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Sea-level transitioning dual bell nozzles

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Abstract

A detailed study was conducted to evaluate the impact of sea-level transitioning dual bell nozzles on the payload mass delivered into geostationary transfer orbit by Ariane 5 ECA. For this purpose, a multitude of Vulcain 2 and Vulcain 2.1 nozzle extension contours were designed. The two variable parameters were the position of the wall inflection and the constant wall pressure of the nozzle extension. Accounting for the two variable parameters, an approved analytical method was applied to predict the impact of the dual bell nozzles on the payload mass.

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Abbreviations

\(A_\mathrm {inf}\) :

Wall inflection cross-sectional area

\(A_\mathrm {e}\) :

Nozzle exit area

\(A_\mathrm {th}\) :

Nozzle throat area

F :

Thrust

\(I_\mathrm {sp,vac}\) :

Vacuum specific impulse

\(I_\mathrm {sp,vac+}\) :

Vacuum specific impulse gain

\(L_\mathrm {inf}\) :

Wall inflection position

\(L_\mathrm {tot}\) :

Total supersonic nozzle length

R :

Radial coordinate

\(R_\mathrm {th}\) :

Nozzle throat radius

X :

Axial coordinate

\(h_\mathrm {tr}\) :

Mode transition altitude

\(m_\mathrm {noz}\) :

Nozzle mass

\(m_\mathrm {noz+}\) :

Nozzle mass increase

\(m_\mathrm {+}\) :

Engine mass increase

\(m_\mathrm {PL+}\) :

Payload gain

\(p_\mathrm {a}\) :

Ambient pressure

\(p_\mathrm {cc}\) :

Combustion chamber pressure

\(p_\mathrm {w}\) :

Wall pressure

\(p_\mathrm {wext}\) :

Dual bell extension wall pressure

\(\alpha _\mathrm {e}\) :

Wall exit angle

\(\alpha _\mathrm {inf}\) :

Wall inflection angle

\(\epsilon\) :

Area ratio, \(A/A_\mathrm {th}\)

\(\epsilon _\mathrm {inf}\) :

Base nozzle area ratio, \(A_\mathrm {inf}/A_\mathrm {th}\)

\(\epsilon _\mathrm {e}\) :

Nozzle exit area ratio, \(A_\mathrm {e}/A_\mathrm {th}\)

\(\Delta F\) :

Thrust increment

\(\Delta I_\mathrm {sp}\) :

Specific impulse increment

NPR :

Nozzle pressure ratio, \(p_\mathrm {cc}/p_\mathrm {a}\)

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Acknowledgements

Financial support has been provided by the German Research Foundation (Deutsche Forschungsgemeinschaft) in the framework of the Sonderforschungsbereich Transregio 40 (SFB-TRR40).

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Authors and Affiliations

  1. German Aerospace Center, 74239, Lampoldshausen, Germany

    Ralf Stark & Chloé Génin

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  1. Ralf Stark
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  2. Chloé Génin
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Correspondence to Ralf Stark.

Additional information

This paper is based on a presentation at the Space Propulsion 2016 conference, 2–6 May, 2016, Rome, Italy.

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Stark, R., Génin, C. Sea-level transitioning dual bell nozzles. CEAS Space J 9, 279–287 (2017). https://doi.org/10.1007/s12567-017-0154-8

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