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Pore size effect on the wake shear layer of a metal foam covered cylinder at relatively high
Reynolds number
Iman Ashtiani Abdi
Department of Mechanical and Mining Engineering
University of Queensland
St. Lucia, Queensland, Australia
i.ashtiani@uq.edu.au
Mostafa Odabaee, Morteza Khashehchi, Kamel Hooman
Department of Mechanical and Mining Engineering
Unviersity of Queensland
St. Lucia, Queensland, Australia
m.odabaee@uq.edu.au, m.khashehchi@uq.edu.au
, k.hooman@uq.edu.au
Abstract
In this paper, hot-wire anemometry is used to compare
the energy spectra of stream-wise velocity fluctuations on the
wake shear layer of two different metal foam-wrapped tubes (5PPI
& 40PPI) at Reynolds number of 40000 based on outer diameter.
The standard case of cross-flow over a bare tube, i.e. no surface
extension, is also tested as a benchmark. Results show that using
5PPI foam delays the separation and increases the magnitude of
fluctuations inside the wake. However, foams with smaller pores
increase the energy of fluctuations both on and outside the shear
layer compared to the one with larger pore size.
Introduction
The flow around a porous medium is a complex one.
The rate at which flow goes through the pores is not easy to
predict since this flow rate depends on different parameters.
Studies show the flow behaviour around a foam-wrapped tube is
significantly different from the one around a bare tube [1-6].
Nevertheless, being conductive, permeable and having high
surface area, metal foams are appropriate for various thermal
applications such as heat exchanger, heat sink and heat pipes [7,
8]. It is, therefore, of great interest to understand the flow
behaviour around and through the foam. The flow field is linked to
various instabilities that are identified by the Reynolds number,
wake, separated shear layer and boundary layer. Specifically, in
heat exchanger, having a good understanding of the cylinder’s
shear layer size and characteristics is of importance, since increase
in its size is proportional to the whole system’s pressure drop [9,
10]. Bonnet et al. [11] performed experiments on both liquid and
gaseous flows to analyse their permeability into the metal foams.
They correlated the permeability and inertia factor to the pore size.
Bhattacharya et al. [12] formulated a theoretical model to
represent metal foam structure also the results of experiments
shows that the effective thermal conductivity of the foam is highly
dependent on the porosity, however no systematic dependency on
pore density was found. Phanikumar and Mahajan [13] also
performed experiments on metal foams with different pore sizes to
investigate pore size and porosity effect on natural convection in
porous metal foams.
The present study, however, analyses the pore size effect
on the shear layer formation and energy of turbulent fluctuations
on and outside the shear layer by mean of a hot-wire anemometry.
Experimental setup
The experiments are performed in an open loop suction
wind tunnel. The inlet velocity is controlled via a pitot tube. To
decrease the turbulence intensity, a honeycomb containing 1700
cardboard tubes and removable flow smoothing screens are used at
the inlet of the wind tunnel. The contraction is three-dimensional
with a 5.5:1 area ratio. Test section is
. The
schematic of the experiment within the wind tunnel is shown in
Figure 1. In the figure, the stream-wise and transverse directions
are indicated by “X” and “Z” axis, respectively. The free stream
turbulence level of empty test section is calculated to be 0.24% at
10ms
-1
. The experiment is done on 32mm diameter bare tube
covered with 15mm aluminium foam layer of different pore sizes
(5 and 40 PPI). Both foams have the same effective density of 5%.
In addition, a bare cylinder with 62mm diameter is used as a
benchmark case with the same frontal area as the foam-wrapped
tubes. The length of all tubes is 600mm.
Dantec 55P15 single sensor hot-wire probe is used in
this experiment. The probe has 1.25mm long platinum-plated
tungsten wire sensing elements of 5µ diameter and is operated in
constant temperature mode with an over-heat ratio set to 1.8. The
1
June 30 - July 3, 2015 Melbourne, Australia
9
P-01
probe is calibrated in the free stream using Dantec 54T29
reference velocity probe and is mounted to a computer controlled
three-axis traverse system. Velocity fluctuations are acquired at
logarithmic spaced points with a resolution of 50μm on straight
lines normal to the cylinder surface as indicated by the red line in
Figure 1. Measurements started 500μm (0.008D) from the surface
all the way down to a point located 90.532mm (1.46D) far from
the surface on the same normal line to the tube surface. Sufficient
sampling frequency of 25 kHz is used to resolve the smallest
scales and also the sampling lengths are sufficiently long (120 sec)
for statistical convergence. The relatively uncertain maximum
velocity at 95% confidence is calculated to be 0.8%
Figure 1 : Side view of the experimental setup – velocity profile is taken on the red line
Results and discussion
The effect of pore size density (PPI) on the shear layer
of a foam covered tube is studied for inlet velocity of 10m/s.
Figure 2 compares the velocity profiles of the three samples (5, 40
PPI and bare) at θ = 90°. It is clear that the wake size for the foam
covered cylinders is considerably larger than that of the bare case
at the same velocity similar to what reported by Khashehchi el al.
[2]. Moreover, the figure shows the velocity profile inside the
shear layer of the foam covered cylinders follows a different trend
than the bare one. This could be due to the fouling in the media
that blocks the inner pores and the ones near the downstream,
which eventually lead the permeated flow to be redirected; then it
exits from the pores near the surface. This affects the shear layer
by pushing it back from the surface and changing the flow
structures by mixing with the flow inside the inner layer. This
effect is pronounced by decreasing the size of pores. This is
because, the smaller pores size, compared to the bigger pores size,
inject the redirected flow out by higher velocity, and also the
surface of the foam for the case with smaller pore sizes could be
considered as a rough surface that lets the flow to pass over it.
Hence to analyse the shear layer for these cases we need to use
some statistical tools like skewness and turbulence intensity.
Figure 3 and Figure 4 demonstrate the comparison for
the same cases for skewness and turbulence intensity,
consecutively. Both these tools can be used to identify where
shear layer is forming. Skewness is a measure of the symmetry of
the data around the sample mean. A large deviation from unity for
skewness (>> 1 or <<1) shows a non-normal distribution that is
happening near the position of maximum shear. Besides,
turbulence intensity is a scale characterizing the turbulence. A
large value of this number indicates large magnitude of
fluctuations compare to the sample mean. The following equations
are used to calculate skewness and turbulence intensity;
(1)
(2)
Where
is the instantaneous velocity and is the
average velocity. By analysing both Figure 3 and Figure 4, it is
possible to locate and characterize the shear layer. Surprisingly, in
both figures the magnitude of skewness and turbulence intensity at
the position of the maximum shear is significantly different from
those for the bare cylinder. The maximum skewness in the
compared profile for the bare cylinder is 8 times larger than the
foam covered cylinder with 5PPI and 35 times larger than the one
with 40PPI. However, the numerical value of turbulence intensity
for both foam covered cylinders is within the same order of
magnitude yet half of what has been obtained for the bare case.
This is an interesting result indicating that mixing of the injected
flow from the pores and the flow around the cylinder (foam
covered) decreases the skewness of the obtained data which ends
up with more normal distributed results. The pore size is
proportional to the magnitude of skewness. Also, as can be seen in
2
Figure 4, this mixing decreases the magnitude of fluctuations in
the shear layer although for turbulence intensity, the role of pore
size is not significant. Moreover, comparisons show the maximum
shear occurs at Z = 1.6, 3.6 and 5.1 mm away from the surface of
bare tube, foam covered cylinder with 5PPI and 40PPI,
respectively. We use these numbers to compare the energy of the
stream-wise fluctuations on three different points on the velocity
profile at θ = 90° for all three cases. The first point is where the
shear is maximum, the second is where in the skewness peak starts
forming and the last one is 5.7mm from the surface of the cylinder.
Figure 2 : Comparison of normalized velocity profile at θ = 90° at U
i
= 10 m/s
Figure 3 : Comparison of skewness profile at θ = 90° at U
i
= 10m/s
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Figure 4 : Comparison of turbulence intensity profile at θ = 90° at U
i
= 10m/s
Figure 5 and Figure 6 show the energy of stream-wise
velocity fluctuation at the three mentioned points. The former
pertains to the foam covered tube with 5PPI and the latter refers to
the one with 40PPI. Besides, Figure 7, the spectra of stream-wise
velocity fluctuations for the bare tube, is used as a benchmark. To
calculate the power spectra, the velocity time series obtained from
the hotwire is used. Each time series consists of 2
21
points and is
divided into 2
10
segments. For each segment, the local mean
velocity and fluctuation velocities are obtained. Afterward,
Taylor’s frozen-turbulence hypothesis is used and space-for-time
substitution is carried out on the time series
to obtain the
space series . The power spectra for each of the segments, is
the square of the magnitude of the discrete Fourier transfer of
the
. Following [14], the stream-wise power spectra is
obtained by averaging the power spectra over all the segments. It
is worth to note that no filter has been applied to the spectra.
The first observation that can be made is that the bare
tube has the highest magnitude of energy on all the three points on
which the power spectra is calculated. Just ahead of the maximum
shear point the power spectra magnitude for 5PPI foam is 2 orders
and 40PPI 3 orders lower than the bare one. This number is in the
same order for both pore sizes where the maximum shear exists
and is 4 order smaller than the benchmark case. However, in
5.7mm away from the surface, this magnitude is ~ 10
-7
for 5PPI,
~10
-6
for 40PPI and ~ 10
-4
for the bare tube – 5.7mm distance for
the bare case is far away from the shear layer but the same
distance for both foam cases is near the shear layer as seen in
Figure 2. This is an interesting observation, since changing the
pore size doesn’t change the order of magnitude of the
fluctuation’s power on or beyond the shear layer. Moreover, as
expected, this energy starts decreasing by setting back from the
surface of cylinder. Besides, when comparing foams and bare, in
foams the larger frequency range in which the power of
fluctuations remain almost constant (up to almost 1 kHz) is seen.
Moreover, for all the cases there is a large peak at about 8.5 kHz.
However, in 40 PPI case a smaller peak at about 1.5 kHz is also
recognizable. The strange trend inside the boundary layer (the
yellow colour) of the both foam covered tubes is another
remarkable note which could be due to the flow mixing described
earlier.
Further notable observation is that, using foam decreases
the range of fluctuations. As Figure 7 shows for a bare tube, the
range of fluctuation specifically inside the shear layer is
significant, which is not the case for 5 or 40PPI foams. In foam
cases, the plots seems smooth with insignificant fluctuations over
the mean line.
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Figure 5 : Spectra of the stream-wise velocity fluctuations at θ = 90° for the 5PPI foam at U
i
= 10m/s
Figure 6 : Spectra of the stream-wise velocity fluctuations at θ = 90° for the 40PPI foam at U
i
= 10m/s
Figure 7 : Spectra of the stream-wise velocity fluctuations at θ = 90° for the bare cylinder at U
i
= 10m/s
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Conclusion
A Dantec 55P15 single sensor hot-wire probe is utilized
in a low speed wind tunnel to study the effect of the pore size on
the wake shear layer of a metal foam covered tube at relatively
high Reynolds number. Turbulence intensity and skewness as
statistical measures are used to compare the shear layer
characteristics on top of power spectra to measure and analyse the
energy of fluctuations inside and outside the shear layer.
Experiments are conducted on three different cases, a bare tube as
a benchmark and two foam covered tubes with 5 and 40 PPI pore
densities, with the same frontal area as the bare tube. Experiments
are conducted at 10m/s (Re = 40000).
Analysis shows that using the foam with larger pore
sizes delays the separation and increases the magnitude of
fluctuations inside the wake. This is while using the 40PPI foam
increases the energy of fluctuations on and outside the shear layer
considerably. This could be due to the fouling in the media that
blocks the inner pores and the ones near the downstream, which
makes the permeated flow to exit from the pores near the surface.
This pushes the shear layer back from the surface and changes the
flow structures by mixing with the flow inside the shear layer.
References
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analysis of the wake behind a single tube and a one-row tube
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[2] Khashehchi, M., Ashtiani Abdi, I., Hooman, K., and Roesgen,
T., 2014, "A comparison between the wake behind finned and
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