Marginal conditions for thermoacoustic oscillations in resonators
This paper examines marginal conditions for the onset of thermoacoustic oscillations in resonators of a Sondhauss tube and a gas-filled, dumbbell-shaped tube. An analysis is performed using a linear acoustic theory based on the first-order boundary-layer approximation. When a parabolic temperature d...
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| Veröffentlicht in: | Proceedings of the Royal Society. A, Mathematical and physical sciences Mathematical and physical sciences, 2009-11, Vol.465 (2111), p.3531-3552 |
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| container_issue | 2111 |
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| container_title | Proceedings of the Royal Society. A, Mathematical and physical sciences |
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| creator | Sugimoto, Nobumasa Takeuchi, Ryota |
| description | This paper examines marginal conditions for the onset of thermoacoustic oscillations in resonators of a Sondhauss tube and a gas-filled, dumbbell-shaped tube. An analysis is performed using a linear acoustic theory based on the first-order boundary-layer approximation. When a parabolic temperature distribution is assumed along the tube's neck, a frequency equation is available analytically, whose complex solutions are examined numerically. In the case of the dumbbell-shaped tube, two modes of oscillations exist, one being an antisymmetric mode and the other a symmetric one for pressure variations in the neck, while in the case of the Sondhauss tube, only a mode corresponding to the antisymmetric one exists due to the boundary condition at the open end. Marginal conditions are sought numerically, not only for the lowest branches of both modes, but also for second higher branches, but they are available only for the lowest branch of the antisymmetric mode. For the Sondhauss tube, marginal conditions are obtained by taking account of radiation into free space. Some discussions are provided in comparison with experiments. |
| doi_str_mv | 10.1098/rspa.2009.0279 |
| format | Article |
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An analysis is performed using a linear acoustic theory based on the first-order boundary-layer approximation. When a parabolic temperature distribution is assumed along the tube's neck, a frequency equation is available analytically, whose complex solutions are examined numerically. In the case of the dumbbell-shaped tube, two modes of oscillations exist, one being an antisymmetric mode and the other a symmetric one for pressure variations in the neck, while in the case of the Sondhauss tube, only a mode corresponding to the antisymmetric one exists due to the boundary condition at the open end. Marginal conditions are sought numerically, not only for the lowest branches of both modes, but also for second higher branches, but they are available only for the lowest branch of the antisymmetric mode. For the Sondhauss tube, marginal conditions are obtained by taking account of radiation into free space. 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A, Mathematical and physical sciences, 2009-11, Vol.465 (2111), p.3531-3552</ispartof><rights>Copyright 2009 The Royal Society</rights><rights>2009 The Royal Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c712t-4b279765991805e34d4406873b9a8cb28ac6c95aeabbd49d504f89b66994452e3</citedby><cites>FETCH-LOGICAL-c712t-4b279765991805e34d4406873b9a8cb28ac6c95aeabbd49d504f89b66994452e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/30243451$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/30243451$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,27901,27902,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>Sugimoto, Nobumasa</creatorcontrib><creatorcontrib>Takeuchi, Ryota</creatorcontrib><title>Marginal conditions for thermoacoustic oscillations in resonators</title><title>Proceedings of the Royal Society. A, Mathematical and physical sciences</title><addtitle>Proc. R. Soc. A</addtitle><addtitle>Proc. R. Soc. A</addtitle><description>This paper examines marginal conditions for the onset of thermoacoustic oscillations in resonators of a Sondhauss tube and a gas-filled, dumbbell-shaped tube. An analysis is performed using a linear acoustic theory based on the first-order boundary-layer approximation. When a parabolic temperature distribution is assumed along the tube's neck, a frequency equation is available analytically, whose complex solutions are examined numerically. In the case of the dumbbell-shaped tube, two modes of oscillations exist, one being an antisymmetric mode and the other a symmetric one for pressure variations in the neck, while in the case of the Sondhauss tube, only a mode corresponding to the antisymmetric one exists due to the boundary condition at the open end. Marginal conditions are sought numerically, not only for the lowest branches of both modes, but also for second higher branches, but they are available only for the lowest branch of the antisymmetric mode. For the Sondhauss tube, marginal conditions are obtained by taking account of radiation into free space. Some discussions are provided in comparison with experiments.</description><subject>Approximation</subject><subject>Boundary conditions</subject><subject>Boundary layers</subject><subject>Boundary-Layer Theory</subject><subject>Marginal Condition</subject><subject>Oscillation</subject><subject>Resonators</subject><subject>Sondhauss Tube</subject><subject>Symmetry</subject><subject>Temperature distribution</subject><subject>Temperature gradients</subject><subject>Temperature ratio</subject><subject>Thermoacoustics</subject><subject>Wall temperature</subject><issn>1364-5021</issn><issn>0962-8444</issn><issn>1471-2946</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp9Uk2P0zAUjBBILAtXbkg5wSnF37FvVCs-tQhEF8TtyXGcrbtpnLUdoPx63AatVCF6sqWZN29m7KJ4itECIyVfhjjqBUFILRCp1b3iDLMaV0QxcT_fqWAVRwQ_LB7FuEGZxmV9Viw_6nDtBt2Xxg-tS84Psex8KNPahq3Xxk8xOVP6aFzf6xl3Qxls9INOPsTHxYNO99E--XueF1_fvL66eFddfnr7_mJ5WZkak1SxJpuqBVcKS8QtZS1jSMiaNkpL0xCpjTCKa6ubpmWq5Yh1UjVCKMUYJ5aeFy9m3TH428nGBFsXjc2mBptNghQ5UVanmfn8JJNyhGhNUSYuZqIJPsZgOxiD2-qwA4xg3ynsO4V9p7DvNA_czAPB73JWb5xNO9j4KeQGI3xZfV7-YII7gjEGJClGLL-BgN9unKUyCC7GycKBciz_7zZ6att_PT6bpzYxP89dIooIo4zjjFcz7mKyv-5wHW5A1LTm8E0y-L66-rCqlQCR-a9m_tpdr3-6YOHIzmF7_jvJDukQ7xCMcoqhm_oexrbLEuSkhN-NIerjafoH2bLgTg</recordid><startdate>20091108</startdate><enddate>20091108</enddate><creator>Sugimoto, Nobumasa</creator><creator>Takeuchi, Ryota</creator><general>The Royal Society</general><general>The Royal Society Publishing</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope><scope>F1W</scope><scope>H96</scope><scope>L.G</scope></search><sort><creationdate>20091108</creationdate><title>Marginal conditions for thermoacoustic oscillations in resonators</title><author>Sugimoto, Nobumasa ; Takeuchi, Ryota</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c712t-4b279765991805e34d4406873b9a8cb28ac6c95aeabbd49d504f89b66994452e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Approximation</topic><topic>Boundary conditions</topic><topic>Boundary layers</topic><topic>Boundary-Layer Theory</topic><topic>Marginal Condition</topic><topic>Oscillation</topic><topic>Resonators</topic><topic>Sondhauss Tube</topic><topic>Symmetry</topic><topic>Temperature distribution</topic><topic>Temperature gradients</topic><topic>Temperature ratio</topic><topic>Thermoacoustics</topic><topic>Wall temperature</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sugimoto, Nobumasa</creatorcontrib><creatorcontrib>Takeuchi, Ryota</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</collection><jtitle>Proceedings of the Royal Society. A, Mathematical and physical sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sugimoto, Nobumasa</au><au>Takeuchi, Ryota</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Marginal conditions for thermoacoustic oscillations in resonators</atitle><jtitle>Proceedings of the Royal Society. A, Mathematical and physical sciences</jtitle><stitle>Proc. R. Soc. A</stitle><addtitle>Proc. R. Soc. A</addtitle><date>2009-11-08</date><risdate>2009</risdate><volume>465</volume><issue>2111</issue><spage>3531</spage><epage>3552</epage><pages>3531-3552</pages><issn>1364-5021</issn><issn>0962-8444</issn><eissn>1471-2946</eissn><abstract>This paper examines marginal conditions for the onset of thermoacoustic oscillations in resonators of a Sondhauss tube and a gas-filled, dumbbell-shaped tube. An analysis is performed using a linear acoustic theory based on the first-order boundary-layer approximation. When a parabolic temperature distribution is assumed along the tube's neck, a frequency equation is available analytically, whose complex solutions are examined numerically. In the case of the dumbbell-shaped tube, two modes of oscillations exist, one being an antisymmetric mode and the other a symmetric one for pressure variations in the neck, while in the case of the Sondhauss tube, only a mode corresponding to the antisymmetric one exists due to the boundary condition at the open end. Marginal conditions are sought numerically, not only for the lowest branches of both modes, but also for second higher branches, but they are available only for the lowest branch of the antisymmetric mode. For the Sondhauss tube, marginal conditions are obtained by taking account of radiation into free space. Some discussions are provided in comparison with experiments.</abstract><pub>The Royal Society</pub><doi>10.1098/rspa.2009.0279</doi><tpages>22</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Approximation Boundary conditions Boundary layers Boundary-Layer Theory Marginal Condition Oscillation Resonators Sondhauss Tube Symmetry Temperature distribution Temperature gradients Temperature ratio Thermoacoustics Wall temperature |
| title | Marginal conditions for thermoacoustic oscillations in resonators |
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