Publicação
On the dynamics and linear stability of one-dimensional steady detonation waves
| Resumo: | A detailed analysis of the dynamics and linear stability of a steady one-dimensional detonation wave propagating in a binary reactive system with an Arrhenius chemical kinetics of type A + A = B + B is carried out. Starting from the frame of the kinetic theory, the binary reactive mixture is modelled at the mesoscopic scale by the reactive Boltzmann equation (BE), assuming hard sphere cross sections for elastic collisions and step cross sections with activation energy for reactive interactions. The corresponding hydrodynamic limit is based on a second-order non-equilibrium solution of the BE obtained in a previous paper, using the Chapman-Enskog method in a chemical regime for which the reactive interactions are less frequent than the elastic collisions. The resulting hydrodynamic governing equations are the reactive Euler equations, including a rate law which exhibits an explicit dependence on the reaction heat and forward activation energy of the chemical reaction. These equations are used to describe the spatial structure of the steady detonation wave solution and investigate how this structure varies with the reaction heat. The response of the steady solution to one-dimensional disturbances is studied using a normal mode linear approach which leads to an initial value problem for the state variable disturbances in the reaction zone. The stability problem is treated numerically, using an iterative shooting technique to determine the unstable modes. The analysis here developed emphasizes the influence of the chemical reaction heat and activation energy on the linear stability spectra. |
|---|---|
| Autores principais: | Carvalho, Filipe |
| Outros Autores: | Soares, A. J. |
| Assunto: | Kinetic theory Boltzmann equation Chemical reactions Reactive flows Steady detonation waves Hydrodynamic stability |
| Ano: | 2012 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| _version_ | 1867439601990238208 |
|---|---|
| author | Carvalho, Filipe |
| author2 | Soares, A. J. |
| author2_role | author |
| author_facet | Carvalho, Filipe Soares, A. J. |
| author_role | author |
| contributor_name_str_mv | RepositóriUM - Universidade do Minho |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Carvalho, Filipe\"},{\"Person.name\":\"Soares, A. J.\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | RepositóriUM - Universidade do Minho |
| datacite.creators.creator.creatorName.fl_str_mv | Carvalho, Filipe Soares, A. J. |
| datacite.date.Accepted.fl_str_mv | 2012-05-29T00:00:00Z |
| datacite.date.available.fl_str_mv | 2012-05-07T09:56:16Z |
| datacite.date.embargoed.fl_str_mv | 2012-05-07T09:56:16Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Kinetic theory Boltzmann equation Chemical reactions Reactive flows Steady detonation waves Hydrodynamic stability |
| datacite.titles.title.fl_str_mv | On the dynamics and linear stability of one-dimensional steady detonation waves |
| dc.contributor.none.fl_str_mv | RepositóriUM - Universidade do Minho |
| dc.creator.none.fl_str_mv | Carvalho, Filipe Soares, A. J. |
| dc.date.Accepted.fl_str_mv | 2012-05-29T00:00:00Z |
| dc.date.available.fl_str_mv | 2012-05-07T09:56:16Z |
| dc.date.embargoed.fl_str_mv | 2012-05-07T09:56:16Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/1822/19131 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | IOP Publishing |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Kinetic theory Boltzmann equation Chemical reactions Reactive flows Steady detonation waves Hydrodynamic stability |
| dc.title.fl_str_mv | On the dynamics and linear stability of one-dimensional steady detonation waves |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | A detailed analysis of the dynamics and linear stability of a steady one-dimensional detonation wave propagating in a binary reactive system with an Arrhenius chemical kinetics of type A + A = B + B is carried out. Starting from the frame of the kinetic theory, the binary reactive mixture is modelled at the mesoscopic scale by the reactive Boltzmann equation (BE), assuming hard sphere cross sections for elastic collisions and step cross sections with activation energy for reactive interactions. The corresponding hydrodynamic limit is based on a second-order non-equilibrium solution of the BE obtained in a previous paper, using the Chapman-Enskog method in a chemical regime for which the reactive interactions are less frequent than the elastic collisions. The resulting hydrodynamic governing equations are the reactive Euler equations, including a rate law which exhibits an explicit dependence on the reaction heat and forward activation energy of the chemical reaction. These equations are used to describe the spatial structure of the steady detonation wave solution and investigate how this structure varies with the reaction heat. The response of the steady solution to one-dimensional disturbances is studied using a normal mode linear approach which leads to an initial value problem for the state variable disturbances in the reaction zone. The stability problem is treated numerically, using an iterative shooting technique to determine the unstable modes. The analysis here developed emphasizes the influence of the chemical reaction heat and activation energy on the linear stability spectra. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://repositorium.uminho.pt/bitstreams/6f6464d9-243f-4b88-9ec8-e795e75c35ba/download |
| id | rum_71a129b9bcb25a7e2b2b36aaba5fc826 |
| identifier.url.fl_str_mv | https://hdl.handle.net/1822/19131 |
| instacron_str | repositorium |
| institution | Universidade do Minho |
| instname_str | Universidade do Minho |
| language | eng |
| network_acronym_str | rum |
| network_name_str | RepositóriUM - Universidade do Minho |
| oai_identifier_str | oai:repositorium.uminho.pt:1822/19131 |
| organization_str_mv | urn:organizationAcronym:repositorium |
| person_str_mv | Carvalho, Filipe Soares, A. J. |
| publishDate | 2012 |
| publisher.none.fl_str_mv | IOP Publishing |
| reponame_str | RepositóriUM - Universidade do Minho |
| repository_id_str | urn:repositoryAcronym:rum |
| service_str_mv | urn:repositoryAcronym:rum |
| spelling | engIOP PublishingporA detailed analysis of the dynamics and linear stability of a steady one-dimensional detonation wave propagating in a binary reactive system with an Arrhenius chemical kinetics of type A + A = B + B is carried out. Starting from the frame of the kinetic theory, the binary reactive mixture is modelled at the mesoscopic scale by the reactive Boltzmann equation (BE), assuming hard sphere cross sections for elastic collisions and step cross sections with activation energy for reactive interactions. The corresponding hydrodynamic limit is based on a second-order non-equilibrium solution of the BE obtained in a previous paper, using the Chapman-Enskog method in a chemical regime for which the reactive interactions are less frequent than the elastic collisions. The resulting hydrodynamic governing equations are the reactive Euler equations, including a rate law which exhibits an explicit dependence on the reaction heat and forward activation energy of the chemical reaction. These equations are used to describe the spatial structure of the steady detonation wave solution and investigate how this structure varies with the reaction heat. The response of the steady solution to one-dimensional disturbances is studied using a normal mode linear approach which leads to an initial value problem for the state variable disturbances in the reaction zone. The stability problem is treated numerically, using an iterative shooting technique to determine the unstable modes. The analysis here developed emphasizes the influence of the chemical reaction heat and activation energy on the linear stability spectra.application/pdfporOn the dynamics and linear stability of one-dimensional steady detonation wavesCarvalho, FilipeSoares, A. J.HostingInstitutionOrganizationalRepositóriUM - Universidade do Minhoe-mailmailto:repositorium@usdb.uminho.ptrepositorium@usdb.uminho.ptISSNIsPartOf1751-8113EISSNIsPartOf1751-8121DOIIsPartOf10.1088/1751-8113/45/25/2555012012-05-07T09:56:16Z2012-05-292011-12-222012-05-29T00:00:00ZHandlehttps://hdl.handle.net/1822/19131http://purl.org/coar/access_right/c_abf2open accessKinetic theoryBoltzmann equationChemical reactionsReactive flowsSteady detonation wavesHydrodynamic stability330578 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorium.uminho.pt/bitstreams/6f6464d9-243f-4b88-9ec8-e795e75c35ba/download |
| spellingShingle | On the dynamics and linear stability of one-dimensional steady detonation waves Carvalho, Filipe Kinetic theory Boltzmann equation Chemical reactions Reactive flows Steady detonation waves Hydrodynamic stability |
| status | SINGLETON |
| subject.fl_str_mv | Kinetic theory Boltzmann equation Chemical reactions Reactive flows Steady detonation waves Hydrodynamic stability |
| title | On the dynamics and linear stability of one-dimensional steady detonation waves |
| title_full | On the dynamics and linear stability of one-dimensional steady detonation waves |
| title_fullStr | On the dynamics and linear stability of one-dimensional steady detonation waves |
| title_full_unstemmed | On the dynamics and linear stability of one-dimensional steady detonation waves |
| title_short | On the dynamics and linear stability of one-dimensional steady detonation waves |
| title_sort | On the dynamics and linear stability of one-dimensional steady detonation waves |
| topic | Kinetic theory Boltzmann equation Chemical reactions Reactive flows Steady detonation waves Hydrodynamic stability |
| topic_facet | Kinetic theory Boltzmann equation Chemical reactions Reactive flows Steady detonation waves Hydrodynamic stability |
| url | https://hdl.handle.net/1822/19131 |
| visible | 1 |