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

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Abstract

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.

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References

  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)

    Article  Google Scholar 

  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). https://doi.org/10.1016/j.jcp.2018.08.030

    Article  MathSciNet  MATH  Google Scholar 

  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). https://doi.org/10.1007/s10494-013-9472-x

    Article  Google Scholar 

  4. Berland, J., Bogey, C., Bailly, C.: Numerical study of screech generation in a planar supersonic jet. Phys. Fluids 19(7), 075,105 (2007). https://doi.org/10.1063/1.2747225

    Article  MATH  Google Scholar 

  5. Birkby, P.: Numerical studies of reacting and non-reacting underexpanded sonic jets. Ph.D. thesis, Loughborough University (1998)

  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)

    Article  Google Scholar 

  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)

  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)

  9. Cook, A.W., Cabot, W.H.: Hyperviscosity for shock-turbulence interactions. J. Comput. Phys. 203(2), 379–385 (2005). https://doi.org/10.1016/j.jcp.2004.09.011

    Article  MATH  Google Scholar 

  10. Crist, S., Glass, D.R., Sherman, P.M.: Study of the highly underexpanded sonic jet. AIAA J. 4(1), 68–71 (1966). https://doi.org/10.2514/3.3386

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  12. Crowe, C.T., Sommerfeld, M., Tsuji, Y.: Multiphase Flows with Droplets and Particles. CRC Press, Boca Raton (1998)

    Google Scholar 

  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)

  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). https://doi.org/10.1017/S0022112071000053

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  16. Elghobashi, S.: On predicting particle-laden turbulent flows. Appl. Sci. Res. 52 (4), 309–329 (1994). https://doi.org/10.1007/BF00936835

    Article  Google Scholar 

  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). https://doi.org/10.1063/1.3247158

    Article  MATH  Google Scholar 

  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). https://doi.org/10.1017/S0022112092001678

    Article  MATH  Google Scholar 

  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). https://doi.org/10.1007/s00348-018-2614-0

    Article  Google Scholar 

  20. Garnier, E., Adams, N., Sagaut, P.: Large Eddy Simulation for Compressible Flows. Springer Science & Business Media, Berlin (2009)

    Book  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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). https://doi.org/10.2514/3.50770

    Article  Google Scholar 

  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)

  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). https://doi.org/10.1016/j.ijhydene.2014.10.016

    Article  Google Scholar 

  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). https://doi.org/10.1016/j.compfluid.2016.12.024

    Article  MathSciNet  MATH  Google Scholar 

  26. Hirsch, C.: Numerical Computation of Internal and External Flows. Volume 2: Computational Methods for Inviscid and Viscous Flows. Wiley, New York (1990)

    MATH  Google Scholar 

  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)

  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. https://doi.org/10.2514/6.1998-2802 (1998)

  29. Kawai, S., Lele, S.K.: Large-eddy simulation of jet mixing in supersonic crossflows. AIAA J. 48(9), 2063–2083 (2010). https://doi.org/10.2514/1.J050282

    Article  Google Scholar 

  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). https://doi.org/10.1007/s00193-010-0260-4

    Article  MATH  Google Scholar 

  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). https://doi.org/10.1177/0954410011424984

    Article  Google Scholar 

  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). https://doi.org/10.1021/je000236i

    Article  Google Scholar 

  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). https://doi.org/10.2514/1.43281

    Article  Google Scholar 

  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). https://doi.org/10.1063/1.4818553

    Google Scholar 

  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)

    MATH  Google Scholar 

  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). https://doi.org/10.1016/j.ijhydene.2004.10.001

    Article  Google Scholar 

  37. Moin, P., Kim, J.: Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377 (1982)

    Article  MATH  Google Scholar 

  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). https://doi.org/10.1063/1.4937948

    Article  Google Scholar 

  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)

  40. Peng, D.Y., Robinson, D.B.: A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15(1), 59–64 (1976). https://doi.org/10.1021/i160057a011

    Article  Google Scholar 

  41. Pirozzoli, S.: Numerical methods for high-speed flows. Annu. Rev. Fluid Mech. 43(1), 163–194 (2011). https://doi.org/10.1146/annurev-fluid-122109-160718

    Article  MathSciNet  MATH  Google Scholar 

  42. Pope, S.B.: Turbulent Flows, 6th edn. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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). https://doi.org/10.1016/j.ijthermalsci.2014.11.019

    Article  Google Scholar 

  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. Sagaut, P.: Large Eddy Simulation for Incompressible Flows, 3rd edn. Springer, Berlin (2005)

    MATH  Google Scholar 

  47. Settles, G.S.: Schlieren and Shadowgraph Techniques, First edn. Experimental Fluid Mechanics Book Series. Springer International Publishing, New York (2001)

    Book  Google Scholar 

  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). https://doi.org/10.1016/j.ijhydene.2012.05.142

    Article  Google Scholar 

  49. Vreman, B., Geurts, B., Kuerten, H.: Large-eddy simulation of the turbulent mixing layer. J. Fluid Mech. 339, 357–390 (1997). https://doi.org/10.1017/S0022112097005429

    Article  MathSciNet  MATH  Google Scholar 

  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). https://doi.org/10.1063/1.4772192

    Article  Google Scholar 

  51. Wen, C., Yu, Y.: Mechanics of fluidization. Chem. Eng. Prog. Symp. Ser. 62 (62), 100–111 (1966)

    Google Scholar 

  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). https://doi.org/10.1016/j.jcp.2017.06.009

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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). https://doi.org/10.1016/j.jngse.2012.05.003

    Article  Google Scholar 

  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), https://doi.org/10.2514/6.2003-917

  56. Zhu, J., Shih, T.H.: A numerical study of confined turbulent jets. J. Fluids Eng. 116(4), 702–706 (1994)

    Article  Google Scholar 

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Acknowledgments

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.

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Correspondence to Berend van Wachem.

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Xiao, CN., Fond, B., Beyrau, F. et al. Numerical Investigation and Experimental Comparison of the Gas Dynamics in a Highly Underexpanded Confined Real Gas Jet. Flow Turbulence Combust 103, 141–173 (2019). https://doi.org/10.1007/s10494-019-00014-2

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