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Compressible integral representation of rotational and axisymmetric rocket flow
This work focuses on the development of a semi-analytical model that is appropriate for the rotational, steady, inviscid, and compressible motion of an ideal gas, which is accelerated uniformly along the length of a right-cylindrical rocket chamber. By overcoming some of the difficulties encountered...
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Published in: | Journal of fluid mechanics 2016-12, Vol.809, p.213-239 |
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description | This work focuses on the development of a semi-analytical model that is appropriate for the rotational, steady, inviscid, and compressible motion of an ideal gas, which is accelerated uniformly along the length of a right-cylindrical rocket chamber. By overcoming some of the difficulties encountered in previous work on the subject, the present analysis leads to an improved mathematical formulation, which enables us to retrieve an exact solution for the pressure field. Considering a slender porous chamber of circular cross-section, the method that we follow reduces the problem’s mass, momentum, energy, ideal gas, and isentropic relations to a single integral equation that is amenable to a direct numerical evaluation. Then, using an Abel transformation, exact closed-form representations of the pressure distribution are obtained for particular values of the specific heat ratio. Throughout this effort, Saint-Robert’s power law is used to link the pressure to the mass injection rate at the wall. This allows us to compare the results associated with the axisymmetric chamber configuration to two closed-form analytical solutions developed under either one- or two-dimensional, isentropic flow conditions. The comparison is carried out assuming, first, a uniformly distributed mass flux and, second, a constant radial injection speed along the simulated propellant grain. Our amended formulation is consequently shown to agree with a one-dimensional solution obtained for the case of uniform wall mass flux, as well as numerical simulations and asymptotic approximations for a constant wall injection speed. The numerical simulations include three particular models: a strictly inviscid solver, which closely agrees with the present formulation, and both
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and Spalart–Allmaras computations. |
doi_str_mv | 10.1017/jfm.2016.654 |
format | article |
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and Spalart–Allmaras computations.</description><subject>Axisymmetric</subject><subject>Computer simulation</subject><subject>Constants</subject><subject>Exact solutions</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Thrust chambers</subject><subject>Walls</subject><issn>0022-1120</issn><issn>1469-7645</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNqFkD1PwzAQhi0EEqWw8QMyMpDgs2MnHlHFl1SpC8yW41wqlyQudirov8dVOyKx3J3unnuHh5BboAVQqB423VAwCrKQojwjMyilyitZinMyo5SxHIDRS3IV44ZS4FRVM7Ja-GEbMEbX9Ji5ccJ1MH0W8LDEcTKT82Pmuyz445yOZmwz8-PifhhwCs6mm_3EKet6_31NLjrTR7w59Tn5eH56X7zmy9XL2-JxmVte1VMuRaNqxlF1JefMKlGhtEawtgEDUDYNLZmQUlaKio6qWqZqJVUcO7AtAp-Tu2PuNvivHcZJDy5a7Hszot9FDSollMBr_j9aq4pLJVL6nNwfURt8jAE7vQ1uMGGvgeqDYp0U64NinRQnvDjhZmiCa9eoN34XkqP498MvNUN-PQ</recordid><startdate>20161225</startdate><enddate>20161225</enddate><creator>Akiki, M.</creator><creator>Majdalani, J.</creator><general>Cambridge University Press</general><scope>IKXGN</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7UA</scope><scope>C1K</scope><scope>F1W</scope><scope>H96</scope><scope>L.G</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0001-9129-8292</orcidid></search><sort><creationdate>20161225</creationdate><title>Compressible integral representation of rotational and axisymmetric rocket flow</title><author>Akiki, M. ; Majdalani, J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c378t-65b9823e9f4332c957e6ca52db1a114bb04256667905f09865f0c6093ef1cde13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Axisymmetric</topic><topic>Computer simulation</topic><topic>Constants</topic><topic>Exact solutions</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Thrust chambers</topic><topic>Walls</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Akiki, M.</creatorcontrib><creatorcontrib>Majdalani, J.</creatorcontrib><collection>Cambridge University Press:Open Access Journals</collection><collection>CrossRef</collection><collection>Water Resources Abstracts</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of fluid mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Akiki, M.</au><au>Majdalani, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Compressible integral representation of rotational and axisymmetric rocket flow</atitle><jtitle>Journal of fluid mechanics</jtitle><addtitle>J. Fluid Mech</addtitle><date>2016-12-25</date><risdate>2016</risdate><volume>809</volume><spage>213</spage><epage>239</epage><pages>213-239</pages><issn>0022-1120</issn><eissn>1469-7645</eissn><notes>ObjectType-Article-1</notes><notes>SourceType-Scholarly Journals-1</notes><notes>ObjectType-Feature-2</notes><notes>content type line 23</notes><abstract>This work focuses on the development of a semi-analytical model that is appropriate for the rotational, steady, inviscid, and compressible motion of an ideal gas, which is accelerated uniformly along the length of a right-cylindrical rocket chamber. By overcoming some of the difficulties encountered in previous work on the subject, the present analysis leads to an improved mathematical formulation, which enables us to retrieve an exact solution for the pressure field. Considering a slender porous chamber of circular cross-section, the method that we follow reduces the problem’s mass, momentum, energy, ideal gas, and isentropic relations to a single integral equation that is amenable to a direct numerical evaluation. Then, using an Abel transformation, exact closed-form representations of the pressure distribution are obtained for particular values of the specific heat ratio. Throughout this effort, Saint-Robert’s power law is used to link the pressure to the mass injection rate at the wall. This allows us to compare the results associated with the axisymmetric chamber configuration to two closed-form analytical solutions developed under either one- or two-dimensional, isentropic flow conditions. The comparison is carried out assuming, first, a uniformly distributed mass flux and, second, a constant radial injection speed along the simulated propellant grain. Our amended formulation is consequently shown to agree with a one-dimensional solution obtained for the case of uniform wall mass flux, as well as numerical simulations and asymptotic approximations for a constant wall injection speed. The numerical simulations include three particular models: a strictly inviscid solver, which closely agrees with the present formulation, and both
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subjects | Axisymmetric Computer simulation Constants Exact solutions Mathematical analysis Mathematical models Thrust chambers Walls |
title | Compressible integral representation of rotational and axisymmetric rocket flow |
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