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Behavior of probability density functions in a binary gas jet

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Abstract

A helium/air mixture free round jet into still air was investigated using a laser Doppler anemometer and a hot-wire type concentration probe. The jet Reynolds number was 4,300 and the jet-to-ambient fluid density ratio was set at 0.64. Simultaneous measurements of the mixture density and the axial and radial velocities were carried out in both the near and far fields of the jet. A detailed analysis of the turbulent mass transfer and jet characteristics has been presented by So et al. (1990). This paper reports on the higher order statistics and the characteristics of the single and joint probability density distributions of the mixture density and the axial and radial velocities. The behavior of these distributions across and along the jet is analyzed and compared with other single and joint probability density distributions.

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Abbreviations

a, b :

constants in beta distribution

c :

instantaneous helium volume concentration

D :

jet nozzle diameter

f, g :

time series of u/U j, ν/U j or ϱ/ϱ a

K u, K ν, K θ, K ϱ :

kurtosis of u, ν, θ, and ϱ, respectively

p(f) :

single pdf of f

P(f,g) :

joint pdf of f and g

r :

radial coordinate measured from jet centerline

Re :

jet Reynolds number, U j D/vj

S u,S ν,S θ,S ϱ :

skewness of u, ν, θ, and ϱ, respectively

u :

instantaneous axial velocity

u′:

fluctuating part of u

U j :

mean jet exit velocity

ν :

instantaneous radial velocity

ν′:

fluctuating part of ν

x :

axial coordinate measured from jet nozzle exit

α :

density ratio parameter \(\left( {{{\varrho _h } \mathord{\left/ {\vphantom {{\varrho _h } {\varrho _a - 1}}} \right. \kern-\nulldelimiterspace} {\varrho _a - 1}}} \right)\)

δ u :

jet half width based on \(\bar U\) profile

δ θ :

jet half width based on \(\bar \theta \) profile

δ ϱ :

jet half width based on \(\bar \varrho \) profile

θ :

instantaneous mixture mass fraction or temperature

θ′:

fluctuating part of θ

ϱ :

instantaneous mixture density

ϱ′:

fluctuating part of ϱ

ϱ j :

mean jet fluid density

σ 1 :

jet density ratio, ϱ j/ϱ a

ν :

fluid kinematic viscosity

a :

air

h :

helium

j :

jet

0:

centerline

-:

time-averaged value

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Author notes

  1. J. Y. Zhu

    Present address: Mechanical Engineering Department, University of California, Irvine, 92717, Irvine, CA, USA

Authors and Affiliations

  1. Mechanical and Aerospace Engineering, Arizona State University, 85287, Tempe, AZ, USA

    R. M. C. So & J. Y. Zhu

  2. Aerospace Engineering Department, Polytechnic University, 11735, Farmingdale, NY, USA

    M. V. Ötügen

  3. David Taylor Research Center, 21402, Annapolis, MD, USA

    B. C. Hwang

Authors
  1. R. M. C. So
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  2. J. Y. Zhu
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  3. M. V. Ötügen
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  4. B. C. Hwang
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So, R.M.C., Zhu, J.Y., Ötügen, M.V. et al. Behavior of probability density functions in a binary gas jet. Experiments in Fluids 11, 227–242 (1991). https://doi.org/10.1007/BF00192749

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