Numerical quadrature for the Prandtl Meyer function at high temperature with application for air in nozzles
When the stagnation temperature of the combustion chamber or ambient air increases, the specific heats and their ratio do not remain constant any more, and start to vary with this temperature. The gas remains perfect, except, it will be calorically imperfect and thermally perfect. A new generalized...
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| Format: | Article |
| Language: | English |
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Renewable Energy Development Center (CDER)
2011-12-01
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| Series: | Revue des Énergies Renouvelables |
| Subjects: | |
| Online Access: | https://revue.cder.dz/index.php/rer/article/view/290 |
| _version_ | 1818354217987866624 |
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| author | T. Zebbiche |
| author_facet | T. Zebbiche |
| author_sort | T. Zebbiche |
| collection | DOAJ |
| description | When the stagnation temperature of the combustion chamber or ambient air increases, the specific heats and their ratio do not remain constant any more, and start to vary with this temperature. The gas remains perfect, except, it will be calorically imperfect and thermally perfect. A new generalized form of the Prandtl Meyer function is developed, by adding the effect of variation of this temperature, lower than the threshold of dissociation. The new relation is presented in the form of integral of a complex analytical function, having an infinite derivative at the critical temperature. A robust numerical integration quadrature is presented in this context. The classical form of the Prandtl Meyer function of a perfect gas becomes a particular case of the developed form. The comparison is made with the perfect gas model for aim to present a limit of its application. The application is for air. |
| first_indexed | 2024-12-13T19:21:55Z |
| format | Article |
| id | doaj.art-5983d536898342f1b6bc18946fb02174 |
| institution | Directory Open Access Journal |
| issn | 1112-2242 2716-8247 |
| language | English |
| last_indexed | 2024-12-13T19:21:55Z |
| publishDate | 2011-12-01 |
| publisher | Renewable Energy Development Center (CDER) |
| record_format | Article |
| series | Revue des Énergies Renouvelables |
| spelling | doaj.art-5983d536898342f1b6bc18946fb021742022-12-21T23:34:08ZengRenewable Energy Development Center (CDER)Revue des Énergies Renouvelables1112-22422716-82472011-12-01144675 – 685675 – 685290Numerical quadrature for the Prandtl Meyer function at high temperature with application for air in nozzlesT. Zebbiche0University Saâd Dahleb of Blida, B.P. 270 Blida, AlgeriaWhen the stagnation temperature of the combustion chamber or ambient air increases, the specific heats and their ratio do not remain constant any more, and start to vary with this temperature. The gas remains perfect, except, it will be calorically imperfect and thermally perfect. A new generalized form of the Prandtl Meyer function is developed, by adding the effect of variation of this temperature, lower than the threshold of dissociation. The new relation is presented in the form of integral of a complex analytical function, having an infinite derivative at the critical temperature. A robust numerical integration quadrature is presented in this context. The classical form of the Prandtl Meyer function of a perfect gas becomes a particular case of the developed form. The comparison is made with the perfect gas model for aim to present a limit of its application. The application is for air.https://revue.cder.dz/index.php/rer/article/view/290supersonic flowhigh temperatureprandtl meyer functiongauss legendre quadraturerelative error |
| spellingShingle | T. Zebbiche Numerical quadrature for the Prandtl Meyer function at high temperature with application for air in nozzles Revue des Énergies Renouvelables supersonic flow high temperature prandtl meyer function gauss legendre quadrature relative error |
| title | Numerical quadrature for the Prandtl Meyer function at high temperature with application for air in nozzles |
| title_full | Numerical quadrature for the Prandtl Meyer function at high temperature with application for air in nozzles |
| title_fullStr | Numerical quadrature for the Prandtl Meyer function at high temperature with application for air in nozzles |
| title_full_unstemmed | Numerical quadrature for the Prandtl Meyer function at high temperature with application for air in nozzles |
| title_short | Numerical quadrature for the Prandtl Meyer function at high temperature with application for air in nozzles |
| title_sort | numerical quadrature for the prandtl meyer function at high temperature with application for air in nozzles |
| topic | supersonic flow high temperature prandtl meyer function gauss legendre quadrature relative error |
| url | https://revue.cder.dz/index.php/rer/article/view/290 |
| work_keys_str_mv | AT tzebbiche numericalquadraturefortheprandtlmeyerfunctionathightemperaturewithapplicationforairinnozzles |