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The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field

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Abstract

Three-dimensional density information of a double free air jet was acquired using optical tomography. The projections of the density field were measured using the background oriented schlieren method (BOS). Preceding the free jet measurements, the sensitivity, accuracy and resolution of the BOS method were investigated. The sensitivity depends mostly on the focal length of the lens used, the relative position of the object between camera and background and the smallest detectable shift in the image plane. The accuracy was found to be sufficiently high to apply a tomographic reconstruction process. The resolution is determined by the transfer function of the BOS-method. It is not constant and depends on the size of the interrogation windows used for the cross-correlation-algorithm. The reconstruction of the free jet was computed, using filtered back projection. The reconstructed 3D density field shows with good resolution the typical diamond structure of the density distribution in under-expanded free jets.

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Abbreviations

f :

focal length (m)

g :

overall length of a BOS-set-up (m)

h :

size of an interrogation window

K :

Gladstone–Dale-constant

k :

polar coordinate in the Fourier plane

l :

distance between background and phase object (m)

M :

magnification

m :

distance between camera lens and phase object (m)

n :

index of refraction

p :

pressure (Pa)

R :

gas constant [J/(kg K)]

s :

coordinate in the polar coordinate system (m)

T :

temperature (K)

v px :

shift in the sensor plane (m)

v H :

shift in the background (m)

x, y, z :

Cartesian coordinates (m)

x′, y′:

auxiliary variable (m)

α:

Angle between reference light ray and measurement light ray

ɛ:

Deflection angle of a light ray

θ:

Coordinate in the polar coordinate system

λ:

spatial wavelength (m)

\(\Pi\) :

Window function

ρ:

Density (kg/m³)

\(\varphi_{\text tn }\) :

Angle between light ray and line of sight

References

  • Augenstein E, Leopold F, Richard H, Raffel M (2001) Schlieren techniques in comparison: the background oriented schlieren method versus visualization with holographic filters, 4th international symposium on particle image velocimetry, Göttingen, Germany

  • Kak AC, Slaney M (1988) Principles of computerized tomographic imaging. IEEE Press, New York (1989)

  • Blinkov GN, Fomin NA, Soloukhin MN, Vitkin DE, Yadrevskaya NL (1989) Specle tomography of a gas flame. Exp Fluids 8:72

    Article  Google Scholar 

  • Dalziel B, Hughes GO, Sutherland BR (2000) Whole-field density measurements by ‘synthetic schlieren’. Exp Fluids 28(4):322–335

    Article  Google Scholar 

  • Elsinga E, Oudheusden BW, Scarano F, Watt DW (2004) Assessment and application of quantitative schlieren methods: calibrated color schlieren and background oriented schlieren. Exp Fluids 36(2):309–325

    Article  Google Scholar 

  • Faris G, Byer R (1988) Three-dimensional beam-deflection optical tomography of a supersonic jet. Appl Optics 27(24):5202–5212

    Article  Google Scholar 

  • Formin NA (1997) Speckle photography for fluid mechanics. Springer, Germany pp 195–197

    Google Scholar 

  • Klinge F, Kirmse T, Kompenhans J (2003) Application of quantitative background oriented schlieren (BOS): investigation of a wing tip vortex in a transonic windtunnel. Proceedings of PSFVIP-4, F4097. Charmonix, France

    Google Scholar 

  • Meier G E A (1999) Hintergrundschlierenverfahren, Deutsche Patentanmeldung, DE19942856A1

  • Raffel M, Willert C E, Kompenhans J (1998) Particle image velocimetry: a practical guide. Springer, Germany

    Google Scholar 

  • Meinhart CD, Wereley ST, Santiago JG (2000) A PIV algorithm for estimating time-averaged velocity fields. ASME J Fluids Eng 122(2):285–289

    Article  Google Scholar 

  • Natterer F (1986) The mathematics of computerized tomography. Wiley, USA

    MATH  Google Scholar 

  • Richard H, Raffel M, Rein M, Kompenhans J, Meier GEA (2000) Demonstration of the applicability of a background oriented schlieren (BOS) method. Proceedings 9th international symposium on applied laser techniques to Fluid Mechanics, Lisbon, Portugal

  • Rotteveel St R (1992) Optische Tomographie zur Untersuchung von Zylinderinnenströmungen. VDI Reihe 6 Nr. 278. VDI Verlag, Düsseldorf pp 50

    Google Scholar 

  • Venkatakrishnan L (2004) Density measurements in an axis symmetric underexpandet jet using background oriented schlieren technique, 24 AIAA aerodynamic measurement technology and ground testing conference, paper AIAA 2004–2603, Portland, Oregon

  • Venkatakrishnan L, Meier GEA (2004) Density measurements using background oriented schlieren technique. Exp Fluids 37:237–247, DOI:10.1007/soo348-004-0807-1

    Article  Google Scholar 

  • Nogueira J, Lecuona A, Rodriguez PA (2005) Limits on the resolution of correlation PIV iterative methods. Fundamentals Exp In Fluids 39:305–313, DOI 10.1007/s00348-005-1016-2

    Article  Google Scholar 

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Acknowledgments

Funding from Deutsche Forschungsgemeinschaft under grant Se 1023/3-2 and Ko 1718/6-2 is gratefully acknowledged. The authors gratefully acknowledge one anonymous reviewer’s advice for the simplification of Eq. 8.

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  1. Institute of Turbomachinery and Fluid Dynamics, Leibniz University Hannover, Hannover, Germany

    Erik Goldhahn & Jörg Seume

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  1. Erik Goldhahn
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  2. Jörg Seume
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Correspondence to Erik Goldhahn.

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Goldhahn, E., Seume, J. The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field. Exp Fluids 43, 241–249 (2007). https://doi.org/10.1007/s00348-007-0331-1

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  • DOI: https://doi.org/10.1007/s00348-007-0331-1

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