Effect of a constant radial temperature gradient on a TaylorCouette flow with axial wall slits
Identifieur interne : 000982 ( Istex/Corpus ); précédent : 000981; suivant : 000983Effect of a constant radial temperature gradient on a TaylorCouette flow with axial wall slits
Auteurs : Dong Liu ; Sang-Hyuk Lee ; Hyoung-Bum KimSource :
- Fluid Dynamics Research [ 0169-5983 ] ; 2010.
Abstract
The flow between two concentric cylinders with the inner cylinder rotating with an imposed radial temperature gradient was studied using the digital particle image velocimetry method. Four models of a stationary outer cylinder without and with different numbers of slits (6, 9 and 18) were used. The Grashof number in this study was 1000. The results showed clearly that the buoyant force due to the temperature gradient caused the helical flow; this flow occurred when the Richardson number was larger than 0.0045. The constant temperature gradient considered in this research has little effect on the transition to a turbulent Taylor vortex flow in all models.
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DOI: 10.1088/0169-5983/42/6/065501
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Effect of a constant radial temperature gradient on a TaylorCouette flow with axial wall slits</title><author><name sortKey="Liu, Dong" sort="Liu, Dong" uniqKey="Liu D" first="Dong" last="Liu">Dong Liu</name><affiliation><mods:affiliation>Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</mods:affiliation></affiliation><affiliation><mods:affiliation>School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, People's Republic of China</mods:affiliation></affiliation></author><author><name sortKey="Lee, Sang Hyuk" sort="Lee, Sang Hyuk" uniqKey="Lee S" first="Sang-Hyuk" last="Lee">Sang-Hyuk Lee</name><affiliation><mods:affiliation>Korea Atomic Energy Research Institute, Daejeon 305-353, Korea</mods:affiliation></affiliation></author><author><name sortKey="Kim, Hyoung Bum" sort="Kim, Hyoung Bum" uniqKey="Kim H" first="Hyoung-Bum" last="Kim">Hyoung-Bum Kim</name><affiliation><mods:affiliation>Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</mods:affiliation></affiliation><affiliation><mods:affiliation>School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: kimhb@gsnu.ac.kr</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:8924A003AB4D576436B5E15DA6D4EEFD930C0051</idno><date when="2010" year="2010">2010</date><idno type="doi">10.1088/0169-5983/42/6/065501</idno><idno type="url">https://api.istex.fr/document/8924A003AB4D576436B5E15DA6D4EEFD930C0051/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000982</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Effect of a constant radial temperature gradient on a TaylorCouette flow with axial wall slits</title><author><name sortKey="Liu, Dong" sort="Liu, Dong" uniqKey="Liu D" first="Dong" last="Liu">Dong Liu</name><affiliation><mods:affiliation>Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</mods:affiliation></affiliation><affiliation><mods:affiliation>School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, People's Republic of China</mods:affiliation></affiliation></author><author><name sortKey="Lee, Sang Hyuk" sort="Lee, Sang Hyuk" uniqKey="Lee S" first="Sang-Hyuk" last="Lee">Sang-Hyuk Lee</name><affiliation><mods:affiliation>Korea Atomic Energy Research Institute, Daejeon 305-353, Korea</mods:affiliation></affiliation></author><author><name sortKey="Kim, Hyoung Bum" sort="Kim, Hyoung Bum" uniqKey="Kim H" first="Hyoung-Bum" last="Kim">Hyoung-Bum Kim</name><affiliation><mods:affiliation>Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</mods:affiliation></affiliation><affiliation><mods:affiliation>School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: kimhb@gsnu.ac.kr</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Fluid Dynamics Research</title><title level="j" type="abbrev">Fluid Dyn. Res.</title><idno type="ISSN">0169-5983</idno><imprint><publisher>The Japan Society of Fluid Mechanics and IOP Publishing Ltd</publisher><date type="published" when="2010">2010</date><biblScope unit="volume">42</biblScope><biblScope unit="issue">6</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="16">16</biblScope><biblScope unit="production">Printed in the UK</biblScope></imprint><idno type="ISSN">0169-5983</idno></series><idno type="istex">8924A003AB4D576436B5E15DA6D4EEFD930C0051</idno><idno type="DOI">10.1088/0169-5983/42/6/065501</idno><idno type="articleID">365009</idno><idno type="articleNumber">065501</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0169-5983</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract">The flow between two concentric cylinders with the inner cylinder rotating with an imposed radial temperature gradient was studied using the digital particle image velocimetry method. Four models of a stationary outer cylinder without and with different numbers of slits (6, 9 and 18) were used. The Grashof number in this study was 1000. The results showed clearly that the buoyant force due to the temperature gradient caused the helical flow; this flow occurred when the Richardson number was larger than 0.0045. The constant temperature gradient considered in this research has little effect on the transition to a turbulent Taylor vortex flow in all models.</div></front></TEI><istex><corpusName>iop</corpusName><author><json:item><name>Dong Liu</name><affiliations><json:string>Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</json:string><json:string>School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, People's Republic of China</json:string></affiliations></json:item><json:item><name>Sang-Hyuk Lee</name><affiliations><json:string>Korea Atomic Energy Research Institute, Daejeon 305-353, Korea</json:string></affiliations></json:item><json:item><name>Hyoung-Bum Kim</name><affiliations><json:string>Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</json:string><json:string>School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</json:string><json:string>E-mail: kimhb@gsnu.ac.kr</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>paper</json:string></originalGenre><abstract>The flow between two concentric cylinders with the inner cylinder rotating with an imposed radial temperature gradient was studied using the digital particle image velocimetry method. Four models of a stationary outer cylinder without and with different numbers of slits (6, 9 and 18) were used. The Grashof number in this study was 1000. The results showed clearly that the buoyant force due to the temperature gradient caused the helical flow; this flow occurred when the Richardson number was larger than 0.0045. The constant temperature gradient considered in this research has little effect on the transition to a turbulent Taylor vortex flow in all models.</abstract><qualityIndicators><score>5.534</score><pdfVersion>1.4</pdfVersion><pdfPageSize>595.276 x 841.89 pts (A4)</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>662</abstractCharCount><pdfWordCount>3774</pdfWordCount><pdfCharCount>20086</pdfCharCount><pdfPageCount>16</pdfPageCount><abstractWordCount>105</abstractWordCount></qualityIndicators><title>Effect of a constant radial temperature gradient on a TaylorCouette flow with axial wall slits</title><genre><json:string>research-article</json:string></genre><host><volume>42</volume><publisherId><json:string>fdr</json:string></publisherId><pages><total>16</total><last>16</last><first>1</first></pages><issn><json:string>0169-5983</json:string></issn><issue>6</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><title>Fluid Dynamics Research</title></host><publicationDate>2010</publicationDate><copyrightDate>2010</copyrightDate><doi><json:string>10.1088/0169-5983/42/6/065501</json:string></doi><id>8924A003AB4D576436B5E15DA6D4EEFD930C0051</id><score>0.25568476</score><fulltext><json:item><original>true</original><mimetype>application/pdf</mimetype><extension>pdf</extension><uri>https://api.istex.fr/document/8924A003AB4D576436B5E15DA6D4EEFD930C0051/fulltext/pdf</uri></json:item><json:item><original>false</original><mimetype>application/zip</mimetype><extension>zip</extension><uri>https://api.istex.fr/document/8924A003AB4D576436B5E15DA6D4EEFD930C0051/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/8924A003AB4D576436B5E15DA6D4EEFD930C0051/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Effect of a constant radial temperature gradient on a TaylorCouette flow with axial wall slits</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>The Japan Society of Fluid Mechanics and IOP Publishing Ltd</publisher><availability><p>2010 The Japan Society of Fluid Mechanics and IOP Publishing Ltd</p></availability><date>2010</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Effect of a constant radial temperature gradient on a TaylorCouette flow with axial wall slits</title><author xml:id="author-1"><persName><forename type="first">Dong</forename><surname>Liu</surname></persName><affiliation>Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</affiliation><affiliation>School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, People's Republic of China</affiliation></author><author xml:id="author-2"><persName><forename type="first">Sang-Hyuk</forename><surname>Lee</surname></persName><affiliation>Korea Atomic Energy Research Institute, Daejeon 305-353, Korea</affiliation></author><author xml:id="author-3"><persName><forename type="first">Hyoung-Bum</forename><surname>Kim</surname></persName><email>kimhb@gsnu.ac.kr</email><affiliation>Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</affiliation><affiliation>School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</affiliation></author></analytic><monogr><title level="j">Fluid Dynamics Research</title><title level="j" type="abbrev">Fluid Dyn. Res.</title><idno type="pISSN">0169-5983</idno><imprint><publisher>The Japan Society of Fluid Mechanics and IOP Publishing Ltd</publisher><date type="published" when="2010"></date><biblScope unit="volume">42</biblScope><biblScope unit="issue">6</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="16">16</biblScope><biblScope unit="production">Printed in the UK</biblScope></imprint></monogr><idno type="istex">8924A003AB4D576436B5E15DA6D4EEFD930C0051</idno><idno type="DOI">10.1088/0169-5983/42/6/065501</idno><idno type="articleID">365009</idno><idno type="articleNumber">065501</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2010</date></creation><langUsage><language ident="en">en</language></langUsage><abstract><p>The flow between two concentric cylinders with the inner cylinder rotating with an imposed radial temperature gradient was studied using the digital particle image velocimetry method. Four models of a stationary outer cylinder without and with different numbers of slits (6, 9 and 18) were used. The Grashof number in this study was 1000. The results showed clearly that the buoyant force due to the temperature gradient caused the helical flow; this flow occurred when the Richardson number was larger than 0.0045. The constant temperature gradient considered in this research has little effect on the transition to a turbulent Taylor vortex flow in all models.</p></abstract></profileDesc><revisionDesc><change when="2010">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><original>false</original><mimetype>text/plain</mimetype><extension>txt</extension><uri>https://api.istex.fr/document/8924A003AB4D576436B5E15DA6D4EEFD930C0051/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus iop not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="ISO-8859-1"</istex:xmlDeclaration><istex:docType SYSTEM="http://ej.iop.org/dtd/iopv1_5_2.dtd" name="istex:docType"></istex:docType><istex:document><article artid="fdr365009"><article-metadata><jnl-data jnlid="fdr"><jnl-fullname>Fluid <italic>Dynamics</italic> Research</jnl-fullname><jnl-abbreviation>Fluid Dyn. Res.</jnl-abbreviation><jnl-shortname>FDR</jnl-shortname><jnl-issn>0169-5983</jnl-issn><jnl-coden>FDRSEH</jnl-coden><jnl-imprint>The Japan Society of Fluid Mechanics and IOP Publishing Ltd</jnl-imprint><jnl-web-address>stacks.iop.org/FDR</jnl-web-address></jnl-data><volume-data><year-publication>2010</year-publication><volume-number>42</volume-number></volume-data><issue-data><issue-number>6</issue-number><coverdate>December 2010</coverdate></issue-data><article-data><article-type type="paper" sort="regular"></article-type><type-number type="paper" numbering="article" artnum="065501">065501</type-number><article-number>365009</article-number><first-page>1</first-page><last-page>16</last-page><length>16</length><pii></pii><doi>10.1088/0169-5983/42/6/065501</doi><copyright>2010 The Japan Society of Fluid Mechanics and IOP Publishing Ltd</copyright><ccc>0169-5983/10/065501+16$30.00</ccc><printed>Printed in the UK</printed></article-data></article-metadata><header><title-group><title>Effect of a constant radial temperature gradient on a Taylor–Couette flow with axial wall slits</title><short-title>Effect of a constant radial temperature gradient on a Taylor–Couette flow with axial wall slits</short-title><ej-title>Effect of a constant radial temperature gradient on a Taylor–Couette flow with axial wall slits</ej-title></title-group><author-group><author address="fdr365009ad1" second-address="fdr365009ad4"><first-names>Dong</first-names><second-name>Liu</second-name></author><author address="fdr365009ad2"><first-names>Sang-Hyuk</first-names><second-name>Lee</second-name></author><author address="fdr365009ad1" second-address="fdr365009ad3" email="fdr365009ea1"><first-names>Hyoung-Bum</first-names><second-name>Kim</second-name></author><short-author-list>D Liu <italic>et al</italic></short-author-list></author-group><address-group><address id="fdr365009ad1" showid="yes">Research Center for Aircraft Parts Technology, <orgname>Gyeongsang National University</orgname>, Jinju, Gyeongnam 660-701, <country>Korea</country></address><address id="fdr365009ad2" showid="yes"><orgname>Korea Atomic Energy Research Institute</orgname>, Daejeon 305-353, <country>Korea</country></address><address id="fdr365009ad3" showid="yes">School of Mechanical and Aerospace Engineering, <orgname>Gyeongsang National University</orgname>, Jinju, Gyeongnam 660-701, <country>Korea</country></address><address id="fdr365009ad4" showid="yes">School of Energy and Power Engineering, <orgname>Jiangsu University</orgname>, Zhenjiang 212013, <country>People's Republic of China</country></address><e-address id="fdr365009ea1"><email mailto="kimhb@gsnu.ac.kr">kimhb@gsnu.ac.kr</email></e-address></address-group><history received="4 October 2009" finalform="29 July 2010" online="14 September 2010" recommended="K Suga"></history><abstract-group><abstract><heading>Abstract</heading><p indent="no">The flow between two concentric cylinders with the inner cylinder rotating with an imposed radial temperature gradient was studied using the digital particle image velocimetry method. Four models of a stationary outer cylinder without and with different numbers of slits (6, 9 and 18) were used. The Grashof number in this study was 1000. The results showed clearly that the buoyant force due to the temperature gradient caused the helical flow; this flow occurred when the Richardson number was larger than 0.0045. The constant temperature gradient considered in this research has little effect on the transition to a turbulent Taylor vortex flow in all models.</p></abstract></abstract-group></header><body refstyle="alphabetic"><sec-level1 id="fdr365009s1" label="1"><heading>Introduction</heading><p indent="no">The flow between two concentric cylinders with the inner cylinder rotating or both rotating is known as Taylor–Couette flow. It was first studied by Taylor (<cite linkend="fdr365009bib13">1923</cite>). Since then, many researchers have studied the instability causing Taylor vortices. Various numerical and experimental studies have been performed to solve this eigenvalue problem (Jones <cite linkend="fdr365009bib10">1985</cite>, Wereley and Lueptow <cite linkend="fdr365009bib14">1998</cite>, Rigopoulos <italic>et al</italic> <cite linkend="fdr365009bib11">2003</cite>, Marques and Lopez <cite linkend="fdr365009bib9">2006</cite>). Most Taylor–Couette studies have been performed under plain wall and isothermal conditions. Few works have been conducted that consider both the wall shape of the cylinders and non-isothermal conditions. In engineering applications such as electronic motors, clutches and bearings, the temperatures of the two rotating cylinders are not the same and the wall generally has complex geometries. These factors affect the stability of the fluid flow. Under this condition, two aspects affect the flow region between two cylinders. The first is the centrifugal force caused by the inner cylinder rotation, and the second is the buoyancy caused by the presence of a radial temperature gradient. Here, the Richardson number, <inline-eqn><math-text><italic>Ri</italic></math-text></inline-eqn>, is introduced to identify which force is dominant (Ball <italic>et al</italic> <cite linkend="fdr365009bib1">1989</cite>, Hwang <italic>et al</italic> <cite linkend="fdr365009bib4">2006</cite>). It is defined as <inline-eqn><math-text><italic>Ri</italic>=<italic>Gr</italic>/<italic>Re</italic><sup>2</sup></math-text></inline-eqn>. In this study, the radial temperature gradient remains constant; consequently, the Grashof number does not vary.</p><p>Snyder and Karlsson (<cite linkend="fdr365009bib12">1964</cite>) investigated the effect of a radial temperature gradient on the stability of a Taylor–Couette flow and found that relatively small temperature gradients have a large effect on the critical Taylor number. Lee and Minkowycz (<cite linkend="fdr365009bib6">1989</cite>) studied heat transfer characteristics by using the naphthalene sublimation technique in the annular gap between two short concentric cylinders that had either two smooth walls or one smooth and one axially slit wall. This study yielded qualitative information regarding heat transfer but did not address the flow phenomena inside the annular gap. Lepiller <italic>et al</italic> (<cite linkend="fdr365009bib9">2008</cite>) studied the influence of radial heating on the stability of a circular Couette flow. They found that a radial temperature gradient destabilizes the Couette flow, leading to a pattern of traveling helical vortices occurring near the bottom of the system. The size of the pattern increases as the rotation frequency of the cylinder is increased by varying the Grashof number from <inline-eqn><math-text>−1000</math-text></inline-eqn> to 1000. Kang <italic>et al</italic> (<cite linkend="fdr365009bib5">2009</cite>) studied the effect of a radial temperature gradient on circular Couette flow using numerical simulation. They found that the size of vortices increases with increasing Richardson number. Lee <italic>et al</italic> (<cite linkend="fdr365009bib7">2009</cite>) studied a Taylor–Couette system with different numbers of slits in the outer cylinder by using the digital particle image velocimetry (DPIV) method. They showed that a larger number of axial slits accelerated the transition process. However, their study was limited to isothermal conditions.</p><p>The present work explores the effect of a constant radial temperature gradient quantified by the Grashof number and the presence of slits on the transition process of a Taylor–Couette flow. DPIV is used to measure the flow field inside the gap. This study can not only help improve the performance of fluid machinery but also help understand the flow instability phenomena in a Taylor–Couette flow.</p></sec-level1><sec-level1 id="fdr365009s2" label="2"><heading>Experimental apparatus and method</heading><p indent="no">The general arrangement of the apparatus is shown schematically in figure <figref linkend="fdr365009fig1">1</figref>. The radius of the inner cylinder (<inline-eqn><math-text><italic>r</italic><sub><upright>i</upright></sub></math-text></inline-eqn>) and the inner radius of the outer cylinder (<inline-eqn><math-text><italic>r</italic><sub><upright>o</upright></sub></math-text></inline-eqn>) are 33 mm and 40 mm, respectively. The annular gap (<inline-eqn><math-text><italic>d</italic></math-text></inline-eqn>) between the cylinders is 7 mm and the length of the cylinders (<inline-eqn><math-text><italic>L</italic></math-text></inline-eqn>) is 336 mm. The radius ratio (<inline-eqn><math-text><italic>r</italic><sub><upright>i</upright></sub>/<italic>r</italic><sub><upright>o</upright></sub></math-text></inline-eqn>) and the aspect ratio (<inline-eqn><math-text><italic>L</italic>/<italic>d</italic></math-text></inline-eqn>) of the models are 0.825 and 48, respectively, following the studies of Cole (<cite linkend="fdr365009bib2">1976</cite>) and Wereley and Lueptow (<cite linkend="fdr365009bib14">1998</cite>). The inner cylinder was driven by a micro stepping motor having a resolution of 400 000 steps per revolution. This micro stepper motor was controlled through a computer, which allowed for precise control of the angular velocity (<inline-eqn><math-text>Ω</math-text></inline-eqn>) and the acceleration to the preset velocity. The outer cylinder was kept stationary. A total of four concentric cylinder models were used to investigate the slit wall effect under a constant temperature gradient. Figure <figref linkend="fdr365009fig2">2</figref> shows the geometries of the experimental models used in this study.</p><figure id="fdr365009fig1" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="17.9pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig1.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig1.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc1" label="Figure 1"><p indent="no">Schematic diagram of the experimental apparatus and setup.</p></caption></figure><figure id="fdr365009fig2" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="25.7pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig2.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig2.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc2" label="Figure 2"><p indent="no">Geometries of the experimental models. (a) The plain model, (b) the 18-slit model, (c) nine-slit model and (d) the six-slit model.</p></caption></figure><p>The complex geometry and curved surfaces of the outer cylinders hindered us from obtaining clear images via the particle image velocimetry (PIV) method owing to the difference in refractive indexes. Therefore, we carefully matched refractive indexes between the annulus and the working fluid to obtain clear particle images. A detailed explanation of the apparatus and refractive index matching method is given in a previous paper (Lee <italic>et al</italic> <cite linkend="fdr365009bib7">2009</cite>).</p><p>During the experiment, the temperature of the inner and outer cylinders was carefully controlled to keep the imposed temperature gradients constant. A CNT-coated heating film wrapped around the inner cylinder was used to generate the constant heat flux; it had a thickness of <inline-eqn><math-text>300 μ<upright>m</upright></math-text></inline-eqn>. This film can generate uniform heat flux along the entire surface. A water jacket was installed in the space between the enclosure box and the outer cylinder, which was connected to the constant temperature bath, forming the other closed circuit. The main purpose of this circuit was to maintain a constant temperature condition between the enclosure box and the outer cylinder. The temperature gradient became steady after the two circuits had worked for 10 h. The temperature of the enclosure box and the outer cylinder was maintained at <inline-eqn><math-text><italic>T</italic><sub><upright>out</upright></sub>=24.0 °<upright>C</upright></math-text></inline-eqn>, and the surface temperature of the inner cylinder was maintained at <inline-eqn><math-text><italic>T</italic><sub><upright>in</upright></sub>=25.2 °<upright>C</upright></math-text></inline-eqn>. The effect of the temperature gradient was parametrized by the Grashof number, defined as <inline-eqn><math-text><italic>Gr</italic>=<italic>d</italic><sup>3</sup>β<italic>g</italic>Δ<italic>T</italic>/ν</math-text></inline-eqn>, where <italic>g</italic> is the acceleration due to gravity, <inline-eqn><math-text>β</math-text></inline-eqn> is the coefficient of thermal expansion of the working fluid and <inline-eqn><math-text>Δ<italic>T</italic></math-text></inline-eqn> is the temperature change across the gap. <inline-eqn><math-text>Δ<italic>T</italic></math-text></inline-eqn> is defined as (<inline-eqn><math-text><italic>T</italic><sub><upright>in</upright></sub></math-text></inline-eqn> – <inline-eqn><math-text><italic>T</italic><sub><upright>out</upright></sub></math-text></inline-eqn>) and is thus considered to be positive if the inner cylinder is hotter than the outer cylinder. In this paper, <inline-eqn><math-text>Δ<italic>T</italic>=1.2 °<upright>C</upright></math-text></inline-eqn>, and <inline-eqn><math-text>β=5.7×10<sup>−4</sup> °<upright>C</upright><sup>−1</sup></math-text></inline-eqn> at <inline-eqn><math-text>24 °<upright>C</upright></math-text></inline-eqn>. Therefore, the Grashof number in this study was 1000.</p><p>In this experiment, the rotational speed was expressed as a Reynolds number, <inline-eqn><math-text><italic>Re</italic></math-text></inline-eqn>, which is defined as <inline-eqn><math-text><italic>Re</italic>=<italic>r</italic><sub><upright>i</upright></sub><italic>d</italic>Ω/ν</math-text></inline-eqn>, where <inline-eqn><math-text>Ω</math-text></inline-eqn> is the angular velocity of the inner cylinder.</p></sec-level1><sec-level1 id="fdr365009s3" label="3"><heading>Experimental results and discussion</heading><p indent="no">The radial and axial instantaneous velocity fields between the inner and outer cylinders were measured using the DPIV method. The conventional cross-correlation PIV method was applied, and the interrogation window size was <inline-eqn><math-text>32×32</math-text></inline-eqn> pixels with <inline-eqn><math-text>50%</math-text></inline-eqn> overlap. Various flow regimes were classified quantitatively by measuring the velocity fields with increasing <inline-eqn><math-text><italic>Re</italic></math-text></inline-eqn> number.</p><p>Due to the existence of the constant temperature gradient, a natural convection current was set up. The axial position, <inline-eqn><math-text><italic>Z</italic>*=<italic>z</italic>/<italic>d</italic></math-text></inline-eqn>, and the radial position, <inline-eqn><math-text><italic>R</italic>*=(<italic>r</italic>−<italic>r</italic><sub><upright>i</upright></sub> )/<italic>d</italic></math-text></inline-eqn>, were normalized by the annular gap width so that the latter varied from <inline-eqn><math-text><italic>R</italic>*=0</math-text></inline-eqn> at the inner cylinder to <inline-eqn><math-text><italic>R</italic>*=1</math-text></inline-eqn> at the outer cylinder of a plain model. The region <inline-eqn><math-text><italic>R</italic>*>1</math-text></inline-eqn> refers to the axial slit space in the outer cylinder. When the concentric cylinders were stationary (<inline-eqn><math-text><italic>Re</italic>=0</math-text></inline-eqn>), the axial velocities of the plain and 18-slit models are shown in figure <figref linkend="fdr365009fig3">3</figref>. The positive temperature gradient created an upward flow near the inner wall and a downward flow at the outer wall. For the plain model, the axial velocity is nearly symmetric about the point at the <inline-eqn><math-text><italic>R</italic>*=0.5</math-text></inline-eqn> location, whereas for the 18-slit model, the axial velocity at the slit space is approximately <inline-eqn><math-text>40%</math-text></inline-eqn> higher than the velocity near the inner cylinder.</p><figure id="fdr365009fig3" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="18.5pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig3.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig3.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc3" label="Figure 3"><p indent="no">Axial velocity profile of the plain and 18-slit models at <inline-eqn><math-text><italic>Re</italic>=0</math-text></inline-eqn>.</p></caption></figure><p>As the Reynolds number increased gradually, only one counter-clockwise rotating vortex appeared. It moved helically along the axial direction. This flow did not appear under an isothermal condition. Figure <figref linkend="fdr365009fig4">4</figref> shows this flow regime for the plain model at <inline-eqn><math-text><italic>Re</italic>=78</math-text></inline-eqn>. The time interval of each image is 1 s. The background represents the vorticity distribution, which was calculated from the radial velocity <inline-eqn><math-text><italic>v</italic><sub><upright>r</upright></sub></math-text></inline-eqn> and the axial velocity <inline-eqn><math-text><italic>v</italic><sub><italic>z</italic></sub></math-text></inline-eqn> using the equation <inline-eqn><math-text>ω=<upright>d</upright><italic>v</italic><sub><upright>r</upright></sub> /<upright>d</upright><italic>z</italic>−<upright>d</upright><italic>v</italic><sub><italic>z</italic></sub> /<upright>d</upright><italic>r</italic></math-text></inline-eqn>. And an asterisk symbol marks the vortex centers, which were decided based on the point of maximum swirling strength in the radial–axial plane.</p><figure id="fdr365009fig4" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="19.2pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig4.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig4.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc4" label="Figure 4"><p indent="no">Single helical vortex flow of the plain model at <inline-eqn><math-text><italic>Re</italic>=78</math-text></inline-eqn> (<inline-eqn><math-text>Δ<italic>t</italic>=1 <upright>s</upright></math-text></inline-eqn>).</p></caption></figure><sec-level2 id="fdr365009s3.1" label="3.1"><heading>Helical vortex flow regime</heading><p indent="no">Figure <figref linkend="fdr365009fig5">5</figref> shows the instantaneous flow fields of different models at <inline-eqn><math-text><italic>Re</italic>=115</math-text></inline-eqn> with a time interval of 1 s. At this Reynolds number, two counter-rotating vortices that move helically along the axial direction appeared. In all models, this flow regime first appeared when the Reynolds number was 99, which indicates that the slits do not affect the transition to a helical vortex flow at this <inline-eqn><math-text><italic>Gr</italic></math-text></inline-eqn> number. In the slit wall configurations, the vortices expanded into the axial slit space and the vorticity in the annular gap became weaker as the number of slits increased. In addition, the distance between the vortex pairs became greater as the number of slits increased.</p><figure id="fdr365009fig5" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="left"><graphic-file version="print" format="EPS" width="30.8pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig5.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig5.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc5" label="Figure 5"><p indent="no">Instantaneous velocity field of the helical vortex flow at <inline-eqn><math-text><italic>Re</italic>=115</math-text></inline-eqn> (<inline-eqn><math-text>Δ<italic>t</italic>=1 <upright>s</upright></math-text></inline-eqn>). (a) Plain model, the (b) six-slit model, (c) the nine-slit model and (d) the 18-slit model.</p></caption></figure><p>With this Reynolds number under an isothermal condition, a Taylor vortex flow appeared. Figure <figref linkend="fdr365009fig6">6</figref> shows the radial velocity components along the axial direction for the plain and 18-slit models at the <inline-eqn><math-text><italic>R</italic>*=0.5</math-text></inline-eqn> location. The results of the Taylor vortex flow are from a previous study by Lee <italic>et al</italic> (<cite linkend="fdr365009bib7">2009</cite>). In figure <figref linkend="fdr365009fig6">6</figref>(a), the velocity distribution corresponding to the outflow is narrower and stronger than that corresponding to the inflow, which can be seen not only in the plain model but also in the 18-slit model. This occurs because the distance between the two vortex centers of a vortex pair is shorter than that of two adjacent vortex pairs and because the outflow between the vortex centers of a vortex pair is stronger than the inflow between two adjacent vortex pairs. In figure <figref linkend="fdr365009fig6">6</figref>(b), the velocity distribution corresponding to the outflow is also narrower than that corresponding to the inflow in both models. However, in the plain model, the velocity of the inflow and outflow is nearly identical because in the helical vortex flow regime, the two-vortex core center of the same vortex pair is not at the same radial position of <inline-eqn><math-text><italic>R</italic>*=0.5</math-text></inline-eqn>; the maximum radial velocities of the outflow and inflow were found to be <inline-eqn><math-text>1.95×10<sup>−3</sup></math-text></inline-eqn> and <inline-eqn><math-text>1.27×10<sup>−3</sup> <upright>m</upright> <upright>s</upright><sup>−1</sup></math-text></inline-eqn> at different positions. It was also found that the outflow of the 18-slit model is faster than that of the plain model in both conditions due to the slit wall effect.</p><figure id="fdr365009fig6" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="left"><graphic-file version="print" format="EPS" width="30.8pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig6.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig6.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc6" label="Figure 6"><p indent="no">Radial velocity profile along the axial direction. (a) Taylor vortex flow and (b) helical vortex flow.</p></caption></figure><p>Figure <figref linkend="fdr365009fig7">7</figref> shows the vortex moving velocity along the axial direction of the plain model. This figure shows that in the helical vortex flow regime, as <inline-eqn><math-text><italic>Re</italic></math-text></inline-eqn> increases, the vortex moving velocity increases.</p><figure id="fdr365009fig7" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="20.0pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig7.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig7.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc7" label="Figure 7"><p indent="no">Vortex moving velocity along the axial direction of the plain model.</p></caption></figure></sec-level2><sec-level2 id="fdr365009s3.2" label="3.2"><heading>First helical wavy vortex flow (HWVF) regime</heading><p indent="no">Figure <figref linkend="fdr365009fig8">8</figref> shows the instantaneous flow fields of the first HWVF at <inline-eqn><math-text><italic>Re</italic>=132</math-text></inline-eqn> under the influence of the convection flow. We chose instantaneous velocity fields with different time intervals for clearly showing vortex flow. At the same Reynolds number, a wavy vortex flow (WVF) appeared under an isothermal condition. In this study, the inner region had a higher temperature than the outer region; therefore, the direction of the convection current is upwards near the inner cylinder and downwards near the outer cylinder (Deters and Egbers <cite linkend="fdr365009bib3">2005</cite>). As a result, the vortices have the same direction of circulation as the natural convection current increases in size. The counter-rotating vortices, on the other hand, decrease in size. For this reason, vortices with different shapes were formed in an HWVF.</p><figure id="fdr365009fig8" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="left"><graphic-file version="print" format="EPS" width="30.6pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig8.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig8.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc8" label="Figure 8"><p indent="no">First HWVF at <inline-eqn><math-text><italic>Re</italic>=132</math-text></inline-eqn>. (i) <inline-eqn><math-text><italic>t</italic>=0 <upright>s</upright></math-text></inline-eqn>, (ii) <inline-eqn><math-text>Δ<italic>t</italic>=0.8 <upright>s</upright></math-text></inline-eqn>, (iii) <inline-eqn><math-text>Δ<italic>t</italic>=1.6 <upright>s</upright></math-text></inline-eqn> and (iv) <inline-eqn><math-text>Δ<italic>t</italic>=2.6 <upright>s</upright></math-text></inline-eqn>. (a) The plain model, (b) the six-slit model, (c) the nine-slit model and (d) the 18-slit model.</p></caption></figure><p>For the six-slit model, a transition to an HWVF occurred at <inline-eqn><math-text><italic>Re</italic>=127</math-text></inline-eqn>, which was identical to what was observed in the plain model. However, for the nine-slit and 18-slit models, an HWVF occurred slightly earlier than in the plain and six-slit models at <inline-eqn><math-text><italic>Re</italic>=119</math-text></inline-eqn>.</p></sec-level2><sec-level2 id="fdr365009s3.3" label="3.3"><heading>Random helical vortex flow regime (RHVF)</heading><p indent="no">With further increase in the Reynolds number, another transition was made to an RHVF at <inline-eqn><math-text><italic>Re</italic>=143</math-text></inline-eqn> in the plain and six-slit models, which is shown in figure <figref linkend="fdr365009fig9">9</figref>. However, for the nine-slit and 18-slit models, the transition to RHVF was somewhat accelerated, at <inline-eqn><math-text><italic>Re</italic>=135</math-text></inline-eqn> and 129, respectively. In the random helical vortex, the vortices appeared randomly and the motion of the vortices was irregular.</p><figure id="fdr365009fig9" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="left"><graphic-file version="print" format="EPS" width="30.7pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig9.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig9.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc9" label="Figure 9"><p indent="no">Random HWVF at <inline-eqn><math-text><italic>Re</italic>=143</math-text></inline-eqn>. (a) The plain model, (b) the six-slit model, (c) the nine-slit model and (d) the 18-slit model.</p></caption></figure><p>An RHVF has an irregular flow regime similar to a weak turbulent Taylor vortex flow (TTVF). However, the turbulence intensity of this flow regime is much smaller than that of TTVF. The turbulence intensity of the RHVF was close to <inline-eqn><math-text>0.2%</math-text></inline-eqn>.</p></sec-level2><sec-level2 id="fdr365009s3.4" label="3.4"><heading>Second HWVF regime</heading><p indent="no">After the RHVF, an HWVF appeared again at <inline-eqn><math-text><italic>Re</italic>=286</math-text></inline-eqn> in the plain and six-slit models. This phenomenon also occurred in the nine-slit model at <inline-eqn><math-text><italic>Re</italic>=268</math-text></inline-eqn>, but did not appear in the 18-slit model. Figure <figref linkend="fdr365009fig10">10</figref> shows this flow regime at <inline-eqn><math-text><italic>Re</italic>=409</math-text></inline-eqn>. The time intervals are also different like in figure <figref linkend="fdr365009fig8">8</figref>. The differences between the first and second HWVF regimes were the wavy frequency and the vortex moving velocity. Table <tabref linkend="fdr365009tab1">1</tabref> shows the wavy frequency at the first and second HWVF regimes. The wavy frequencies of the three models are identical in the first HWVF regime and the values increase in the second HWVF regime. The wavy frequency decreases slightly as the number of slits increases in this HWVF regime.</p><figure id="fdr365009fig10" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="left"><graphic-file version="print" format="EPS" width="30.8pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig10.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig10.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc10" label="Figure 10"><p indent="no">Second HWVF at <inline-eqn><math-text><italic>Re</italic>=409</math-text></inline-eqn>. (i) <inline-eqn><math-text><italic>t</italic>=0 <upright>s</upright></math-text></inline-eqn>, (ii) <inline-eqn><math-text>Δ<italic>t</italic>=0.8 <upright>s</upright></math-text></inline-eqn>, (iii) <inline-eqn><math-text>Δ<italic>t</italic>=1.4 <upright>s</upright></math-text></inline-eqn> and (iv) <inline-eqn><math-text>Δ<italic>t</italic>=2.4 <upright>s</upright></math-text></inline-eqn>. (a) The plain model, (b) the six-slit model and (c) the nine-slit model.</p></caption></figure><table id="fdr365009tab1" frame="topbot" position="float" width="fit" place="top"><caption type="table" id="fdr365009tc1" label="Table 1"><p>Wavy frequency for different <inline-eqn><math-text><italic>Re</italic></math-text></inline-eqn> values in helical wavy vortex flow regimes.</p></caption><tgroup cols="7"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="center"></colspec><colspec colnum="3" colname="col3" align="center"></colspec><colspec colnum="4" colname="col4" align="center"></colspec><colspec colnum="5" colname="col5" align="center"></colspec><colspec colnum="6" colname="col6" align="center"></colspec><colspec colnum="7" colname="col7" align="center"></colspec><thead><row><entry></entry><entry namest="col1" nameend="col2" align="center">The plain model</entry><entry namest="col1" nameend="col2" align="center">The six-slit model</entry><entry namest="col1" nameend="col2" align="center">The nine-slit model</entry></row></thead><tbody><row><entry><inline-eqn><math-text><italic>Re</italic></math-text></inline-eqn></entry><entry>132</entry><entry>409</entry><entry>132</entry><entry>409</entry><entry>132</entry><entry>409</entry></row><row><entry>Frequency (Hz)</entry><entry>0.23</entry><entry>0.60</entry><entry>0.23</entry><entry>0.55</entry><entry>0.23</entry><entry>0.50</entry></row></tbody></tgroup></table></sec-level2><sec-level2 id="fdr365009s3.5" label="3.5"><heading>WVF regime</heading><p indent="no">The WVF regime appeared in the plain model, the six-slit model and the nine-slit model before the transition to a TTVF. Figure <figref linkend="fdr365009fig11">11</figref> shows WVF fields of different models with a time interval of 0.8 s. For the six-slit and nine-slit models, the vorticity is distributed in an oval shape because the vortices expanded into the slit space. A detailed explanation of this flow regime in an isothermal condition is given in a previous paper (Lee <italic>et al</italic> <cite linkend="fdr365009bib7">2009</cite>).</p><figure id="fdr365009fig11" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="left"><graphic-file version="print" format="EPS" width="30.6pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig11.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig11.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc11" label="Figure 11"><p indent="no">Instantaneous velocity field of a WVF at <inline-eqn><math-text><italic>Re</italic>=573</math-text></inline-eqn> (<inline-eqn><math-text>Δ<italic>t</italic>=0.8 <upright>s</upright></math-text></inline-eqn>). (a) The plain model, (b) the six-slit model and (c) the nine-slit model.</p></caption></figure><p>For the plain model, the WVF first appeared at <inline-eqn><math-text><italic>Re</italic>=471</math-text></inline-eqn>. The flow regime was similar to that of the isothermal condition when the Reynolds number was larger than this value. It was found that when the Reynolds number is smaller than 471, that is, when <inline-eqn><math-text><italic>Ri</italic></math-text></inline-eqn> is larger than 0.0045, both the temperature gradient and the rotational forces affect the flow characteristics. As the rotation speed of the inner cylinder increases gradually and as <italic>Ri</italic> becomes smaller than 0.0045, the rotational forces are predominant; the helical feature of the vortex flow caused by the temperature gradient effect weakens and the temperature gradient has only a slight effect on the wavy frequency and the amplitude of axial movement of the wavy vortex, as shown in figure <figref linkend="fdr365009fig12">12</figref>. Under an isothermal condition, the wavy frequency is higher than that in a non-isothermal condition with the same <inline-eqn><math-text><italic>Re</italic></math-text></inline-eqn>. This difference increases as <inline-eqn><math-text><italic>Re</italic></math-text></inline-eqn> increases, but the amplitude of the wave in the isothermal condition is nearly <inline-eqn><math-text>30%</math-text></inline-eqn> smaller. This does not change regardless of the Reynolds number.</p><figure id="fdr365009fig12" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="left"><graphic-file version="print" format="EPS" width="30.8pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig12.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig12.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc12" label="Figure 12"><p indent="no">Variation of the frequency and the mean distance of axial motion of a wavy vortex. (a) Variation of the frequency. (b) Variation of axial motion. <inline-eqn><math-text>δ</math-text></inline-eqn> is the mean distance of axial motion.</p></caption></figure></sec-level2><sec-level2 id="fdr365009s3.6" label="3.6"><heading>TTVF regime</heading><p indent="no">The flow of the plain and six-slit models finally changed to a TTVF as the rotating Reynolds number increased to 1909, which also occurred in the isothermal condition according to Lee <italic>et al</italic> (<cite linkend="fdr365009bib7">2009</cite>). For the nine-slit and 18-slit models, it was found that the transition to a TTVF was accelerated, as in that under the isothermal condition, at <inline-eqn><math-text><italic>Re</italic>=880</math-text></inline-eqn> and 585, respectively. For the 18-slit model, the TTVF was distinguished from the RHVF by the turbulence intensity. The turbulence intensity is greater than <inline-eqn><math-text>1%</math-text></inline-eqn> at <inline-eqn><math-text><italic>Re</italic>=585</math-text></inline-eqn>.</p><p>The transition processes of Taylor–Couette flow with a constant temperature gradient in the slit wall configuration according to rotating Reynolds numbers are summarized in figure <figref linkend="fdr365009fig13">13</figref>.</p><figure id="fdr365009fig13" parts="single" width="column" position="float" pageposition="top" printstyle="normal" orientation="port"><graphic position="indented"><graphic-file version="print" format="EPS" width="25.0pc" printcolour="no" filename="fdr_42_6_065501eps/fdr365009fig13.eps"></graphic-file><graphic-file version="ej" format="JPEG" printcolour="no" filename="fdr_42_6_065501img/fdr365009fig13.jpg"></graphic-file></graphic><caption type="figure" id="fdr365009fc13" label="Figure 13"><p indent="no">Flow type in different models for various <inline-eqn><math-text><italic>Re</italic></math-text></inline-eqn> values. The scale of the <inline-eqn><math-text><italic>x</italic></math-text></inline-eqn>-axis does not represent the actual scale.</p></caption></figure></sec-level2></sec-level1><sec-level1 id="fdr365009s4" label="4"><heading>Conclusion</heading><p indent="no">An experimental study was performed for a Taylor–Couette flow with a constant temperature gradient between concentric cylinders with a slit wall. By adjusting the rotation speed of the inner cylinder gradually, different flow regimes between two cylinders were investigated, from a laminar flow to a turbulent flow.</p><p>From the results for the plain model, when <inline-eqn><math-text><italic>Ri</italic></math-text></inline-eqn> is larger than 0.0045, the radial temperature gradient affects the flow transition processes, including the helical vortex flow, HWVF and random helical vortex flow. In the WVF mode, the transition process of the non-isothermal condition is nearly identical to that of the isothermal condition regardless of the differences in the cylinder models. This indicates that the temperature gradient has little effect when <inline-eqn><math-text><italic>Ri</italic></math-text></inline-eqn> is less than 0.0045.</p><p>Comparing the results to those in an isothermal condition obtained by Lee <italic>et al</italic> (<cite linkend="fdr365009bib7">2009</cite>), we can conclude that the temperature gradient has a greater influence on the plain and six-slit models, as it changes the vortex shape and vortex center location in these models. Each core of vortex pairs has the same radial position under an isothermal condition in the case of the plain and six-slit models. However, under a non-isothermal condition, the locations of the vortex core have different radial positions. In the case of the nine-slit and 18-slit models, the core always has a different radial location regardless of the existence of the temperature gradient. In addition, it was found that the existence of temperature gradient has little effect on the transition to a TTVF.</p><p>The effect of the slit wall on the transition process is similar to that in an isothermal condition. The plain and six-slit models showed the same critical Reynolds number and acceleration in the transition process as the number of slits increased.</p><p>This research showed the flow transition of a Taylor–Couette flow for a slit wall and a temperature gradient. Although the CNT film used in this study can generate the constant heat flux precisely, it only made a small temperature difference with negative temperature gradient. We are rebuilding the apparatus with two heat exchangers and constant temperature baths, and different temperature gradients can be generated between two cylinders by adjusting the temperature and flow rate of a constant temperature bath. We expect that the results from this study can help understand the effect of various temperature gradients on the flow transition of a Taylor–Couette flow.</p></sec-level1><acknowledgment><heading>Acknowledgment</heading><p indent="no">This work was supported by Priority Research Centers Program (2009-0094016) and Pioneer Research Center Program (2009-0082813) of the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology.</p></acknowledgment></body><back><references><heading>References</heading><reference-list type="alphabetic"><journal-ref id="fdr365009bib1" author="Ball et al" year-label="1989"><authors><au><second-name>Ball</second-name><first-names>K S</first-names></au><au><second-name>Farouk</second-name><first-names>B</first-names></au><au><second-name>Dixit</second-name><first-names>V C</first-names></au></authors><year>1989</year><art-title>An experimental study of heat transfer in a vertical annulus with a rotating inner cylinder</art-title><jnl-title>Int. 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Fluid Mech.</jnl-title><volume>364</volume><pages>59–80</pages><crossref><cr_doi>http://dx.doi.org/10.1017/S0022112098008969</cr_doi><cr_issn type="print">00221120</cr_issn><cr_issn type="electronic">14697645</cr_issn></crossref></journal-ref></reference-list></references></back></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="eng"><title>Effect of a constant radial temperature gradient on a TaylorCouette flow with axial wall slits</title></titleInfo><titleInfo type="abbreviated"><title>Effect of a constant radial temperature gradient on a TaylorCouette flow with axial wall slits</title></titleInfo><titleInfo type="alternative" lang="eng"><title>Effect of a constant radial temperature gradient on a TaylorCouette flow with axial wall slits</title></titleInfo><name type="personal"><namePart type="given">Dong</namePart><namePart type="family">Liu</namePart><affiliation>Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</affiliation><affiliation>School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, People's Republic of China</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Sang-Hyuk</namePart><namePart type="family">Lee</namePart><affiliation>Korea Atomic Energy Research Institute, Daejeon 305-353, Korea</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Hyoung-Bum</namePart><namePart type="family">Kim</namePart><affiliation>Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</affiliation><affiliation>School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea</affiliation><affiliation>E-mail: kimhb@gsnu.ac.kr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="paper">paper</genre><originInfo><publisher>The Japan Society of Fluid Mechanics and IOP Publishing Ltd</publisher><dateIssued encoding="w3cdtf">2010</dateIssued><copyrightDate encoding="w3cdtf">2010</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><note type="production">Printed in the UK</note></physicalDescription><abstract>The flow between two concentric cylinders with the inner cylinder rotating with an imposed radial temperature gradient was studied using the digital particle image velocimetry method. Four models of a stationary outer cylinder without and with different numbers of slits (6, 9 and 18) were used. The Grashof number in this study was 1000. The results showed clearly that the buoyant force due to the temperature gradient caused the helical flow; this flow occurred when the Richardson number was larger than 0.0045. The constant temperature gradient considered in this research has little effect on the transition to a turbulent Taylor vortex flow in all models.</abstract><relatedItem type="host"><titleInfo><title>Fluid Dynamics Research</title></titleInfo><titleInfo type="abbreviated"><title>Fluid Dyn. Res.</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">0169-5983</identifier><identifier type="PublisherID">fdr</identifier><identifier type="CODEN">FDRSEH</identifier><identifier type="URL">stacks.iop.org/FDR</identifier><part><date>2010</date><detail type="volume"><caption>vol.</caption><number>42</number></detail><detail type="issue"><caption>no.</caption><number>6</number></detail><extent unit="pages"><start>1</start><end>16</end><total>16</total></extent></part></relatedItem><identifier type="istex">8924A003AB4D576436B5E15DA6D4EEFD930C0051</identifier><identifier type="DOI">10.1088/0169-5983/42/6/065501</identifier><identifier type="articleID">365009</identifier><identifier type="articleNumber">065501</identifier><accessCondition type="use and reproduction" contentType="copyright">2010 The Japan Society of Fluid Mechanics and IOP Publishing Ltd</accessCondition><recordInfo><recordContentSource>IOP</recordContentSource><recordOrigin>2010 The Japan Society of Fluid Mechanics and IOP Publishing Ltd</recordOrigin></recordInfo></mods></metadata><enrichments><json:item><type>multicat</type><uri>https://api.istex.fr/document/8924A003AB4D576436B5E15DA6D4EEFD930C0051/enrichments/multicat</uri></json:item></enrichments><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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