{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/300649"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/300649","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"2D PIV Study of Grid Turbulence","abstract":"The aim of the current project was to analyse grid turbulence with a technique that allows for a direct measurement of velocity derivative statistics. Two-dimensional particle image velocimetry ($2D~PIV$) of highly resolved grid turbulence at $Re_{M}=U_{\\infty}M/\\nu = 16000$ where $M$ is the grid rod spacing was analysed. Data spanning the downstream range $65 < x/M < 145$ was captured separately on planes parallel to a water channel's floor and walls with a $PIV$ resolution within three times the Kolmogorov microscale $\\eta_{_{K}}$. Isotropic turbulence ($IT$), axisymmetric turbulence ($AT$), homogeneous turbulence ($HT$), all these theoretical frameworks have been checked against velocity derivative data. It was found that the data complies most satisfactorily with $HT$ only, and to a lesser extent with $IT$ and $AT$. The $2\\times 2$ velocity-gradient tensor $VGT$ that can be formed from $2D~PIV$ data was used in a novel manner by plotting the joint probability density function ($PDF$) of its trace $p$ and determinant $q$. Under the assumptions of \\textit{locally} isotropic turbulence, the observed asymmetry in this joint $PDF$ was explained as the result of the predominance of enstrophy amplification by vortex stretching. The observations were validated when compared with $2D$ slices of $3D$ data from a direct numerical simulation of isotropic flow. Finally, a study of homogenisation was carried out by mapping an area of $14M\\times 4M$ in the down- and cross-stream directions respectively starting immediately at the grid. This unprecedented attempt was achieved by using $2D~PIV$ over the stitched fields of view of three cameras put side-by-side. The statistics - based on 10600 vector fields per case - in the wake of two carefully chosen grids were studied, showing that homogenisation is a rapid but gradual process. Collapse of statistics across the different grid geometries was achieved passed the region of initial flow transients by taking into account all relevant parameters: differences in grid geometry \\textit{and} work done on the flow. This hints at a unique dependency of grid turbulence dynamics in the region of cross-stream homogenised flow. Two-point spatial correlation functions were used to study the footprint of the grid on the flow statistics, exhibiting complex $Re_{M}-$dependent wake interactions between the grid rods. Their impact, however, is quickly washed away by the turbulence.","abstract_html":"The aim of the current project was to analyse grid turbulence with a technique that allows for a direct measurement of velocity derivative statistics. Two-dimensional particle image velocimetry ($2D~PIV$) of highly resolved grid turbulence at <span class=\"etd-inline-math\">Re<sub>M</sub>=U<sub>\\infty</sub>M/\\nu = 16000</span> where $M$ is the grid rod spacing was analysed. Data spanning the downstream range $65 &lt; x/M &lt; 145$ was captured separately on planes parallel to a water channel&#x27;s floor and walls with a $PIV$ resolution within three times the Kolmogorov microscale <span class=\"etd-inline-math\">\\eta<sub><sub>K</sub></sub></span>. Isotropic turbulence ($IT$), axisymmetric turbulence ($AT$), homogeneous turbulence ($HT$), all these theoretical frameworks have been checked against velocity derivative data. It was found that the data complies most satisfactorily with $HT$ only, and to a lesser extent with $IT$ and $AT$. The $2\\times 2$ velocity-gradient tensor $VGT$ that can be formed from $2D~PIV$ data was used in a novel manner by plotting the joint probability density function ($PDF$) of its trace $p$ and determinant $q$. Under the assumptions of \\textit{locally} isotropic turbulence, the observed asymmetry in this joint $PDF$ was explained as the result of the predominance of enstrophy amplification by vortex stretching. The observations were validated when compared with $2D$ slices of $3D$ data from a direct numerical simulation of isotropic flow. Finally, a study of homogenisation was carried out by mapping an area of $14M\\times 4M$ in the down- and cross-stream directions respectively starting immediately at the grid. This unprecedented attempt was achieved by using $2D~PIV$ over the stitched fields of view of three cameras put side-by-side. The statistics - based on 10600 vector fields per case - in the wake of two carefully chosen grids were studied, showing that homogenisation is a rapid but gradual process. Collapse of statistics across the different grid geometries was achieved passed the region of initial flow transients by taking into account all relevant parameters: differences in grid geometry \\textit{and} work done on the flow. This hints at a unique dependency of grid turbulence dynamics in the region of cross-stream homogenised flow. Two-point spatial correlation functions were used to study the footprint of the grid on the flow statistics, exhibiting complex <span class=\"etd-inline-math\">Re<sub>M</sub>-</span>dependent wake interactions between the grid rods. Their impact, however, is quickly washed away by the turbulence.","abstract_has_math":true,"creators":["Cardesa Dueñas, José Ignacio"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Dawson, James R.","Nickels, Timothy Bruce"],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-19","date_published":"2012-05-19","updated_at":"2026-07-22T22:24:16Z","subjects":["fluid mechanics","turbulence","particle image velocimetry","velocity gradient tensor","invariants","isotropic turbulence","axisymmetric turbulence","homogeneous turbulence"],"languages":["en"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/e7e117b5-fa35-47cf-8a9e-b868f138f947/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["0000000238635285","0000000230696948"],"render_values":[{"text":"0000-0002-3863-5285","href":"https://orcid.org/0000-0002-3863-5285","code":true},{"text":"0000-0002-3069-6948","href":"https://orcid.org/0000-0002-3069-6948","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.47724","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Dawson, James R.","Nickels, Timothy Bruce"]},{"key":"dc:contributor.sponsor","label":"Sponsor","values":["EPSRC Doctoral Training Account"]},{"key":"dc:creator","label":"Author","values":["Cardesa Dueñas, José Ignacio"]},{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["0000000238635285","0000000230696948"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2012-05-19"]},{"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/1810/300649"]},{"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":["fluid mechanics","turbulence","particle image velocimetry","velocity gradient tensor","invariants","isotropic turbulence","axisymmetric turbulence","homogeneous turbulence"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/e7e117b5-fa35-47cf-8a9e-b868f138f947/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.17863/CAM.47724"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/4a1c4ae5-9740-439d-9c04-d311b12f5ebd/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The aim of the current project was to analyse grid turbulence with a technique that allows for a direct measurement of velocity derivative statistics. 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Under the assumptions of \\textit{locally} isotropic turbulence, the observed asymmetry in this joint $PDF$ was explained as the result of the predominance of enstrophy amplification by vortex stretching. The observations were validated when compared with $2D$ slices of $3D$ data from a direct numerical simulation of isotropic flow. Finally, a study of homogenisation was carried out by mapping an area of $14M\\times 4M$ in the down- and cross-stream directions respectively starting immediately at the grid. This unprecedented attempt was achieved by using $2D~PIV$ over the stitched fields of view of three cameras put side-by-side. The statistics - based on 10600 vector fields per case - in the wake of two carefully chosen grids were studied, showing that homogenisation is a rapid but gradual process. Collapse of statistics across the different grid geometries was achieved passed the region of initial flow transients by taking into account all relevant parameters: differences in grid geometry \\textit{and} work done on the flow. This hints at a unique dependency of grid turbulence dynamics in the region of cross-stream homogenised flow. Two-point spatial correlation functions were used to study the footprint of the grid on the flow statistics, exhibiting complex $Re_{M}-$dependent wake interactions between the grid rods. 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Data spanning the downstream range $65 < x/M < 145$ was captured separately on planes parallel to a water channel's floor and walls with a $PIV$ resolution within three times the Kolmogorov microscale $\\eta_{_{K}}$. Isotropic turbulence ($IT$), axisymmetric turbulence ($AT$), homogeneous turbulence ($HT$), all these theoretical frameworks have been checked against velocity derivative data. It was found that the data complies most satisfactorily with $HT$ only, and to a lesser extent with $IT$ and $AT$. The $2\\times 2$ velocity-gradient tensor $VGT$ that can be formed from $2D~PIV$ data was used in a novel manner by plotting the joint probability density function ($PDF$) of its trace $p$ and determinant $q$. Under the assumptions of \\textit{locally} isotropic turbulence, the observed asymmetry in this joint $PDF$ was explained as the result of the predominance of enstrophy amplification by vortex stretching. The observations were validated when compared with $2D$ slices of $3D$ data from a direct numerical simulation of isotropic flow. Finally, a study of homogenisation was carried out by mapping an area of $14M\\times 4M$ in the down- and cross-stream directions respectively starting immediately at the grid. This unprecedented attempt was achieved by using $2D~PIV$ over the stitched fields of view of three cameras put side-by-side. The statistics - based on 10600 vector fields per case - in the wake of two carefully chosen grids were studied, showing that homogenisation is a rapid but gradual process. Collapse of statistics across the different grid geometries was achieved passed the region of initial flow transients by taking into account all relevant parameters: differences in grid geometry \\textit{and} work done on the flow. This hints at a unique dependency of grid turbulence dynamics in the region of cross-stream homogenised flow. Two-point spatial correlation functions were used to study the footprint of the grid on the flow statistics, exhibiting complex $Re_{M}-$dependent wake interactions between the grid rods. 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