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Conceptual Aerodynamic Design of Pintle Nozzle for Variable-Thrust Propulsion

  • Vignesh SaravananEmail author
  • Jeongwoo Ko
  • Soogab Lee
  • Nijanthan Murugan
  • V. R. Sanal Kumar
Original Paper
  • 18 Downloads

Abstract

Comprehensive theoretical studies have been carried out for the geometry optimization of a pintle nozzle for variable-thrust propulsion. We designed the pintle such that, at the final pintle position, the integrated shape facilitates the scaled-down version of the shockless main nozzle. Numerical studies have been carried out using a validated two-dimensional transient, an implicit Reynolds-averaged Navier–Stokes equations (RANS) solver with a kω Menter’s shear stress transport (SST) turbulence model. At the quasi-steady and dynamic conditions, the numerical results have shown excellent agreement with the theoretical results. In the dynamic condition, the effects of shock train, shock impinging, and the shock location on the overall thrust are studied, and we observed a monotonic increase in thrust during the pintle movement toward the exit and achieved the maximum thrust at the highest area ratio (nozzle exit area to throat area) position. The diminishing of the shock–strength pattern and the movement of the shock-impinging point towards the nozzle exit are captured in the numerical simulation and reported herein. We concluded that the prudent aerodynamic shape optimization of the external surface contour of the pintle and the inner surface contour of its associated nozzle ensures improved performance for the variable-thrust propulsion of aerospace vehicles.

Keywords

Pintle nozzle Aerodynamic design Quasi-dynamic analysis Nozzle performance 

List of symbols

\( A_{\text{e}} \)

Nozzle exit area, m2

\( A_{\text{t}} \)

Nozzle throat area, m2

\( A_{\text{t,wop}} \)

Nozzle throat area without pintle, m2

\( C_{\text{F}} \)

Thrust coefficient

\( F \)

Thrust, N

\( F_{\text{ref}} \)

Thrust at the initial pintle position, N

h

Grid size, mm

L

Length of the pintle, m

\( M_{\text{e}} \)

Nozzle exit Mach number

\( \mathop m\limits^{ \circ } \)

Mass flow rate, kg/s

\( P \)

Pressure, N/m2

\( P_{0} \)

Total pressure, N/m2

\( P_{\text{a}} \)

Ambient pressure, N/m2

\( P_{\text{c}} \)

Chamber pressure, N/m2

\( P_{\text{e}} \)

Nozzle exit pressure, N/m2

\( P_{\text{ref}} \)

Pressure at initial pintle position, N/m2

\( P_{{0,{\text{t}}}} \)

Total pressure at nozzle throat, N/m2

\( R_{\text{G}} \)

Gas constant, J/kg K

\( R \)

Radius of the arc, m

\( r \)

Radius or distance in Y direction, m

\( r_{\text{e}} \)

Nozzle exit radius, m

\( r_{\text{t,o}} \)

Nozzle throat area at the initial position, m2

\( r_{\text{t,f}} \)

Nozzle throat area at the final position, m2

\( T_{\text{c}} \)

Chamber temperature, K

\( T_{\text{t}} \)

Static temperature at nozzle throat, K

\( T_{{0,{\text{t}}}} \)

Total temperature at nozzle throat, K

\( X \)

Distance in the x-direction, m

\( X_{\text{t}} \)

Throat distance from the nozzle inlet, m

\( X_{\text{L}} \)

Pintle stroke distance, m

\( \alpha \)

Non-dimensional distance affected by lip shock wave

\( \beta \)

Non-dimensional distance affected by trailing shock wave

\( \gamma \)

Specific heat ratio (= 1.4)

\( \theta \)

Angle, °

Subscripts

a

Ambient

c

Chamber

e

Exit

F

Thrust

L

Length

p

Pintle

t

Throat

wop

Without pintle

0

Total

Superscript

\( ^\circ \)

Flow rate

Notes

Acknowledgements

This work was supported by the Advanced Research Center Program (NRF-2013R1A5A1073861) through a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) contracted through the Advanced Space Propulsion Research Center at Seoul National University.

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Copyright information

© The Korean Society for Aeronautical & Space Sciences 2019

Authors and Affiliations

  1. 1.Department of Aerospace and Mechanical EngineeringSeoul National UniversitySeoulRepublic of Korea
  2. 2.Department of Aeronautical EngineeringKumaraguru College of TechnologyCoimbatoreIndia

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