{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/68509"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/68509","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Numerical Analysis of Two- and Three-Dimensional 90-Degree Bend Flow","abstract":"The two basic methods of numerical viscous flow calculation--the vorticity-transport and primitive-variable schemes--are applied to the finite-difference analysis of flow through a two-dimensional 90-degree bend between sections of straight conduit. Additionally, the vorticity-transport method is employed in two approaches--one a direct calculation in rectangular and polar coordinates, the other via a non-orthogonal coordinate transform by which calculations are performed in a square mesh field. The solutions for all three methods were in agreement for (//R) = 72. The two-dimensional primitive-variable methodology was then successfully transferred to the three-dimensional 90-degree curved pipe problem and solutions have been generated up to (//R) = 100.","abstract_html":"The two basic methods of numerical viscous flow calculation--the vorticity-transport and primitive-variable schemes--are applied to the finite-difference analysis of flow through a two-dimensional 90-degree bend between sections of straight conduit. Additionally, the vorticity-transport method is employed in two approaches--one a direct calculation in rectangular and polar coordinates, the other via a non-orthogonal coordinate transform by which calculations are performed in a square mesh field. The solutions for all three methods were in agreement for (//R) = 72. The two-dimensional primitive-variable methodology was then successfully transferred to the three-dimensional 90-degree curved pipe problem and solutions have been generated up to (//R) = 100.","abstract_has_math":false,"creators":["Liou, Ren-Jei"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Theoretical and Applied Mechanics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-14T14:42:20Z","date_published":"2014-12-14T14:42:20Z","updated_at":"2026-07-22T22:25:59Z","subjects":["Applied Mechanics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8026548"],"render_values":[{"text":"(UMI)AAI8026548","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/68509","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Liou, Ren-Jei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-14T14:42:20Z","10000-01-01","1980"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Theoretical and Applied Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied Mechanics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/68509","(UMI)AAI8026548"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The two basic methods of numerical viscous flow calculation--the vorticity-transport and primitive-variable schemes--are applied to the finite-difference analysis of flow through a two-dimensional 90-degree bend between sections of straight conduit. Additionally, the vorticity-transport method is employed in two approaches--one a direct calculation in rectangular and polar coordinates, the other via a non-orthogonal coordinate transform by which calculations are performed in a square mesh field. The solutions for all three methods were in agreement for (//R) = 72. The two-dimensional primitive-variable methodology was then successfully transferred to the three-dimensional 90-degree curved pipe problem and solutions have been generated up to (//R) = 100.","The two- and three-dimensional bend flows show many similarities except that no secondary flow occurs in two-dimensional bend. The axial velocity increases in the inner wall upstream junction region and outer wall downstream junction region while the axial pressure gradient increases in both regions. The axial velocity decreases in the outer wall upstream junction region and inner wall downstream junction region while the axial pressure gradient reverses in both regions. There is a strong secondary flow developed in the three-dimensional bend region and extends into the downstream straight pipe.","Made available in DSpace on 2014-12-14T14:42:20Z (GMT). No. of bitstreams: 1 8026548.pdf: 4605082 bytes, checksum: 2a5a2d3c5ee327bda71d53e81d47861b (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 68687 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","143 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."]},{"key":"dc:title","label":"Title","values":["Numerical Analysis of Two- and Three-Dimensional 90-Degree Bend Flow"]}]}],"canonical_facts":{"dc:creator":["Liou, Ren-Jei"],"dc:date":["2014-12-14T14:42:20Z","10000-01-01","1980"],"dc:description":["The two basic methods of numerical viscous flow calculation--the vorticity-transport and primitive-variable schemes--are applied to the finite-difference analysis of flow through a two-dimensional 90-degree bend between sections of straight conduit. Additionally, the vorticity-transport method is employed in two approaches--one a direct calculation in rectangular and polar coordinates, the other via a non-orthogonal coordinate transform by which calculations are performed in a square mesh field. The solutions for all three methods were in agreement for (//R) = 72. The two-dimensional primitive-variable methodology was then successfully transferred to the three-dimensional 90-degree curved pipe problem and solutions have been generated up to (//R) = 100.","The two- and three-dimensional bend flows show many similarities except that no secondary flow occurs in two-dimensional bend. The axial velocity increases in the inner wall upstream junction region and outer wall downstream junction region while the axial pressure gradient increases in both regions. The axial velocity decreases in the outer wall upstream junction region and inner wall downstream junction region while the axial pressure gradient reverses in both regions. There is a strong secondary flow developed in the three-dimensional bend region and extends into the downstream straight pipe.","Made available in DSpace on 2014-12-14T14:42:20Z (GMT). No. of bitstreams: 1 8026548.pdf: 4605082 bytes, checksum: 2a5a2d3c5ee327bda71d53e81d47861b (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 68687 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","143 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."],"dc:identifier":["http://hdl.handle.net/2142/68509","(UMI)AAI8026548"],"dc:language":["eng"],"dc:subject":["Applied Mechanics"],"dc:title":["Numerical Analysis of Two- and Three-Dimensional 90-Degree Bend Flow"],"dc:type":["text"],"thesis:degree_discipline":["Theoretical and Applied Mechanics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:59Z"}