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


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.


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


Grid size, mm


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, °

















Without pintle




\( ^\circ \)

Flow rate



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.


  1. 1.
    Unmack KE (1987) Wide range thrust throttling of a solid rocket motor. In: AIAA/SAE/ASME/ASEE 23rd joint propulsion conference, AIAA Paper No 1987-2085, June–July 1987Google Scholar
  2. 2.
    Kent SR, Loh TH, Chwalowski P (1995) Analytical contouring of pintle nozzle exit cone using computational fluid dynamics. In: 31st AIAA/ASME/SAE/ASEE joint propulsion conference and exhibit, AIAA Paper 1995-2877, July 1995.
  3. 3.
    Burroughs S (2001) Status of army pintle technology for controllable thrust propulsion. In: 37th AIAA/ASME/SAE/ASEE joint propulsion conference and exhibit, AIAA Paper 2001-3598, July 2001.
  4. 4.
    Sun P, Zhao X, Gao J (2013) Influencing analysis to nozzle’s inner flow field of different pintle radius and shapes. J Appl Sci 13(14):2744–2751. CrossRefGoogle Scholar
  5. 5.
    Kim JG (2011) Study on the effects of pintle shapes and position in nozzle flow field, and thrust in a solid rocket motor with pintle nozzle. Ph.D. dissertation, Dept. of Mechanical Design Engineering, Chungnam National Univ., Daejeon, ROKGoogle Scholar
  6. 6.
    Lee JY (2012) A study on the static and dynamic characteristics of pintle-perturbed conical nozzle flows. Ph.D. dissertation, Dept. of Mechanical Engineering, Yonsei Univ., Seoul, ROKGoogle Scholar
  7. 7.
    Ji Hyung L, Byung Hoon P, Woongsup Y (2013) Parametric investigation of the pintle-perturbed conical nozzle flows. Aerosp Sci Technol 26(1):268–279. CrossRefGoogle Scholar
  8. 8.
    Junyoung H, Kiyeon J, Hong-Gye S (2015) Numerical study of the dynamic characteristics of pintle nozzles for variable thrust. J Propuls Power 31(1):230–237. CrossRefGoogle Scholar
  9. 9.
    Hong-Gye S, Kiyeon J, Junyoung H (2017) Performance characteristics of a pintle nozzle using the conformal sliding mesh technique. Aerosp Sci Technol 61:85–94. CrossRefGoogle Scholar
  10. 10.
    Nijanthan M, Vignesh S, Doddi HN, Pavithra M, Mohammed NN, Sanal Kumar VR (2017) Conceptual design and shape optimization of a pintle nozzle for controllable thrust propulsion and steering. In: 53rd AIAA/SAE/ASEE joint propulsion conference, AIAA Paper 2017-4870, July 2017.
  11. 11.
    Sutton PG, Biblarz O (2000) rocket propulsion elements, 7th edn. A Wiley-Interscience Publication, New York, pp 45–96 (ISBN: 0471326429) Google Scholar
  12. 12.
    Barth TJ, Jespersen D (1989) The design and application of upwind schemes on unstructured meshes. In: 27th Aerospace sciences meeting, aerospace sciences meetings, AIAA Paper 1989-0366, January 1989.
  13. 13.
    Menter FR (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32(8):1598–1605. CrossRefGoogle Scholar
  14. 14.
    Hunter AC (2004) Experimental investigation of separated nozzle flows. J Propuls Power 20(3):527–532. MathSciNetCrossRefGoogle Scholar
  15. 15.
    Sanal Kumar VR, Vigneshwaran S, Nichith C, Vignesh S, Vishnu N, Sathyan P, Ajith S, Sivabalan M, Tharikaa R, Hema Sai ND, Krithika V, Sharad S, Pavithra M, Ganesh Shankar S, Niyasdeen NM, Roshan VB, Sulthan Ariff Rahman MR, Ukeshkumar H, Vivek S (2018) A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers. AIP Adv. Google Scholar

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

Personalised recommendations