{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/343053"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/343053","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Turbulent Line Plumes and Filling Boxes","abstract":"Turbulent line plumes have been studied for over half a century, yet key questions regarding their behaviour remain unanswered. In this thesis, we use a combination of simplified theoretical modelling, flow visualisations, and experimental measurements to address the following questions. First, what is the entrainment coefficient of a turbulent line plume? Second, how does real two-dimensional filling box behaviour differ from the commonly used Baines & Turner (1969) filling box model? Third, what are the changes to filling box behaviour when the plume source is not centred in the filling box? The entrainment coefficient is a crucial component of simplified models of plume behaviour, and an accurate value is thus necessary for reliable quantitative predictions. However, reported values for the entrainment coefficient vary from 0.1 to 0.2, severely hindering the use of these models. Furthermore, there has not been a comprehensive attempt to assess the reported variation nor has a value within this range been accepted as a consensus. Using a multifaceted approach combining theoretical developments to plume theory, a thorough assessment of the reported values, and new measurements of the entrainment coefficient, we conclude that the entrainment coefficient is 0.111 ± 15%. This range, considerably smaller than the range in reported values, should result in improved confidence in predictions using plume theory and allow more detailed quantitative comparisons between line plumes and related flows. Filling boxes are commonly interpreted with the Baines & Turner model in which a plume fills a confined environment with a series of infinitesimally thin and passive layers. Flow visualisations show that this idealised filling process does not represent the real behaviour in a two-dimensional filling box: the `layers' created by the plume are relatively thick (approximately 20% of the box height) and play an active role in the filling process. Consequently, the Baines \\& Turner model significantly underpredicts the time required for buoyant fluid to reach a given height in a box, with considerable implications for fire safety. At late times in the filling process, the Baines & Turner model makes more reasonable predictions, although still neglects important aspects of the flow. Based on the visualisations and experimental measurements, we propose a hybrid filling box model, combining the Baines & Turner model with a well-mixed region, which more accurately captures filling box behaviour. An off-centred line plume source in a filling box offers the intriguing possibility that the plume could act as a fluid barrier, dividing two regions with different flow conditions. We developed simple models to predict the buoyancy difference that the plume could create and maintain, concluding that the plume could create a practically significant buoyancy difference, given an appropriate box geometry and a sufficiently strong plume. We conducted experiments to measure the buoyancy difference created by an off-centred plume, confirming the models and the premise that an off-centred plume can support a buoyancy difference across it.","abstract_html":"Turbulent line plumes have been studied for over half a century, yet key questions regarding their behaviour remain unanswered. In this thesis, we use a combination of simplified theoretical modelling, flow visualisations, and experimental measurements to address the following questions. First, what is the entrainment coefficient of a turbulent line plume? Second, how does real two-dimensional filling box behaviour differ from the commonly used Baines & Turner (1969) filling box model? Third, what are the changes to filling box behaviour when the plume source is not centred in the filling box? The entrainment coefficient is a crucial component of simplified models of plume behaviour, and an accurate value is thus necessary for reliable quantitative predictions. However, reported values for the entrainment coefficient vary from 0.1 to 0.2, severely hindering the use of these models. Furthermore, there has not been a comprehensive attempt to assess the reported variation nor has a value within this range been accepted as a consensus. Using a multifaceted approach combining theoretical developments to plume theory, a thorough assessment of the reported values, and new measurements of the entrainment coefficient, we conclude that the entrainment coefficient is 0.111 ± 15%. This range, considerably smaller than the range in reported values, should result in improved confidence in predictions using plume theory and allow more detailed quantitative comparisons between line plumes and related flows. Filling boxes are commonly interpreted with the Baines & Turner model in which a plume fills a confined environment with a series of infinitesimally thin and passive layers. Flow visualisations show that this idealised filling process does not represent the real behaviour in a two-dimensional filling box: the `layers' created by the plume are relatively thick (approximately 20% of the box height) and play an active role in the filling process. Consequently, the Baines \\& Turner model significantly underpredicts the time required for buoyant fluid to reach a given height in a box, with considerable implications for fire safety. At late times in the filling process, the Baines & Turner model makes more reasonable predictions, although still neglects important aspects of the flow. Based on the visualisations and experimental measurements, we propose a hybrid filling box model, combining the Baines & Turner model with a well-mixed region, which more accurately captures filling box behaviour. An off-centred line plume source in a filling box offers the intriguing possibility that the plume could act as a fluid barrier, dividing two regions with different flow conditions. We developed simple models to predict the buoyancy difference that the plume could create and maintain, concluding that the plume could create a practically significant buoyancy difference, given an appropriate box geometry and a sufficiently strong plume. We conducted experiments to measure the buoyancy difference created by an off-centred plume, confirming the models and the premise that an off-centred plume can support a buoyancy difference across it.","abstract_has_math":false,"creators":["Richardson, James"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Hunt, Gary"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-06-01","date_published":"2021-06-01","updated_at":"2026-07-22T22:24:07Z","subjects":["entrainment","filling box","plume"],"languages":["eng"],"rights":[],"rights_urls":["https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["0000000253304046"],"render_values":[{"text":"0000-0002-5330-4046","href":"https://orcid.org/0000-0002-5330-4046","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.90464","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Hunt, Gary"]},{"key":"dc:creator","label":"Author","values":["Richardson, James"]},{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["0000000253304046"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2021-06-01"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/343053"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["entrainment","filling box","plume"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.17863/CAM.90464"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/18fb28ec-ad83-4708-abb0-448e70083ade/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Turbulent line plumes have been studied for over half a century, yet key questions regarding their behaviour remain unanswered. In this thesis, we use a combination of simplified theoretical modelling, flow visualisations, and experimental measurements to address the following questions. First, what is the entrainment coefficient of a turbulent line plume? Second, how does real two-dimensional filling box behaviour differ from the commonly used Baines & Turner (1969) filling box model? Third, what are the changes to filling box behaviour when the plume source is not centred in the filling box? The entrainment coefficient is a crucial component of simplified models of plume behaviour, and an accurate value is thus necessary for reliable quantitative predictions. However, reported values for the entrainment coefficient vary from 0.1 to 0.2, severely hindering the use of these models. Furthermore, there has not been a comprehensive attempt to assess the reported variation nor has a value within this range been accepted as a consensus. Using a multifaceted approach combining theoretical developments to plume theory, a thorough assessment of the reported values, and new measurements of the entrainment coefficient, we conclude that the entrainment coefficient is 0.111 ± 15%. This range, considerably smaller than the range in reported values, should result in improved confidence in predictions using plume theory and allow more detailed quantitative comparisons between line plumes and related flows. Filling boxes are commonly interpreted with the Baines & Turner model in which a plume fills a confined environment with a series of infinitesimally thin and passive layers. Flow visualisations show that this idealised filling process does not represent the real behaviour in a two-dimensional filling box: the `layers' created by the plume are relatively thick (approximately 20% of the box height) and play an active role in the filling process. Consequently, the Baines \\& Turner model significantly underpredicts the time required for buoyant fluid to reach a given height in a box, with considerable implications for fire safety. At late times in the filling process, the Baines & Turner model makes more reasonable predictions, although still neglects important aspects of the flow. Based on the visualisations and experimental measurements, we propose a hybrid filling box model, combining the Baines & Turner model with a well-mixed region, which more accurately captures filling box behaviour. An off-centred line plume source in a filling box offers the intriguing possibility that the plume could act as a fluid barrier, dividing two regions with different flow conditions. We developed simple models to predict the buoyancy difference that the plume could create and maintain, concluding that the plume could create a practically significant buoyancy difference, given an appropriate box geometry and a sufficiently strong plume. We conducted experiments to measure the buoyancy difference created by an off-centred plume, confirming the models and the premise that an off-centred plume can support a buoyancy difference across it."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["832f5bb547b3b232a93a7f4bc9e1d21b"]},{"key":"dc:title","label":"Title","values":["Turbulent Line Plumes and Filling Boxes"]}]}],"canonical_facts":{"dc:contributor.advisor":["Hunt, Gary"],"dc:creator":["Richardson, James"],"dc:creator.authoridentifier":["0000000253304046"],"dc:date.issued":["2021-06-01"],"dc:description.abstract":["Turbulent line plumes have been studied for over half a century, yet key questions regarding their behaviour remain unanswered. In this thesis, we use a combination of simplified theoretical modelling, flow visualisations, and experimental measurements to address the following questions. First, what is the entrainment coefficient of a turbulent line plume? Second, how does real two-dimensional filling box behaviour differ from the commonly used Baines & Turner (1969) filling box model? Third, what are the changes to filling box behaviour when the plume source is not centred in the filling box? The entrainment coefficient is a crucial component of simplified models of plume behaviour, and an accurate value is thus necessary for reliable quantitative predictions. However, reported values for the entrainment coefficient vary from 0.1 to 0.2, severely hindering the use of these models. Furthermore, there has not been a comprehensive attempt to assess the reported variation nor has a value within this range been accepted as a consensus. Using a multifaceted approach combining theoretical developments to plume theory, a thorough assessment of the reported values, and new measurements of the entrainment coefficient, we conclude that the entrainment coefficient is 0.111 ± 15%. This range, considerably smaller than the range in reported values, should result in improved confidence in predictions using plume theory and allow more detailed quantitative comparisons between line plumes and related flows. Filling boxes are commonly interpreted with the Baines & Turner model in which a plume fills a confined environment with a series of infinitesimally thin and passive layers. Flow visualisations show that this idealised filling process does not represent the real behaviour in a two-dimensional filling box: the `layers' created by the plume are relatively thick (approximately 20% of the box height) and play an active role in the filling process. Consequently, the Baines \\& Turner model significantly underpredicts the time required for buoyant fluid to reach a given height in a box, with considerable implications for fire safety. At late times in the filling process, the Baines & Turner model makes more reasonable predictions, although still neglects important aspects of the flow. Based on the visualisations and experimental measurements, we propose a hybrid filling box model, combining the Baines & Turner model with a well-mixed region, which more accurately captures filling box behaviour. An off-centred line plume source in a filling box offers the intriguing possibility that the plume could act as a fluid barrier, dividing two regions with different flow conditions. We developed simple models to predict the buoyancy difference that the plume could create and maintain, concluding that the plume could create a practically significant buoyancy difference, given an appropriate box geometry and a sufficiently strong plume. We conducted experiments to measure the buoyancy difference created by an off-centred plume, confirming the models and the premise that an off-centred plume can support a buoyancy difference across it."],"dc:format.checksum.md5":["832f5bb547b3b232a93a7f4bc9e1d21b"],"dc:identifier.doi":["10.17863/CAM.90464"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/18fb28ec-ad83-4708-abb0-448e70083ade/download"],"dc:language":["eng"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/343053"],"dc:rights":["https://www.rioxx.net/licenses/all-rights-reserved/"],"dc:subject":["entrainment","filling box","plume"],"dc:title":["Turbulent Line Plumes and Filling Boxes"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-22T22:24:07Z"}