Grid criteria for numerical simulation of hypersonic aerothermodynamics in transition regime
Grid is an important factor in numerical simulation of hypersonic aerothermodynamics. This paper introduces three criteria for determining grid size in the transition flow regime when using the computational fluid dynamics (CFD) method or the direct simulation Monte Carlo (DSMC) method. The numerica...
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Veröffentlicht in: | Journal of fluid mechanics 2019-12, Vol.881, p.585-601 |
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description | Grid is an important factor in numerical simulation of hypersonic aerothermodynamics. This paper introduces three criteria for determining grid size in the transition flow regime when using the computational fluid dynamics (CFD) method or the direct simulation Monte Carlo (DSMC) method. The numerical relationship between these three criteria sizes is deduced according to the one-dimensional fluid theory. Then, the relationship is verified using the CFD method to simulate the flow around a two-dimensional cylinder. At the same time, the dependence of simulation accuracy on grid size in the CFD and DSMC methods is studied and the mechanism is given. The result shows that the simulation accuracy of heat flux especially depends on the normal grid size next to surfaces, where the $Re_{\mathit{cell},w}$ criterion and the $\unicode[STIX]{x1D706}_{w}$ criterion based on local parameters are applicable and equivalent, while the $Re_{\mathit{cell},\infty }$ criterion based on the free-stream parameter is only applicable under the assumption of constant viscosity coefficient and constant temperature wall conditions. On the other hand, the trend of the heat flux changing with grid size obtained by CFD and DSMC is exactly the opposite. Therefore, the grid size must be strictly satisfied with the grid criteria when comparing CFD with DSMC and even the hybrid DSMC with Navier–Stokes method. |
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This paper introduces three criteria for determining grid size in the transition flow regime when using the computational fluid dynamics (CFD) method or the direct simulation Monte Carlo (DSMC) method. The numerical relationship between these three criteria sizes is deduced according to the one-dimensional fluid theory. Then, the relationship is verified using the CFD method to simulate the flow around a two-dimensional cylinder. At the same time, the dependence of simulation accuracy on grid size in the CFD and DSMC methods is studied and the mechanism is given. The result shows that the simulation accuracy of heat flux especially depends on the normal grid size next to surfaces, where the $Re_{\mathit{cell},w}$ criterion and the $\unicode[STIX]{x1D706}_{w}$ criterion based on local parameters are applicable and equivalent, while the $Re_{\mathit{cell},\infty }$ criterion based on the free-stream parameter is only applicable under the assumption of constant viscosity coefficient and constant temperature wall conditions. On the other hand, the trend of the heat flux changing with grid size obtained by CFD and DSMC is exactly the opposite. Therefore, the grid size must be strictly satisfied with the grid criteria when comparing CFD with DSMC and even the hybrid DSMC with Navier–Stokes method.</description><identifier>ISSN: 0022-1120</identifier><identifier>EISSN: 1469-7645</identifier><identifier>DOI: 10.1017/jfm.2019.756</identifier><language>eng</language><publisher>Cambridge: Cambridge University Press</publisher><subject>Accuracy ; Aerodynamics ; Aerothermodynamics ; Computational fluid dynamics ; Computer applications ; Computer simulation ; Criteria ; Cylinders ; Direct simulation Monte Carlo method ; Flow simulation ; Fluid dynamics ; Heat ; Heat flux ; Heat transfer ; Hydrodynamics ; Mathematical models ; Methods ; Monte Carlo simulation ; Parameters ; Reynolds number ; Simulation ; Statistical methods ; Theory ; Time dependence ; Transition flow ; Two dimensional flow ; Viscosity ; Viscosity coefficient ; Viscosity coefficients</subject><ispartof>Journal of fluid mechanics, 2019-12, Vol.881, p.585-601</ispartof><rights>2019 Cambridge University Press</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c193t-42c0b2734067c8abca6dc066014335793dae2a288f1cedeec8f9dbd90fb217213</citedby><cites>FETCH-LOGICAL-c193t-42c0b2734067c8abca6dc066014335793dae2a288f1cedeec8f9dbd90fb217213</cites><orcidid>0000-0001-8045-0922</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,781,785,27929,27930</link.rule.ids></links><search><creatorcontrib>Ren, Xiang</creatorcontrib><creatorcontrib>Yuan, Junya</creatorcontrib><creatorcontrib>He, Bijiao</creatorcontrib><creatorcontrib>Zhang, Mingxing</creatorcontrib><creatorcontrib>Cai, Guobiao</creatorcontrib><title>Grid criteria for numerical simulation of hypersonic aerothermodynamics in transition regime</title><title>Journal of fluid mechanics</title><description>Grid is an important factor in numerical simulation of hypersonic aerothermodynamics. This paper introduces three criteria for determining grid size in the transition flow regime when using the computational fluid dynamics (CFD) method or the direct simulation Monte Carlo (DSMC) method. The numerical relationship between these three criteria sizes is deduced according to the one-dimensional fluid theory. Then, the relationship is verified using the CFD method to simulate the flow around a two-dimensional cylinder. At the same time, the dependence of simulation accuracy on grid size in the CFD and DSMC methods is studied and the mechanism is given. The result shows that the simulation accuracy of heat flux especially depends on the normal grid size next to surfaces, where the $Re_{\mathit{cell},w}$ criterion and the $\unicode[STIX]{x1D706}_{w}$ criterion based on local parameters are applicable and equivalent, while the $Re_{\mathit{cell},\infty }$ criterion based on the free-stream parameter is only applicable under the assumption of constant viscosity coefficient and constant temperature wall conditions. On the other hand, the trend of the heat flux changing with grid size obtained by CFD and DSMC is exactly the opposite. Therefore, the grid size must be strictly satisfied with the grid criteria when comparing CFD with DSMC and even the hybrid DSMC with Navier–Stokes method.</description><subject>Accuracy</subject><subject>Aerodynamics</subject><subject>Aerothermodynamics</subject><subject>Computational fluid dynamics</subject><subject>Computer applications</subject><subject>Computer simulation</subject><subject>Criteria</subject><subject>Cylinders</subject><subject>Direct simulation Monte Carlo method</subject><subject>Flow simulation</subject><subject>Fluid dynamics</subject><subject>Heat</subject><subject>Heat flux</subject><subject>Heat transfer</subject><subject>Hydrodynamics</subject><subject>Mathematical models</subject><subject>Methods</subject><subject>Monte Carlo simulation</subject><subject>Parameters</subject><subject>Reynolds number</subject><subject>Simulation</subject><subject>Statistical methods</subject><subject>Theory</subject><subject>Time dependence</subject><subject>Transition flow</subject><subject>Two dimensional flow</subject><subject>Viscosity</subject><subject>Viscosity coefficient</subject><subject>Viscosity coefficients</subject><issn>0022-1120</issn><issn>1469-7645</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</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>eNotkE1OwzAUhC0EEqWw4wCW2JLy_JM4WaIKClIlNrBEluPY1FVjl-dk0dtwFk5GqrKaWXyakT5CbhksGDD1sPX9ggNrFqqszsiMyaopVCXLczID4LxgjMMlucp5C8AENGpGPlcYOmoxDA6DoT4hjWM_dWt2NId-3JkhpEiTp5vD3mFOMVhqHKZh47BP3SGaPthMQ6QDmpjDEf_9QfcVendNLrzZZXfzn3Py8fz0vnwp1m-r1-XjurCsEUMhuYWWKyGhUrY2rTVVZ6GqgEkhStWIzjhueF17Zl3nnK1907VdA77lTHEm5uTutLvH9D26POhtGjFOl5oLyWU5bcuJuj9RFlPO6LzeY-gNHjQDfRSoJ4H6KFBPAsUfIbFmhA</recordid><startdate>20191225</startdate><enddate>20191225</enddate><creator>Ren, Xiang</creator><creator>Yuan, Junya</creator><creator>He, 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criteria for numerical simulation of hypersonic aerothermodynamics in transition regime</title><author>Ren, Xiang ; Yuan, Junya ; He, Bijiao ; Zhang, Mingxing ; Cai, Guobiao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c193t-42c0b2734067c8abca6dc066014335793dae2a288f1cedeec8f9dbd90fb217213</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Accuracy</topic><topic>Aerodynamics</topic><topic>Aerothermodynamics</topic><topic>Computational fluid dynamics</topic><topic>Computer applications</topic><topic>Computer simulation</topic><topic>Criteria</topic><topic>Cylinders</topic><topic>Direct simulation Monte Carlo method</topic><topic>Flow simulation</topic><topic>Fluid dynamics</topic><topic>Heat</topic><topic>Heat flux</topic><topic>Heat transfer</topic><topic>Hydrodynamics</topic><topic>Mathematical models</topic><topic>Methods</topic><topic>Monte Carlo simulation</topic><topic>Parameters</topic><topic>Reynolds number</topic><topic>Simulation</topic><topic>Statistical methods</topic><topic>Theory</topic><topic>Time dependence</topic><topic>Transition flow</topic><topic>Two dimensional flow</topic><topic>Viscosity</topic><topic>Viscosity coefficient</topic><topic>Viscosity coefficients</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ren, Xiang</creatorcontrib><creatorcontrib>Yuan, Junya</creatorcontrib><creatorcontrib>He, Bijiao</creatorcontrib><creatorcontrib>Zhang, Mingxing</creatorcontrib><creatorcontrib>Cai, Guobiao</creatorcontrib><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 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mechanics</jtitle><date>2019-12-25</date><risdate>2019</risdate><volume>881</volume><spage>585</spage><epage>601</epage><pages>585-601</pages><issn>0022-1120</issn><eissn>1469-7645</eissn><abstract>Grid is an important factor in numerical simulation of hypersonic aerothermodynamics. This paper introduces three criteria for determining grid size in the transition flow regime when using the computational fluid dynamics (CFD) method or the direct simulation Monte Carlo (DSMC) method. The numerical relationship between these three criteria sizes is deduced according to the one-dimensional fluid theory. Then, the relationship is verified using the CFD method to simulate the flow around a two-dimensional cylinder. At the same time, the dependence of simulation accuracy on grid size in the CFD and DSMC methods is studied and the mechanism is given. The result shows that the simulation accuracy of heat flux especially depends on the normal grid size next to surfaces, where the $Re_{\mathit{cell},w}$ criterion and the $\unicode[STIX]{x1D706}_{w}$ criterion based on local parameters are applicable and equivalent, while the $Re_{\mathit{cell},\infty }$ criterion based on the free-stream parameter is only applicable under the assumption of constant viscosity coefficient and constant temperature wall conditions. On the other hand, the trend of the heat flux changing with grid size obtained by CFD and DSMC is exactly the opposite. Therefore, the grid size must be strictly satisfied with the grid criteria when comparing CFD with DSMC and even the hybrid DSMC with Navier–Stokes method.</abstract><cop>Cambridge</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2019.756</doi><tpages>17</tpages><orcidid>https://orcid.org/0000-0001-8045-0922</orcidid></addata></record> |
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subjects | Accuracy Aerodynamics Aerothermodynamics Computational fluid dynamics Computer applications Computer simulation Criteria Cylinders Direct simulation Monte Carlo method Flow simulation Fluid dynamics Heat Heat flux Heat transfer Hydrodynamics Mathematical models Methods Monte Carlo simulation Parameters Reynolds number Simulation Statistical methods Theory Time dependence Transition flow Two dimensional flow Viscosity Viscosity coefficient Viscosity coefficients |
title | Grid criteria for numerical simulation of hypersonic aerothermodynamics in transition regime |
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