Skip to main content
SpringerLink
Log in

Systematic errors in mixing measurements using filtered Rayleigh scattering in supersonic flows

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

When performing non-reacting mixing enhancement experimental studies in supersonic flow, helium is often used as an injectant which serves as a simulant gas for hydrogen fuel. The resulting distribution of helium mole fraction in the binary mixture of air and helium can be quantified using filtered Rayleigh scattering (FRS). The FRS technique requires two independent experiments in supersonic flow, one with helium injection and the other with air injection. The helium mole fraction is retrieved under the key assumptions that the number density profiles and the extent of the Doppler shift that is associated with each of the two independent experiments at the measuring plane are identically the same. This work is centered on the analysis of the impact of a departure from the aforementioned assumptions with the aid of a reduced-order model developed for a canonical rectangular jet in supersonic flow. The results, derived from the implementation of the model, are used to identify key driving phenomena that concurrently contribute to violate the key assumptions and are compared and discussed in the light of available experimental data. Additionally, the analysis suggests that the newly developed model can be used in the design of FRS experiments by minimizing the extent of mismatch in the number density profile and thus reducing the systematic bias error associated with the mixture’s composition measurements.

Graphic abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  • Allison PM, McManus TA, Sutton JA (2016) Quantitative fuel vapor/air mixing imaging in droplet/gas regions of an evaporating spray flow using filtered rayleigh scattering. Opt Lett 41(6):1074–1077

    Google Scholar 

  • Anderson JD, Wendt J (1995) Computational fluid dynamics, vol 206. Springer, Berlin

    Google Scholar 

  • Arnberg B, Britton C, Seidl W (1974) Discharge coefficient correlations for circular-arc venturi flowmeters at critical (sonic) flow. J Fluids Eng 96(2):111–123

    Google Scholar 

  • Barber MJ, Schetz JA, Roe LA (1997) Normal, sonic helium injection through a wedge-shaped orifice into supersonic flow. J Propul Power 13(2):257–263

    Google Scholar 

  • Billig FS (1993) Research on supersonic combustion. J Propul Power 9(4):499–514

    Google Scholar 

  • Boguszko M, Elliott G (2004) Measurements in fluid flows using molecular filter-based techniques. In: 42nd AIAA aerospace sciences meeting and exhibit, p 18

  • Boguszko M, Elliott GS (2005) On the use of filtered rayleigh scattering for measurements in compressible flows and thermal fields. Exp Fluids 38(1):33–49

    Google Scholar 

  • Boyd RW (2003) Nonlinear optics. Elsevier, New York

    Google Scholar 

  • Charrier L, Pont G, Marie S, Brenner P, Grasso F (2017) Simulation of a supersonic coaxial he/air jet experiment with a hybrid rans/les variable turbulent schmidt number model. In: 23rd AIAA computational fluid dynamics conference, p 4280

  • Donaldson CD, Gray K (1966) Theoretical and experimental investigation of the compressible free mixing of two dissimilar gases. AIAA J 4(11):2017–2025

    Google Scholar 

  • Elliot G, Boguszko M, Carter C (2001) Filtered rayleigh scattering-toward multiple property measurements. In: 39th aerospace sciences meeting and exhibit, p 301

  • Ferri A (1973) Mixing-controlled supersonic combustion. Annual Rev Fluid Mech 5(1):301–338

    Google Scholar 

  • Forkey J, Finkelstein N, Lempert W, Miles R (1996) Demonstration and characterization of filtered rayleigh scattering for planar velocity measurements. AIAA J 34(3):442–448

    Google Scholar 

  • Gatski TB, Bonnet JP (2013) Compressibility, turbulence and high speed flow. Academic Press, Cambridge

    Google Scholar 

  • Glawe D, Donbar J, Nejad A, Sekar B, Chen T, Samimy M, Driscoll J (1994) Parallel fuel injection from the base of an extended strut into supersonic flow. American Institute of Aeronautics and Astronautics, New York

    Google Scholar 

  • Ground C, Vergine F, Maddalena L (2016) The effect of vortex merging and non-merging on the transfer of modal turbulent kinetic energy content. Exp Fluids 57(8):131

    MATH  Google Scholar 

  • Ground C, Viganó D, Maddalena L (2018a) Comparison of intrusive and non-intrusive mixture composition measurements in supersonic flow. J Propul Power 34(6):1574–1585

    Google Scholar 

  • Ground CR, Gopal V, Maddalena L (2018b) Filtered rayleigh scattering mixing measurements of merging and non-merging streamwise vortex interactions in supersonic flow. Exp Fluids 59(4):67

    Google Scholar 

  • Gutmark E, Schadow K, Yu K (1995) Mixing enhancement in supersonic free shear flows. Annual Rev Fluid Mech 27(1):375–417

    Google Scholar 

  • Hirschel EH et al (2005) Basics of aerothermodynamics. Springer, Berlin

    Google Scholar 

  • Javed A, Rajan N, Chakraborty D (2015) Behaviour of turbulent prandtl/schmidt number in compressible mixing layer. Proc Inst Mech Eng Part G J Aerosp Eng 229(7):1349–1359

    Google Scholar 

  • Kearney S, Beresh S, Grasser T (2003) A filtered rayleigh scattering instrument for gas-phase and combustion temperature imaging. In: 41st Aerospace sciences meeting and exhibit, p 584

  • Kearney S, Beresh S, Grasser T, Schefer R (2004) Filtered rayleigh scattering thermometry in vortex-strained and sooting flames. In: 42nd AIAA aerospace sciences meeting and exhibit, p 1358

  • Kwok F, Andrew P, Ng W, Schetz J (1991) Experimental investigation of a supersonic shear layer with slot injection of helium. AIAA J 29(9):1426–1435

    Google Scholar 

  • Lele SK (1994) Compressibility effects on turbulence. Annual Rev Fluid Mech 26(1):211–254

    MathSciNet  MATH  Google Scholar 

  • Maddalena L, Vergine F, Crisanti M (2014) Vortex dynamics studies in supersonic flow: merging of co-rotating streamwise vortices. Phys Fluids 26:046101

    Google Scholar 

  • Mcmanus TA, Monje IT, Sutton JA (2019) Experimental assessment of the tenti s6 model for combustion-relevant gases and filtered rayleigh scattering applications. Appl Phys B 125(1):13

    Google Scholar 

  • Miles R, Lempert W, Forkey J (1991) Instantaneous velocity fields and background suppression by filteredrayleigh scattering. In: 29th Aerospace sciences meeting, p 357

  • Miles RB, Lempert WR, Forkey JN (2001) Laser rayleigh scattering. Measur Sci Technol 12(5):R33

    Google Scholar 

  • Miller M, Bowman C, Mungal M (1998) An experimental investigation of the effects of compressibility on a turbulent reacting mixing layer. J Fluid Mech 356:25–64

    Google Scholar 

  • Murakami E, Papamoschou D (2000) Mixing layer characteristics of coaxial supersonic jets. In: 6th Aeroacoustics conference and exhibit, p 2060

  • Pan X, Shneider MN, Miles RB (2004) Coherent rayleigh-brillouin scattering in molecular gases. Phys Rev A 69(3):033814

    Google Scholar 

  • Patel RP (1978) Effects of stream turbulence on free shear flows. Aeron Q 29(1):33–43

    Google Scholar 

  • Prandtl L (1942) Bemerkungen zur theorie der freien turbulenz. ZAMM 22(5):241–243

    MathSciNet  MATH  Google Scholar 

  • Reynolds A (1976) The variation of turbulent prandtl and schmidt numbers in wakes and jets. Int J Heat Mass Transfer 19(7):757–764

    Google Scholar 

  • Rudy DH, Bushnell DM (1973) A rational approach to the use of prandtl’s mixing length model in free turbulent shear flow calculations. Technical Report NASA-SP-321

  • Schetz JA, Bowersox RD (2011) Boundary layer analysis. American Institute of Aeronautics and Astronautics, New York

    Google Scholar 

  • Schlichting H, Gersten K (2016) Boundary-layer theory. Springer, Berlin

    MATH  Google Scholar 

  • Seasholtz R, Buggele A, Seasholtz R, Buggele A (1997a) Study of injection of helium into supersonic air flow using rayleigh scattering. In: 35th Aerospace sciences meeting and exhibit, p 155

  • Seasholtz RG, Buggele AE, Reeder MF (1997b) Flow measurements based on rayleigh scattering and fabry-perot interferometer. Opt Lasers Eng 27(6):543–570

    Google Scholar 

  • Seiner JM, Dash S, Kenzakowski D (2001) Historical survey on enhanced mixing in scramjet engines. J Propul Power 17(6):1273–1286

    Google Scholar 

  • Shapiro AH (1954) The dynamics and thermodynamics of compressible fluid flow (vol2). The Ronald Press Company, Technical report

  • Smits AJ, Dussauge JP (2006) Turbulent shear layers in supersonic flow. Springer, Berlin

    Google Scholar 

  • Tenti G, Boley C, Desai RC (1974) On the kinetic model description of rayleigh-brillouin scattering from molecular gases. Can J Phys 52(4):285–290

    Google Scholar 

  • Vergine F, Maddalena L (2014) Stereoscopic particle image velocimetry measurements of supersonic, turbulent, and interacting streamwise vortices: challenges and application. Prog Aerosp Sci 66:1–16

    Google Scholar 

  • Vergine F, Crisanti M, Maddalena L, Miller V, Gamba M (2014) Supersonic combustion of pylon-injected hydrogen in high-enthalpy flow with imposed vortex dynamics. AIAA J Propul Power 31:89

    Google Scholar 

  • Vergine F, Ground C, Maddalena L (2016) Turbulent kinetic energy decay in supersonic streamwise interacting vortices. J Fluid Mech 807:353–385

    MathSciNet  MATH  Google Scholar 

  • Xiao X, Edwards JR, Hassan HA, Culter AD (2006) Variable turbulent schmidt-number formulation for scramjet applications. AIAA J 44(3):593–599

    Google Scholar 

  • Yip S, Nelkin M (1964) Application of a kinetic model to time-dependent density correlations in fluids. Phys Rev 135(5A):A1241

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Aerodynamics Research Center, University of Texas at Arlington, Arlington, TX, 76019, USA

    Vijay Gopal & Luca Maddalena

Authors
  1. Vijay Gopal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luca Maddalena
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vijay Gopal.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gopal, V., Maddalena, L. Systematic errors in mixing measurements using filtered Rayleigh scattering in supersonic flows. Exp Fluids 61, 130 (2020). https://doi.org/10.1007/s00348-020-02956-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00348-020-02956-0

Search

Navigation