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Experiments in Fluids

, Volume 43, Issue 2–3, pp 241–249 | Cite as

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

  • Erik GoldhahnEmail author
  • Jörg Seume
Research Article

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.

Keywords

Deflection Angle Density Field Interrogation Window Tomographic Reconstruction Interrogation Window Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

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)

vpx

shift in the sensor plane (m)

vH

shift in the background (m)

x, y, z

Cartesian coordinates (m)

x′, y′

auxiliary variable (m)

Greek symbols

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

Notes

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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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Institute of Turbomachinery and Fluid DynamicsLeibniz University HannoverHannoverGermany

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