Slowly mixing cylinder in a cone-shaped nozzle
Juergen Linke Æ Peter Neumeyer Æ
Matthias Waechter Æ Joachim Peinke
Received: 24 February 2005 / Revised: 5 March 2007 / Accepted: 5 March 2007 / Published online: 21 March 2007
Abstract We report on a surprising phenomenon in a
turbulent jet setup which uses a cone-shaped nozzle with an
excentric inlet. Inside the nozzle a slowly mixing, rotating
cylinder surface was observed. The speed of mixing on this
cylinder surface is reduced by approximately a factor of 8
compared to the remaining ﬂow ﬁeld of the nozzle. The
phenomenon seems to be independent of the Reynolds
number and the pressure distribution inside the nozzle.
Vortices are fundamental structures in the mechanics of
disordered and turbulent ﬂuids. Their general meaning was
already discovered by Leonardo da Vinci, see for example
Frisch (1995). Later, Richardson’s pioneering work on the
turbulent cascade (Richardson 1922) of vortices built the
basis for today’s understanding of turbulent ﬂuids. Vortices
play a key role especially for the mixing properties of
turbulent structures, ranging from the smallest length scales
at the viscosity limit up to atmospheric phenomenons like,
This article describes the surprising phenomenon of a
non-mixing manifold in a turbulent ﬂow which is observed
in a specialized experimental setup. The laser-induced
etching process (Stephen et al. 2004) under investigation
uses a cone-shaped nozzle to apply etching ﬂuid to the
workpiece. The thermochemical etching reaction is locally
initiated by a laser beam heating the workpiece.
In this setup we have investigated the mixing properties
of a dye added to the inﬂow which gets mixed in the nozzle
chamber. Surprisingly, a cylindric structure of the dye
showed up in the rotating turbulent ﬂow inside the nozzle.
This cylindric structure has an extremely slow mixing
property, and does not depend sensitively on the Reynolds
This contribution is organized as follows. In Sect. 2
we introduce the experimental setup, followed by the
description of the experiments and observations in Sect. 3.
The results are then shortly discussed in Sect. 4.
2 Experimental setup
The experiment was designed to visualize mixing pro-
cesses in a cone-shaped nozzle. For this visualization the
setup of the above-mentioned etching process was rebuilt
from plexiglas (PMMA) in a 10:1 scale. Figures 1 and 2
show the apparatus. The excentric inlet induces a rotating
ﬂow inside the nozzle.
At the nozzle exit velocities between 0.35 and 0.76 m/s
were realized, resulting in nozzle exit based Reynolds
numbers ranging from 7,000 to 15,000. A constant ﬂow
velocity was achieved using an overﬂow basin in an
adjustable height above the nozzle. The water level in the
overﬂow basin was kept constant with an accuracy better
than ±1 mm. Thus a precision of the Reynolds number in the
range of a few percent could be realized. Below the nozzle
and normal to its main axis a plate of plexiglas is placed in a
distance of several centimeters, representing the workpiece.
It should be noted that the distance to this plate had no
fundamental inﬂuence on the phenomenon reported here.
J. Linke Á P. Neumeyer
M. Waechter Á J. Peinke (&)
Institute of Physics, Carl von Ossietzky University of Oldenburg,
Exp Fluids (2007) 42:811–814