Jens Heinlein Æ Udo Fritsching
Droplet clustering in sprays
Received: 22 April 2005 / Revised: 8 November 2005 / Accepted: 13 November 2005 / Published online: 13 December 2005
Ó Springer-Verlag 2005
Abstract In this contribution, the spatial particle distri-
bution in sprays of diﬀerent atomizers is analyzed.
Steady and unsteady particle structures are identiﬁed by
evaluating the interparticle arrival time statistics at a
certain position, which is the time increment between
two succeeding particles. In addition to its characteris-
tics of size and velocity, each particle exhibits an indi-
vidual interparticle arrival time that is used to identify
unsteady characteristics in the ﬂow. Unsteadiness in
sprays is thereby of interest for several reasons and in
several applications, for example, in the combustion
industry. A typical example of an unsteady spray
behaviour is droplet clustering which can be caused, for
example, by pulsating liquid disintegration procedures
or particle interaction with large-scale eddy structures in
the gas. The aim of the investigation is the analysis of
such unsteady spray conditions. The evaluation of spray
unsteadiness is done by means of point wise and time
resolved PDA measurements in the spray of a pressure
and twin-ﬂuid atomizer, respectively.
Dispersed gas/particle ﬂows often are characterized ei-
ther in their global structure or at a single point in time
or space. For the global ﬂow structure, such a descrip-
tion provides information such as a measure of the local
number concentration or ﬂux rate. Particle measurement
techniques such as the Phase Doppler anemometry are
capable of obtaining times series information in dis-
persed two-phase ﬂows also. In this context, Edwards
and Marx (1995a, b) developed a multipoint statistical
description of a dispersed ﬂow. Based on this theoretical
framework, it is possible to distinguish between steady
and unsteady dispersed structures by using the inter-
particle arrival time, s. Steady dispersed ﬂows are de-
ﬁned as those whose interparticle arrival time
distributions obey inhomogeneous Poisson statistics.
Conversely, unsteady dispersed ﬂows are deﬁned as
those whose interparticle arrival time distributions do
not obey inhomogeneous Poisson statistics.
An example of unsteady behaviour is droplet clus-
tering in sprays, which is of interest for several reasons,
for example, in the combustion industry, where prob-
lems are related to the unsteady ﬂow of fuel into and
through the combustion chamber. In recent years, sev-
eral experimental and numerical investigations have
been made on unsteadiness in dispersed two-phase ﬂows.
Zimmer (2002), for example, investigated the droplet
dynamics and fuel concentration proﬁles with and
without combustion by means of planar laser methods.
Furthermore, Luong and Sojka (1999) showed that in
the spray of an eﬀervescent atomizer, only droplets
within a certain diameter range exhibit unsteady
behaviour while other droplets are incapable of follow-
ing the turbulent ﬂow. Their results indicate that eﬀer-
vescent atomization is an inherently unsteady process.
Rouson and Eaton (2001) showed by means of a direct
numerical simulation that two extremes exist in dis-
persed particles’ response to turbulence. Their results
indicate that high-stokes-number particles respond to so
little of the spectrum of turbulent eddies that their mo-
tion lacks coherent mechanisms for non-random clus-
tering. Low-stokes-number particles act as ﬂow tracers.
Their mean spacing is ﬁxed by the continuity constraint,
so, they are precluded from clustering near a point.
Between these two extremes exists a range of stokes
number within which particles respond to some eddies
but not to others. One expects these particles to prefer-
entially concentrate in certain ﬂow structures.
In this context, the relevance of droplet clustering
eﬀects is studied within the spray cones of two diﬀerent
kinds of atomizers, namely a pressure atomizer and a
J. Heinlein Æ U. Fritsching (&)
Department of Chemical Engineering, University of Bremen,
Badgasteiner Str. 3, 28359 Bremen, Germany
Experiments in Fluids (2006) 40: 464–472