melting Tank Ungan, A.; Viskanta, R. Journal of the American Ceramic Society, Vol. 69, Issue 5 https://doi.org/10.1111/j.1151-2916.1986.tb04765.x	journal	May 1986
Control of Radioactive Waste Glass Melters: II, Residence Time and Melt Rate Limitations Bickford, Dennis F.; Hrma, Pavel; Bowan, Bradley W. Journal of the American Ceramic Society, Vol. 73, Issue 10 https://doi.org/10.1111/j.1151-2916.1990.tb06693.x	journal	October 1990
Nuclear Waste Vitrification in the United States: Recent Developments and Future Options: Nuclear Waste Vitrification in the United States. Vienna, John D. International Journal of Applied Glass Science, Vol. 1, Issue 3 https://doi.org/10.1111/j.2041-1294.2010.00023.x	journal	September 2010
Conductive and Radiative Properties of Soda‐Lime Silicate Glassmelts with Different Iron Contents from 1100°C to 1500°C Liu, Hua; Kitamura, Rei; Xia, Xinlin Journal of the American Ceramic Society, Vol. 99, Issue 4 https://doi.org/10.1111/jace.14095	journal	January 2016
Effects of heating rate, quartz particle size, viscosity, and form of glass additives on high‐level waste melter feed volume expansion Lee, SeungMin; VanderVeer, Bradley J.; Hrma, Pavel Journal of the American Ceramic Society, Vol. 100, Issue 2 https://doi.org/10.1111/jace.14629	journal	October 2016
Thermal properties of simulated Hanford waste glasses Rodriguez, Carmen P.; Chun, Jaehun; Crum, Jarrod V. Journal of the American Ceramic Society, Vol. 100, Issue 6 https://doi.org/10.1111/jace.14786	journal	March 2017
X‐ray tomography of feed‐to‐glass transition of simulated borosilicate waste glasses Harris, William H.; Guillen, Donna P.; Klouzek, Jaroslav Journal of the American Ceramic Society, Vol. 100, Issue 9 https://doi.org/10.1111/jace.14895	journal	May 2017
Rheology of simulated radioactive waste slurry and cold cap during vitrification McCarthy, Benjamin P.; George, Jaime L.; Dixon, Derek R. Journal of the American Ceramic Society, Vol. 101, Issue 11 https://doi.org/10.1111/jace.15755	journal	June 2018
Heat transfer from glass melt to cold cap: Gas evolution and foaming Hrma, Pavel; Klouzek, Jaroslav; Pokorny, Richard Journal of the American Ceramic Society, Vol. 102, Issue 10 https://doi.org/10.1111/jace.16484	journal	April 2019
Viscosity of glass‐forming melt at the bottom of high‐level waste melter‐feed cold caps: Effects of temperature and incorporation of solid components Lee, Seung Min; McCarthy, Benjamin P.; Hrma, Pavel Journal of the American Ceramic Society, Vol. 103, Issue 3 https://doi.org/10.1111/jace.16876	journal	October 2019
Simplified melting rate correlation for radioactive waste vitrification in electric furnaces Lee, SeungMin; Ferkl, Pavel; Pokorny, Richard Journal of the American Ceramic Society, Vol. 103, Issue 10 https://doi.org/10.1111/jace.17281	journal	June 2020
Conversion kinetics of container glass batch melting Ueda, Nanako; Vernerová, Miroslava; Kloužek, Jaroslav Journal of the American Ceramic Society, Vol. 104, Issue 1 https://doi.org/10.1111/jace.17406	journal	August 2020
Corrosion of glass contact refractories for the vitrification of radioactive wastes: a review Bingham, P. A.; Connelly, A. J.; Hyatt, N. C. International Materials Reviews, Vol. 56, Issue 4 https://doi.org/10.1179/1743280410Y.0000000005	journal	July 2011
Magma / Suspension Rheology Kolzenburg, Stephan; Chevrel, Magdalena O.; Dingwell, Donald B. Reviews in Mineralogy and Geochemistry, Vol. 87, Issue 1 https://doi.org/10.2138/rmg.2022.87.14	journal	May 2022
Strain Localization in Magmas Lavallée, Yan; Kendrick, Jackie E. Reviews in Mineralogy and Geochemistry, Vol. 87, Issue 1 https://doi.org/10.2138/rmg.2022.87.15	journal	May 2022
Models for Viscosity of Geological Melts Russell, James K.; Hess, Kai-Uwe; Dingwell, Donald B. Reviews in Mineralogy and Geochemistry, Vol. 87, Issue 1 https://doi.org/10.2138/rmg.2022.87.18	journal	May 2022

Similar Records

Heat Transfer from Glass Melt to Cold Cap: Gas Evolution and Foaming

Journal Article · Tue Oct 01 00:00:00 EDT 2019 · Journal of the American Ceramic Society · OSTI ID:1571518

Viscosity of glass‐forming melt at the bottom of high‐level waste melter‐feed cold caps: Effects of temperature and incorporation of solid components

Journal Article · Mon Nov 11 19:00:00 EST 2019 · Journal of the American Ceramic Society · OSTI ID:1581841

Viscosity of glass-forming melt at the bottom of high-level waste melter feed cold caps: Effects of temperature and incorporation of solid components

Journal Article · Sun Mar 01 23:00:00 EST 2020 · Journal of American Ceramic Society · OSTI ID:1608763

Related Subjects

36 MATERIALS SCIENCE
Foam stability
Glass melting
Primary foam
Production rate
Thermal conductivity

Effect of cold-cap-bottom shear stress on primary foam stability

Citation Formats

References (69)

Similar Records

Related Subjects