Proceedings of HT05
2005 Summer Heat Transfer Conference
July 17-22, 2005 Westin St. Francis, San Francisco, CA, USA
HT2005-72766
THE WAKE BEHAVIOR BEHIND A HEATED CYLINDER IN FORCED AND MIXED
CONVECTION REGIMES
Hu, H.*
Department of Aerospace Engineering
Iowa State University, Ames, Iowa 50011
Email: huhui@iastate.edu
ABSTRACT
The effect of buoyancy on the wake instability of a heated
circular cylinder in a contra flow arrangement is investigated
experimentally in the present study. A novel optical diagnostic
technique, Molecular Tagging Velocimetry and Thermometry
(MTV&T), was used for qualitative flow visualization and
quantitative simultaneous measurements of velocity and
temperature fields in the wake of the heated cylinder. The
experiment was conducted in a water channel with the
temperature and Reynolds number of the approaching flow
being held constant at T∞ = 24 oC and Re = ρ ∞U ∞ D / µ ∞ = 130 .
The temperature of the heated cylinder varied between
o
24 o C (unheated cylinder) and 85 C , corresponding to a
Richardson number (Ri) varying between zero (unheated) and
unity. The heat transfer process around the heated cylinder
changes from the forced convection regime to the mixed
convection regime. With increasing Richardson number,
significant modifications of the wake instability were revealed
from both qualitative flow visualization images and quantitative
simultaneous velocity and temperature fields. The effect of
buoyancy on the wake instability of the heated cylinder was
discussed in the terms of vortex shedding pattern, vortex
shedding frequency, turbulent heat flux distribution, the wake
closure length and averaged Nusselt number of the heated
cylinder.
INTRODUCTION
An understanding of the flow around a bluff body is of
great importance due to its fundamental nature as well as many
related engineering applications. A circular cylinder is a most
commonly studied bluff body. Despite of its simple shape, a
circular cylinder generates a wake that is dynamically complex.
By varying the Reynolds number, a variety of flow patterns and
Koochesfahani, M. M.
Department of Mechanical Engineering
Michigan State University
East Lansing, Michigan 48824
vortex shedding characteristics in the wake of a circular
cylinder have already been observed and discussed in literature.
The wake behavior behind a heated circular cylinder is
physically more complicated due to the buoyancy effect added
to the viscous phenomena. The heat transfer from the surface of
a heated cylinder to surrounding fluids can be either pure
forced convection, free convection or mixed convection
depending on the Richardson number ( Ri = Gr / Re 2 ) of the
case. In the forced convection (Ri<<1) regime, where the effect
of buoyancy is neglected, the heat transfer is a function of
Reynolds (Re) number and the Prandtl (Pr) number. In free
convection (Ri>>1) regime, where the forced convection is
negligible, the heat transfer is a function of the Grashof (Gr)
number and the Prandtl ( Pr = ν / a ) number. In the mixed
convection regime, both forced convention and free convection
are important, and the heat transfer is a function of the Grashof
number ( G r = gβ (Tw − T∞ ) D3 / ν 2 ), the Reynolds Number (Re),
the Prandtl number and the forced flow direction. Despite the
fact of that mixed convection around bluff bodies is of great
importance for various engineering applications (for example,
electronics cooling, compact heat exchangers, etc. ), the
thermal effect (buoyancy effect) on the wake stability of a bluff
body in mixed convection regime has received little attention
compared to that in forced convection regime.
When a heated cylinder operates in mixed convection
regime, buoyancy force plays an important role to the flow
pattern in the wake of a heated cylinder. As shown in Fig. 1, for
a horizontal heated cylinder, the forced flow approaching to the
heated cylinder can be either horizontal, parallel (vertically
upward) or contra (vertically down) depending on the angle
between the buoyancy force acting on the fluid around the
heated cylinder and the approaching flow direction.
* Author to whom all correspondence should be addressed.
1
Copyright © 2005 by ASME
contra
flow
gravity
direction
buoyancy force
direction
horizontal
heated cylinder
Tc > T∞
parallel
flow
Fig. 1. Schematic of approaching forced flow arrangements
around a heated cylinder
Most of the earlier studies about heated cylinders in mixed
convection regime were focused on the determination of the
global effect of thermal induced flows on the heat transfer
coefficients compared with those in forced convection regime.
It turned out that the heat transfer coefficient was influenced
considerably by the thermal induced flow when the Richardson
number is larger than a critical value. It was also found that the
value of the critical Richardson number changes with the angle
between the buoyancy force and the approaching forced flow
direction. Oosthuizen and Madan [1,2] studied a heated circular
cylinder placed in a horizontal, parallel and contra flow of air
as well as 135 degrees with respect to gravity force. They gave
the following critical Richardson numbers, and suggested that
above these critical Richardson numbers the heat convention
would transit from forced convection to mixed convection.
Parallel flow
Ri > 0.10
Horizontal flow
Ri > 0.53
135 degrees
R i > 0.04
Contra flow
R i > 0.01
More detailed studies about the effect of buoyancy on the
vortex shedding in the wake of a heated cylinder in mixed
convection regime were carried out slightly later, and some
remarkable results were obtained. Noto and Matsumoto [3]
studied the wake flow of a horizontal heated cylinder placed in
a parallel flow, where the direction of the approaching forced
flow is vertically upward. By increasing the heat input
(increasing Ri), the Strouhal number of the vortex shedding was
found to increase at first. However, above a critical Richardson
number, the Strouhal number became zero abruptly and the
vortex shedding is suppressed. The “Karman” vortex street at
the downstream of the heated cylinder converts to two steady
vortices in the near wake. A further increasing of the heat input
(increasing Ri) causes the twin vortices to disappear, ending
with a thermal plume at the downstream of the heated cylinder.
The influences of buoyancy force on the vortex shedding
frequency were further analyzed numerically by Chang and Sa
[4]. The same results were also reported in the experimental
study of Michaux-Leblond and Belorgey [5], and the dualism
between buoyancy and viscous effects were considered to be
responsible for the abrupt disappearance of the vortex shedding
phenomenon for a heated cylinder exposed in a parallel flow.
More recently, Kieft et al. [6] and Steenhoveen and
Rindt[7] studied the effect of buoyancy on the wake instability
of a heated cylinder exposed in a horizontal cross flow. In their
studies, the direction of the approaching forced flows is
horizontal, which is perpendicular to the direction of the
buoyancy force acting on the fluid surround the heated
cylinder. They found that the non-parallelism between the
horizontal forced flow and the vertical buoyancy force caused
the flow pattern to become asymmetrical with the strength of
the vortices in the upper vortex row being different from those
in the lower row. The strength difference of the shedding vortex
increases with the increasing Richardson number. As a result,
the shedding vortices are found to move slight downward,
which is a rather unexpected behaviors in considering the
upward action of buoyancy force. Using an electrochemical tin
precipitation method, Maas et al. [8] visualized the wake
structures behind a heated circular cylinder placed in a
horizontal cross flow. They found that the wake become threedimensional when Ri>0.3. For small Richardson values
(Ri<1.0), the warm fluid is initially collected in the coherent
vortex structures shedding from the heated cylinder. Thermal
plumes were found to originate from these vortex structures at
further downstream. For larger Richardson values (Ri>1.0), the
upward buoyancy force was found to prevent the formation of
the coherent vortex structures and the wake structures were
found to transit to be three-dimensional already at the rear end
of the heated cylinder.
To the best of author’s knowledge, there is no literature
available to report a detailed experimental study about the
effect of buoyancy on the wake instability of a heated cylinder
exposed in a contra flow, where the direction of the
approaching forced flow is opposing to the direction of
buoyancy force acting on the fluid around the heated cylinder.
So far, only the numerical study of Chang and Sa [4] may be
considered to involve this topic. Instead of studying a heated
horizontal cylinder in a vertically downward forced flow,
Chang and Sa [4] presented their numerical results (streaklines,
streamlines and iso-thermal contours) of a cooled circular
cylinder in a vertically upward forced air, where the direction
of the approaching forced flow is reverse to the buoyancy force
acting on the fluid around the cooled circular cylinder.
In the present study, the effect of buoyancy on the wake
instability of a heated cylinder exposed in a contra flow is
investigated experimentally. A novel optical diagnostic
technique, Molecular Tagging Velocimetry and Thermometry
(MTV&T), is used for qualitative flow visualization and
quantitative simultaneous measurements of velocity and
temperature fields in the wake of the heated cylinder. The effect
of buoyancy on the wake instability of the heated cylinder is
discussed in the terms of vortex shedding pattern, Strouhal
number of vortex shedding (St), the distributions of turbulent
heat flux (correlation terms between turbulent velocity and
temperature), the wake closure length (lc) and averaged Nusselt
number (Nu) of the heated cylinder.
2
Copyright © 2005 by ASME
MOLECULAR TAGGING VELOCIMETRY AND
THERMOMETRY TECHNIQUE
The Molecular Tagging Velocimetry and Thermometry
(MTV&T) technique used in the present study is a novel
molecule-based flow diagnostic technique. Instead of using
particle tracers, MTV&T technique utilizes specially-designed
molecules, which can be turned into long lifetime tracers upon
excitation by photons of an appropriate wavelength, as tracers
for simultaneous velocity and temperature measurements.
The specially-designed tracer molecules used in the present
study are the supramolecules of phosphorescent triplex (1BrNp⋅Gβ-CD⋅ROH). The phosphorescent triplex is actually the
mixture of three different chemicals, which are lumophore
(indicated collectively by 1-BrNp), glucosyl-β-cyclodextrin
(indicated collectively by Gβ-CD) and alcohols (indicated
collectively by ROH). In the present study, we used a
concentration of 2×10−4 M for Gβ-CD, a saturated
(approximately 1×10−5 M) solution of 1-BrNp and a
concentration of 0.06 M for the cyclohexanol (ROH), as
suggested by Gendrich et al. [9].
Flow Velocity Distribution Measurement
The MTV&T technique can be thought as the molecular
counterpart of the PIV technique for the flow velocity
measurement. Typically a pulsed laser is used to “tag” the
regions of interest, and those regions are interrogated at two
successive times within the photoluminescence emission
lifetime of the molecular tracers. The tagged molecules form a
“glowing net” that convects, bends, and folds as the tracer
molecules move with the working fluid. The Lagrangian
displacement vectors of the tagged molecules over the
prescribed time delay between the two interrogations provide
the estimates of flow velocity vectors.
Figure 2 shows an example of the MTV measurement of a
vortex ring impacting a solid wall at normal incidence [9]. The
figure shows both the initially tagged regions and their
subsequent evolution after a time delay, together with the
resultant velocity vector field derived from the image pair using
a spatial correlation method.
(a)
(b)
(c)
Fig. 2. Typical MTV image pairs and the resultant velocity
field. (a) grid image 1 µs after the laser pulse; (b) same grid
imaged 8 ms later; (c) velocity field derived from (a) and (b).
Flow Temperature Distribution Measurement
According to quantum theory [10], for a diluted solution
and unsaturated laser excitation, the decay of phosphorescence
emission intensity follows an exponential law, and can be
expressed as:
I p = I i C ε Φ p e −t / τ
(1)
where Ii is the local incident laser intensity, C is the
concentration of the phosphorescence dye, ε is the absorption
coefficient of the phosphorescence dye, Φp is phosphorescence
quantum yield, and τ is the lifetime of the phosphorescence
emission, which refers to the time when the intensity drops to
37% (i.e. 1/e) of the initial intensity.
For some phosphorescent dyes like the phosphorescent
triplex (1-BrNp⋅Gβ-CD⋅ROH) used in the present study, the
phosphorescence quantum efficiency (Φp) and the lifetime of
the phosphorescence emission (τ) are temperature dependent.
Therefore, the phosphorescence intensity may be considered, in
principle, to depend only on temperature if the excitation laser
intensity is uniform and the phosphorescent dye concentration
remains constant in the measurement region.
By referring phosphorescent emission intensity to
temperature directly, Thomson and Maynes [11] have
demonstrated the possibility for fluid temperature measurement
by measuring the phosphorescence intensity of the
phosphorescent triplex (1-BrNp⋅Gβ-CD⋅ROH). It should be
noted that since the phosphorescence intensity is also the
function of incident laser intensity, therefore, the spatial and
temporal variations of the incident laser intensity would have to
be corrected for separately in order to extract quantitative
temperature data from phosphorescence images by using the
method suggested by Thomson and Maynes [11]. However, in
practice, it is usually very difficult, if not impossible, to ensure
a non-varying incident laser intensity distribution, especially
for unsteady flows with index of refraction variations. This may
cause significant error in the temperature measurement.
In order to overcome this problem, a novel ratiometric
technique, named as lifetime-based thermometry technique, has
been developed recently by the authors [12, 13], which
achieves the quantitative temperature mapping of a fluid flow
by taking advantage of the temperature dependence of the
phosphorescence lifetime of the phosphorescent triplex
molecules (1-BrNp⋅Gβ-CD⋅ROH).
Figure 3 shows the calibration curve of the
phosphorescence lifetime of the phosphorescent triplex (1BrNp⋅Gβ-CD⋅ROH) changing with temperature. It can be seen
that the phosphorescence lifetime of the phosphorescent triplex
(1-BrNp⋅Gβ-CD⋅ROH) varies significantly with increasing
temperature. The relative temperature sensitivity of the
phosphorescence lifetime ranges about 5.0% per degree at
20.0oC to about 20.0% per degree at 50.0o C. The temperature
sensitivity is much higher than those of most commonly used
LIF dyes (for example, the temperature sensitivity of
Rhodamine B is about 2.0%).
3
Copyright © 2005 by ASME
In summary, the MTV&T technique achieve the
simultaneous measurements of velocity and temperature in
fluid flows by using a pulsed laser to “tag” the regions of
interest. The tagged regions are interrogated at two successive
times within the lifetime of the photoluminescence of the tracer
molecules. The measured Lagrangian displacement vector of
the “tagged” molecules between the two interrogations provides
the estimate of velocity vector. The simultaneous temperature
measurement is achieved by taking advantage of the
temperature dependence of phosphorescence lifetime, which is
estimated from the phosphorescence intensity ratio of the two
interrogations. Further information about the technical basis,
system setup, calibration procedure, and image processing
algorithm of the MTV&T technique is available at [12, 13].
overflow
constant power
DC supply
12-bit intensified
CCD camera
pulsed
laser grid
Y
x
reserve tank
Data Set 1
Data Set 2
Data Set 3
Data Set 4
polynomial fit
1.0
DICAM-PRO
thermometer
To laser
Quartz
windows
1.2
honeycomb
mesh structure
heated
cylinder
1.4
Normalized lifetime (τ/τT=25oC)
constant head tank
Digital delay
generator
host
computer
valv
pum
0.8
Fig. 4 Experiment setup
0.6
0.4
0.2
0
20
25
30
35
40
45
50
o
Temperature ( C)
Fig. 3 Phosphorescence lifetime versus temperature profile
EXPERIMENTAL SETUP AND FLOW CONDITIONS
A schematic of the experimental setup used in the present
study is shown in Fig. 4. The experiment was conducted in a
small vertical water channel. A constant head tank with an
overflow system was used to maintain a constant flow
condition in the water channel during the experiment. The
aqueous solution of the phosphorescent triplex (1-BrNp⋅GβCD⋅ROH) in the constant head tank was filled from a reserve
tank by an electric pump. Honeycomb and mesh structures
were used at the inlet of the water channel to insure a uniform
flow condition at the upstream of the test cylinder. A copper
tube with outer diameter of 4.76mm (D=4.74mm) and inner
diameter of 4.00mm was used as the test cylinder in the present
study. A rod cartridge heater (Watlow Firerod™ ) with the outer
diameter of 3.1mm was stuffed inside the copper cylinder to
obtain the desire cylinder temperature. High thermal
conductivity paste (OMEGATHERM 201) was pressed in to
fill the gap between the cartridge heater and the inner wall of
the test cylinder. Two J-type thermocouples were embedded in
the gap at mid-span of the heated cylinder. The thermocouples
were connected to a two-channel thermometer (Omega HH23),
which has a resolution of ±0.1OC, to monitor the temperature of
the test cylinder.
A Lambda-physik XeCl Excimer UV laser (wavelength
λ=308 nm, energy 100 mJ/pulse, pulse width 20ns) with a set
of optics was used to generate illuminating grids in the
measurement region to achieve qualitative flow visualization
and quantitative simultaneous measurements of velocity and
temperature fields in the wake of the test cylinder. A 12-bit
(1280 × 1024 pixels) gated intensified CCD camera (PCO
DICAM-Pro) was used in the present study to conduct image
recording. The camera was operated in the dual-frame mode,
where two full-frame images of phosphorescence were acquired
in quick succession from the same laser excitation pulse. The
laser and the camera were synchronized using a digital delay
generator (SRS DDG535), which controlled the timing of the
laser illumination and the CCD camera data acquisition.
In the present study, the heated cylinder was placed
horizontally in the middle of the water channel, and the
approaching flow is vertically downward. Such arrangement
makes the heated cylinder operates in a contra flow, i.e. the
direction of the approaching flow opposes the direction of the
buoyancy force acting on the fluid around the heated cylinder.
The velocity of the approaching flow was about U∞ =
0.0255m/s. The temperature of the approaching flow in the
constant head tank was T∞ = 24.0 OC. The corresponding
Reynolds number is Re=130. During the experiment, the
temperature of the test cylinder was changed at several
temperature levels, which varied form 24.0 oC (unheated
cylinder) to 85.0 oC. The corresponding Richardson number
(Ri) changes from 0.0 to 1.05. With increasing Richardson
number, the heat transfer process around the heated cylinder
changes from force convection regime to mixed convection
regime.
4
Copyright © 2005 by ASME
EXPERIMENTAL RESULTS AND DISCUSSIONS
1. Flow Visualization and Simultaneous Velocity and
Temperature Measurement Results
Figure 5(a) and 5(b) show a typical pair of
phosphorescence images for the qualitative flow visualization
and simultaneous quantitative MTV&T measurement in the
wake of the heated cylinder when the temperature of the heated
cylinder is 35OC (Ri=0.19). The resultant velocity vectors
derived from the image pair by using a cross-correlation
method is shown in Fig. 5(c).
In the phosphorescence images, well defined structures in
the form of “dark clusters” can be seen clearly in the wake
region of the heated cylinder. The “dark clusters” are actually
the warmer fluid shedding periodically from the hot boundary
layer around the heated cylinder. As described above, the
phosphorescence intensity of the phosphorescent triplex (1BrNp⋅Gβ-CD⋅ROH) is temperature sensitive, the warmer
phosphorescent triplex molecules from the hot boundary around
the heated cylinder served as the tracers to visualize the
alternative shedding of the “Karman” vortices in the wake of
the heated cylinder. Since the phosphorescence intensity of the
warmer phosphorescent triplex molecules decays faster than
that in ambient fluid, the “dark clusters” are revealed more
clearly in the second phosphorescence image than those in the
first image.
In order to construct simultaneous temperature field from
the phosphorescence images, small interrogation windows were
chosen in the first phosphorescence image. The corresponding
positions of the interrogation windows in the second
phosphorescence image were determined based on the
measured velocity vectors as shown in Fig. 5(c). The
phosphorescence lifetime of the “tagged” phosphorescent
triplex molecules contained in each interrogation window was
calculated based on the intensity ratio of the interrogation
windows in the first and the second phosphorescence images
[12, 13]. Then, the simultaneous temperature field was
constructed by using the calibration curve of phosphorescence
lifetime versus temperature shown in Fig. 3. The resultant
temperature distribution extracted from the phosphorescence
image pair is shown in Fig. 5(d).
Corresponding to the “dark clusters” in the
phosphorescence images, two sets of “warm blobs” at the two
sides of the heated cylinder can be seen clearly in the
temperature distribution, which are generated by the periodical
shedding of the warmer fluids from the hot boundary layer
around the heated cylinder. The “warm blobs” and the heated
cylinder were connected by “braids” at the two sides of the
heated cylinder. The “warm blobs” were found to grow in size
as they traveled downstream. It should also be noted that even
although the difference of the fluid temperature in the wake of
the heated cylinder is quite small for this case (only about 2.0
o
C), the shedding of the warmer fluid in the form of “warm
blobs” can still be revealed very clearly in the simultaneous
temperate distribution by using the present MTV&T technique.
Based on 360 frames of instantaneous measurement
results, the ensemble-averaged velocity and temperature
distributions in the wake of the heated cylinder were calculated,
and the result are shown in Fig. 5(e) and Fig. 5(f). A
recirculation zone at the downstream of the heated cylinder
with a length of about 3 diameters is revealed clearly in the
ensemble-averaged velocity field. The ensemble-averaged
temperature field reveals that high-temperature regions exist at
the two sides of the wake region, which are corresponding to
the shedding paths of the “Karman” vortices and “warm blobs”
revealed in the instantaneous measurement results.
Figure 6 shows the phosphorescence images and the
corresponding MTV&T measurement results in the wake of the
heated cylinder when the temperature of the heated cylinder
increased to 53 OC (Ri = 0.50). Compared with the case of
smaller Richardson number (Ri=0.19) described earlier, the
shedding process of the “Karman” vortices and “warm bulbs”
in the wake was found to change significantly due to the
stronger buoyancy effect. Although the shedding of the
“Karman” vortices and the “warm blobs” still occur
alternatively at the two sides of the heated cylinder, the
shedding process was found to be “delayed”, and the locations
of the first appearance of the concentrated “Karman” vortices
and the “warm blobs” was pushed farther downstream. The
“braids”, which are the connection between the “warm blobs”
and the heated cylinder, were found to become much longer
and thicker. The ensemble-averaged velocity and temperature
distributions revealed that the recirculation zone at the
downstream of the heated cylinder become much wider and
longer compared that of the Ri=0.19 case.
Figure 7 shows a pair of typical phosphorescence images
and the resultant MTV&T measurement results in the wake of
the heated cylinder when the temperature of the heated cylinder
increased to 85.0 oC ( Ri = 1.05 ). The flow pattern and the
vortex shedding in the wake of the heated cylinder for this case
were found to be very different from the cases described before.
Rather than having alternative shedding of vortical structures or
“warm blobs”, the shedding of the vortical structures or “warm
blobs” were found to occur almost concurrently at the two sides
of the heated cylinder. The sizes of these vortical structures
were found to be smaller than that of the cases with smaller
Richardson number, and they behaved more like “KelvinHelmholtz” type structures rather than “Karman” type vortical
structures. The adjacent smaller vortical structures or “warm
blobs” at the same side were found to merge together to form
bigger vortical structures or larger “warm blobs” at further
downstream. The merge process is quite similar to the “pairing
process” of “Kelvin-Helmholtz” vortical structures. The merge
processes of the smaller vortical structures and “warm blobs”
were found to occur alternatively at the two side of the heated
cylinder, which resulted in the alternative shedding of bigger
vortical structures and larger “warm blobs” at far field.
The ensemble-averaged velocity and temperature
distributions revealed that the wake region of the heated
cylinder becomes even wider and longer at this Richardson
number (Ri=1.05). The recirculation zone downstream of the
heated cylinder became so long that its length was about 10
cylinder diameters.
5
Copyright © 2005 by ASME
a. first image (1ms after laser pulse )
b. second image (6ms after laser pulse)
-1
-1
0
0
6
7
10
9
1
1
0.026 m/s
2
2
3
3
4
4
Temperature
O
( C)
5
12
6
7
7
8
8
9
9
10
10
9
6
5
X/D
2
5
7
26.000
25.900
25.800
25.700
25.600
25.500
25.400
25.300
25.200
25.100
25.000
24.900
24.800
24.700
24.600
24.500
4
3
9
11
-5
-4
-3
-2
-1
0
1
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11
7
-5
-4
-3
-2
-1
0
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Y/D
Y/D
c. instantaneous velocity field
d. simultaneous temperature field
-1
-1
0
0
7
6
0.026 m/s
8
1
1
64
8
1
4
5
5
2
2
O
Temperature ( C )
2
3
3
3
11
10
9
8
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5
4
3
2
1
6
4
4
X/D
3
2
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3
1
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8
2
7
25.500
25.400
25.300
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25.100
25.000
24.900
24.800
24.700
24.600
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1
9
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1
X/D
X/D
3
9 7
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Y/D
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0
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6
7
Y/D
e. averaged velocity (U, V)
f. averaged temperature(T)
Fig. 5 MTV&T measurement results ( Tc = 35.0 O C , Ri=0.19)
6
Copyright © 2005 by ASME
b. second image (6ms after laser pulse)
-1
0
0
16
11
9
5
10
10
4
4
9
1
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9
3
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95 3
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X/D
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X/D
68
5
10
6
-5
-4
-3
-2
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0
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11
7
-5
-4
-3
-2
-1
0
1
Y/D
2
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Y/D
c. instantaneous velocity field
d. simultaneous temperature field
-1
-1
0
0
0.026 m/s
8
4
7
9
2
5
3
1
10
1
1
6
2
O
Temperature ( C )
7
86
3
4
5
6
5
12
3
X/D
4
5
7
8
8
9
3
6
7
28.500
28.100
27.700
27.300
26.900
26.500
26.100
25.700
25.300
24.900
24.500
3
9
10
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10
9
8
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5
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1
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X/D
28.500
28.300
28.100
27.900
27.700
27.500
27.300
27.100
26.900
26.700
26.500
26.300
26.100
25.900
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24.500
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0.026 m/s
2
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1
3
1
Temperature
O
( C)
1
180
15
17
2
a. first image (1ms after laser pulse )
-1
10
11
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
11
-5
Y/D
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Y/D
e. averaged velocity (U, V)
f. averaged temperature(T)
Fig. 6 MTV&T measurement results ( Tc
7
= 53.0 O C , Ri=0.50)
Copyright © 2005 by ASME
b. second image (6ms after laser pulse)
-1
0
0
1
Temperature
O
( C)
4
15
20
1 417
1
2
19 8
21
a. first image (1ms after laser pulse )
-1
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
3
11
9
4
4
X/D
3
1
53
5
5
9
6
5
6
6
7
7
8
8
9
9
10
10
5
9
4
6
2
2
4
3
11
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
11
7
-5
-4
-3
-2
-1
0
1
Y/D
2
3
4
5
29.500
29.250
29.000
28.750
28.500
28.250
28.000
27.750
27.500
27.250
27.000
26.750
26.500
26.250
26.000
25.750
25.500
25.250
25.000
24.750
24.500
6
7
Y/D
c. instantaneous velocity field
d. simultaneous temperature field
-1
-1
0
0
6
0.026 m/s
8
1
34
6
1
2
1
2
O
Temperature ( C )
7
3
5
2
3
11
10
9
8
7
6
5
4
3
2
1
2
4
4
5
6
3
X/D
4
1
5
3
6
7
7
8
8
9
9
10
30.000
29.450
28.900
28.350
27.800
27.250
26.700
26.150
25.600
25.050
24.500
3
X/D
X/D
1
4
8
3
10
13
2
7 10
2
12
5
0.026 m/s
10
11
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
11
Y/D
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Y/D
e. averaged velocity (U, V)
f. averaged temperature(T)
Fig. 7 MTV&T measurement results ( Tc = 85.0 O C , Ri=1.05)
8
Copyright © 2005 by ASME
-1
-1
0
0
tubulent thermal flux vector
1
-1
0
tubulent thermal flux vector
1
0.1
3
3
3
4
4
4
5
X/D
2
5
5
6
6
6
7
7
7
8
8
8
9
9
9
10
10
10
11
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
11
-5
-4
-3
-2
-1
0
Y/D
a. Ri=0.19
tubulent thermal flux vector
1
0.1
2
X/D
X/D
0.1
2
1
2
3
4
5
6
7
11
-5
-4
-3
-2
-1
Y/D
0
1
2
3
4
5
6
7
Y/D
b. Ri=0.50
c. Ri=1.05
Fig. 8. Turbulent heat flux vector plots in the wake of the heated cylinder
2. Turbulent Heat Flux
Since the velocity and temperature fields were measured
simultaneously by using the MTV&T technique, turbulent heat
fluxes, which are the correlation terms between the velocity and
temperature fluctuations, could be calculated based on the
simultaneously
measured
velocity
and
temperature
distributions. Figure 8 shows the distributions of the mean
turbulent heat flux ( u j 'T ' ) vectors in the wake of the heated
cylinder. The distributions of the mean turbulent heat flux
vectors indicate how the heat fluxes were propagated in the
wake of the heated cylinder. The effect of buoyancy on the heat
transportation process in the wake of the heated cylinder is also
revealed clearly from the comparison of the turbulent heat flux
vector distributions. As shown in Fig. 8, the structure of u j 'T '
in the near wake is dominated by two large counter-rotating
vortex-like structures, which is almost symmetrical about the
wake centerline. As the Richardson number increasing, the
counter-rotating vortex-like structures were found to move
farther downstream, which are corresponding to the delayed
appearances of the “Karman”vortex structures and “warm
blobs” revealed in the measured velocity and temperature
distributions. Therefore, the structures are believed to be the
result of the large entrainment of the cold free stream fluid by
the shedding of “Karman” vortices in the wake behind the
heated cylinder.
3. The Wake Closure Length (lC),
Figure 9 shows the ensemble-averaged velocity profiles
along the wake centerline at difference Richardson number
levels. Since the flow condition of the approaching forced flow
is kept in constant during the experiment, all the velocity
profiles are found to collapse to one single curve at the
upstream of the test cylinder as it is expected. Due to the effect
of buoyancy, the velocity profiles were found to vary
significantly at the downstream of the test cylinder.
As a typical behavior of the wake behind an unheated
cylinder, the present MTV&T measurement result of unheated
cylinder case (Ri=0.0) reveals that the streamwise velocity of
the wake flow becomes negative at the near downstream of the
test cylinder. The negative streamwise velocity reaches it peak
value at the downstream location of X /D ≈ 2.2 , then the
velocity deficit is found to recover gradually as the downstream
distance increasing. The value of the streamwise velocity is
found to change its sign and become positive again at the
downstream locations of X /D > 3.5 .
For the heated cylinder cases, the existence of sharp
negative velocity peaks near the rear end of the heated cylinder
indicates that there is a strong reversing flow zone near the rear
end of the heated cylinder. In the reversing flow zone, the flow
direction is upward. The upward reversing velocity was found
to become stronger and stronger as the Richardson number
increasing. It may be explained by that since the fluid around
the heated cylinder was heated up, the warmer fluid near the
trailing edge of the heated cylinder were pushed upwardly due
to the effect of buoyancy force. As the temperature of the
heated cylinder increasing (i. e. Richardson number increasing),
the buoyancy force become stronger and stronger, which results
in a stronger and stronger upward reversing flow near the rear
end of the heated cylinder.
When the Richardson number is relatively small (Ri<0.31),
the streamwise velocity far away from the heated cylinder
(X/D>1.5) are found to behave very similarly as that in the
wake of an unheated cylinder (Ri=0.0 case). The velocity
deficits were found to recover gradually as the downstream
distance increasing. However, when the Richardson number
becoming big enough (Ri>0.5), the streamwise velocity profiles
at downstream far away from the heated cylinder (X/D>1.5)
were found to behave very different from that in the wake of an
unheated cylinder (Ri=0.0 case). As shown in the ensembleaveraged velocity distributions shown in Fig. 6 and Fig. 7, a
“dead flow” zone (in which the streamwise velocity being
almost zero) was found in the wake of the heated cylinder.
9
Copyright © 2005 by ASME
Another strong recirculation zone exists at the downstream of
the “dead flow” zone. As the Richardson number increasing, the
strong recirculation zone was found to be pushed to farther
downstream. The recovery rate of the streamwise velocity
deficit was found to become slower and slower as the
Richardson number increasing.
0.9
Ri=0.00
Ri=0.19
Ri=0.31
Ri=0.50
Ri=0.72
Ri=1.05
U c/U ∞
0.6
0.3
0
-0.3
-0.6
-1
0
1
2
3
4
5
6
7
8
9
10
streamwise distance (X/D)
Fig. 9. Mean velocity profiles along the wake centerline
4. The Strouhal Number of the Vortex Shedding
Based on the time sequence of the instantaneous MTV&T
measurement results, the shedding frequency of the “Karman”
vortex structures in the wake of the heated cylinder can be
obtained, and the result is given in Fig. 11. In the present study,
the horizontal heated cylinder is placed in a vertically
downward flow, i.e, in a contra flow. According to the results
shown in Figure 11, the Strouhal number ( St = f D / U ∞ ) of the
vortex shedding in the wake of the heated cylinder is found to
decrease with the increasing Richardson number.
The
numerical results of Chang and Sa [4] for a cooled cylinder
placed in a contra air flow at the condition of Re=100 is also
shown in the figure. It can be seen that both the present
experimental data and the numerical simulation results of
Chang and Sa [4] revealed the same decreasing trend of the
Strouhal number of the vortex shedding with the increasing
Richardson number.
0.18
8
Re=130 (present experiment)
Re=100 (Chang & Sa)
6
Re=130
0.16
Strouhal number(St)
The wake closure length (L C /D)
10
heated cylinder is found to become shorter than that of the
unheated cylinder (Ri=0.0). As Richardson number being
bigger than 0.3, the wake closure length (lC) of the heated
cylinder is found to become longer than that in the wake of the
unheated cylinder. As Richardson number increasing, the wake
closure length (lC) were found to become longer and longer.
The wake closure length (lC) was found to be about 9 cylinder
diameters when the Richardson number increases to 1.05.
4
2
0
0
0.2
0.4
0.6
0.8
1.0
0.14
0.12
0.10
1.2
Richardson number (Ri)
Fig. 10. The change of the wake closure length ( l C ) with
Richardson Number (Ri)
0.08
0
0.2
0.4
0.6
0.8
1.0
1.2
Richardson number (Ri)
Based on the streamwise velocity profiles along the
centerline of the test cylinder, the wake closure length (lC),
which is defined as the distance from the rear end of the test
cylinder to the point where the centerline velocity becomes zero
and changes its sign, can be calculated. The results are shown in
Fig. 10.
For the unheated cylinder case (Ri=0.0), the wake closure
length (lC) is found to be about 3.0 diameters of the test
cylinder. This result is found to be consistent with the result
reported by Michaux-Lebloand and Belorgey [5] at the
Reynolds level of 130. When the Richardson number is
relatively small (Ri < 0.19), the wake closure length (lC) of the
Fig. 11. Strouhal number (St) versus Richardson number (Ri)
5. Averaged Nusselt Number (Nu)
In the present study, the voltage supplied to the cartridge
heater and the strength of the electrical current in the circuit
were measured during the experiment. Considering the power
losses through end pieces of the cartridge heater, 90% of the
total electrical power supplied to the heater is assumed to be
dissipated by the approaching flow inside the water channel.
The averaged Nusselt numbers ( Nu ) of the heated cylinder at
10
Copyright © 2005 by ASME
Avearged Nusselt number (Nu)
different Richardson number levels can be calculated by using
following equation:
q
q
D
πL(Tw − T∞ )
hD A(Tw − T∞ )
(2)
Nu =
=
=
k∞
k∞
k∞
where the q is heat flux dissipated by the approaching forced
flow, L is the spanwise length of the cartridge heater inside the
water channel, k ∞ is the thermal conductivity of the
approaching flow. Tw and T∞ are the temperature of the heated
cylinder and temperature of the approaching flow respectively.
Figure 12 shows the experimental results of the present
study. The predictions of two most commonly-used empirical
models (Hilpert’s model [14] and Morgan’s model [15]) at the
present experimental conditions are also given in the figure.
14
convection and free convection (i.e. mixed convection) rather
than by forced convection alone. The role of the free convection
becomes more and more pronounced as the Richardson number
increasing. Therefore, the difference between the prediction of
Hilpert’s model [14] and the present experimental data becomes
bigger and bigger as the Richardson number increasing.
With the contribution of the free convection being taken
into account, Morgan’s model [15] predicts that the averaged
Nusselt number of the heated cylinder decreases with the
increasing Richardson number, which is consistent with the
present experiment data qualitatively. When the Richardson
number is relatively small (Ri<0.31), the prediction of
Morgan’s model [15] were found to agree with the present
experimental data reasonably well. The Morgan’s model was
found to underestimate the averaged Nusselt number when the
Richardson number becoming relative big (Ri>0.31). The
similar result was also reported by Krauce and Tareiuk [16] in
their study of the heat transfer process from a heated cylinder
placed in a contra air flow.
12
10
8
6
present experiment
Morgan's model
Hilpert's model
4
2
0
0
0.2
0.4
0.6
0.8
1.0
1.2
Richardson number (Ri)
Fig. 12. Nusselt number (Nu.) vs. Richardson Number (Ri).
The experimental data of the present study shown in Fig.
12 reveal that the averaged Nusselt number of the heated
cylinder decreases almost linearly with the increasing of the
Richardson number when a heated cylinder placed in a contra
flow. Compared with the present experimental data, the
prediction of Hilpert’s model [14] is found to overestimate the
averaged Nusselt number. The difference between the present
experimental data and the prediction of Hilpert’s model [14]
becomes bigger and bigger as the Richardson number
increasing. Instead of predicting a decreasing trend of the
averaged Nusselt number, the Hilpert’ model [14] predicts a
opposite trend with the averaged Nusselt number becoming
bigger and bigger as the Richardson number increasing. This
may be explained by that the empirical models proposed by
Hilpert [14] is based on the assumption of that the heated
cylinder operates in forced convection regime, where the effect
of the thermal induced flow (or buoyancy effect) on the heat
transfer process is negligible. As the Richardson number
increasing, the thermal effect (or buoyancy effect) becomes
stronger and stronger. The heat transfer from the heated
cylinder to surrounding fluid is conducted by both forced
CONCLUSIONS
The effect of buoyancy on the wake instability of a heated
circular cylinder in a contra flow arrangement is investigated
experimentally in the present study. A novel optical diagnostic
technique, Molecular Tagging Velocimetry and Thermometry
(MTV&T), was used for qualitative flow visualization and
quantitative simultaneous measurements of velocity and
temperature fields in the wake of the heated cylinder. The
experiment was conducted in a water channel with the
temperature and Reynolds number of the approaching forced
flow being held constant at T∞=24OC and Re=130. The
temperature of the heated cylinder varied between 24OC
(unheated cylinder) and 84OC, corresponding to a Richardson
number (Ri) varying between zero (unheated) and unity. The
heat transfer process around the heated cylinder changes from
the forced convection regime to the mixed convection regime.
Due to the effect of buoyancy force, the wake instability
behind the heated circular cylinder was found to become much
more complicated compared with that behind an unheated
cylinder. With the increasing Richardson number, significant
modifications of the wake instability were revealed from both
qualitative flow visualization images and quantitative
simultaneous velocity and temperature fields. Following facts
were found as the results of the present experimental study:
1. When the Richardson number is relatively small
(Ri<0.31), the flow pattern and the vortex shedding mechanism
in the wake of the heated cylinder is found to be similar as those
in the wake of an unheated cylinder.
2. When the Richardson number becoming big enough
(Ri>0.31), the shedding of the “Karman” vortices in the wake
of the heated cylinder is found to change significantly due to the
strong buoyancy effect. Compared with that in the wake of an
unheated cylinder, the “Karman” vortex shedding process was
found to be delayed and occurred at much farther downstream.
3. As the Richardson number approaching unity (Ri>0.72),
the effect of buoyancy become so strong that the alternative
shedding of the “Karman” vortices was suppressed in the near
field of the wake flow. Smaller vortices generated almost
11
Copyright © 2005 by ASME
concurrently were found to shed at the two sides of the heated
cylinder. These smaller vortices behave more like “KelvinHemholz”-typed vortex structures rather than “Karman”-typed
vortices.
4. Within the Richardson number range investigated
(0≤Ri≤1.05), the shedding frequency of the “Karman” vortex
structures in the wake of the heated cylinder was found to
decrease with the Richardson number increasing.
5. When the Richardson number being relatively small
(Ri<0.31), the wake closure length (lC) of a heated cylinder is
found to be shorter than that of an unheated cylinder. When the
Richardson number becoming big enough (Ri>0.31), the wake
closure length (lC) become longer and longer as the Richardson
number increasing.
6. The average Nusselt number (Nu) of the heated cylinder
was found to decrease almost linearly with the increasing
Richardson number when the heated cylinder is placed in the
contra flow.
ACKNOWLEDGMENTS
This work was supported by the MRSEC Program of NSF,
Award No. DMR-9809688 and the CRC Program of NSF,
Grant No. CHE-0209898
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12
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