Flow, Turbulence and Combustion

, Volume 103, Issue 1, pp 141–173 | Cite as

Numerical Investigation and Experimental Comparison of the Gas Dynamics in a Highly Underexpanded Confined Real Gas Jet

  • Cheng-Nian Xiao
  • Benoit Fond
  • Frank Beyrau
  • Christophe T’Joen
  • Ruud Henkes
  • Peter Veenstra
  • Berend van WachemEmail author


A numerical study for a supersonic underexpanded argon gas jet driven by a pressure ratio of 120 is described in this work, and the results are compared to experiments. A single phase large-eddy simulation (LES) employing a fully-coupled pressure-based finite volume solver framework is carried out. The numerical results are validated against experimental Schlieren and particle-image-velocimetry (PIV) measurements taken under the same conditions. Due to the high pressure conditions imposed on the gas, real gas effects are taken into account via the Peng-Robinson equation of state. This approach enables the accurate prediction of the gas properties throughout all pressure conditions encountered within this study. Flow velocity data obtained from numerical simulations and experiments are presented, leading to valuable insights into the features of the flow. Comparisons between experimental and numerical Schlieren images show a very good agreement for the location and shape of the main shock structure in the near nozzle exit region. The predicted velocity field further downstream, at a stream-wise distance over 100 nozzle diameters from the nozzle exit, is reasonably close to the PIV data, with less than 25% difference between the root-mean-square (RMS) simulated and experimental velocity field. The agreement obtained in this study is remarkable in light of the challenging flow configuration involving a vast range of flow speeds and time scales. There are also discrepancies, predominantly for the near-throat velocity profiles obtained from PIV measurements and numerical simulations: in the immediate post-shock region the simulation results predict a major converging throat of low, subsonic fluid velocity surrounded by the supersonic shear layer, which is not observed in the experiment.


Under-expanded jets Large-eddy simulation Joule-Thomson cooling Industry safety PIV measurements 



The authors are grateful for the financial support provided by Shell Projects & Technology. The use of HPC as well as laboratory facilities of Imperial College is also gratefully acknowledged.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


  1. 1.
    Barchilon, M., Curtet, R.: Some details of the structure of an axisymmetric confined jet with backflow. J. Basic Eng. 86(4), 777–787 (1964)Google Scholar
  2. 2.
    Bartholomew, P., Denner, F., Abdol-Azis, M., Marquis, A., van Wachem, B.: Unified formulation of the momentum-weighted interpolation for collocated variable arrangements. J. Comput. Phys. 375, 177–208 (2018). MathSciNetzbMATHGoogle Scholar
  3. 3.
    Baumann, M., di Mare, F., Janicka, J.: On the validation of large eddy simulation applied to internal combustion engine flows part II: Numerical analysis. Flow Turbul. Combust. 92(1–2), 299–317 (2014). Google Scholar
  4. 4.
    Berland, J., Bogey, C., Bailly, C.: Numerical study of screech generation in a planar supersonic jet. Phys. Fluids 19(7), 075,105 (2007). zbMATHGoogle Scholar
  5. 5.
    Birkby, P.: Numerical studies of reacting and non-reacting underexpanded sonic jets. Ph.D. thesis, Loughborough University (1998)Google Scholar
  6. 6.
    Bonelli, F., Viggiano, A., Magi, V.: A numerical analysis of hydrogen underexpanded jets under real gas assumption. J. Fluids Eng. 135(12), 121,101 (2013)Google Scholar
  7. 7.
    Chauveau, C., Davidenko, D.M., Sarh, B., Gökalp, I., Avrashkov, V., Fabre, C.: PIV measurements in an underexpanded hot free jet. In: 13th International Symposium on the Application of Laser Techniques to Fluids Mechanics. Lisbon, Portugal (2006)Google Scholar
  8. 8.
    Chenoweth, D.R.: Gas-transfer analysis. Section h-real gas results via the van der Waals equation of state and virial expansion extension of its limiting Abel-Noble form. Tech. rep., Sandia National Labs., Albuquerque, NM (USA) (1983)Google Scholar
  9. 9.
    Cook, A.W., Cabot, W.H.: Hyperviscosity for shock-turbulence interactions. J. Comput. Phys. 203(2), 379–385 (2005). zbMATHGoogle Scholar
  10. 10.
    Crist, S., Glass, D.R., Sherman, P.M.: Study of the highly underexpanded sonic jet. AIAA J. 4(1), 68–71 (1966). Google Scholar
  11. 11.
    Crowe, C.T., Sharma, M.P., Stock, D.E.: The Particle-Source-In Cell (PSI-CELL) model for gas-Droplet flows. J. Fluids Eng. 99(2), 325–333 (1977)Google Scholar
  12. 12.
    Crowe, C.T., Sommerfeld, M., Tsuji, Y.: Multiphase Flows with Droplets and Particles. CRC Press, Boca Raton (1998)Google Scholar
  13. 13.
    Denner, F., van Wachem, B.: Accurate advection of sharp interfaces on arbitrary meshes. In: 2nd International Conference on Numerical Methods in Multiphase Flows. 30 June - 2 July 2014. Darmstadt, Germany (2014)Google Scholar
  14. 14.
    Donaldson, C., Snedeker, R.S.: A study of free jet impingement. Part 1. Mean properties of free and impinging jets. J. Fluid Mech. 45(02), 281–319 (1971). Google Scholar
  15. 15.
    Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C., Poinsot, T.: Large-eddy simulation of the shock/turbulence interaction. J. Comput. Phys. 152, 517–549 (1999)zbMATHGoogle Scholar
  16. 16.
    Elghobashi, S.: On predicting particle-laden turbulent flows. Appl. Sci. Res. 52 (4), 309–329 (1994). Google Scholar
  17. 17.
    Emmert, T., Lafon, P., Bailly, C.: Numerical study of self-induced transonic flow oscillations behind a sudden duct enlargement. Phys. Fluids 21(10), 106,105 (2009). zbMATHGoogle Scholar
  18. 18.
    Erlebacher, G., Hussaini, M.Y., Speziale, C.G., Zang, T.A.: Toward the large-eddy simulation of compressible turbulent flows. J. Fluid Mech. 238, 155–185 (1992). zbMATHGoogle Scholar
  19. 19.
    Fond, B., Xiao, C.-N., T’Joen, C., Henkes, R., Veenstra, P., van Wachem, B.G.M., Beyrau, F.: Investigation of a highly underexpanded jet with real gas effects confined in a channel: flow field measurements. Exp. Fluids 59, 160 (2018). Google Scholar
  20. 20.
    Garnier, E., Adams, N., Sagaut, P.: Large Eddy Simulation for Compressible Flows. Springer Science & Business Media, Berlin (2009)zbMATHGoogle Scholar
  21. 21.
    Garnier, E., Mossi, M., Sagaut, P., Comte, P., Deville, M.: On the use of shock-capturing schemes for large-eddy simulation. J. Comput. Phys. 153, 273–311 (1999)zbMATHGoogle Scholar
  22. 22.
    Meier, G.E.A., Grabitz, G., Jungowski, W.M., Witczak, K.J., Anderson, J.S.: Oscillations of the supersonic flow downstream of an abrupt increase in duct cross section. AIAA J. 18(4), 394–395 (1980). Google Scholar
  23. 23.
    Gosman, A., Khalil, E., Whitelaw, J.: The calculation of two-dimensional turbulent recirculating flows. In: Turbulent Shear Flows I, pp 237–255. Springer (1979)Google Scholar
  24. 24.
    Hamzehloo, A., Aleiferis, P.: Large eddy simulation of highly turbulent under-expanded hydrogen and methane jets for gaseous-fuelled internal combustion engines. Int. J. Hydrogen Energy 39(36), 21,275–21,296 (2014). Google Scholar
  25. 25.
    Hempert, F., Boblest, S., Ertl, T., Sadlo, F., Offenhäuser, P., Glass, C., Hoffmann, M., Beck, A., Munz, C.D., Iben, U.: Simulation of real gas effects in supersonic methane jets using a tabulated equation of state with a discontinuous Galerkin spectral element method. Comput. Fluids 145, 167–179 (2017). MathSciNetzbMATHGoogle Scholar
  26. 26.
    Hirsch, C.: Numerical Computation of Internal and External Flows. Volume 2: Computational Methods for Inviscid and Viscous Flows. Wiley, New York (1990)zbMATHGoogle Scholar
  27. 27.
    Hopkins, A.: Lessons from Esso’s gas plant explosion at Longford. In: Lessons from Disasters: Seminar Notes. Institution of Engineers, Australia, pp 17–24 (2000)Google Scholar
  28. 28.
    Hussaini, M.: On large-eddy simulation of compressible flows. In: 29th AIAA, Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics, Albuquerque, NM, USA. (1998)
  29. 29.
    Kawai, S., Lele, S.K.: Large-eddy simulation of jet mixing in supersonic crossflows. AIAA J. 48(9), 2063–2083 (2010). Google Scholar
  30. 30.
    Khaksarfard, R., Kameshki, M.R., Paraschivoiu, M.: Numerical simulation of high pressure release and dispersion of hydrogen into air with real gas model. Shock Waves 20(3), 205–216 (2010). zbMATHGoogle Scholar
  31. 31.
    Lijo, V., Kim, H.D., Setoguchi, T.: Numerical investigation of the effects of base size on supersonic flow through a sudden duct enlargement. Proceedings of the Institution of Mechanical Engineers Part G: Journal of Aerospace Engineering 226(12), 1562–1572 (2012). Google Scholar
  32. 32.
    Linstrom, P.J., Mallard, W.G.: The NIST chemistry WebBook: a chemical data resource on the internet. J. Chem. Eng. Data 46(5), 1059–1063 (2001). Google Scholar
  33. 33.
    Liu, J., Kailasanath, K., Ramamurti, R., Munday, D., Gutmark, E., Lohner, R.: Large-eddy simulations of a supersonic jet and its near-field acoustic properties. AIAA J. 47(8), 1849–1865 (2009). Google Scholar
  34. 34.
    Mallouppas, G., George, W.K., van Wachem, B.G.M.: New forcing scheme to sustain particle-laden homogeneous and isotropic turbulence. Phys. Fluids 25(083304), 1–14 (2013). Google Scholar
  35. 35.
    Martin, M.P., Piomelli, U., Candler, G.V.: Subgrid-scale models for compressible large-eddy simulations. Theor. Comput. Fluid Dyn. 13(5), 361–376 (2000)zbMATHGoogle Scholar
  36. 36.
    Mohamed, K., Paraschivoiu, M.: Real gas simulation of hydrogen release from a high-pressure chamber. Int. J. Hydrogen Energy 30(8), 903–912 (2005). Google Scholar
  37. 37.
    Moin, P., Kim, J.: Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377 (1982)zbMATHGoogle Scholar
  38. 38.
    Müller, H., Niedermeier, C.A., Matheis, J., Pfitzner, M., Hickel, S.: Large-eddy simulation of nitrogen injection at trans- and supercritical conditions. Phys. Fluids 28(1), 015,102 (2016). Google Scholar
  39. 39.
    Munday, D., Gutmark, E., Liu, J., Kailasanath, K.: Flow and acoustic radiation from realistic tactical jet CD nozzles. In: 14Th AIAA/CEAS Aeroacoustics Conference 29Th AIAA Aeroacoustics Conference), p 2838 (2008)Google Scholar
  40. 40.
    Peng, D.Y., Robinson, D.B.: A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15(1), 59–64 (1976). Google Scholar
  41. 41.
    Pirozzoli, S.: Numerical methods for high-speed flows. Annu. Rev. Fluid Mech. 43(1), 163–194 (2011). MathSciNetzbMATHGoogle Scholar
  42. 42.
    Pope, S.B.: Turbulent Flows, 6th edn. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  43. 43.
    Rathore, S.K., Das, M.K.: Comparison of two low-Reynolds number turbulence models for fluid flow study of wall bounded jets. Int. J. Heat Mass Transf. 61, 365–380 (2013)Google Scholar
  44. 44.
    Rathore, S.K., Das, M.K.: A comparative study of heat transfer characteristics of wall-bounded jets using different turbulence models. Int. J. Therm. Sci. 89, 337–356 (2015). Google Scholar
  45. 45.
    Rowe, P.N.: Drag forces in a hydraulic model of a fluidized bed, part II. Trans. Inst. Chem. Engs. 39, 175–180 (1961)Google Scholar
  46. 46.
    Sagaut, P.: Large Eddy Simulation for Incompressible Flows, 3rd edn. Springer, Berlin (2005)zbMATHGoogle Scholar
  47. 47.
    Settles, G.S.: Schlieren and Shadowgraph Techniques, First edn. Experimental Fluid Mechanics Book Series. Springer International Publishing, New York (2001)Google Scholar
  48. 48.
    Velikorodny, A., Kudriakov, S.: Numerical study of the near-field of highly underexpanded turbulent gas jets. Int. J. Hydrogen Energy 37 (22), 17,390–17,399 (2012). Google Scholar
  49. 49.
    Vreman, B., Geurts, B., Kuerten, H.: Large-eddy simulation of the turbulent mixing layer. J. Fluid Mech. 339, 357–390 (1997). MathSciNetzbMATHGoogle Scholar
  50. 50.
    Vuorinen, V., Yu, J., Tirunagari, S., Kaario, O., Larmi, M., Duwig, C., Boersma, B.J.: Large-eddy simulation of highly underexpanded transient gas jets. Phys. Fluids 25(1), 016,101 (2013). Google Scholar
  51. 51.
    Wen, C., Yu, Y.: Mechanics of fluidization. Chem. Eng. Prog. Symp. Ser. 62 (62), 100–111 (1966)Google Scholar
  52. 52.
    Xiao, C.N., Denner, F., van Wachem, B.: Fully-coupled pressure-based finite-volume framework for the simulation of fluid flows at all speeds in complex geometries. J. Comput. Phys. 346, 91–130 (2017). MathSciNetzbMATHGoogle Scholar
  53. 53.
    Yeung, P.K., Pope, S.B.: An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence. J. Comput. Phys. 79, 373–416 (1988)zbMATHGoogle Scholar
  54. 54.
    Yu, J., Vuorinen, V., Hillamo, H., Sarjovaara, T., Kaario, O., Larmi, M.: An experimental investigation on the flow structure and mixture formation of low pressure ratio wall-impinging jets by a natural gas injector. J. Nat. Gas Sci. Eng. 9, 1–10 (2012). Google Scholar
  55. 55.
    Yuceil, B., Otugen, V., Arik, E.: Interferometric Rayleigh scattering and PIV measurements in the near field of underexpanded sonic jets. In: 41st Aerospace SciencesMeeting and Exhibit. American Institute of Aeronautics and Astronautics (2003),
  56. 56.
    Zhu, J., Shih, T.H.: A numerical study of confined turbulent jets. J. Fluids Eng. 116(4), 702–706 (1994)Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringImperial College LondonLondonUK
  2. 2.Faculty of Systems and Process EngineeringOtto-von-Guericke-Universität MagdeburgMagdeburgGermany
  3. 3.Shell Global SolutionsAmsterdamThe Netherlands

Personalised recommendations