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Density measurements using the Background Oriented Schlieren technique

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Abstract

This paper describes the implementation of a novel technique called Background Oriented Schlieren that can produce quantitative visualization of density in a flow. This technique uses only a digital still camera, a structured background, and inverse tomographic algorithms which can extract two-dimensional slices from a three-dimensional flow. This has been applied to obtain the density field for an axisymmetric supersonic flow over a cone-cylinder model. Comparisons with cone tables show excellent agreement.

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Abbreviations

β :

wave angle

θ :

viewing angle

ρ :

density (kg/m3)

λ :

wavelength (m)

ε :

angle of deflection

D :

diameter of cylinder

f :

focal length of imaging lens

G(λ):

Gladstone-Dale number

j :

\({\sqrt { - 1} }\)

n :

refractive index

M :

Mach number

P :

projection

S :

surface

x :

horizontal distance (along axis of symmetry)

y :

vertical distance

Δy :

image displacement

Δy′:

virtual image displacement

ΔZ D :

half-width of region of disturbance

Z :

horizontal distance (origin on background plane)

∞:

freestream conditions

B:

background

D:

dot pattern

i:

image

s:

surface

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Acknowledgements

This work was supported by a grant from the Aeronautical Research and Development Board Government of India. The technical support of the NAL 0.3m trisonic wind tunnel staff during the imaging is acknowledged. The authors wish to thank the two anonymous referees who helped make the methodology clearer to the reader and user, and the referee who drew the attention to earlier work and current effort along similar lines.

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Authors and Affiliations

  1. Experimental Aerodynamics Division, National Aerospace Laboratories, Bangalore, India

    L. Venkatakrishnan

  2. DLR Institute of Fluid Mechanics, Göttingen, Germany

    G. E. A. Meier

Authors
  1. L. Venkatakrishnan
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  2. G. E. A. Meier
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Correspondence to L. Venkatakrishnan.

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Venkatakrishnan, L., Meier, G.E.A. Density measurements using the Background Oriented Schlieren technique. Exp Fluids 37, 237–247 (2004). https://doi.org/10.1007/s00348-004-0807-1

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