{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/84016"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/84016","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"A Morphing Continuum Analysis of Energy Transfer in Turbulent Flow","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Cheikh, Mohamad Ibrahim"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Chen, James","Mechanical and Aerospace Engineering"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-06-21T15:47:04Z","date_published":"2022-06-21T15:47:04Z","updated_at":"2026-07-27T19:05:28Z","subjects":["mechanical engineering"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/84016","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chen, James","Mechanical and Aerospace Engineering"]},{"key":"dc:creator","label":"Author","values":["Cheikh, Mohamad Ibrahim"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-06-21T15:47:04Z","2020"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["mechanical engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/84016"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","The study aims at understanding the relationship between the kinematics of the small-scale eddies and the energy cascade in turbulent flows. In particular, the work decouples small-scale rotational motions from the translational motions and tries to explain the impact of each movement of the energy flow. Resorting to Navier-Stokes (NS) based methods to showcase this energy flow is tedious considering the strong coupling between translational and rotational motions of the fluid. The present work is on the basis of a morphing continuum theory (MCT), a high order continuum theory. MCT is a multi-scale continuum theory that incorporates small-scale structures in its continuum. The MCT small-scale structure has its own independent degrees of freedom and allows decoupling of the rotational motion from the translational motion of the flow, giving the fluid element a total of six-degrees of motion. The study will then assume and prove that the MCT small-scale structures can adopt the role of the smallest eddies in a turbulent flow. The MCT balance laws are presented, and their relationship to the classical fluid theory balance law is addressed. The MCT conservation laws for linear momentum, angular momentum, and energy are derived from the spatial symmetry being applied to the balance laws. The conservation laws show similarities between the morphing continuum theory and the classical Navier-Stokes in the conservation of linear momentum, but the difference in the conservation of angular momentum. The conservation of energy shows that by segregating the kinetic energy into its rotational and translational components, one can realize new energy routes not found in the classical theory. The current work aims at exploiting these routes to investigate the effect of the small-scale motions on the turbulent flows. Since the kinematics of turbulent flows is highly dependent on the behavior of the smallest relevant eddies, the study will prove that MCT small-scale structures can adopt the role of the smallest relevant eddies. Numerical methodologies for solving the compressible and incompressible MCT governing laws are also presented. The incompressible scheme is a pressure-based solver, based upon the famous SIMPLE scheme, while the compressible scheme is a density-based solver. Both schemes are validated and show at least a 2nd degree of accuracy. Preliminary numerical simulations of the MCT governing equations are employed for two turbulent flows. The first case employs the MCT incompressible scheme to investigate the energy flow in homogeneous isotropic turbulence (HIT). The study begins by presenting a model to reproduce the Navier-Stokes HIT case into the presented MCT framework. The study compares the results of both cases and assesses the accuracy of the proposed MCT model. The two cases show similar results on the global scale by having equivalent mean kinetic energy and on the small-scale by agreeing to Kolmogorov 5/3 law. The study implements the MCT conservation law to investigate the impact of the rotational and translational motion on the flow of energy. The second example showcases MCT in predicting the compressible turbulent flow. A supersonic flow with a 2.93 Mach over an 8-degree ramp is considered. The study shows that MCT is a much more computationally friendly theory than the classicalNS equations. The dynamics of energy cascade at the length-scale of individual eddies is illuminated through the subscale rotation introduced by MCT. In this regard, a statistical averaging procedure for capturing energy transfer incompressible turbulence is employed. The analysis show the existence of a statistical coupling between the internal energy and the translational and rotational kinetic energy indicating a multi-scale transfer of energy. In conclusion, MCT gives a new characterization of the energy cascade within compressible turbulence without the use of excessive computational resources.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A Morphing Continuum Analysis of Energy Transfer in Turbulent Flow"]}]}],"canonical_facts":{"dc:contributor":["Chen, James","Mechanical and Aerospace Engineering"],"dc:creator":["Cheikh, Mohamad Ibrahim"],"dc:date":["2022-06-21T15:47:04Z","2020"],"dc:description":["Ph.D.","The study aims at understanding the relationship between the kinematics of the small-scale eddies and the energy cascade in turbulent flows. In particular, the work decouples small-scale rotational motions from the translational motions and tries to explain the impact of each movement of the energy flow. Resorting to Navier-Stokes (NS) based methods to showcase this energy flow is tedious considering the strong coupling between translational and rotational motions of the fluid. The present work is on the basis of a morphing continuum theory (MCT), a high order continuum theory. MCT is a multi-scale continuum theory that incorporates small-scale structures in its continuum. The MCT small-scale structure has its own independent degrees of freedom and allows decoupling of the rotational motion from the translational motion of the flow, giving the fluid element a total of six-degrees of motion. The study will then assume and prove that the MCT small-scale structures can adopt the role of the smallest eddies in a turbulent flow. The MCT balance laws are presented, and their relationship to the classical fluid theory balance law is addressed. The MCT conservation laws for linear momentum, angular momentum, and energy are derived from the spatial symmetry being applied to the balance laws. The conservation laws show similarities between the morphing continuum theory and the classical Navier-Stokes in the conservation of linear momentum, but the difference in the conservation of angular momentum. The conservation of energy shows that by segregating the kinetic energy into its rotational and translational components, one can realize new energy routes not found in the classical theory. The current work aims at exploiting these routes to investigate the effect of the small-scale motions on the turbulent flows. Since the kinematics of turbulent flows is highly dependent on the behavior of the smallest relevant eddies, the study will prove that MCT small-scale structures can adopt the role of the smallest relevant eddies. Numerical methodologies for solving the compressible and incompressible MCT governing laws are also presented. The incompressible scheme is a pressure-based solver, based upon the famous SIMPLE scheme, while the compressible scheme is a density-based solver. Both schemes are validated and show at least a 2nd degree of accuracy. Preliminary numerical simulations of the MCT governing equations are employed for two turbulent flows. The first case employs the MCT incompressible scheme to investigate the energy flow in homogeneous isotropic turbulence (HIT). The study begins by presenting a model to reproduce the Navier-Stokes HIT case into the presented MCT framework. The study compares the results of both cases and assesses the accuracy of the proposed MCT model. The two cases show similar results on the global scale by having equivalent mean kinetic energy and on the small-scale by agreeing to Kolmogorov 5/3 law. The study implements the MCT conservation law to investigate the impact of the rotational and translational motion on the flow of energy. The second example showcases MCT in predicting the compressible turbulent flow. A supersonic flow with a 2.93 Mach over an 8-degree ramp is considered. The study shows that MCT is a much more computationally friendly theory than the classicalNS equations. The dynamics of energy cascade at the length-scale of individual eddies is illuminated through the subscale rotation introduced by MCT. In this regard, a statistical averaging procedure for capturing energy transfer incompressible turbulence is employed. The analysis show the existence of a statistical coupling between the internal energy and the translational and rotational kinetic energy indicating a multi-scale transfer of energy. In conclusion, MCT gives a new characterization of the energy cascade within compressible turbulence without the use of excessive computational resources.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/84016"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["mechanical engineering"],"dc:title":["A Morphing Continuum Analysis of Energy Transfer in Turbulent Flow"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:28Z"}