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Optical measurement of velocity and drag coefficient of droplets accelerated by shock waves

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Abstract

The drag coefficient of micron-sized droplets accelerated by a shock wave has been investigated. The motion of the droplets was studied by an optical measurement system, and an inertial relaxation in the mist flow is discussed in detail. An expansion-shock tube was employed in the present experiment, in which water droplets were produced by a homogeneous condensation when humid nitrogen gas expanded adiabatically in the test section. The local mean diameter and local number density of the droplet cloud were 1.0 μm and on the order of 1012 particles/m3, respectively, as estimated using a light scattering measurement in a preliminary experiment. The droplet cloud accelerated behind a shock wave was observed using a direct shadowgraph method with a spatial filter. Since the intensity of transmitted light through the mist flow is a function of the radius and number density of droplets, we can obtain the locally averaged number density distribution under an adequate approximation. The transmitted light intensity was related to the velocity distribution of droplets under the adequate assumption. So, the acceleration of droplets was estimated from the velocity ratio between the droplets and gas flow. Then, the drag coefficient was calculated for the particle Reynolds number. The experimental result was also compared to a numerical prediction.

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Abbreviations

C D :

Drag coefficient

D p :

Drag force

I :

Light intensity

K :

Logarithmic light extinction rate

Kn :

Knudsen number

M p :

Rate of mass transfer

M S :

Incident shock Mach number

M r :

Relative flow Mach number

N :

Number density of droplets

Pr :

Prandtl number

Q p :

Rate of heat transfer

R :

Gas constant

Re p :

Particle Reynolds number

T :

Temperature

T′:

Interface temperature between the droplet and ambient gas

U :

Velocity in shock fixed frame

We :

Weber number

a :

Acceleration

h :

Enthalpy

l :

Width of test section

m :

Mass of a droplet

p :

Pressure

p s :

Saturation pressure

q :

Condensation coefficient

r p :

Radius of droplet

u :

Velocity in laboratory frame

t :

Time

α :

Particle size parameter

δ :

Mean free path

ρ :

Density

κ :

Heat conductivity

λ :

Light wave length

μ :

Viscosity

σ sca :

Scattering cross section

ς :

Surface tension stress

g:

Gas

p:

Droplet

1:

Upstream of shock wave

2:

Downstream of shock wave

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Acknowledgements

The authors are grateful to Mr. H. Kubota, a student of the Graduate School of Science and Engineering, Saitama University, Japan for his helpful assistance. This study was supported by a Grant-in-Aid for Scientific Research (no. 09450073) from the Ministry of Education of Japan.

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  1. Faculty of Engineering, Saitama University, 255 Shimo-Okubo, Sakura, Saitama, 338-8570, Japan

    H. Hirahara & M. Kawahashi

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  1. H. Hirahara
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  2. M. Kawahashi
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Correspondence to H. Hirahara.

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Hirahara, H., Kawahashi, M. Optical measurement of velocity and drag coefficient of droplets accelerated by shock waves. Exp Fluids 38, 258–268 (2005). https://doi.org/10.1007/s00348-004-0907-y

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