Modelling and analysis of an endothermic reacting counter-current flow

We study the endothermic reaction and flow of a granular solid reactant, where energy for the reaction is provided by a counter-current flow of hot gases through the porous reactant bed. Research into reacting flows typically focusses on exothermic combustion processes. However, endothermic processe...

Ful tanımlama

Detaylı Bibliyografya
Asıl Yazarlar: Luckins, EK, Oliver, J, Please, C, Sloman, B, Van Gorder, R
Materyal Türü: Journal article
Dil:English
Baskı/Yayın Bilgisi: Cambridge University Press 2022
_version_ 1826309629929324544
author Luckins, EK
Oliver, J
Please, C
Sloman, B
Van Gorder, R
author_facet Luckins, EK
Oliver, J
Please, C
Sloman, B
Van Gorder, R
author_sort Luckins, EK
collection OXFORD
description We study the endothermic reaction and flow of a granular solid reactant, where energy for the reaction is provided by a counter-current flow of hot gases through the porous reactant bed. Research into reacting flows typically focusses on exothermic combustion processes. However, endothermic processes are common in the metallurgy industry, including the production of cement, silicon and rutile titanium dioxide. Several common features are observed in experimental and numerical studies of these processes, including critical temperatures of the reactant at which the chemical reaction begins, and regions of the reactor with uniform reactant temperature. Motivated specifically by the processes in a silicon furnace, we analyse a model of endothermic, reacting counter-current flow using the method of matched asymptotic expansions. Assuming the Péclet number in the solid is large, we explore the full range of values for the dimensionless inter-phase heat-transfer rate, finding six distinguished limits. In all limits, we find a diffusive boundary layer in which there is a fast chemical reaction rate due to the high temperatures, analogous to exothermic flame fronts. Outside this region, the counter-current flow is crucial to the chemical processes. For intermediate values of the heat-transfer rate, we find the same qualitative properties as those observed across the metallurgy industry, and we quantify the dependence of these properties on the flow rate and heat-transfer rate. In the limit of large heat-transfer coefficient, we derive the single-temperature limit, in which the solution structure is dependent on the direction of net heat flux through the domain.
first_indexed 2024-03-07T07:38:36Z
format Journal article
id oxford-uuid:dc62bacc-eafe-40c3-a75a-2f00cf7ad2a9
institution University of Oxford
language English
last_indexed 2024-03-07T07:38:36Z
publishDate 2022
publisher Cambridge University Press
record_format dspace
spelling oxford-uuid:dc62bacc-eafe-40c3-a75a-2f00cf7ad2a92023-03-29T08:25:27ZModelling and analysis of an endothermic reacting counter-current flowJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:dc62bacc-eafe-40c3-a75a-2f00cf7ad2a9EnglishSymplectic ElementsCambridge University Press2022Luckins, EKOliver, JPlease, CSloman, BVan Gorder, RWe study the endothermic reaction and flow of a granular solid reactant, where energy for the reaction is provided by a counter-current flow of hot gases through the porous reactant bed. Research into reacting flows typically focusses on exothermic combustion processes. However, endothermic processes are common in the metallurgy industry, including the production of cement, silicon and rutile titanium dioxide. Several common features are observed in experimental and numerical studies of these processes, including critical temperatures of the reactant at which the chemical reaction begins, and regions of the reactor with uniform reactant temperature. Motivated specifically by the processes in a silicon furnace, we analyse a model of endothermic, reacting counter-current flow using the method of matched asymptotic expansions. Assuming the Péclet number in the solid is large, we explore the full range of values for the dimensionless inter-phase heat-transfer rate, finding six distinguished limits. In all limits, we find a diffusive boundary layer in which there is a fast chemical reaction rate due to the high temperatures, analogous to exothermic flame fronts. Outside this region, the counter-current flow is crucial to the chemical processes. For intermediate values of the heat-transfer rate, we find the same qualitative properties as those observed across the metallurgy industry, and we quantify the dependence of these properties on the flow rate and heat-transfer rate. In the limit of large heat-transfer coefficient, we derive the single-temperature limit, in which the solution structure is dependent on the direction of net heat flux through the domain.
spellingShingle Luckins, EK
Oliver, J
Please, C
Sloman, B
Van Gorder, R
Modelling and analysis of an endothermic reacting counter-current flow
title Modelling and analysis of an endothermic reacting counter-current flow
title_full Modelling and analysis of an endothermic reacting counter-current flow
title_fullStr Modelling and analysis of an endothermic reacting counter-current flow
title_full_unstemmed Modelling and analysis of an endothermic reacting counter-current flow
title_short Modelling and analysis of an endothermic reacting counter-current flow
title_sort modelling and analysis of an endothermic reacting counter current flow
work_keys_str_mv AT luckinsek modellingandanalysisofanendothermicreactingcountercurrentflow
AT oliverj modellingandanalysisofanendothermicreactingcountercurrentflow
AT pleasec modellingandanalysisofanendothermicreactingcountercurrentflow
AT slomanb modellingandanalysisofanendothermicreactingcountercurrentflow
AT vangorderr modellingandanalysisofanendothermicreactingcountercurrentflow