Open-loop control of cavity oscillations with harmonic forcings
This article deals with open-loop control of open-cavity flows with harmonic forcings. Two-dimensional laminar open-cavity flows usually undergo a supercritical Hopf bifurcation at some critical Reynolds number: a global mode becomes unstable and its amplitude converges towards a limit cycle. Such b...
Gespeichert in:
Veröffentlicht in: | Journal of fluid mechanics 2012-10, Vol.708, p.439-468 |
---|---|
1. Verfasser: | |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 468 |
---|---|
container_issue | |
container_start_page | 439 |
container_title | Journal of fluid mechanics |
container_volume | 708 |
creator | Sipp, Denis |
description | This article deals with open-loop control of open-cavity flows with harmonic forcings. Two-dimensional laminar open-cavity flows usually undergo a supercritical Hopf bifurcation at some critical Reynolds number: a global mode becomes unstable and its amplitude converges towards a limit cycle. Such behaviour may be accurately captured by a Stuart–Landau equation, which governs the amplitude of the global mode. In the present article, we study the effect on such a flow of a forcing characterized by its frequency
${\omega }_{f} $
, its amplitude
${E}^{\ensuremath{\prime} } $
and its spatial structure
${\mathbi{f}}_{E} $
. The system reacts like a forced Van der Pol oscillator. In the general case, such a forcing modifies the linear dynamics of the global mode. It is then possible to predict preferred forcing frequencies
${\omega }_{f} $
, at which the global mode may be stabilized with the smallest possible forcing amplitude
${E}^{\ensuremath{\prime} } $
. In the case of a forcing frequency close to the frequency of the global mode, a locking phenomenon may be observed if the forcing amplitude
${E}^{\ensuremath{\prime} } $
is sufficiently high: the frequency of the flow on the limit cycle may be modified with a very small forcing amplitude
${E}^{\ensuremath{\prime} } $
. In each case, we compute all harmonics of the flow field and all coefficients that enter the amplitude equations. In particular, it is possible to find preferred forcing structures
${\mathbi{f}}_{E} $
that achieve strongest impact on the flow field. In the general case, these are the optimal forcings, which are defined as the forcings that trigger the strongest energy response. In the case of a forcing frequency close to the frequency of the global mode, a forcing structure equal to the adjoint global mode ensures the lowest forcing amplitude
${E}^{\ensuremath{\prime} } $
. All predictions given by the amplitude equations are checked against direct numerical simulations conducted at a supercritical Reynolds number. We show that a global mode may effectively be stabilized by a high-frequency harmonic forcing, which achieves suppression of the perturbation frequencies that are lower than the forcing frequency, and that a near-resonant forcing achieves locking of the flow onto the forcing frequency, as predicted by the amplitude equations. |
doi_str_mv | 10.1017/jfm.2012.329 |
format | Article |
fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1709748577</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_jfm_2012_329</cupid><sourcerecordid>2767545841</sourcerecordid><originalsourceid>FETCH-LOGICAL-c398t-c808bfb8b6526c0c95a107050c38cf79214489e6397158b360c8e6ce04455b243</originalsourceid><addsrcrecordid>eNqNkE1r3DAQhkVIIZttbv0BhhLIIXZH39IplCVpC4FckrORp3Kixba2krdh_3207FJKyaGnuTzzvDMvIZ8oNBSo_rLux4YBZQ1n9oQsqFC21krIU7IAYKymlMEZOc95DUA5WL0gNw8bP9VDjJsK4zSnOFSxr9D9DvOuihnDMLg5xClXr2F-qV5cGuMUsOpjwjA954_kQ--G7C-Oc0me7m4fV9_r-4dvP1Zf72vk1sw1GjBd35lOSaYQ0EpHQYME5AZ7bRkVwlivuNVUmo4rQOMVehBCyo4JviRXB-8mxV9bn-d2DBl9uW7ycZtbqss7wkit_welwtAiLejnf9B13KapPNJSEJIrq9Q--_pAYYo5J9-3mxRGl3YFavfFt6X4dl98W4ov-OVR6jK6oU9uwpD_7DDFFVN0zzVHrRu7FH4--7_T3xG_AQ-Rj48</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1045369664</pqid></control><display><type>article</type><title>Open-loop control of cavity oscillations with harmonic forcings</title><source>Cambridge University Press Journals Complete</source><creator>Sipp, Denis</creator><creatorcontrib>Sipp, Denis</creatorcontrib><description>This article deals with open-loop control of open-cavity flows with harmonic forcings. Two-dimensional laminar open-cavity flows usually undergo a supercritical Hopf bifurcation at some critical Reynolds number: a global mode becomes unstable and its amplitude converges towards a limit cycle. Such behaviour may be accurately captured by a Stuart–Landau equation, which governs the amplitude of the global mode. In the present article, we study the effect on such a flow of a forcing characterized by its frequency
${\omega }_{f} $
, its amplitude
${E}^{\ensuremath{\prime} } $
and its spatial structure
${\mathbi{f}}_{E} $
. The system reacts like a forced Van der Pol oscillator. In the general case, such a forcing modifies the linear dynamics of the global mode. It is then possible to predict preferred forcing frequencies
${\omega }_{f} $
, at which the global mode may be stabilized with the smallest possible forcing amplitude
${E}^{\ensuremath{\prime} } $
. In the case of a forcing frequency close to the frequency of the global mode, a locking phenomenon may be observed if the forcing amplitude
${E}^{\ensuremath{\prime} } $
is sufficiently high: the frequency of the flow on the limit cycle may be modified with a very small forcing amplitude
${E}^{\ensuremath{\prime} } $
. In each case, we compute all harmonics of the flow field and all coefficients that enter the amplitude equations. In particular, it is possible to find preferred forcing structures
${\mathbi{f}}_{E} $
that achieve strongest impact on the flow field. In the general case, these are the optimal forcings, which are defined as the forcings that trigger the strongest energy response. In the case of a forcing frequency close to the frequency of the global mode, a forcing structure equal to the adjoint global mode ensures the lowest forcing amplitude
${E}^{\ensuremath{\prime} } $
. All predictions given by the amplitude equations are checked against direct numerical simulations conducted at a supercritical Reynolds number. We show that a global mode may effectively be stabilized by a high-frequency harmonic forcing, which achieves suppression of the perturbation frequencies that are lower than the forcing frequency, and that a near-resonant forcing achieves locking of the flow onto the forcing frequency, as predicted by the amplitude equations.</description><identifier>ISSN: 0022-1120</identifier><identifier>EISSN: 1469-7645</identifier><identifier>DOI: 10.1017/jfm.2012.329</identifier><identifier>CODEN: JFLSA7</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Acoustics ; Aeroacoustics, atmospheric sound ; Amplitudes ; Computational fluid dynamics ; Dynamics ; Exact sciences and technology ; Fluid dynamics ; Fluid flow ; Fluid mechanics ; Fundamental areas of phenomenology (including applications) ; Harmonics ; Hydrodynamic stability ; Locking ; Mathematical analysis ; Nonlinearity (including bifurcation theory) ; Physics ; Reynolds number ; Simulation</subject><ispartof>Journal of fluid mechanics, 2012-10, Vol.708, p.439-468</ispartof><rights>Copyright © Cambridge University Press 2012</rights><rights>2015 INIST-CNRS</rights><rights>Copyright © Cambridge University Press 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c398t-c808bfb8b6526c0c95a107050c38cf79214489e6397158b360c8e6ce04455b243</citedby><cites>FETCH-LOGICAL-c398t-c808bfb8b6526c0c95a107050c38cf79214489e6397158b360c8e6ce04455b243</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0022112012003291/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,780,784,27924,27925,55628</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=26362619$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Sipp, Denis</creatorcontrib><title>Open-loop control of cavity oscillations with harmonic forcings</title><title>Journal of fluid mechanics</title><addtitle>J. Fluid Mech</addtitle><description>This article deals with open-loop control of open-cavity flows with harmonic forcings. Two-dimensional laminar open-cavity flows usually undergo a supercritical Hopf bifurcation at some critical Reynolds number: a global mode becomes unstable and its amplitude converges towards a limit cycle. Such behaviour may be accurately captured by a Stuart–Landau equation, which governs the amplitude of the global mode. In the present article, we study the effect on such a flow of a forcing characterized by its frequency
${\omega }_{f} $
, its amplitude
${E}^{\ensuremath{\prime} } $
and its spatial structure
${\mathbi{f}}_{E} $
. The system reacts like a forced Van der Pol oscillator. In the general case, such a forcing modifies the linear dynamics of the global mode. It is then possible to predict preferred forcing frequencies
${\omega }_{f} $
, at which the global mode may be stabilized with the smallest possible forcing amplitude
${E}^{\ensuremath{\prime} } $
. In the case of a forcing frequency close to the frequency of the global mode, a locking phenomenon may be observed if the forcing amplitude
${E}^{\ensuremath{\prime} } $
is sufficiently high: the frequency of the flow on the limit cycle may be modified with a very small forcing amplitude
${E}^{\ensuremath{\prime} } $
. In each case, we compute all harmonics of the flow field and all coefficients that enter the amplitude equations. In particular, it is possible to find preferred forcing structures
${\mathbi{f}}_{E} $
that achieve strongest impact on the flow field. In the general case, these are the optimal forcings, which are defined as the forcings that trigger the strongest energy response. In the case of a forcing frequency close to the frequency of the global mode, a forcing structure equal to the adjoint global mode ensures the lowest forcing amplitude
${E}^{\ensuremath{\prime} } $
. All predictions given by the amplitude equations are checked against direct numerical simulations conducted at a supercritical Reynolds number. We show that a global mode may effectively be stabilized by a high-frequency harmonic forcing, which achieves suppression of the perturbation frequencies that are lower than the forcing frequency, and that a near-resonant forcing achieves locking of the flow onto the forcing frequency, as predicted by the amplitude equations.</description><subject>Acoustics</subject><subject>Aeroacoustics, atmospheric sound</subject><subject>Amplitudes</subject><subject>Computational fluid dynamics</subject><subject>Dynamics</subject><subject>Exact sciences and technology</subject><subject>Fluid dynamics</subject><subject>Fluid flow</subject><subject>Fluid mechanics</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Harmonics</subject><subject>Hydrodynamic stability</subject><subject>Locking</subject><subject>Mathematical analysis</subject><subject>Nonlinearity (including bifurcation theory)</subject><subject>Physics</subject><subject>Reynolds number</subject><subject>Simulation</subject><issn>0022-1120</issn><issn>1469-7645</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNqNkE1r3DAQhkVIIZttbv0BhhLIIXZH39IplCVpC4FckrORp3Kixba2krdh_3207FJKyaGnuTzzvDMvIZ8oNBSo_rLux4YBZQ1n9oQsqFC21krIU7IAYKymlMEZOc95DUA5WL0gNw8bP9VDjJsK4zSnOFSxr9D9DvOuihnDMLg5xClXr2F-qV5cGuMUsOpjwjA954_kQ--G7C-Oc0me7m4fV9_r-4dvP1Zf72vk1sw1GjBd35lOSaYQ0EpHQYME5AZ7bRkVwlivuNVUmo4rQOMVehBCyo4JviRXB-8mxV9bn-d2DBl9uW7ycZtbqss7wkit_welwtAiLejnf9B13KapPNJSEJIrq9Q--_pAYYo5J9-3mxRGl3YFavfFt6X4dl98W4ov-OVR6jK6oU9uwpD_7DDFFVN0zzVHrRu7FH4--7_T3xG_AQ-Rj48</recordid><startdate>20121010</startdate><enddate>20121010</enddate><creator>Sipp, Denis</creator><general>Cambridge University Press</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7TB</scope><scope>7U5</scope><scope>7UA</scope><scope>7XB</scope><scope>88I</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>C1K</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>F1W</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>H8D</scope><scope>H96</scope><scope>HCIFZ</scope><scope>KR7</scope><scope>L.G</scope><scope>L6V</scope><scope>L7M</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>S0W</scope></search><sort><creationdate>20121010</creationdate><title>Open-loop control of cavity oscillations with harmonic forcings</title><author>Sipp, Denis</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c398t-c808bfb8b6526c0c95a107050c38cf79214489e6397158b360c8e6ce04455b243</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Acoustics</topic><topic>Aeroacoustics, atmospheric sound</topic><topic>Amplitudes</topic><topic>Computational fluid dynamics</topic><topic>Dynamics</topic><topic>Exact sciences and technology</topic><topic>Fluid dynamics</topic><topic>Fluid flow</topic><topic>Fluid mechanics</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Harmonics</topic><topic>Hydrodynamic stability</topic><topic>Locking</topic><topic>Mathematical analysis</topic><topic>Nonlinearity (including bifurcation theory)</topic><topic>Physics</topic><topic>Reynolds number</topic><topic>Simulation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sipp, Denis</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Water Resources Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>Earth, Atmospheric & Aquatic Science Collection</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Aerospace Database</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>SciTech Premium Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Earth, Atmospheric & Aquatic Science Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>DELNET Engineering & Technology Collection</collection><jtitle>Journal of fluid mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sipp, Denis</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Open-loop control of cavity oscillations with harmonic forcings</atitle><jtitle>Journal of fluid mechanics</jtitle><addtitle>J. Fluid Mech</addtitle><date>2012-10-10</date><risdate>2012</risdate><volume>708</volume><spage>439</spage><epage>468</epage><pages>439-468</pages><issn>0022-1120</issn><eissn>1469-7645</eissn><coden>JFLSA7</coden><abstract>This article deals with open-loop control of open-cavity flows with harmonic forcings. Two-dimensional laminar open-cavity flows usually undergo a supercritical Hopf bifurcation at some critical Reynolds number: a global mode becomes unstable and its amplitude converges towards a limit cycle. Such behaviour may be accurately captured by a Stuart–Landau equation, which governs the amplitude of the global mode. In the present article, we study the effect on such a flow of a forcing characterized by its frequency
${\omega }_{f} $
, its amplitude
${E}^{\ensuremath{\prime} } $
and its spatial structure
${\mathbi{f}}_{E} $
. The system reacts like a forced Van der Pol oscillator. In the general case, such a forcing modifies the linear dynamics of the global mode. It is then possible to predict preferred forcing frequencies
${\omega }_{f} $
, at which the global mode may be stabilized with the smallest possible forcing amplitude
${E}^{\ensuremath{\prime} } $
. In the case of a forcing frequency close to the frequency of the global mode, a locking phenomenon may be observed if the forcing amplitude
${E}^{\ensuremath{\prime} } $
is sufficiently high: the frequency of the flow on the limit cycle may be modified with a very small forcing amplitude
${E}^{\ensuremath{\prime} } $
. In each case, we compute all harmonics of the flow field and all coefficients that enter the amplitude equations. In particular, it is possible to find preferred forcing structures
${\mathbi{f}}_{E} $
that achieve strongest impact on the flow field. In the general case, these are the optimal forcings, which are defined as the forcings that trigger the strongest energy response. In the case of a forcing frequency close to the frequency of the global mode, a forcing structure equal to the adjoint global mode ensures the lowest forcing amplitude
${E}^{\ensuremath{\prime} } $
. All predictions given by the amplitude equations are checked against direct numerical simulations conducted at a supercritical Reynolds number. We show that a global mode may effectively be stabilized by a high-frequency harmonic forcing, which achieves suppression of the perturbation frequencies that are lower than the forcing frequency, and that a near-resonant forcing achieves locking of the flow onto the forcing frequency, as predicted by the amplitude equations.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2012.329</doi><tpages>30</tpages></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0022-1120 |
ispartof | Journal of fluid mechanics, 2012-10, Vol.708, p.439-468 |
issn | 0022-1120 1469-7645 |
language | eng |
recordid | cdi_proquest_miscellaneous_1709748577 |
source | Cambridge University Press Journals Complete |
subjects | Acoustics Aeroacoustics, atmospheric sound Amplitudes Computational fluid dynamics Dynamics Exact sciences and technology Fluid dynamics Fluid flow Fluid mechanics Fundamental areas of phenomenology (including applications) Harmonics Hydrodynamic stability Locking Mathematical analysis Nonlinearity (including bifurcation theory) Physics Reynolds number Simulation |
title | Open-loop control of cavity oscillations with harmonic forcings |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-24T02%3A11%3A58IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Open-loop%20control%20of%20cavity%20oscillations%20with%20harmonic%20forcings&rft.jtitle=Journal%20of%20fluid%20mechanics&rft.au=Sipp,%20Denis&rft.date=2012-10-10&rft.volume=708&rft.spage=439&rft.epage=468&rft.pages=439-468&rft.issn=0022-1120&rft.eissn=1469-7645&rft.coden=JFLSA7&rft_id=info:doi/10.1017/jfm.2012.329&rft_dat=%3Cproquest_cross%3E2767545841%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1045369664&rft_id=info:pmid/&rft_cupid=10_1017_jfm_2012_329&rfr_iscdi=true |