{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/77764"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/77764","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"A numerical simulation of two-dimensional separated flow in a symmetric open-channel expansion using the depth-integrated two-equation (K-E) turbulence closure model","abstract":"Many of the free surface flow problems encountered by hydraulic engineers can be suitably analyzed by means of the depth-integrated equations of motion. A consequence of adopting a depth-integrated modeling approach is that closure approximations must be implemented to represent the so-called effective stresses. The effective stresses consist of the depth-integrated viscous stresses, which are usually small and neglected, the depth-integrated turbulent Reynold's stresses, and additional stresses resulting from the depth-integration of the nonlinear convective accelerations (here after called momentum dispersion). Existing closure schemes for momentum dispersion lack sufficient numerical and experimental verification to warrant consideration at this time, so consequently, attention is focused on examining closure for the depth-integrated turbulent Reynold's stresses. In the present study, an application at the depth-integrated (k-ε) turbulence model is presented for separated flow in a wide, shallow, rectangular channel with an abrupt expansion in width. The well-known numerical problems associated with the use of upwind and central finite differences for convection is overcome by the adoption of the spatially third-order accurate QUICK finite difference technique. Results presented show that modification of the depth-integrated (k-ε) turbulence closure model for streamline curvature leads to significant improvement in the agreement between model predictions and experimental measurements.","abstract_html":"Many of the free surface flow problems encountered by hydraulic engineers can be suitably analyzed by means of the depth-integrated equations of motion. A consequence of adopting a depth-integrated modeling approach is that closure approximations must be implemented to represent the so-called effective stresses. The effective stresses consist of the depth-integrated viscous stresses, which are usually small and neglected, the depth-integrated turbulent Reynold's stresses, and additional stresses resulting from the depth-integration of the nonlinear convective accelerations (here after called momentum dispersion). Existing closure schemes for momentum dispersion lack sufficient numerical and experimental verification to warrant consideration at this time, so consequently, attention is focused on examining closure for the depth-integrated turbulent Reynold's stresses. In the present study, an application at the depth-integrated (k-ε) turbulence model is presented for separated flow in a wide, shallow, rectangular channel with an abrupt expansion in width. The well-known numerical problems associated with the use of upwind and central finite differences for convection is overcome by the adoption of the spatially third-order accurate QUICK finite difference technique. Results presented show that modification of the depth-integrated (k-ε) turbulence closure model for streamline curvature leads to significant improvement in the agreement between model predictions and experimental measurements.","abstract_has_math":false,"creators":["Chapman, Raymond Scott"],"institution":"Virginia Polytechnic Institute and State University","degree_name":"Ph. 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A consequence of adopting a depth-integrated modeling approach is that closure approximations must be implemented to represent the so-called effective stresses. The effective stresses consist of the depth-integrated viscous stresses, which are usually small and neglected, the depth-integrated turbulent Reynold's stresses, and additional stresses resulting from the depth-integration of the nonlinear convective accelerations (here after called momentum dispersion). Existing closure schemes for momentum dispersion lack sufficient numerical and experimental verification to warrant consideration at this time, so consequently, attention is focused on examining closure for the depth-integrated turbulent Reynold's stresses. In the present study, an application at the depth-integrated (k-ε) turbulence model is presented for separated flow in a wide, shallow, rectangular channel with an abrupt expansion in width. The well-known numerical problems associated with the use of upwind and central finite differences for convection is overcome by the adoption of the spatially third-order accurate QUICK finite difference technique. Results presented show that modification of the depth-integrated (k-ε) turbulence closure model for streamline curvature leads to significant improvement in the agreement between model predictions and experimental measurements."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A numerical simulation of two-dimensional separated flow in a symmetric open-channel expansion using the depth-integrated two-equation (K-E) turbulence closure model"]}]}],"canonical_facts":{"dc:contributor.department":["Civil Engineering"],"dc:creator":["Chapman, Raymond Scott"],"dc:date.accessioned":["2017-05-24T18:19:01Z"],"dc:date.available":["2017-05-24T18:19:01Z"],"dc:date.issued":["1982"],"dc:description.abstract":["Many of the free surface flow problems encountered by hydraulic engineers can be suitably analyzed by means of the depth-integrated equations of motion. A consequence of adopting a depth-integrated modeling approach is that closure approximations must be implemented to represent the so-called effective stresses. The effective stresses consist of the depth-integrated viscous stresses, which are usually small and neglected, the depth-integrated turbulent Reynold's stresses, and additional stresses resulting from the depth-integration of the nonlinear convective accelerations (here after called momentum dispersion). Existing closure schemes for momentum dispersion lack sufficient numerical and experimental verification to warrant consideration at this time, so consequently, attention is focused on examining closure for the depth-integrated turbulent Reynold's stresses. In the present study, an application at the depth-integrated (k-ε) turbulence model is presented for separated flow in a wide, shallow, rectangular channel with an abrupt expansion in width. The well-known numerical problems associated with the use of upwind and central finite differences for convection is overcome by the adoption of the spatially third-order accurate QUICK finite difference technique. Results presented show that modification of the depth-integrated (k-ε) turbulence closure model for streamline curvature leads to significant improvement in the agreement between model predictions and experimental measurements."],"dc:description.degree":["Ph. D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/77764"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute and State University"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["A numerical simulation of two-dimensional separated flow in a symmetric open-channel expansion using the depth-integrated two-equation (K-E) turbulence closure model"],"dc:type":["Dissertation"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Civil Engineering"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. 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