ETH Library
Vortex shedding from confined
micropin arrays
Journal Article
Author(s):
Renfer, A.; Tiwari, M. K.; Meyer, F.; Brunschwiler, T.; Michel, B.; Poulikakos, D.
Publication date:
2013
Permanent link:
https://doi.org/10.3929/ethz-b-000070649
Rights / license:
In Copyright - Non-Commercial Use Permitted
Originally published in:
Microfluidics and Nanofluidics 15(2), https://doi.org/10.1007/s10404-013-1137-5
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RESEARCH PAPER
Vortex shedding from confined micropin arrays
Adrian Renfer
•
Manish K. Tiwari
•
Ferdinand Meyer
•
Thomas Brunschwiler
•
Bruno Michel
•
Dimos Poulikakos
Received: 27 September 2012 / Accepted: 7 January 2013 / Published online: 23 January 2013
Ó Springer-Verlag Berlin Heidelberg 2013
Abstract The hydrodynamics in microcavities populated
with cylindrical micropins was investigated using dynamic
pressure measurements and fluid pathline visualization.
Pressure signals were Fourier-analyzed to extract the flow
fluctuation frequencies, which were in the kHz range for
the tested flow Reynolds numbers (Re) of up to 435. Three
different sets of flow dependent characteristic frequencies
were identified, the first due to vortex shedding, the second
due to lateral flow oscillation and the third due to a tran-
sition between these two flow regimes. These frequencies
were measured at different locations along the chip (e.g.
inlet, middle and outlet). It is established that vortex
shedding initiates at the outlet and then travels upstream
with increase in Re. The pathline visualization technique
provided direct optical access to the flow field without
any intermediate post-processing step and could be used
to interpret the frequencies determined through pressure
measurements. Microcavities with different micropin
height-to-diameter aspect ratios and pitch-to-diameter
ratios were tested. The tests confirmed an increase in the
Strouhal number (associated with the vortex shedding) with
increased confinement (decrease in the aspect ratio or the
pitch), in agreement with macroscale measurements. The
compact nature of the microscale geometry tested, and
the measurement technique demonstrated, readily enabled
us to investigate the flow past 4,420 pins with various degrees
of confinements; this makes the measurements performed
and the techniques developed here an important tool for
investigating large arrays of similar objects in a flow field.
Keywords Flow pathline visualization Microscale flows
Vortex shedding Strouhal number Confinement effect
1 Introduction
Hydrodynamics of flow past obstacles confined in micro-
cavities is relevant to a variety of microfluidic applications
such as microfluidic memory and control elements (Gro-
isman et al. 2003), micro-reactors (Moghtaderi 2007),
electronics cooling (Renfer et al. 2011) and microporous
media (Sen et al. 2012). From the fluidics point of view,
flows past such micropin arrays are particularly interesting.
Unlike flow through a microchannel, where hydrodynamic
transition from laminar to turbulent flow occurs at rela-
tively high Reynolds numbers (Re), a complex flow tran-
sition in confined micropin arrays triggers unstable flow
phenomena even at low Re. The understanding of the fluid
dynamics in micro-total analysis systems (lTAS) and in
Electronic supplementary material The online version of this
article (doi:10.1007/s10404-013-1137-5) contains supplementary
material, which is available to authorized users.
A. Renfer M. K. Tiwari F. Meyer D. Poulikakos (&)
Department of Mechanical and Process Engineering,
ETH Zurich, 8092 Zurich, Switzerland
e-mail: dimos.poulikakos@ethz.ch;
dimos.poulikakos@sl.ethz.ch
A. Renfer
e-mail: arenfer@ethz.ch
M. K. Tiwari
e-mail: mtiwari@ethz.ch
F. Meyer
e-mail: maxmeyer@student.ethz.ch
T. Brunschwiler B. Michel
Advanced Thermal Packaging, IBM Research-Zurich,
8803 Rueschlikon, Switzerland
e-mail: tbr@zurich.ibm.com
B. Michel
e-mail: bmi@zurich.ibm.com
123
Microfluid Nanofluid (2013) 15:231–242
DOI 10.1007/s10404-013-1137-5
fluid based microelectromechanical systems (MEMS)
relies on the advances in microscale flow visualization and
characterization to improve the device efficiency (Osman
et al. 2012). Also within the growing field of lab-on-chip
applications it is important to understand the detailed flow
distribution in microchannel networks (Gunther and Jensen
2006). Flow visualization in microfluidic systems is clearly
emerging as an interdisciplinary technology driving sci-
entific achievements in various research fields, such as
single-cell biomechanical perfusion systems (Rossi et al.
2009), microscale pumping technologies (Nabavi 2009),
mass transfer enhancement using chemical micro-mixers
(Hoffmann et al. 2006; Chung et al. 2004), mixing of fluids
in microchannels (Stroock et al. 2002) and cooling of 3D
integrated electronics (Renfer et al. 2011) to name but a
few. With respect to the latter, there is a clear impact of
fluid dynamics on heat transfer in integrated devices: with
the advancing miniaturization of high power density elec-
trical devices, liquid based cooling solutions will become a
conceivable strategy in the near future. Especially, for
compact systems as concentrated photovoltaics, power
amplifiers and integrated circuits, the fluidics and related
cooling at the microscale and nanoscale are becoming a
crucial technology to further improve their performance.
To exemplify, the concept of integrated water cooling has
received much attention (Brunschwiler et al. 2009; Dang
et al. 2010; Alfieri et al. 2012). Given the clear coupling of
thermal transport with fluidics, the investigation of the
detailed flow behavior is of paramount importance.
Whereas numerous studies are devoted to macroscopic
cylinder arrays (Ziada 2006; Sweeney and Meskell 2003),
fluidics aspects involved in the corresponding microscale
analog of flow past cylindrical arrangements have rarely
been addressed in the literature. The compact nature of the
microfluidic geometry allows fitting, several thousands of
confined micropins in a small area. Such high numbers are
unparalleled compared to macroscopic tube bundles, which
also do not contain the confinement effect of their micro-
scopic counterparts. Our results herein show that large
micropin arrays furnish transient effects and multiple flow
fluctuation frequencies. Flow fluctuations in macro-flow
geometries are measured by means of hot-wire and Laser
Doppler Anemometry (LDA) techniques that require either
direct contact of the probe with the flow or sufficiently
large optical access. Visualization methods in general
require high intensity light sources and fast charge coupled
device (CCD) cameras to capture the fluid dynamics with a
high temporal resolution. This is required since vortex-
induced flow field fluctuations in tube arrays range from a
few Hz up to several hundreds of Hz.
For the hydrodynamic investigation of flow through
micropin arrays, on the other hand, standard experimental
techniques cannot be applied. Therefore, the development of
novel measurement approaches that are specifically targeted
to microfluidics is clearly warranted. The frequency of vor-
tex shedding in micropin arrays is one order of magnitude
higher compared to the macroscopic pendant and in combi-
nation with the inevitably low illumination conditions
in microstructures, direct observation of unsteady flow
processes remains challenging. Even state-of-the art micro-
particle image velocimetry (lPIV), one of the most sophis-
ticated visualization techniques for microscale flows, is
unable to resolve the full dynamic picture of kHz frequency
flow fluctuations. The two-frame cross-correlation technique
in lPIV resolves flow processes with a high temporal reso-
lution in the microsecond time scale to instantly freeze flow
fluctuation patterns in microcavities (Natrajan and Chris-
tensen 2010; Renfer et al. 2011). The limitation, however, is
given by the slow repetition frequency of a few Hz for state-
of-the art intensified CCD cameras and consequently the
unsteady dynamics of the flow cannot be captured. Use of
dynamic pressure sensors is an attractive option to capture
the flow fluctuation frequencies and the corresponding
dynamics. However, contrary to large scale tube bundle
measurements, microscale flow fluctuations introduce only a
small disturbance to the pressure oscillations that are also
inevitably present in any external pump driven flows.
Therefore, an accurate and systematic experimental meth-
odology needs to be developed to distinguish the fluidic
fluctuations from the system noise.
Based on the above, the flow visualization and quantitative
assessment of the microfluidics involved in flow past con-
fined arrays of micropins is the main focus of our work. To
this end, first the measured dynamic pressure helped quantify
the vortex-induced fluctuations; the frequency of flow fluc-
tuations was established to be in the kHz regime. In addition,
to corroborate the results from the pressure sensor, a new
large field-of-view optical technique is introduced to visual-
ize unsteady microscale flows. The technique relies on using
scattered light from the seed particles in the flow and is
realized by modifying a commercial lPIV setup. The tech-
nique enabled us to accurately capture the flow fluctuation
and vortex dynamics in flows past confined arrays of micro-
pins. Consequently, the flow fluctuation frequency was
determined independently through dynamic pressure mea-
surements including frequency domain analysis of the pres-
sure signal and flow field analysis. A good agreement was
obtained between the flow fluctuations of visualization and
pressure measurements. Our investigation provides a new
way to investigate unsteady flows in microfluidic systems
with fluctuation frequencies up to tens of kHz. While the
focus of this work is entirely on the fluidic aspect of vortex
shedding and flow fluctuations in basic arrays of microscale
geometries, the presented microfluidic chips could simulate
the fluidic behavior a single layer in interlayer cooling
structures for three-dimensional electronic chip stacks.
232 Microfluid Nanofluid (2013) 15:231–242
123
2 Experimental section
2.1 Microfluidic chip fabrication
The microfluidic chips were prepared using standard
micro-fabrication techniques. Figure 1a and b shows the
pictures and the schematics of the chips used in the study,
respectively. The cylindrical micropins as well as the fluid
ports were etched into silicon with deep reactive ion
etching (DRIE) followed by anodic bonding of a 500 lm
thick glass plate to the top of the chip to seal the cavity.
The glass plate allowed optical access for flow visualiza-
tion. The resulting microfluidic chip cavity was square
shaped in top-view (10 9 10 mm
2
) and two different chip
cavity heights of 200 and 100 lm were tested. The chip
had four pressure ports located along the cavity edge at 0,
1, 5, and 10 mm in flow direction (see Fig. 1a). However,
for our measurements only two ports were used to inves-
tigate the pressure fluctuations along the flow direction.
The port at 1 mm was used to measure the pressures at the
chip inlet and outlet (by reversing the flow direction), and
the port at 5 mm was used for the measurement in the
middle of the chip. The pressure ports were all identical
and reached into the cavity as shown in the scanning
electron microscope (SEM) image in the inset of Fig. 1a.
The chip cavity was connected to a water tank using two
rectangular 1 9 10 mm
2
inlet and outlet slots.
In total, three different cavity designs with 1,250–4,420
pins in the flow area of the chip were used as shown in
Fig. 1b. The first geometry was a fully populated micropin
cell with equal transversal and longitudinal pitch
(p = p
t
= p
l
); with a pin pitch of 150 lm and a pin
diameter d = p/2. The second set of geometries was a half
populated cell arrangement of pins with the same trans-
versal pitch p
t
= 200 lm but different longitudinal pitch
(p
l
= 300 lm and p
l
= 400 lm, respectively); both with a
pin diameter of 100 lm(d = p
t
/2). For the half populated
cell, the larger longitudinal pitch reduces the pin density in
flow direction.
2.2 Measurement method and experimental conditions
Given the low amplitude of the pressure fluctuations in
flow past micropins, it was crucial to minimize external
flow fluctuations to improve the overall signal quality in
micropin arrays.
With a home-built pressure-driven flow loop, pump-
induced flow fluctuations were almost completely avoided
resulting in a highly stable flow rate (±0.5 %, up to
260 ml/min). The flow was measured with a Cubemass
DCI Coriolis flow meter (Endress ? Hauser, Switzerland)
with an accuracy of 0.1 %. The frequency signals were
recorded with a dynamic pressure quartz sensor (Kistler,
Switzerland) connected to the pressure ports for local
pressure sensing and in contact with the chip cover glass
for a global measurement (sensor diameter 9.5 mm),
respectively (see Fig. 2a). The natural frequency of the
dynamic pressure sensor given by the manufacturer is
around 70 kHz, which permitted frequency measurements
up to *25 kHz (*1/3 of the natural frequency). The
signals were low-pass filtered, at 30 kHz, for anti-aliasing,
before recording at a sample rate of 100 kHz to fulfill the
Nyquist criterion. Fast Fourier transformation (FFT) was
used to express the time series in the frequency domain to
analyze the dominant frequencies. With a total sampling
time of 500 ms, a frequency resolution of 2 Hz is
achieved. Since the flow fluctuation frequency regime
investigated ranges from 3 to 14 kHz, the relative fre-
quency resolution of the signal acquisition system is
\0.07 %. Each frequency peak for a given Reynolds
number was calculated by averaging 20 data sets in the
frequency domain; each calculated from the FFT of the
pressure signal acquired over a time interval of 500 ms.
This results in a flow fluctuation frequency peak obtained
over a time period of 10 s. There was a readout delay of
*1 s between individual 500-ms data sets. Averaging
multiple frequency signals reduces random noise and only
frequencies stable in time will withstand such an ensem-
ble signal conditioning, thereby improving the signal to
noise ratio.
Figure 2b shows the fluid loop and the optics used for
flow visualization. In the visualization experiments, the
flow was driven with a magnetically coupled gear pump
(Fluidotech, Italy) and the flow rate was measured with a
laminar pressure gradient flow sensor (range: 0–500 ml/
min, full scale accuracy of 2 %, Omega, USA). The optical
setup consisted of an epifluorescent microscope system
used for lPIV (FlowMaster Mitas, LaVision, Goettingen,
Germany) with a modified sample illumination to image
Fig. 1 a Photograph and SEM image of the microfluidic chip with
the pressure ports and inlet/outlet slots indicted. b Schematic of the
chips with fully and half populated micropin arrays. The different
pitch values used are also shown (top) with an SEM image of the
micropins in the flow cavity (bottom)
Microfluid Nanofluid (2013) 15:231–242 233
123
the light scattered by particles seeded into the flow. By
altering the exposure time of the camera, the pathlines of
the seeded particles could be recorded. The micropin
array chips were placed on the x–y–z stage of the setup to
change the location of the observed (focused) area. Seeding
the flow with silver-coated polystyrene particles (4.2 lm
in diameter, microparticles GmbH, Berlin, Germany)
enhanced the scattering intensity compared to non-reflec-
tive particles. The tracer particles were illuminated with a
continuous 532 nm DPSS Nd:YAG laser (300 mW, Crys-
taLaser, Reno, USA) and the scattered light was recorded
with a 2,048 9 2,048 pixel intensified CCD camera. A 59
microscope objective (NA = 0.16) was used providing a
quadratic 1.2 mm
2
field-of-view. The grayscale visualiza-
tion images were rescaled with a green color scale for
better visibility of the pathlines. With the pathline visual-
ization technique it is possible to visualize the trajectory of
a tracer particle and, therefore, the fluid path is seen
directly without any intermediate correlation method,
which, in contrast, is required for lPIV. In addition, to
produce qualitative flow patterns, the tracer particle density
can be significantly lowered to reduce the measurement
complexity (e.g. mitigation of clogging). All measurements
were conducted at room temperature with de-ionized (DI)
water as the working fluid.
2.3 Frequency validation
Three distinct procedures were used to ensure the accuracy
and validate the frequency results obtained using pressure
measurements and visualization of flow fluctuations in a
micropin array. The latter investigation will be presented in
Sect. 3.
The pressure sensor calibration ensures an accurate fre-
quency read-out including signal conditioning. Figure 3a
shows the FFT spectrum of the signal from the pressure
sensor fitted to a vibration exciter (type 4809, Bru
¨
el & Kjær,
Bremen, Germany) with a fundamental natural frequency of
10 kHz. The sensor signal was acquired with the presence
of the adapter (needed for local port pressure measurements
as seen in Fig. 2a) to simulate actual experiments. The
sharp frequency peak at 9.9996 kHz with a full width at half
maximum (FWHM) of 3 Hz (inset in Fig. 2a) establishes
the good accuracy of the pressure sensor including the
signal conditioning procedure. The peak at *20 kHz is the
second harmonic of the exciter.
In the flow regime investigated, vortex-induced pressure
fluctuations are expected to be a linear function of the
Reynolds number, resulting in a constant Strouhal number.
Therefore, hydrodynamic frequencies can be distinguished
from the inevitably present structural resonant frequencies
of the chips by changing the flow rate. The presence of
structural vibration was confirmed by performing separate
measurements on chips with microchannels filling the
microcavity. Unlike in the case of micropin arrays, we do
not expect to observe any vortices in the microchannel
configuration. This fact can serve as an additional confir-
mation to the frequency measurements reported for flow
past micropin arrays. Therefore, global vibration mea-
surements (see Fig. 2a) were conducted with a micro-
channel chip (p = 200 lm, h = 200 lm). As expected, the
results presented in Fig. 3b only show the structural fre-
quencies that lack any dependence on Re, which is a unique
feature of the hydrodynamic frequencies recorded from
micropin chips (discussed below). Within the measurement
error, Fig. 3b only captures two modes of the structural
Fig. 2 a Local and global
sensing modes were applied to
measure the fluctuating pressure
of micropin cavities.
b Schematic of the particle
scattering flow visualization
system with the microfluidic
chip connected to a water loop
234 Microfluid Nanofluid (2013) 15:231–242
123