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Measurement of the turbulent diffusivity in the near field of variable density jets using conditional velocimetry

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Abstract

Pulsed laser Mie scattering and laser Doppler velocimetry (LDV), both conditioned on the origin of the seed particles, have been successively performed in turbulent jets with variable density. In the early stages of the jet developments, significant differences are measured between the ensemble average LDV data obtained by jet seeding and those obtained by seeding the ambient air. Careful analysis of the marker statistics shows that this difference is a quantitative measure of the turbulent mixing. The good agreement with gradient–diffusion modelling suggests the validity of a general diffusion equation where the velocities involved are expressed in terms of ensemble conditional Favre averages. This operator accounts for all events (including intermittent ones) and for variations in the density of the marked fluid whose velocity is still specified by the binary origin of the marker.

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Abbreviations

D L :

laminar diffusivity, m2/s

D T :

turbulent diffusivity, m2/s

d :

diameter of the jet nozzle, m

F r :

Froude number

J :

diffusion vector, m/s

k :

global sensitivity of the detection system for one particle (signal level)

N P :

number of seed particles in the probe volume

N P,i :

number of seed particles in sample i

N P (i) :

value of N P in channel i

N B :

number of Doppler bursts

\( {\dot{N}_{{\rm{B}}} } \) :

count rate of bursts, s−1

N v :

number of validated Doppler bursts

\( {\dot{N}_{{\rm{V}}} } \) :

count rate of validated bursts, s−1

N id :

number of ideal particles

N id*:

number of marked ideal particles

P*:

probability that an ideal particle be marked by a seed particle

P(ρz):

probability density function for ρz, m3/kg

\( {P_{{(N_{{\rm{P}}} = k)}} } \) :

probability to have k seed particles in the probe volume

\( {P_{{(N_{{\rm{P}}} = k\left| {\rho z)} \right.}} } \) :

probability of having k seed particle conditioned on a given value of ρz

r :

radial coordinate, m

R ρ :

=ρ (1)/ρ (2), density ratio

S1 :

local signal level with jet seeding

S 1 (1) :

reference signal level in pure stream 1 with jet seeding

s 1 :

= S1/S1 (1), normalized signal

v c :

volumic capacity of the probe volume, m3

V :

velocity vector, m/s

V x :

axial velocity component, m/s

V r :

radial velocity component, m/s

V P :

particulate velocity vector, m/s

V Pj :

velocity vector of particle j, m/s

V Pij :

velocity vector of the jth particle in sample i, m/s

V i :

velocity vector of the marked flow for realization i, m/s

V 1,i :

velocity vector of the flow such it is marked in realization i by particles issuing only from stream 1, m/s

x :

axial coordinate, m

Y i :

local mass fraction of species i

Z :

mixture fraction:local mass fraction of jet fluid

Z i :

mixture fraction for realization i

ρ :

local density, kg/m3

ρ i :

local density for realization i, kg/m3

ρ (1) :

density in stream 1 (density of the jet fluid), kg/m3

τ 1 :

time of flight of jet seed particles to reach the probe volume, s

τ B :

duration of a Doppler burst, s

<A>:

ensemble average of A

Ā:

time average of A

\( {\overline{\overline A} } \) :

Favre average, \( {\overline{\overline A} = {{\overline{{\rho A}} } \over {\overline{\rho } }}} \), (\( {\overline{\overline A} \equiv \tilde{A}} \)) the present notation is only due to printing problems

A″:

Favre fluctuation, \( {{A}'' = A - \overline{\overline A} } \)

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Authors and Affiliations

  1. UMR 6614-CORIA, Site Universitaire du Madrillet, CNRS et Université de Rouen, Av. de l'Université, BP 12, 76801, Saint Etienne du Rouvray, Cedex, France

    D. Stepowski & J. C. Sautet

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  1. D. Stepowski
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  2. J. C. Sautet
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Correspondence to D. Stepowski.

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Stepowski, D., Sautet, J.C. Measurement of the turbulent diffusivity in the near field of variable density jets using conditional velocimetry. Exp Fluids 35, 397–407 (2003). https://doi.org/10.1007/s00348-003-0662-5

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  • DOI: https://doi.org/10.1007/s00348-003-0662-5

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