Shock-Structure Formation in Circular and Non-Circular Sonic Jets at Underexpanded Conditions

Document Type : Regular Article


1 School of Aeronautical Sciences, Hindustan Institute of Technology and Science, Chennai, Tamilnadu, 603103, India

2 Department of Aerospace Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, 721302, India

3 Department of Aerospace Engineering, JAIN (Deemed-to-be University), Bangalore, Karnataka, 560069, India

4 Department of Aerospace Engineering, Madras Institute of Technology, Chennai, Tamil Nadu, 600044, India



The generation of shock waves and their repercussions in high-speed vehicles are inevitable. Particularly, the hot plume from the aircraft exhaust ejecting at a high speed, as well as the emitted aeroacoustic noise, have several consequences. Besides, the occurrence of the supersonic core length and the emission of high screech noise are mostly due to the shock cells, prevailing in high-speed jets. Therefore, understanding the shock cell structures developed at the exit of aircraft or rocket nozzles is vital in improving mixing and thereby the noise characteristics. Essentially, non-circular nozzle shapes are well known for enhancing entrainment characteristics and mitigating the noise due to their differential spreading over the nozzle's perimeter. The current study examines the shock structures of circular, elliptic, and square jets at various sonic underexpansion levels. In this investigation, the nozzle geometries are considered to have the same exit area. The Nozzle Pressure Ratio (NPR) was adjusted to 3, 4, and 5 to achieve moderate and highly underexpansion conditions. The shadowgraph visualization method is used to study the development of shock cells from axisymmetric and asymmetric nozzles. It is interesting to observe that the incident and reflected shock structures exist only at moderate and high underexpansion levels. Besides, the elliptic and the square jets have distinctive flow patterns along their different axis planes. The intercepting shock appears on the elliptic jet in the minor axis rather than the major axis direction. The curvature of the intercepting shock wave was found to be greater for the elliptic jet than that for the circular jet. In addition, the square jet in the symmetry plane diverges from the jet centerline, but the jet in the diagonal direction converges. Moreover, the estimated shock cell lengths using shadowgraph images were compared to a theoretical model where the experimentally obtained results are in good agreement with the theoretical values.


Adamson, T. C. and J. A. Nicholls (1959). On the Structure of Jets from Highly Underexpanded Nozzles into Still Air. Journal of Aerospace Sciences 26, 16–24.##
Addy, A. L. (1981). Effects of axisymmetric sonic nozzle geometry on Mach disk characteristics. AIAA Journal 19, 121–122.##
Austin, T. and C. M. Ho (1992). Controlled entrainment in a 2:1 Aspect-Ratio Subsonic Elliptic Nozzle. AIAA 92-0537, 30th Aerospace Sciences Meeting and Exhibit, Reno, NV 1–11.##
Gutmark, E. and C. M. Ho (1986). Visualization of a forced elliptic jet. AIAA Journal 24, 684–685.##
Ho, C. M. and E. Gutmark (1987). Vortex induction and mass entrainment in a small-aspect-ratio elliptic jet. Journal of Fluid Mechanics 179, 383–405.##
Ilakkiya, S. and B. T. N. Sridhar (2018). An experimental study on the effect of square grooves on decay characteristics of a supersonic jet from a circular nozzle. Journal of Mechanical Science and Technology 32, 4721–4729.##
Jana, T. and M. Kaushik (2021). Performance of corrugated actuator-tabs of aspect ratio 2.0 on supersonic jet mixing enhancement. Journal of Mechanical Science and Technology 35, 1087–1097.##
Jiang, Z., O. Onodera and K. Takayama (1999). Evolution of shock waves and the primary vortex loop discharged from a square cross-sectional tube. Shock Waves 9, 1–10.##
Jothi, T. J. S. and K. Srinivasan (2013). Turbulent mixing noise from underexpanded non-circular slot jets. Acta Acustica united with Acustica 99, 514–523.##
Jothi, T. J. S. and K. Srinivasan (2019). Shock structures of underexpanded non-circular slot jets. Sādhanā 44, 1–9.##
Kaushik, M. (2019). Theoretical and Experimental Aerodynamics. 1st edition, Springer Nature, Singapore.##
Lee, S. J., Y. G. Jang and Y. S. Choi (2012). Stereoscopic-PIV measurement of turbulent jets issuing from a sharp-edged circular nozzle with multiple triangular tabs. Journal of Mechanical Science and Technology 26, 2765–2771.##
Menon, N. and B. W. Skews (2010). Shock wave configurations and flow structures in non-axisymmetric underexpanded sonic jets. Shock Waves 20, 175–190.##
Mitchell, D. M., D. R. Honnery and J. Soria (2013). Near-field structure of underexpanded elliptic jets. Experiments in Fluids 54.##
Rajakuperan, E. and M. A.  Ramaswamy (1998). An experimental investigation of underexpanded jets from oval sonic nozzles. Experiments in Fluids 24, 291–299.##
Rathakrishnan, E. (2007). Instrumentation, Measurements, and Experiments in Fluids. CRC Press, Boca Raton, FL.##
Schadow, K. C., E. Gutmark, S. Koshigoe and K. J. Wilson (1989). Combustion-related shear-flow dynamics in elliptic supersonic jets. AIAA Journal 27, 1347–1353.##
Tam, C. K. W. (1988). The shock-cell structures and screech tone frequencies of rectangular and non-axisymmetric supersonic jets. Journal of Sound and Vibration 121, 135–147.##
Tanna, H. K. (1977). An experimental study of jet noise part II: Shock associated noise. Journal of Sound and Vibration 50, 429–444.##
Thangaraj, T., M. Kaushik, D. Deb, M. Unguresan and V. Muresan (2022). Survey on Vortex Shedding Tabs as Supersonic Jet Control. Frontiers in Physics 9, 1–17.##
Tsutsumi, S., S. Teramoto, K. Yamaguchi and T. Nagashima (2006). Structure of underexpanded jets from square nozzles. AIAA Journal 44, 1287–1291.##
Verma, S. B. and E. Rathakrishnan (2001). Effect of Mach number on the acoustic field of 2:1 elliptic-slot jet. The Aeronautical Journal 105, 9–16.##
Verma, S. B. and E. Rathakrishnan (1998). Mixing Enhancement and Noise Attenuation in Notched Elliptic-Slot Free Jets. International Journal of Turbo and Jet Engines 15, 7–25.##
Zare-Behtash, H., K. Kontis and N. Gongora-Orozco (2008). Experimental investigations of compressible vortex loops. Physics of Fluids 20, 1–18.##
Zhang, H., Z. Chen., Z. Guo and X. Sun (2017). Characteristic behavior of shock pattern and primary vortex loop of a supersonic square jet. International Journal of Heat and Mass Transfer 115, 347–363.##
Volume 15, Issue 6 - Serial Number 67
November and December 2022
Pages 1913-1921
  • Received: 22 April 2022
  • Revised: 06 July 2022
  • Accepted: 13 July 2022
  • First Publish Date: 07 September 2022