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Quantitative concentration measurements in a turbulent helium jet using rainbow schlieren deflectometry

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Abstract

Rainbow schlieren deflectometry (RSD) is applied to acquire quantitative concentration measurements in a turbulent environment for the first time. RSD methodology is developed and validated using Rayleigh scattering data available in the literature. Experiments were performed in an initially laminar, momentum-driven helium jet injected into ambient air. Full-field measurements are acquired that span the laminar, transition, and fully turbulent regions of the jet. The RSD results are shown to provide accurate measurements in each region and also confirm the self-similar nature of the fully turbulent jet. Analysis shows that the transition from laminar to turbulent flow occurs across an axial span that decreases with increasing Reynolds number. Experiments with a long exposure time were conducted to evaluate the limitations of hardware averaging of the RSD signal in comparison with software averaging.

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References

  • Abramovich GN, Schindel L (1963) The theory of turbulent jets. MIT Press, Cambridge, MA, pp 3–8

    Google Scholar 

  • Agrawal AK, Wanstall CT (2018) Rainbow schlieren deflectometry for scalar measurements in fluid flows. J Flow Vis Image Processing 25(3–4):329–357

    Article  Google Scholar 

  • Agrawal A, Alammar K, Gollahalli S (2002) Application of rainbow schlieren deflectometry to measure temperature and oxygen concentration in a laminar gas-jet diffusion flame. Exp Fluid 32(6):689–691

    Article  Google Scholar 

  • Al-Ammar K, Agrawal A, Gollahalli S, Griffind (1998) Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium jet. Exp Fluid 25(2):89–95

    Article  Google Scholar 

  • Bracewell RN, Bracewell RN (1986) The Fourier transform and its applications. McGraw-Hill, New York

    MATH  Google Scholar 

  • Buch KA, Dahm WJ (1998) Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. part 2. sc\(\approx\)1. J Fluid Mech 364:1–29

    Article  MATH  Google Scholar 

  • Chen CJ, Rodi W (1980) Vertical turbulent buoyant jets: a review of experimental data. NASA STI/Recon Tech Rep A 80:23073

    Google Scholar 

  • Davis M (1971) Measurements in a subsonic turbulent jet using a quantitative schlieren technique. J Fluid Mech 46(4):631–656

    Article  Google Scholar 

  • Davis M (1972) Quantitative schlieren measurements in a supersonic turbulent jet. J Fluid Mech 51(3):435–447

    Article  Google Scholar 

  • Davis M (1975) Intensity, scale and convection of turbulent density fluctuations. J Fluid Mech 70(3):463–479

    Article  Google Scholar 

  • Dowling DR (1991) The estimated scalar dissipation rate in gas-phase turbulent jets. Phys Fluids A Fluid Dyn 3(9):2229–2246

    Article  Google Scholar 

  • Dowling DR, Dimotakis PE (1990) Similarity of the concentration field of gas-phase turbulent jets. J Fluid Mech 218:109–141

    Article  Google Scholar 

  • Dowling D, Dimotakis P (1988) On mixing and structure of the concentration field of turbulent jets. In: 1st national fluid dynamics conference, p 3611

  • Gardiner W Jr, Hidaka Y, Tanzawa T (1981) Refractivity of combustion gases. Combust Flame 40:213–219

    Article  Google Scholar 

  • Greenberg PS, Klimek RB, Buchele DR (1995) Quantitative rainbow schlieren deflectometry. Appl Opt 34(19):3810–3825

    Article  Google Scholar 

  • Ko H, Kihm K (1991) An extended algebraic reconstruction technique (art) for density-gradient projections: laser speckle photographic tomography. Exp Fluid 27(6):542–550

    Article  Google Scholar 

  • Kolhe PS, Agrawal AK (2009a) Abel inversion of deflectometric data: comparison of accuracy and noise propagation of existing techniques. Appl Opt 48(20):3894–3902

    Article  Google Scholar 

  • Kolhe PS, Agrawal AK (2009b) A novel spectral analysis algorithm to obtain local scalar field statistics from line-of-sight measurements in turbulent flows. Meas Sci Technol 20(11):115402

    Article  Google Scholar 

  • Kwon SJ, Seo IW (2005) Reynolds number effects on the behavior of a non-buoyant round jet. Exp Fluid 38(6):801–812

    Article  Google Scholar 

  • Libby PA (1996) An introduction to turbulence. CRC Press, Florida

    Google Scholar 

  • Mastorakos E, Shibasaki M, Hishida K (1996) Mixing enhancement in axisymmetric turbulent isothermal and buoyant jets. Exp Fluid 20(4):279–290

    Article  Google Scholar 

  • Mistry D, Philip J, Dawson JR, Marusic I (2016) Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet. J Fluid Mech 802:690–725

    Article  MathSciNet  Google Scholar 

  • Papanicolaou PN, List EJ (1988) Investigations of round vertical turbulent buoyant jets. J Fluid Mech 195:341–391

    Article  Google Scholar 

  • Pasumarthi KS, Agrawal AK (2003) Schlieren measurements and analysis of concentration field in self-excited helium jets. Phys Fluid 15(12):3683–3692

    Article  MATH  Google Scholar 

  • Pelliccia-Kraft B, Wattd (2000) Three-dimensional imaging of a turbulent jet using shearing interferometry and optical tomography. Exp Fluid 29(6):573–581

    Article  Google Scholar 

  • Pitts WM (1991a) Effects of global density ratio on the centerline mixing behavior of axisymmetric turbulent jets. Exp Fluid 11(2–3):125–134

    Article  Google Scholar 

  • Pitts WM (1991b) Reynolds number effects on the mixing behavior of axisymmetric turbulent jets. Exp Fluid 11(2–3):135–141

    Article  Google Scholar 

  • Pitts WM, Kashiwagi T (1984) The application of laser-induced rayleigh light scattering to the study of turbulent mixing. J Fluid Mech 141:391–429

    Article  Google Scholar 

  • Prandtl L (1925) Bericht über untersuchungen zur ausgebildeten turbulenz. ZAMM J Appl Mathe Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 5(2):136–139

    Article  MATH  Google Scholar 

  • Richards CD, Pitts WM et al (1993) Global density effects on the self-preservation behaviour of turbulent free jets. J Fluid Mech 254:417–417

    Article  Google Scholar 

  • Singh S, Panigrahi P, Muralidhar K (2007) Effect of buoyancy on the wakes of circular and square cylinders: a schlieren-interferometric study. Exp Fluid 43(1):101–123

    Article  Google Scholar 

  • Su L, Helmer D, Brownell C (2010) Quantitative planar imaging of turbulent buoyant jet mixing. J Fluid Mech 643:59–95

    Article  MATH  Google Scholar 

  • Takano H, Kamikihara D, Ono D, Nakao S, Yamamoto H, Miyazato Y (2016) Three-dimensional rainbow schlieren measurements in underexpanded sonic jets from axisymmetric convergent nozzles. J Therm Sci 25(1):78–83

    Article  Google Scholar 

  • Vasil\(^{\prime }\)ev LA (1971) Schlieren methods. Schlieren methods. Jerusalem, Israel Program; distributed by Keter New York, pp 19–21

  • Vyas A, Mishra B, Agrawal A, Srivastava A (2018) Non-intrusive investigation of flow and heat transfer characteristics of a channel with a built-in circular cylinder. Phys Fluid 30(3):033602

    Article  Google Scholar 

  • Vyas A, Mishra B, Srivastava A (2020) Investigation of the effect of blockage ratio on flow and heat transfer in the wake region of a cylinder embedded in a channel using whole field dynamic measurements. Int J Therm Sci 153:106322

    Article  Google Scholar 

  • Wanstall CT, Agrawal AK, Bittle JA (2017) Quantifying liquid boundary and vapor distributions in a fuel spray by rainbow schlieren deflectometry. Appl Opt 56(30):8385–8393

    Article  Google Scholar 

  • Wanstall CT, Agrawal AK, Bittle JA (2019) Phase boundary detection in transient, evaporating high-pressure fuel sprays by rainbow schlieren deflectometry. Appl Opt 58(25):6791–6801

    Article  Google Scholar 

  • Watanabe T, Sakai Y, Nagata K, Ito Y, Hayase T (2014) Enstrophy and passive scalar transport near the turbulent/non-turbulent interface in a turbulent planar jet flow. Phys Fluid 26(10):105103

    Article  Google Scholar 

  • Watt D, Vest CM (1990) Turbulent flow visualization by interferometric integral imaging and computed tomography. Exp Fluid 8(6):301–311

    Article  Google Scholar 

  • Westerweel J, Hofmann T, Fukushima C, Hunt J (2002) The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet. Exp Fluid 33(6):873–878

    Article  Google Scholar 

  • Westerweel J, Fukushima C, Pedersen J, Hunt J (2005) Mechanics of the turbulent-nonturbulent interface of a jet. Phys Rev Lett 95(17):174501

    Article  Google Scholar 

  • Yildirim B, Agrawal A (2005) Full-field measurements of self-excited oscillations in momentum-dominated helium jets. Exp Fluid 38(2):161–173

    Article  Google Scholar 

Download references

Acknowledgements

This work was performed with support by the Department of Energy, Office of Energy Efficiency and Renewable Energy (EERE) and the Department of Defense, Tank and Automotive Research, Development, and Engineering Center (TARDEC), under Award Number DE-EE0007301.

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  1. The University of Alabama, Tuscaloosa, Alabama, USA

    C. Taber Wanstall, Joshua A. Bittle & Ajay K. Agrawal

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  1. C. Taber Wanstall
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  2. Joshua A. Bittle
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  3. Ajay K. Agrawal
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Correspondence to Ajay K. Agrawal.

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Wanstall, C.T., Bittle, J.A. & Agrawal, A.K. Quantitative concentration measurements in a turbulent helium jet using rainbow schlieren deflectometry. Exp Fluids 62, 53 (2021). https://doi.org/10.1007/s00348-021-03154-2

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  • DOI: https://doi.org/10.1007/s00348-021-03154-2

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