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Rocket nozzles: 75 years of research and development

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Abstract

The nozzle forms a large segment of the rocket engine structure, and as a whole, the performance of a rocket largely depends upon its aerodynamic design. The principal parameters in this context are the shape of the nozzle contour and the nozzle area expansion ratio. A careful shaping of the nozzle contour can lead to a high gain in its performance. As a consequence of intensive research, the design and the shape of rocket nozzles have undergone a series of development over the last several decades. The notable among them are conical, bell, plug, expansion-deflection and dual bell nozzles, besides the recently developed multi nozzle grid. However, to the best of authors’ knowledge, no article has reviewed the entire group of nozzles in a systematic and comprehensive manner. This paper aims to review and bring all such development in one single frame. The article mainly focuses on the aerodynamic aspects of all the rocket nozzles developed till date and summarizes the major findings covering their design, development, utilization, benefits and limitations. At the end, the future possibilities of development are also recommended.

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Abbreviations

A e :

Nozzle exit area (m2)

A t :

Throat area (m2)

C fv :

Vacuum thrust coefficient

C fvc :

Conical nozzle vacuum thrust coefficient

C fvi :

Ideal nozzle vaccum thrust coefficient

C Fbase :

Total base thrust

C F :

Thrust coefficient

C F , X :

Axial thrust coefficient

C Fi :

Ideal thrust coefficient

D t :

Throat diameter (m)

F v :

Thrust when discharging to vaccum

H N :

Nozzle projected height (m)

I sp :

Specific impulse (sec)

L :

Nozzle length (m)

L n :

Nozzle axial length from throat to exit plane (m)

L N :

Nozzle projected length (m)

L f :

Desired fractional length (m)

p a :

Ambient pressure (Pa)

p c :

Chamber pressure (Pa)

p des :

Design pressure (Pa)

p e :

Pressure at the exit (Pa)

p t :

Stagnation pressure (Pa)

p w :

Wall pressure (Pa)

R :

Radius of circular arc (m)

R t :

Throat radius (m)

V e :

Nozzle exit velocity (m/s

α :

Divergent cone half-angle (deg.)

ρ e :

Density at the exit of nozzle (kg/m3)

γ :

Isentropic exponent

ε :

Nozzle expansion ratio or area ratio

θ :

Nozzle convergent cone section half-angle (deg.)

θ e :

Nozzle exit wall angle (deg.)

θ n :

Initial wall angle of the parabola (deg.)

AR:

Area ratio

CD:

Converging-diverging

CFD:

Computational fluid dynamics

CSN:

Conventional single nozzle

E-D:

Expansion-deflection

EEC:

Extendable exit cone

ESA:

European space agency

ESN:

Equivalent single nozzle

FESTIP:

Future European space transportation investigations programme

FSS:

Free shock separation

MDO:

Multi-disciplinary optimization

MNG:

Multi nozzle grid

MOC:

Method of characteristics

NASA:

National aeronautics and space administration

NPR:

Nozzle pressure ratio

PSP:

Pressure-sensitive paint

RSS:

Restricted shock separation

SRM:

Solid rocket motor

SSME:

Space shuttle main engine

SST:

Shear stress transport

TIC:

Truncated ideal contour

TOC:

Thrust optimized contour

TOP:

Thrust optimized parabola

1D:

One dimensional

2D:

Two dimensional

3D:

Three dimensional

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Acknowledgements

The authors wish to place on record their sincere gratitude to all the authors of classical and popular papers/reports/theses which formed the framework of the present review work. Appreciation is extended to all the sources of figures and data used in this work. A list of these sources has been included in the references, and the authors apologize if due recognition to any source is left out inadvertently.

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  1. Department of Energy and Process Engineering, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Shivang Khare

  2. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, 781039, India

    Ujjwal K Saha

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Khare, S., Saha, U.K. Rocket nozzles: 75 years of research and development. Sādhanā 46, 76 (2021). https://doi.org/10.1007/s12046-021-01584-6

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