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CSME 2021/06
Volume 42 No.3
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325-330
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Fast Algorithm for the Inverse of the Real Gas Prandtl-Meyer Function
Toufik Yahiaoui a and Toufik Zebbiche a
aInstitute of Aeronautics and Space Studies, University of Blida 1, BP 270 Blida 09000, Algeria.
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Abstract:
The calculation of the flow parameters at the center of a throat expansion of a supersonic nozzle design in the real gas model is of practical interest in aerospace construction. The expansion center is characterized by the end of an infinite Mach lines which will be discretized by a finite number with continuous increase of Mach number and the PM value with a decrease of the temperature, density and the pressure. The flow parameters must be calculated by determining the inverse of the PM. This function depends on two variables which are the temperature and the density. The aim of this work is to develop a fast algorithm allowing to do the inverse of the PM in the context of real gas model by the determination of the temperature and the density corresponding to the given PM deviation which is itself depends on the flow deviation according to the shape of the supersonic nozzle. The Bernoulli equation must be added to construct two nonlinear algebraic equations with two coupled unknowns. The corresponding Mach number and pressure will be determined by analytic equations. The two equations are presented as integral of four complex functions, where the integration is made by the Gauss Legendre's quadrature. The numerical solving of system of equations is done by combining the successive approximation algorithm and the bipartition algorithm. The initial solution is chosen as the parameters corresponding to the previous Mach line to ensure the convergence and accelerate the numerical process. The comparison is made with previous algorithm.
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Keywords: Supersonic nozzle. Prandtl Meyer function. Successive approximation method. bipartition algorithm. Stagnation temperature. Stagnation pressure. Real Gas. Berthelot state equation. Thermodynamic ratios. Gauss Legendre quadrature. Tolerance.
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©
2021
CSME , ISSN 0257-9731
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