Supersonic Two-Dimensional Minimum Length Nozzle Design at High Temperature. Application for Air.

Zebbiche, Toufik; Youbi, Z.

doi:10.2514/6.2006-4599

Cited by 10 publications

(19 citation statements)

References 1 publication

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“…[1] GL quadrature For the trapezoid and Simpson's quadratures, one has to control of fixation of the digits decimal for wanted precision. Since the error relations of these quadratures does not give any information's on the minimum number of points which it is necessary to obtain the desired precision, considering the properties (4).…”

Section: Simpson Simpsonmentioning

confidence: 99%

Numerical quadrature for the Prandtl Meyer function at high temperature with application for air

Zebbiche

2010

JCM

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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. Résumé-Lorsque la température de stagnation de la chambre de combustion ou de l'air ambiant augmente, la chaleur spécifique et de leur rapport ne reste pas plus constant, et commence à varier avec cette température. Le gaz reste parfait, à l'exception, il sera imparfait en calories et parfait thermiquement. Une nouvelle forme générale de la fonction de Prandtl Meyer est développée, en ajoutant l'effet de variation de cette température, qui est basse au seuil de dissociation. La nouvelle relation est présentée sous la forme d'une intégrale d'une fonction analytique complexe, et ayant une dérivée infinie à la température critique. Une intégration quadratique numérique robuste est présentée dans ce contexte. La forme classique de la fonction de Prandtl Meyer d'un gaz parfait devient un cas particulier de la forme développée. La comparaison est faite avec le modèle d'un gaz parfait ayant pour but de présenter une limite de son application. L'application est l'air.

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Section: Simpson Simpsonmentioning

confidence: 99%

Numerical quadrature for the Prandtl Meyer function at high temperature with application for air

Zebbiche

2010

JCM

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“…The present development is based on the laws of conservation of mass, momentum and energy and on the equation of state of a perfect gas [1,3,6,8,12,13] and they are given by:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Equations (12) and (13) constitute a system of nonlinear equations with two unknowns, T 2 and x ρ 82 T. Zebbiche / Effect of the stagnation temperature on the normal shock wave…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The ratio T * /T 0 and T 1 /T 0 corresponding to T 0 and M 1 can be determined as a result. The ratio ρ 1 /ρ 0 1 can be calculated using the following relationship when i = 1, presented in [3,6,12,13], using the Simpson formulae [5] with condensation of nodes [3] by:…”

Section: Calculation Proceduresmentioning

confidence: 99%

“…In reference [14], we find, for air, a table containing some values of C P and γ depending on the temperature in the interval 55 K and 3550 K. An interpolation polynomial is made to the values of the table [10,11] to find an analytical function C P (T) [3,6,12,13]. The presented mathematical relationships are valid in the general case regardless of the form of interpolation and substance, but our results are presented by the choice of an interpolation by a polynomial of the 9th degree [3,6,12,13], and substance chosen is the air. The comparison is made with the PG model to determine a limit for applying this model.…”

Section: Introductionmentioning

confidence: 99%

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Effect of the stagnation temperature on the normal shock wave

Zebbiche

2009

JCM

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When the stagnation temperature increases, the specific heat does not remain constant and start to vary with this temperature. The gas is perfect; its state equation remains always valid, except, it was called by calorically imperfect gas or gas at high temperature. The purpose of this work is to develop a mathematical model for a normal shock wave at high temperature when the stagnation temperature is taken into account, less than the dissociation of the molecules. A generalisation model for a perfect gas for constant heat specific is obtained. A study on the error given by the perfect gas model compared to our model is presented in order to find a limit of application of the perfect gas model. The application is for air.

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Modified Method of Characteristics for Analysing Cold Flow in Bell-Type Rocket Nozzle

Panigrahi

Maity

Sinha

et al. 2020

Lecture Notes in Mechanical Engineering

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Supersonic Two-Dimensional Minimum Length Nozzle Design at High Temperature. Application for Air.

Cited by 10 publications

References 1 publication

Numerical quadrature for the Prandtl Meyer function at high temperature with application for air

Numerical quadrature for the Prandtl Meyer function at high temperature with application for air

Effect of the stagnation temperature on the normal shock wave

Modified Method of Characteristics for Analysing Cold Flow in Bell-Type Rocket Nozzle

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