Closure of non-integer moments arising in multiphase flow phenomena
In this paper we consider closure problem for non-integer moments of form 〈xp〉,p∈R which are encountered in the moment evolution equations of many multiphase flow systems involving polydispersed particles, heat and mass transfer, chemical reactions, agglomeration or break-up. Two different categorie...
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| Veröffentlicht in: | Chemical engineering science 2012-06, Vol.75, p.424-434 |
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| creator | Haeri, S. Shrimpton, J.S. |
| description | In this paper we consider closure problem for non-integer moments of form 〈xp〉,p∈R which are encountered in the moment evolution equations of many multiphase flow systems involving polydispersed particles, heat and mass transfer, chemical reactions, agglomeration or break-up. Two different categories of methods are considered: the first method is based on the reconstruction of the underlying PDF using Laguerre polynomials and the other is based on the direct calculation of non-integer moments using the fractional derivatives of moment generating function (MGF). By applying the results of fractional calculus an explicit equation is derived to express non-integer moments as a function of any arbitrary number of integer moments. The proposed methods are tested on several highly non-Gaussian analytical PDFs in addition to experimental agglomeration data and direct numerical simulation of fluid–particle turbulent multiphase flows.
► In this paper we consider closure problem for non-integer moments for Eulerian particle systems. ► Laguerre polynomials and fractional derivatives of the moment generating function are used and compared. ► Both methods can be considered general with the latter method possessing more desirable properties. |
| doi_str_mv | 10.1016/j.ces.2012.03.052 |
| format | Article |
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► In this paper we consider closure problem for non-integer moments for Eulerian particle systems. ► Laguerre polynomials and fractional derivatives of the moment generating function are used and compared. ► Both methods can be considered general with the latter method possessing more desirable properties.</description><subject>Agglomeration</subject><subject>Applied sciences</subject><subject>Categories</subject><subject>Chemical engineering</subject><subject>chemical reactions</subject><subject>Closure problem</subject><subject>equations</subject><subject>Eulerian–Eulerian turbulent models</subject><subject>Exact sciences and technology</subject><subject>Fractional moments</subject><subject>heat</subject><subject>Heat and mass transfer. Packings, plates</subject><subject>Hydrodynamics of contact apparatus</subject><subject>Laguerre polynomial</subject><subject>Mass transfer</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Moment generating function</subject><subject>Multiphase flow</subject><subject>Portable document format</subject><subject>Reactors</subject><subject>Reconstruction</subject><subject>Sintering, pelletization, granulation</subject><subject>Solid-solid systems</subject><issn>0009-2509</issn><issn>1873-4405</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNp9kE1rGzEQQEVpoK6TH5BT9lLoZbf63NXSUzFJWjD0kPosxtqRLbMrOdK6of8-Mg459jQMvHkMj5BbRhtGWfvt0FjMDaeMN1Q0VPEPZMF0J2opqfpIFpTSvuaK9p_I55wPZe06RhdktRpjPiWsoqtCDLUPM-4wVVOcMMy5guSzD7vKh2o6jbM_7iFj5cb4Uh33GM4UXJMrB2PGm7e5JJuH-z-rn_X69-Ov1Y91bYWWc90JZYUVzLbbrVQMpQBGseOgASw4wUQr9YCD01vXDr2ElqNtUfcda7et5mJJvl68xxSfT5hnM_lscRwhYDxlw6jQXMleiYKyC2pTzDmhM8fkJ0j_CmTOwczBlGDmHMxQYUqwcvPlTQ_ZwugSBOvz-yFXPdO9PLvvLpyDaGBXApnNUxGpEpX3gspCfL8QWGr89ZhMth6DxcEntLMZov_PH6-ZZYln</recordid><startdate>20120618</startdate><enddate>20120618</enddate><creator>Haeri, S.</creator><creator>Shrimpton, J.S.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>FBQ</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>L7M</scope></search><sort><creationdate>20120618</creationdate><title>Closure of non-integer moments arising in multiphase flow phenomena</title><author>Haeri, S. ; Shrimpton, J.S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c384t-735c3c31c6bb451e43a10e72a8aacaf313648dedf8bf6d94a62ec6e89716b6823</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Agglomeration</topic><topic>Applied sciences</topic><topic>Categories</topic><topic>Chemical engineering</topic><topic>chemical reactions</topic><topic>Closure problem</topic><topic>equations</topic><topic>Eulerian–Eulerian turbulent models</topic><topic>Exact sciences and technology</topic><topic>Fractional moments</topic><topic>heat</topic><topic>Heat and mass transfer. Packings, plates</topic><topic>Hydrodynamics of contact apparatus</topic><topic>Laguerre polynomial</topic><topic>Mass transfer</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Moment generating function</topic><topic>Multiphase flow</topic><topic>Portable document format</topic><topic>Reactors</topic><topic>Reconstruction</topic><topic>Sintering, pelletization, granulation</topic><topic>Solid-solid systems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Haeri, S.</creatorcontrib><creatorcontrib>Shrimpton, J.S.</creatorcontrib><collection>AGRIS</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Chemical engineering science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Haeri, S.</au><au>Shrimpton, J.S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Closure of non-integer moments arising in multiphase flow phenomena</atitle><jtitle>Chemical engineering science</jtitle><date>2012-06-18</date><risdate>2012</risdate><volume>75</volume><spage>424</spage><epage>434</epage><pages>424-434</pages><issn>0009-2509</issn><eissn>1873-4405</eissn><coden>CESCAC</coden><abstract>In this paper we consider closure problem for non-integer moments of form 〈xp〉,p∈R which are encountered in the moment evolution equations of many multiphase flow systems involving polydispersed particles, heat and mass transfer, chemical reactions, agglomeration or break-up. 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| subjects | Agglomeration Applied sciences Categories Chemical engineering chemical reactions Closure problem equations Eulerian–Eulerian turbulent models Exact sciences and technology Fractional moments heat Heat and mass transfer. Packings, plates Hydrodynamics of contact apparatus Laguerre polynomial Mass transfer Mathematical analysis Mathematical models Moment generating function Multiphase flow Portable document format Reactors Reconstruction Sintering, pelletization, granulation Solid-solid systems |
| title | Closure of non-integer moments arising in multiphase flow phenomena |
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