Journal of Visualization

, Volume 22, Issue 1, pp 35–49 | Cite as

Extracting mole fraction measurements from the visualization of a shock reflection

  • Jeff L. Edwards
  • W. Schuyler Hinman
  • Craig T. JohansenEmail author
Regular Paper


A novel method of determining the local mole fraction in a binary mixture from the visualization of a shock reflection was developed and tested in a shock tube. Incident and reflected shock wave velocities extracted from high-speed shadowgraphy and surface pressure data obtained from piezoelectric pressure sensors were used in combination with classical shock theory to perform the measurements. The mole fraction was determined from the analysis of the mixture properties, including the specific heat capacity and molecular weight. The sensitivity of measurement uncertainty to the camera resolution and framing rate was analyzed. Based on shock tube tests of helium–nitrogen mixtures, the accuracy of the mole fraction measurement technique is 4%.

Graphical abstract


Mole fraction Shadowgraphy Shock reflection 



The authors would like to acknowledge Defence Research and Development Canada (DRDC) for loaning the shock tube for these experiments.


  1. Aghsaee M, Abdali A, Duerrstein SH, Schulz C (2011) A shock-tube with high-repetition-rate time-of-flight mass spectrometry for the study of complex reaction systems. In: 28th International symposium on shock waves Vol 1, Springer, Heidelberg, New York, Dordrecht, London, Manchester, UK, pp 191–196.
  2. Alexandrino K, Alzueta MU, Curran HJ (2018) An experimental and modeling study of the ignition of dimethyl carbonate in shock tubes and rapid compression machine. Combust Flame 188:212–226.,
  3. Allen JD (2015) Dynamics of nanoparticle combustion. Ph.d. thesis, University of Illinois.
  4. Barraza-Botet CL, Wooldridge MS (2018) Combustion chemistry of iso-octane/ethanol blends: Effects on ignition and reaction pathways. Combust Flame 188:324–336.,
  5. Bazyn T, Krier H, Glumac N (2006) Combustion of nanoaluminum at elevated pressure and temperature behind reflected shock waves. Combust Flame 145(4):703–713.,
  6. Botros KK (2010) Measurements of speed of sound in lean and rich natural gas mixtures at pressures up to 37 MPa using a specialized rupture tube. Int J Thermophys 31(11–12):2086–2102. CrossRefGoogle Scholar
  7. Cengel YA, Boles MA (2006) Thermodynamicc an engineering approach, 6th edn. McGraw Hill, New YorkGoogle Scholar
  8. Ciccarelli G, Johansen C, Parravani M (2010) The role of shock-flame interactions on flame acceleration in an obstacle laden channel. Combust Flame 157(11):2125–2136CrossRefGoogle Scholar
  9. Craig RR (1966) A shock tube study of the ignition delay of hydrogen-air mixtures near the second explosion limit. Tech Rep AFAPL-TR-66-74, Air Force Aero Propulsion Laboratory Reasearch and Technology Division, Wright-Patterson Air Force Base, OHI,.
  10. Davidson DF, Hanson RK (2009) Recent advances in shock tube/laser diagnostic methods for improved chemical kinetics measurements. Shock Waves 19:271–283., URL
  11. Davidson DF, Haylett DR, Hanson RK (2008) Development of an aerosol shock tube for kinetic studies of low-vapor-pressure fuels. Combust Flame 155:108–117.,
  12. De Kat R, Van Oudheusden B (2012) Instantaneous planar pressure determination from PIV in turbulent flow. Exp Fluids 52(5):1089–1106CrossRefGoogle Scholar
  13. Edwards JL (2017) Estimation of the local mixture composition associated with a short-duration fuel injection near a shock reflection. Master of science, University of CalgaryGoogle Scholar
  14. Glass II (1990) Over forty years of continuous research. Shock Waves 1:50Google Scholar
  15. Guibert P, Perrard W, Morin C (2002) Concentration Measurements in a Pressurized and Heated Gas Mixture Flow Using Laser Induced Fluorescence. J Fluids Eng 124(2):512–522.,
  16. Hanson RK (1968) An experimental and analytical investigation of shock-wave reflection in a chemically relaxing gas. Ph.d. thesis, Stanford UniversityGoogle Scholar
  17. Hanson RK (1971) Shock-tube study of vibrational relaxation in carbon monoxide using pressure measurements. AIAA J 9(9):1811–1819., URL
  18. Hanson RK, Davidson DF (2014) Recent advances in laser absorption and shock tube methods for studies of combustion chemistry. Prog Energy Combust Sci 44:103–114., URL
  19. Hanson RK, Davidson DF (2015) Advances in shock tube techniques for fundamental studies of combustion kinetics. In: 25th ICDERS., Leeds, UK, pp 1–5Google Scholar
  20. Hargather MJ, Settles GS (2012) A comparison of three quantitative schlieren techniques. Opt Lasers Eng 50(1):8–17., URL
  21. Hargis JW, Petersen EL (2015) Methane ignition in a shock tube with high levels of CO2 dilution: consideration of the reflected-shock bifurcation. Energy Fuels 29:7712–7726.,
  22. Haylett DR (2011) The development and application of aerosol shock tube methods for the study of low-vapor-pressure fuels. Ph.d. thesis, Stanford University.
  23. He J, Yong K, Zhang W, Li P, Zhang C, Li X (2016) Shock tube study of ignition delay characteristics of nnonane and nundecane in argon. Energy Fuels 30:8886–8895.
  24. Herranz LE, Anderson MH, Corradini ML (1998) The effect of light gases in noncondensable mixtures on condensation heat transfer. In: Proceedings of the 11th international heat transfer conference, Kyongju, Korea, pp 415–420Google Scholar
  25. Herzler J, Naumann C (2009) Shock-tube study of the ignition of methane/ethane/hydrogen mixtures with hydrogen contents from 0% to 100% at different pressures. Proc Combust Inst 32:213–220.,
  26. Higashino F, Ishii Y, Sakurai A (1985) Measurement of ignition delay time on unsteady hydrogen jets. In: 10th ICDERS, Berkeley, CA, pp 407–415Google Scholar
  27. Hinman W, Johansen C (2016) Rapid prediction of hypersonic blunt body flows for parametric design studies. Aerosp Sci Technol 58:48–59CrossRefGoogle Scholar
  28. Hinman W, Johansen C, Rodi P (2017) Optimization and analysis of hypersonic leading edge geometries. Aerosp Sci Technol 70:549–558CrossRefGoogle Scholar
  29. Ishii Y, Higashino F, Sakurai A (1986) Ignition of spurting hydrogen jets behind a reflected shock wave. Bulletin of JSME 29(256):3448–3451.,
  30. Johansen C, Ciccarelli G (2009) Visualization of the unburned gas flow field ahead of an accelerating flame in an obstructed square channel. Combust Flame 156(2):405–416CrossRefGoogle Scholar
  31. Kern RD, Singh HJ, Zhang Q (2001) Mass spectrometric methods for chemical kinetics in shock tubes. In: Handbook of shock waves volume 3, chap 16.1Google Scholar
  32. Kogekar G, Karakaya C, Liskovich GJ, Oehlschlaeger MA, Decaluwe SC, Kee RJ (2018) Impact of non-ideal behavior on ignition delay and chemical kinetics in high-pressure shock tube reactors. Combust Flame 189:1–11.,
  33. Liu X, Katz J (2006) Instantaneous pressure and material acceleration measurements using a four-exposure PIV system. Exp Fluids 41(2):227–240CrossRefGoogle Scholar
  34. Loparo ZE, Lopez JG, Neupane S, Partridge WP, Vodopyanov K, Vasu SS (2017) Fuel-rich n-heptane oxidation: a shock tube and laser absorption study. Combustion and Flame 185:220–233.
  35. Lynch PT (2010) High Temperature Spectroscopic Measurements of Aluminum Combustion in a Heterogeneous Shock Tube. Ph.D. thesis, University of Illinois,
  36. Mullaney GJ (1959) Autoignition of liquid fuel sprays. Industrial and Engineering Chemistry 51(6):779–782.
  37. Ninnemann E, Koroglu B, Pryor O, Barak S, Nash L, Loparo Z, Sosa J, Ahmed K, Vasu S (2018) New insights into the shock tube ignition of H2/O2 at low to moderate temperatures using high-speed end-wall imaging. Combustion and Flame 187:11–21.,
  38. Nishida M (2001) Shock tubes and tunnels: facilities, instrumentation, and techniques. In: Handbook of shock waves volume 1, Elsevier Inc, chap 4.1, pp 553–585, 10.1016/B978-012086430-0/50041-5,, arXiv:1011.1669v3
  39. Pang GA, Davidson DF, Hanson RK (2009) Experimental study and modeling of shock tube ignition delay times for hydrogen - oxygen - argon mixtures at low temperatures. Proc Combust Inst 32(1):181–188. CrossRefGoogle Scholar
  40. Porter JM, Jeffries JB, Hanson RK (2011) Mid-infrared laser-absorption diagnostic for vapor-phase fuel mole fraction and liquid fuel film thickness. Appl Phys B Lasers Opt 102(2):345–355., URL
  41. Pryor O, Barak S, Koroglu B, Ninnemann E, Vasu SS (2017) Measurements and interpretation of shock tube ignition delay times in highly CO 2 diluted mixtures using multiple diagnostics. Combust Flame 180:63–76.,
  42. Rasband WS (2016) ImageJ, U. S. National In- stitutes of Health, Bethesda, Maryland, USA. (1997--2016).
  43. Roy C, Blottner F (2006) Review and assessment of turbulence models for hypersonic flows. Prog Aerosp Sci 42:469–530CrossRefGoogle Scholar
  44. Sajid MB, Javed T, Farooq A (2015) Shock tube/laser absorption measurements of methane, acetylene and ethylene during the pyrolysis of n-pentane and iso-pentane. Combust Flame 164:1–9.,
  45. Sakurai A (1985) Auto-ignition of hydrogen by a shock-compressed oxidizer. In: Proceedings of the fifteenth international symposium on shock waves and shock tubes, Berkeley, CA, pp 77–86Google Scholar
  46. Settles GS, Hargather M (2017) A review of recent developments in schlieren and shadowgraph techniques This. Meas Sci Technol p aa5748,
  47. Smiley EF, Winkler EH (1954) Shock-tube measurements of vibrational relaxation. J Chem Phys 22(7):2018–1390.,
  48. Swain M, Grillot E, Swain M (1999) Experimental verification of a hydrogen risk assessment method. Chem Health Safe 6(3):0–4, 10.1016/S1074-9098(00)80037-4.
  49. Takahashi S (1982) An experiment on the ignition of hydrogen injected into a kigh temperature oxidizer. Int J Hydrogen Energy 7(7):589–596CrossRefGoogle Scholar
  50. Tropea C, Yarin A, Foss J (2007) Handbook of experimental fluid mechanics, 1st edn. Springer, BerlinGoogle Scholar
  51. Xing F, Huang Y, Zhao M, Zhao J (2016) The brief introduction of different laser diagnostics methods used in aeroengine combustion research. J Sens 2016:13 p., arXiv:1011.1669v3
  52. Yingjia Z, Zuohua H, Jinhua W, Shengli X (2011) Shock tube study on auto-ignition characteristics of kerosene/air mixtures. Eng Thermophys 56(13):1399–1406.,
  53. YingJia Z, Zuohua H, Liangjie W, Shaodong N (2011) Experimental and kinetic study on ignition delay times of methane/hydrogen/oxygen/nitrogen mixtures by shock tube. Eng Thermophys 56(26):2853–2861., URL

Copyright information

© The Visualization Society of Japan 2018

Authors and Affiliations

  • Jeff L. Edwards
    • 1
  • W. Schuyler Hinman
    • 1
  • Craig T. Johansen
    • 1
    Email author
  1. 1.University of Calgary Schulich School of EngineeringCalgaryCanada

Personalised recommendations