This document is aiming toward deepening the understanding of the phenomena of mixing and the effect of the initial conditions in the cylindrical & spherical Richtmyer-Meshkov and Rayleigh-Taylor Instabilities. This work is focused on identifying the most energetic structures of the ow in order to define a reduced order model intended for modeling the evolution of the mixing layer after reshocking the density interface. Initially, Simulations are implemented for the two dimensional case of a cylindrical shock wave convergently approaching an initially wave-like perturbed density discontinuity formed by a target of Sulfur Hexauoride immersed into unshocked air with Atwood number of 0.67. The perturbation is varied by setting different values for the wave amplitude and wave-number; the amplitude and wave-number effects on late-time mixing are studied separately and then such perturbation features are coupled together in the analysis of single- and multi-mode well-defined cylindrical perturbations. The simulation data is then utilized as a mechanism for obtaining a model equation intended to predict the mixing layer evolution using a Proper Orthogonal Decomposition. The ultimate goal of the POD is to model the evolution after reshock which has been the main issue to be tackled since available models fail to predict the extent of the mixing layer after reshocking the interface. Considering three-dimensional effects as in spherical shock-interface interaction gives a better depiction of the small-scale interactions but spherical cases are only quickly addressed. The main effect is the vortex stretching affectation on the vorticity evolution. Furthermore, mixing layers in 3D spherical simulations are found to be wider than its 2D simplified framework. Nonetheless, useful insight is gained by reducing the problem under study to a cylindrical two-dimensional symmetrical system.
","abstract_html":"<p>This document is aiming toward deepening the understanding of the phenomena of mixing and the effect of the initial conditions in the cylindrical & spherical Richtmyer-Meshkov and Rayleigh-Taylor Instabilities. This work is focused on identifying the most energetic structures of the ow in order to define a reduced order model intended for modeling the evolution of the mixing layer after reshocking the density interface. Initially, Simulations are implemented for the two dimensional case of a cylindrical shock wave convergently approaching an initially wave-like perturbed density discontinuity formed by a target of Sulfur Hexauoride immersed into unshocked air with Atwood number of 0.67. The perturbation is varied by setting different values for the wave amplitude and wave-number; the amplitude and wave-number effects on late-time mixing are studied separately and then such perturbation features are coupled together in the analysis of single- and multi-mode well-defined cylindrical perturbations. The simulation data is then utilized as a mechanism for obtaining a model equation intended to predict the mixing layer evolution using a Proper Orthogonal Decomposition. The ultimate goal of the POD is to model the evolution after reshock which has been the main issue to be tackled since available models fail to predict the extent of the mixing layer after reshocking the interface. Considering three-dimensional effects as in spherical shock-interface interaction gives a better depiction of the small-scale interactions but spherical cases are only quickly addressed. The main effect is the vortex stretching affectation on the vorticity evolution. Furthermore, mixing layers in 3D spherical simulations are found to be wider than its 2D simplified framework. Nonetheless, useful insight is gained by reducing the problem under study to a cylindrical two-dimensional symmetrical system.</p>","abstract_has_math":false,"creators":["Proaño, Erik S."],"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":2019,"date_issued":"2019-05-01T07:00:00Z","date_published":"2019-05-01T07:00:00Z","updated_at":"2026-07-27T19:25:37Z","subjects":["shock wave","interfacial mixing","Aerospace Engineering"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.erau.edu/edt/450","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Proaño, Erik S."]}]},{"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":["shock wave","interfacial mixing","Aerospace Engineering"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.erau.edu/edt/450"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This document is aiming toward deepening the understanding of the phenomena of mixing and the effect of the initial conditions in the cylindrical & spherical Richtmyer-Meshkov and Rayleigh-Taylor Instabilities. This work is focused on identifying the most energetic structures of the ow in order to define a reduced order model intended for modeling the evolution of the mixing layer after reshocking the density interface. Initially, Simulations are implemented for the two dimensional case of a cylindrical shock wave convergently approaching an initially wave-like perturbed density discontinuity formed by a target of Sulfur Hexauoride immersed into unshocked air with Atwood number of 0.67. The perturbation is varied by setting different values for the wave amplitude and wave-number; the amplitude and wave-number effects on late-time mixing are studied separately and then such perturbation features are coupled together in the analysis of single- and multi-mode well-defined cylindrical perturbations. The simulation data is then utilized as a mechanism for obtaining a model equation intended to predict the mixing layer evolution using a Proper Orthogonal Decomposition. The ultimate goal of the POD is to model the evolution after reshock which has been the main issue to be tackled since available models fail to predict the extent of the mixing layer after reshocking the interface. Considering three-dimensional effects as in spherical shock-interface interaction gives a better depiction of the small-scale interactions but spherical cases are only quickly addressed. The main effect is the vortex stretching affectation on the vorticity evolution. Furthermore, mixing layers in 3D spherical simulations are found to be wider than its 2D simplified framework. Nonetheless, useful insight is gained by reducing the problem under study to a cylindrical two-dimensional symmetrical system.
"]},{"key":"dc:title","label":"Title","values":["Covering Shock Wave Induced Interfacial Mixing: Numerical Study and a Control Primer"]}]}],"canonical_facts":{"dc:creator":["Proaño, Erik S."],"dc:description.abstract":["This document is aiming toward deepening the understanding of the phenomena of mixing and the effect of the initial conditions in the cylindrical & spherical Richtmyer-Meshkov and Rayleigh-Taylor Instabilities. This work is focused on identifying the most energetic structures of the ow in order to define a reduced order model intended for modeling the evolution of the mixing layer after reshocking the density interface. Initially, Simulations are implemented for the two dimensional case of a cylindrical shock wave convergently approaching an initially wave-like perturbed density discontinuity formed by a target of Sulfur Hexauoride immersed into unshocked air with Atwood number of 0.67. The perturbation is varied by setting different values for the wave amplitude and wave-number; the amplitude and wave-number effects on late-time mixing are studied separately and then such perturbation features are coupled together in the analysis of single- and multi-mode well-defined cylindrical perturbations. The simulation data is then utilized as a mechanism for obtaining a model equation intended to predict the mixing layer evolution using a Proper Orthogonal Decomposition. The ultimate goal of the POD is to model the evolution after reshock which has been the main issue to be tackled since available models fail to predict the extent of the mixing layer after reshocking the interface. Considering three-dimensional effects as in spherical shock-interface interaction gives a better depiction of the small-scale interactions but spherical cases are only quickly addressed. The main effect is the vortex stretching affectation on the vorticity evolution. Furthermore, mixing layers in 3D spherical simulations are found to be wider than its 2D simplified framework. Nonetheless, useful insight is gained by reducing the problem under study to a cylindrical two-dimensional symmetrical system.
"],"dc:identifier":["https://commons.erau.edu/edt/450"],"dc:subject":["shock wave","interfacial mixing","Aerospace Engineering"],"dc:title":["Covering Shock Wave Induced Interfacial Mixing: Numerical Study and a Control Primer"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["Thesis - Open Access"],"thesis:degree_name":["Master of Science in Aerospace Engineering"]},"updated_at":"2026-07-27T19:25:37Z"}