The goal of this thesis is to determine a flow model that provides a better blade design over current design techniques utilizing a hybrid vortex model. This hybrid vortex model combines the well-established simple radial equilibrium vortex models into a higher order equation that will establish the basis for a more flow-accurate model. In this paper, we will discuss the basis and derivation of these vortex models, the shortcomings of current techniques, and verification of the new vortex model with empirical data via Computational Fluid Dynamic (CFD). The simple radial equilibrium equation set has been known to the scientific community since the first gas turbine engines designs. Active research into the vortex models associated with radial equilibrium, has declined with the advent of robust CFD solvers capable of representing fluid through turbomachinery. Since there are no closed form of the Navier-Stokes Equations in existence, CFD is bound by errors in modelling turbulence, mixing planes, boundary layer transitions, as well as other loss models that are incorporated into these programs. The Simplified High-Order Vortex Equation was utilized to increase the surge margin of up to 3.32% compared to a rotor designed using the free vortex method.
","abstract_html":"<p>The goal of this thesis is to determine a flow model that provides a better blade design over current design techniques utilizing a hybrid vortex model. This hybrid vortex model combines the well-established simple radial equilibrium vortex models into a higher order equation that will establish the basis for a more flow-accurate model. In this paper, we will discuss the basis and derivation of these vortex models, the shortcomings of current techniques, and verification of the new vortex model with empirical data via Computational Fluid Dynamic (CFD). The simple radial equilibrium equation set has been known to the scientific community since the first gas turbine engines designs. Active research into the vortex models associated with radial equilibrium, has declined with the advent of robust CFD solvers capable of representing fluid through turbomachinery. Since there are no closed form of the Navier-Stokes Equations in existence, CFD is bound by errors in modelling turbulence, mixing planes, boundary layer transitions, as well as other loss models that are incorporated into these programs. The Simplified High-Order Vortex Equation was utilized to increase the surge margin of up to 3.32% compared to a rotor designed using the free vortex method.</p>","abstract_has_math":false,"creators":["Matsumoto, Travis K."],"institution":null,"degree_name":"Master of Science in Aerospace Engineering","degree_level":"Thesis - Open Access","degree_discipline":"Aerospace Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-04-01T07:00:00Z","date_published":"2015-04-01T07:00:00Z","updated_at":"2026-07-27T19:26:08Z","subjects":["high-order","vortex equation","radial equilibrium","computational fluid dynamics","Aerodynamics and Fluid Mechanics","Aerospace Engineering"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.erau.edu/edt/169","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Matsumoto, Travis K."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Aerospace Engineering"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["high-order","vortex equation","radial equilibrium","computational fluid dynamics","Aerodynamics and Fluid Mechanics","Aerospace Engineering"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.erau.edu/edt/169"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The goal of this thesis is to determine a flow model that provides a better blade design over current design techniques utilizing a hybrid vortex model. This hybrid vortex model combines the well-established simple radial equilibrium vortex models into a higher order equation that will establish the basis for a more flow-accurate model. In this paper, we will discuss the basis and derivation of these vortex models, the shortcomings of current techniques, and verification of the new vortex model with empirical data via Computational Fluid Dynamic (CFD). The simple radial equilibrium equation set has been known to the scientific community since the first gas turbine engines designs. Active research into the vortex models associated with radial equilibrium, has declined with the advent of robust CFD solvers capable of representing fluid through turbomachinery. Since there are no closed form of the Navier-Stokes Equations in existence, CFD is bound by errors in modelling turbulence, mixing planes, boundary layer transitions, as well as other loss models that are incorporated into these programs. The Simplified High-Order Vortex Equation was utilized to increase the surge margin of up to 3.32% compared to a rotor designed using the free vortex method.
"]},{"key":"dc:title","label":"Title","values":["Determination of a Simplified High-Order Vortex Equation for Radial Equilibrium with CFD Verification"]}]}],"canonical_facts":{"dc:creator":["Matsumoto, Travis K."],"dc:description.abstract":["The goal of this thesis is to determine a flow model that provides a better blade design over current design techniques utilizing a hybrid vortex model. This hybrid vortex model combines the well-established simple radial equilibrium vortex models into a higher order equation that will establish the basis for a more flow-accurate model. In this paper, we will discuss the basis and derivation of these vortex models, the shortcomings of current techniques, and verification of the new vortex model with empirical data via Computational Fluid Dynamic (CFD). The simple radial equilibrium equation set has been known to the scientific community since the first gas turbine engines designs. Active research into the vortex models associated with radial equilibrium, has declined with the advent of robust CFD solvers capable of representing fluid through turbomachinery. Since there are no closed form of the Navier-Stokes Equations in existence, CFD is bound by errors in modelling turbulence, mixing planes, boundary layer transitions, as well as other loss models that are incorporated into these programs. The Simplified High-Order Vortex Equation was utilized to increase the surge margin of up to 3.32% compared to a rotor designed using the free vortex method.
"],"dc:identifier":["https://commons.erau.edu/edt/169"],"dc:subject":["high-order","vortex equation","radial equilibrium","computational fluid dynamics","Aerodynamics and Fluid Mechanics","Aerospace Engineering"],"dc:title":["Determination of a Simplified High-Order Vortex Equation for Radial Equilibrium with CFD Verification"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["Thesis - Open Access"],"thesis:degree_name":["Master of Science in Aerospace Engineering"]},"updated_at":"2026-07-27T19:26:08Z"}