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High-speed cinematography of compressible mixing layers

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Abstract

Experiments are performed using high-speed film cinematography to temporally resolve compressible planar mixing layer structures using shadowgraphs and planar light sheet visualization. The technique is relatively inexpensive and allows multiple images. The time-dependent shadowgraph and Mie scattering images are documented with a rotating mirror camera operating at approximately 350 kHz. The results show the presence of large scale structures in the mixing layer which flatten as they convect downstream. Both spatial and temporal covariances have been obtained through digital image processing which yield, on average, elliptical structures with convective speeds above the isentropic prediction, and non-isotropic streamwise and transverse scalar transport fluctuations.

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Abbreviations

a :

speed of sound

b :

shear layer thickness

C :

covariance of intensity

f :

mixture fraction

I :

intensity

M :

Mach number

M r :

relative Mach number

N * :

number of points considered

r :

droplet radius

Re b :

Reynolds number based on shear layer thickness

t :

time

U :

freestream velocity

U c :

convective velocity

V :

transverse velocity

ΔU :

difference between high-speed and low-speed stream velocities

x :

streamwise distance

y :

transverse distance

db/dx :

shear layer growth rate

λ u :

ratio of low-speed to high-speed velocities

λ ϱ :

ratio of low-speed to high-speed densities

λ γ :

ratio of low-speed to high-speed specific heat ratios

γ :

specific heat ratio

μ :

coefficient of viscosity

ϱ :

density

σ :

jet spreading parameter

c :

convection value, compressible case

0:

incompressible case

1:

high-speed stream

2:

low-speed stream

( )′:

fluctuating component

( ):

averaged component

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Authors and Affiliations

  1. Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, 61801, Urbana, Illinois, USA

    R. Mahadevan & Eric Loth

Authors
  1. R. Mahadevan
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  2. Eric Loth
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Additional information

The authors would like to acknowledge the support provided by the National Science Foundation (NSF) under contract CTS-9010594 with Stephen P. Traugott as Technical Monitor. We gratefully acknowledge Prof. J. C. Dutton for his helpful suggestions while preparing this manuscript. The authors also acknowledge graduate student Robert Frank for the design and fabrication of the test facility, and undergraduate students Robert Hoffenberg for helping in setting up the facility and Jim Guglielmo and Robert Sprenger for help in conducting the Mie scattering experiments.

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Mahadevan, R., Loth, E. High-speed cinematography of compressible mixing layers. Experiments in Fluids 17, 179–189 (1994). https://doi.org/10.1007/BF00190915

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