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Supersonic Several Bells Design of Minimum Length Nozzle Contours for More Altitudes Level Adaptations

  • Research Article-Mechanical Engineering
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Abstract

This wok focuses to develop a numerical computation program allowing to design new contours of a supersonic nozzle having several bells, adapted to several levels of different altitudes, going from sea level and progressively with the altitude up to space, giving a supersonic uniform and parallel flow to the exit section and a maximum possible thrust without loss, aiming to reduce considerably the side loads caused in the conventional and the dual bell nozzles when the ambient pressure decrease with the altitude. The first bell has a sonic, uniform and parallel inlet to the throat, and a sea level adaptation with a reduced supersonic Mach number, while the other bell have a supersonic, parallel and uniform inlet and an adaptation to a given altitude with a progressed increase of supersonic Mach number. The transition from one level of adaptation to another adjacent is done without mechanical activation. The purpose of this type of nozzle is to have the possibility of flying in several supersonic regimes adapted to several different altitudes with a reduced side loads. This type of nozzle is named by Several Bell Nozzle and has inflection points between bell and adjacent other. The design is done in the context of a calorically and thermally perfect gas. The problem is to design a typical bell having a uniform and parallel supersonic inlet and exit with two given Mach numbers. The design is made by the use of the Method of Characteristics. The resolution of the equations is done numerically by the finite difference corrector predictor algorithm. The validation of the results is controlled by the convergence of the ratio of the critical sections, calculated numerically, to that given by the theory. In this case, all the design parameters converge automatically to the desired solution. The application is made for axisymmetric MLN having 3, 4, 5 and 10 bells.

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Abbreviations

C F :

Thrust coefficient.

C Mass :

Mass coefficient

L :

Length of the nozzle.

M :

Mach number.

MLN:

Abbreviation of Minimum Length Nozzle.

MOC:

Abbreviation of Method of Characteristics.

NPR:

Number of Pressure Ratio of the nozzle.

SBN:

Several Bell Nozzle

b :

Number of the bell of the MLN

P :

Pressure.

PG:

Abbreviation of Perfect Gas.

x, y :

Cartesian components.

θ :

Flow angle deviation.

ν :

Prandtl Meyer function.

μ :

Mach angle.

γ :

Specific heats ratio.

ξ :

Downward Mach line.

η :

Upward Mach line.

Δθ :

Deviation step for ξ at the expansion center.

Δ :

Non dimensional step on the Mach line BS

N :

Node number on the wall.

m :

Additional number of the inserted ξ

0:

Stagnation condition.

*:

Throat condition.

E :

Exit section.

I :

Inlet section

j :

Number of the bell of the nozzle

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Authors and Affiliations

  1. Institute of Aeronautics and Space Studies, University of Blida, 1, BP 270, 09000, Blida, Algeria

    Toufik Yahiaoui & Toufik Zebbiche

Authors
  1. Toufik Yahiaoui
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  2. Toufik Zebbiche
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Correspondence to Toufik Zebbiche.

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Yahiaoui, T., Zebbiche, T. Supersonic Several Bells Design of Minimum Length Nozzle Contours for More Altitudes Level Adaptations. Arab J Sci Eng 46, 11871–11883 (2021). https://doi.org/10.1007/s13369-021-05725-1

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  • DOI: https://doi.org/10.1007/s13369-021-05725-1

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