Stresa, Italy, 2628 April 2006
?TIMA Editions/DTIP 2006 page ISBN: 2916187030
ANALYSIS OF PACKAGING EFFECTS ON THE PERFORMANCE OF THE
MICROFLOWN
J.W. van Honschoten, D.R. Yntema, M. Dijkstra, V.B. Svetovoy, R.J. Wiegerink, M. Elwenspoek
Transducers Technology Laboratory, MESA
+
Research Institute,
University of Twente, the Netherlands.
ABSTRACT
The packaging effects of an acoustic particle velocity
sensor have been analysed both analytically and by means
of finite volume simulations on fluid dynamics. The
results are compared with acoustic experiments that show
a large magnification of the output signal of the sensor
due to the mounting inside a cylindrically shaped
package. The influences of the package consist of a
decrease of the output signal at frequencies below 1 Hz,
whereas signals with frequencies above 10 Hz are
amplified by a constant factor of approximately
3.5 (11 dB). The analysis leads to an improved insight
into the effects of viscosity and fluid flow that play a role
in flow sensing and opens the way for further
optimisation of sensitivity and bandwidth of the sensor.
1. INTRODUCTION
The ?Microflown? is a micromachined acoustic sensor
that measures the particle velocity instead of the sound
pressure, the quantity that is measured by conventional
microphones [16]. Originally a flow sensor [7], it has
been optimised for sound measurements. The sensor
consists of two or three thin platinum wires (length
1500 ?m, spacing 240 ?m) on a silicon nitride carrier,
that are electrically heated to about 600 K (see fig. 1).
The metal pattern acts as temperature sensor and as
heater. When a particle velocity is present, the
temperature distribution around the resistors is
asymmetrically altered. The temperature difference, and
therefore the resistance difference, between the sensor
wires is proportional to the particle velocity associated
with the sound wave.
For measurement purposes, the sensor is placed in a
package: a 7 cm long cylindrical probe of 13 mm
diameter with two small cylinders of about 5 mm
diameter at its end, with the microflown in between (see
fig. 2). These two tiny cylinders on top protect the
fragile wires of the sensor while the holder contains the
electrical connections. Moreover, this packaging of the
sensor influences also the fluid flow. It improves its
sensitivity by a factor 3.5, or approximately 11 dB. That
observation raised the need for a detailed investigation
of these packaging effects, in order to optimise the
sensor performance further. In this paper, this
investigation is achieved both by a numerical analysis
using a finitevolume simulation program, and by a
theoretical description of the flow profile around the two
small cylinders of the package.
Fig. 1. SEM photograph of a twowire type
?Microflown?.
Fig. 2. The current probe, with the flow sensor packaged
in between two tiny cylinders.
2. NUMERICAL SIMULATIONS
2.1. The approach
For numerical calculations on the complex structure of
the package, we used a commercially available software
J.W. van Honschoten et al.
Analysis of packaging effects on the performance of the Microflown
?TIMA Editions/DTIP 2006 page ISBN: 2916187030
program, CFDRC, for fluid dynamical simulations
[12, 13]. This software provides a variety of tools for the
simulation and analysis of fluid flow. In our approach for
the numerical simulation of the fluid behaviour around
the sensor, three successive steps are to be distinguished.
The volume of interest (the solution space) is divided into
discrete control volumes or cells.
The boundary conditions, the initial conditions and the
equations to be solved at each cell are defined, as well as
the numerical technique to solve the equations.
After the simulation, we extract the needed information
from the large amount of data generated in the solution
process.
The solution space was defined as a cylinder of
approximately 8 cm radius and 15 cm height, in which the
probe was positioned. A structured grid of tetrahedric and
prismatic volume elements was designed in the fluid
space around the probe. The number of cells amounted to
about 70,000; in the middle, around the sensor, the cells
were made very dense.
As a boundary condition, a plane propagating wave was
imposed at the wall of the large outer cylinder. This wave
was described by a varying fluid particle velocity of
magnitude u
0
and radial frequency ? :
)cos(),(
0
kytutyu ?= ? ,
with k the wave number in the propagation direction y.
The Navier?Stokes equations were solved at each fluid
space element, together with the noslip boundary
condition on the probe surface and the assumption of a
fully adiabatic process. Besides, a constant temperature
and constant dynamic viscosity of respectively T = 300 K
and ? = 1.5895?10
5
m
2
/s were assumed, an equilibrium
fluid density of ? = 1.1614 kg/m
3
, and an equilibrium
pressure of p
0
= 1.0?10
5
Pa in the fluid around the probe.
It must be mentioned that the temperature effects of the
sensor, that causes a local temperature increase of the
fluid due to the heated wires, have not been taken into
account. Since this temperature effect is very localised
and will therefore only slightly influence the fluid flow
around it [4, 5], this assumption seems to be justified.
The numerical calculations were performed with a
convergence criterion of 10
4
, using the SIMPLEC solution
method, coupled with ideal gas law [11].
2.2. The fluid flow around the probe
In the different simulations, the frequency ? was varied
between 0 and 10
4
rad/s, and the magnitude u
0
was
chosen as 3?10
5
< u
0
< 1?10
3
m/s. Each simulation result
Fig. 3. A grid containing about 70 thousand cells was
defined to model the probe geometry, very densely
structured at the place of interest (the centre).
Fig. 4. Simulation result visualising both the streamlines
and a contour plot of the particle velocity at v
0
=1 mm/s;
f = 1 Hz.
provided the magnitude and phase of the particle velocity
and the pressure at each point in space, such that the
streamline pattern in the fluid could also be investigated
(fig. 4). It was observed that for the region of interest,
3?10
5
< u
0
< 1?10
3
m/s, all dynamics were linear in u
0
,
i.e. an increase of the amplitude of the imposed acoustic
wave led to an entirely equal increase of all velocities and
pressures in space.
We defined a number of points located in and around the
probe to consider in particular:
Point A is located in between the two small cylinders
(where the sensor is placed).
Point B is found at a distance of 8 cm in front of the
probe (on the outer boundary where the acoustic wave is
imposed).
Point C is located at 6.5 cm left from the centre.
Point D as a reference point for the phase of the wave, at
5 cm above A.
J.W. van Honschoten et al.
Analysis of packaging effects on the performance of the Microflown
?TIMA Editions/DTIP 2006 page ISBN: 2916187030
10
0
10
2
0.5
1
1.5
2
2.5
3
3.5
frequency [ Hz ]
v
no
r
m
al
i
s
ed
curve A
curve C
curve B
Fig. 5a. Amplitude of the particle velocity at different
points in and around the probe. Point A: in between the
two cylinders, B: at large distance in front of the probe,
C: left from the probe, 6.5 mm from the center, D: 3 cm
above A.
0 2 4 6 8 10
0
0.5
1
1.5
2
2.5
3
3.5
4
frequency [ Hz ]
v
n
o
r
m
al
i
s
ed
curve A
curve C
curve D
curve B
Fig. 5b. As fig. 5a, on a linear frequency scale.
When the frequency rises, the particle velocity
(normalised to the value u
0
of the imposed wave) is seen
to increase at both point A and C. One sees in fig. 5 that,
especially at A, a large amplification of the particle
velocity is attained. This magnification approaches a
constant value of about 3.2 for frequencies above 10 Hz.
However, for frequencies below 1 Hz, the normalised
particle velocity at A is smaller than 1, and decreases to
0.1 at zero frequency. The same tendency is observed at
C, a representative point for the region just next to the
probe. The normalised signal increases from 0.2 at 0 Hz
up to 1.7 at 10 Hz and then remains constant. The figures
5a and 5b show this behaviour on a linear and logarithmic
frequency scale. At frequencies below the characteristic
frequency of about f
c
= 1.5 Hz, the (scaled) particle
velocity amplitudes at A and C are lower than one,
whereas for f > f
c
, they increase.
3. THEORY
3.1. Introduction
To describe the flow behaviour around the sensor, the full
Navier?Stokes equations for the threedimensional
geometry should be solved. Due to the complex geometry
of the probe, an exact solution cannot be found. However,
the region of interest is well approximated by two parallel
long circular cylinders, so that the problem becomes
actually twodimensional. Oscillatory viscous flows
around bodies of various shapes have been investigated in
literature, see [8, 9]. We consider an incompressible
viscous fluid with kinematic viscosity ? and density ? in
which two separated parallel cylinders are immersed. At
infinity, the fluid oscillates harmonically, perpendicular
to the plane containing their axes, with a velocity
tu ?cos
0
. We show that this problem can be solved
analytically and an explicit expression for the flow profile
around the cylinders is found. Two regions of interest can
be distinguished: a frequency range ? << ?
c
, in which
viscous effects are dominant and the viscous boundary
layers around the cylinders become large, and a region
? >> ?
c
, where the fluid behaviour approaches that of an
ideal gas.
Besides, we show that for the idealgas case, a solution of
the Navier?Stokes equations for this geometry is formed
by vortices. In the entire description of the total solution,
the contribution of vortices around the cylinders is largely
responsible for the large magnitude of the particle
velocity in between the cylinders at the location of the
sensor; the observed ?package gain?.
3.2. Assumptions and problem definition
To find the flow profile in and around the probe, we have
to solve the equations of motion of a viscous fluid, the
Navier?Stokes equations, for the current geometry. To
determine if the fluid in the case of propagating acoustic
waves can be regarded as incompressible, we considered
the conditions under which the assumption of
incompressibility is justified. It was seen that for normal
sound waves and frequencies well below 10 kHz, for the
current geometry one can describe the gas as
incompressible.
In their most general form the Navier?Stokes equations
for an incompressible fluid then read
vpvv
t
v v
v
v
v
v
v
2
1
)( ?+??=??+
?
?
?
?
(1.)
with v
v
the (vectorial) velocity, p the pressure, ? the
kinematic viscosity and ? the fluid density.
Besides, the continuity equation has to be obeyed:
J.W. van Honschoten et al.
Analysis of packaging effects on the performance of the Microflown
?TIMA Editions/DTIP 2006 page ISBN: 2916187030
0)( =??+
?
?
v
t
v
v
?
?
(2.)
For the threedimensional geometry of the probe it is
rather complicated to solve these equations analytically.
But since the flow profile around the package in which
the sensor is located is of main interest, we consider in
particular the two cylindrical tubes of the package with
the microflown in the middle.
Let us assume an infinite incompressible viscous fluid in
which two parallel circular cylinders of radius R are
immersed. The fluid oscillates in the direction
perpendicular to the plane containing the axes of the
cylinders with velocity tu ?cos
0
at infinity where u
0
is
the magnitude of the particle velocity and ? the radial
frequency. The problem can be well described in a two
dimensional system of bipolar cylindrical coordinates
(?,?), defined by the transformations
0,
coscosh
sin
,
coscosh
sinh
>
?
=
?
= c
c
y
c
x
??
?
??
?
(3.)
where x and y are the usual Cartesian coordinates, 0 ? ? <
2? and ? < ? < ? (see fig. 6).
The two cylinders are therefore defined by ? = ?
1
> 0 and
? = ?
2
< 0, where R = c/sinh?
1
 = c/sinh?
2
. The fluid
region is given by ?
2
< ? < ?
1
, 0 ? ? < 2?, while
0==??
at infinity.
The problem is scaled using the dimensionless parameters
?
?
?
?
?
2
2
,
l
t
l
==
(4.)
where l represents a characteristic length, for example the
cylinder radius.
The Navier?Stokes equations in the form (1.) are non
linear because of the second term on the lefthand side.
This nonlinear problem has been analysed by Zapryanov et
al. [8]. They used a perturbation theory in terms of
asymptotic expansions in the inner and outer regions
around the cylinders [8, 9].
3.3. Solution
For the current values in our problem, u
0
~ 2?10
4
m/s, l ~
6?10
3
m, ? ~ 1.5?10
5
m
2
/s, and ? > 60 s
1
, the nonlinear
convection term is of the order u
0
2
/l and therefore
relatively small compared with the other terms. Hence,
we neglect the term vv
v
v
v
)( ?? in the further approach.
Moreover, we can assume ? >> 1.
The Navier?Stokes equations, (1.), are often written in
y
? =  ?
? = ?
e
?
? = 0 e
?
? = 1 ? =1
. . x
(c,0); ? =  ? (c,0); ? = ?
Fig. 6. Representation of the bipolar cylindrical
coordinate system.
terms of the stream function ? , that in this coordinate
system can be defined by
?
??
?
??
??
?
??
??=
?
??
?= )cos(,)cos( chvchv
(5.)
We now have to solve the equations of motion for ?. For
that purpose the fluid region around the two cylinders is
divided in three regions: the two boundary layers adjacent
to the cylinders, of thickness ? ~ ?
1/2
, and a region in
between. The solution ? in the intermediate region forms
the basis for a perturbation approach with a perturbation
parameter ?, in the boundary layers. We deduced that one
can write for the stream function in this region [10]:
)exp(
))arctan((2exp1
))arctan((2exp
))arctan((2exp1
))arctan((2exp
),(
1
1
1
1
?
?
?
?
?
ix
ixy
c
i
ixy
c
i
ixy
c
i
ixy
c
i
yx
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
+
?
?
+
?
+
?
?
+
=?
(6.)
In the boundary layer adjacent to the right cylinder, a
scaled variable ? is defined:
???? )(
1
?=
(7.)
The boundary layer extends from ? = 0 to ? = 1. The
stream function in this region is ?
b
, and ? is large but
finite. The solution ? in the intermediate region forms the
basis for a perturbation approach with a perturbation
parameter ?, in the boundary layers. One finds then for
the stream function in the boundary layer [10]:
))cos(coshsinh(),(
1
????? ?=? iC
bb
(8.)
with
))cos(coshsinh()cos(cosh
cos)exp(2
)cos(cosh
1coscosh
1
)(
11
1
1
2
1
1
????
??
??
??
?
?
??
?+
?
?
?=
?
?
=
ii
nnn
C
n
b
(9.)
J.W. van Honschoten et al.
Analysis of packaging effects on the performance of the Microflown
?TIMA Editions/DTIP 2006 page ISBN: 2916187030
1
0
1
2
3
4
0
1
2
3
4
4
2
0
2
4
?
x
y
Fig. 7 Stream function ?. Contour lines of ? form
streamlines in the flow.
0 1 2 3 4 5 6
1
1.2
1.4
1.6
1.8
2
av
e
r
ag
ed
v
e
loc
i
ty
?
Fig. 8. The averaged normalised velocity as a function of
the ratio of the cylinder radius and the spacing between
the cylinders.
(? = cylinder radius/distance between cylinders).
In figure 7, the stream function according to eq. (6.) is
visualised, for the halfinfinite region x > 0 and a cylinder
radius R = sinh
1
1. (c = ?
1
= 1). Contour lines of ? form
the streamlines of the flow. With the expression obtained
for the stream function, we can investigate the influence
of the geometry on the velocity at the location of the
sensor. Figure 8 shows the dependence of the flow
velocity between the cylinders as a function of the ratio of
the cylinder radius and the cylinder spacing. A good
correspondence to the simulation results can be seen.
4. EXPERIMENTS
To determine the sensor sensitivity as a function of
frequency, both a packaged and an unpackaged sensor
were placed on a ?shaker? providing a broadband
vibration. It was verified before that the response of the
sensors, when both unpackaged, was identical. The ratio
of the output signal of the packaged and unpackaged
sensor was then measured using an audio analyser.
Results are shown in fig. 9. The signal could be measured
accurately down to frequencies of about 1 Hz.
Fig. 9a. Ratio of the output signal of a packaged and an
unpackaged sensor, as measured in a particle velocity
measurement, for 0 < f < 5 Hz. The squares denote
simulation results.
10
0
10
1
10
2
10
3
10
2
10
1
10
0
10
1
frequency (Hz)
r
a
t
i
o p
a
c
k
aged/
unpac
k
a
g
ed (

)
Fig. 9b. As fig. 9a, for the frequency range 1 < f <
500 Hz. The squares represent simulation results.
For f < 4 Hz, the ratio packaged / unpackaged output
signal is smaller than 1, while for f >>4 Hz, it approaches
3.2, remaining almost constant up to 10 kHz.
5. DISCUSSION
The NavierStokes equations were solved for the stream
function ?, that provides all the information about the
fluid velocity, in the different flow regions around the
cylinders. The solution ? in the intermediate region
formed the basis for a perturbation approach with a
perturbation parameter ?, in the boundary layers.
Analysing the form of ? in eq. (6.), one can recognise
three different elementary plane flow contributions
[13, 14]: a contribution of the uniform flow, a ?doublet?
flow or ?dipole? solution, and a socalled vortex flow. It is
this vortex flow, which has an nonzero circulation along
a contour around each of the cylinders, that is mainly
responsible for the large magnification of the velocity in
J.W. van Honschoten et al.
Analysis of packaging effects on the performance of the Microflown
?TIMA Editions/DTIP 2006 page ISBN: 2916187030
between the cylinders. In between the two cylinders, the
contributions of the two vortices around the two cylinders
are of equal sign and therefore add.
This nonzero circulation along a contour around a
cylinder is also observed in the numerical simulations.
Since the frequency parameter ? = ?l
2
/? is proportional
to the frequency ?, the situation ? ? ? describes the
ideal fluid limit, and we are left with the solution for ? in
the intermediate region; the boundary layer thickness
decreases to zero. For ? small, say ? ~ 1 (a low
frequency, small characteristic length or high viscosity),
the perturbation approach used cannot be applied. In this
frequency range, the numerical simulations supplement
the theoretic analysis. One can determine a certain
characteristic frequency at which the boundary layers
extend over all space between the cylinders. For the
current geometry this frequency is approximately
f
c
? 1.5 Hz. This distinction between low and high
frequencies is important for the acoustic measurement
purposes of the microflown. The aim of the sensor is to
measure frequencies in the acoustic range (from 20 Hz to
10 kHz) while lower frequencies are preferably
suppressed. Experiments show that the current geometry
of the probe magnifies signals higher than, and attenuates
signals lower than, f = 4 Hz (which is in the same order of
magnitude as f
c
).
6. CONCLUSIONS
We have analysed the effects of the package of the
microflown on the velocity profile around the flow
sensor. Numerical simulations show a large magnification
of the particle velocity in between the two small cylinders
of the package where the sensor is mounted, for
frequencies above 4 Hz. The magnification increases up
to approximately 3.2 at high frequencies (10 Hz10 kHz)
and then remains constant. An analytic expression for the
flow profile was also deduced, that explains adequately
the package gain at high frequencies. The existence of
vortices in the fluid flow is mainly responsible for this
magnification. For low frequencies, viscous effects
dominate and signals are attenuated. This is important for
acoustic measurement applications, in which low
frequency noise should be suppressed (to prevent
overburding of the amplifier) and higher frequencies be
amplified. We found a good correspondence between
simulations, theory and experiments. This opens the way
for further optimisation of the package geometry.
7. ACKNOWLEDGEMENT
This research was funded by the Dutch Technology
Foundation (STW).
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