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A closed loop pulsating heat pipe (CLPHP),
typically suited for electronics cooling applications, consists of a tube of
capillary dimensions with many U-turns and joined end to end (Figure 1). There
is no additional capillary structure inside it as in a conventional heat pipe.
The tube is first evacuated and then filled partially with a fluid, which
distributes itself naturally in the form of liquid-vapor slugs and bubbles due
to the dominance of surface tension. One end of this tube bundle receives heat
transferring it to the other end by a pulsating action of the liquid-vapor/
slug-bubble system. There may exist an optional adiabatic zone in between.
This type of heat pipe is essentially a non-equilibrium heat transfer device.
The performance success primarily depends on continuous maintenance of these
non-equilibrium conditions in the system. |
The liquid/ vapor slug/bubble
transport is caused by thermally induced pressure pulsations inside the device
and no external mechanical power source is required [1, 2]. To understand the
thermo-fluid dynamic characteristics in a PHP, one primary building block i.e.
a two-phase loop is investigated with the primary aim of preliminary
measurements and phenomenological observations.
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| Figure 1:
Schematic of a closed loop pulsating heat pipe without check valve |
Figure 2:
Schematic of the two-phase loop |
The geometrical details are shown in Figure
2. The loop is first evacuated
(<10-4
mbar) and then filled partially with
ethanol. Temperature measurement is done by a data logger (resolution: 0.1°C,
accuracy: ±0.5°C, time constant: 70 ms) with a measuring frequency of 1 Hz,
coupled with K type thermo-couples of OD1.5 mm. Two thermocouples each are
placed in drilled passages in the evaporator and condenser copper blocks. (avg.
Te and Tc). Two thermocouples (T1, T2) are placed on the wall of adiabatic
glass tubes. Although the temperature recorded by the latter two thermocouples
does not truly represent the fluctuations inside the working fluid and the
recording frequency is also limited to 1 Hz by the data logger, the essence of
the phenomenological condition of the fluid is certainly captured by these
measurements and important conclusions may therefore be drawn. |
2. Results and Discussion |
2.1 Flow patterns
It has been indicated by earlier studies [3, 4] that there is a large number
of parameters which affect the PHP operation. These can be summarized as, (a)
Geometrical parameters i.e. diameter and cross sectional shape of tube, length
of evaporator/condenser section, overall length of the device, number of turns,
(b) Operational parameters i.e. global orientation, use of flow control check
valve in the circuit and (c) Physical parameters i.e. thermophysical
properties of working fluid and its filling ratio. The results of the present
study indicate that the thermal performance of a PHP is not only dependent on
this multitude of parameters but also strongly on the two-phase fluid flow
patterns existing while in operation. Also, this study suggests that the flow
pattern itself is linked to the filling ratio and heat input.
Figure 3: Observed flow patterns in
the loop and corresponding temperature profiles
It is established that the zone of interest for a PHP operation
is achieved when the FR is between about 20% to 80% [5, 6]. Below FR≈20%, there are not enough distinct liquid slugs and the operation becomes 'unstable'
resulting in large unacceptable variations in average Te. Above FR≈80% there
are not enough bubbles to provide the pumping action and so the performance
drastically deteriorates. Within the operating range of filling ratios, it has
been observed in the present experiments that various flow patterns may exist
depending on the applied boundary conditions.
Figure 3 depicts the observed phenomena in the loop operated in vertical
heater down position, with FR = 60% ethanol and increasing input heat power.
The corresponding recorded temperatures, Te, T1 and T2, for each case along
with the performance parameters are also shown. At low heating power, case A,
low amplitude oscillations with slug flow in both tube sections are observed.
Individual bubbles oscillate about a mean position and there is very little
bubble agglomeration. In fact, the bubbles in the adiabatic section act as
isolators, not allowing the hot side fluid to come in contact with the fluid
on the cold side. The hot slugs remain oscillating in the evaporator zone and
the performance is very poor. As the heat input is increased, case B and C,
the oscillation amplitude increases. As it becomes comparable to the overall
length of the loop and hot fluid is able to reach the condenser there is
considerable improvement in the performance. A complete turning of fluid
starts sometimes in the clockwise and sometimes anti-clockwise direction until
the stage represented by case D is reached. Here, the flow turns in one
direction for a considerable time before a direction reversal takes place.
This is also clearly seen by the changing pattern of T1 and T2 for case D.
During this time the hotter tube section starts to develop annular flow which
changes back to slug flow by liquid bridging action as the fluid travels
towards the cold end. When the input power is further increased the flow
direction reversal completely stops. The fluid flow takes an arbitrary
direction, either clockwise or anti-clockwise, but then remains in the same
fixed direction thereafter. In such a condition, fully developed annular flow
is observed in one section (the up-header/ hot fluid line) and bubbly/slug
flow is observed in the other section (down-header/cold feeder line). The
device performance is observed to be the best in such a situation. As the heat
power is further increased, the flow pattern remains similar and the size of
the bubbles in the down-header/cold feeder line keeps on shrinking (and even
becomes smaller than tube diameter since the overall system is isochoric). As
the FR goes on increasing, it becomes more and more difficult to sustain
annular flow and the tendency is towards slug flow in both tube sections. This
reduces the performance again. If the flow pattern remains strictly slug flow
in the entire system, it has been shown by experimental and simulation studies
that latent heat will play an insignificant role in the overall heat transfer
[4, 7]. In the present case of existence of annular flow with corresponding
increase in the performance, the contribution of latent heat needs
reevaluation.
2.2 Role of Gravity
In the present experiments satisfactory self oscillating operation of the
device was only possible till about 10° from the horizontal (heater down). All
oscillations stopped at horizontal orientation. This can be explained as
follows:
2.2.1 Vertical operation
In the vertical orientation, gravitational body force acts on each slug and
bubble (effect on bubble is negligible). In a static condition, the
probability that sections X-C-Y and section X-F-Y (refer Figure 2) have
exactly the same volume fraction (or mass fraction) of the respective phases
is extremely rare. Moreover, the individual lengths of the slugs will also
vary in these sections. Further, it is evident that the summation of static
pressure by traversing once along the entire loop must be zero. The above
facts necessarily suggest that the menisci geometry of individual slugs must
be different so as to satisfy both the above conditions.
Since the mass distribution (and lengths) of individual phases is different in
sections X-C-Y and X-F-Y respectively, the dynamic pressure drop (or force)
required to push the fluid by a small amount in anti-clockwise direction (X-C-Y-F-X)
is different than in the reverse direction (X-F-Y-C-X). This is true even if
the condition of no dynamic contact angle hysteresis is assumed and only the
net effects of wall shear stress and gravity are considered. As a bubble forms
in the evaporator and expands, a preferential direction of motion is
automatically set depending on the path of least resistance (say X-F-Y-C-X).
Figure 4: Static pressure distribution
in different cases, (a) Vertical (b) Horizontal
This explains the start-up direction of the two-phase loop. After the start-up,
the section at the outlet of the evaporator (A-F-E) has a higher vapor volume
fraction than the other loop section (D-C-B) because of evaporation and
condensation processes. The process continues for at least some finite time
before a combination of interfacial waves, perturbations, internal
inhomogeneity of the heating/cooling process and continued non-equilibrium
metastable conditions cause a flow direction reversal. The analysis of facts
leading to a flow reversal phenomenon needs further investigation.
2.2.2 Horizontal operation
In horizontal orientation, in the absence of gravity, the static pressure
distribution is quite different from that of the vertical case. This is
highlighted in Figure 4 a, b where static pressure distributions of three
different cases are compared. Although the two sections X-C-Y and X-F-Y will
have different mass distributions, as in the vertical case, this does not
necessitate the contact angles of the various menisci to be different for
maintaining the static pressure integral to be zero across the loop. If a
bubble in the evaporator has to expand, in the absence of any external/internal
perturbations, dynamic contact angle hysteresis, etc. apparently there seems
to be no preferred direction of least resistance. The first set of
experimental results with a two-phase loop clearly demonstrate that horizontal
operation (without gravity) is not possible. Several results from other
sources [1, 2] for a multi-turn PHP suggest that horizontal operation is
possible albeit not as good as vertical. In our earlier studies with
multi-turn PHPs too [8], proper horizontal operation was hardly observed.
These apparently uncomplimentary and contradictory results seem to suggest
that reasons for proper horizontal operation may be attributed to (a) more
number of PHP turns, which is responsible for higher degree of internal system
perturbations and inhomogeneity, (b) a high input heat flux leading to higher
internal operating pressure. The second point is supported by the fact that
even for vertical operation, there is a critical minimum input heat flux
requirement to initiate self exited oscillations. In the absence of gravity
this minimum critical heat flux is likely to be higher. This fact is yet to be
experimentally demonstrated.
2.3 Thermodynamic considerations
There exist pressure differentials in the system caused by both, expanding
bubbles in the evaporator and contracting bubbles in the cooler. While the
system as a whole is isochoric having no associated PdV work, local control
volumes in the evaporator and condenser are essentially involved with work
interactions with adjoining fluid particles having reverse signs. Heat
addition along with 'positive pumping' by the expanding bubbles is taking
place in the evaporator. In the condenser, the bubbles collapse giving up the
heat and in turn do a 'negative pumping' work on the adjoining fluid particles.
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| Figure 5:
Instantaneous thermo-dynamic cycle of the single loop (For notations refer
Figure 2) |
Figure 6: Volumetric ratio of
vapor to vapor mass quality in the operating range of a pulsating heat
pipe |
When bulk movement of the fluid is taking place, in general, the quality of
two-phase mixture coming out of the condenser is certainly inferior to that
existing at the evaporator outlet. Simultaneously, the fluid pressure is also
lower at the condenser outlet. So, considering the P-h diagram as shown in
Figure 5, although exact positions are not known, relative locations of the
state of fluid at condenser and evaporator outlet are certainly known (it is
emphasized that these are strictly instantaneous positions). In the two
adiabatic fluid transport sections, an isenthalpic pressure drop seems to be a
very satisfactory assumption. By applying this, the condenser inlet and
evaporator inlet points are also known. What happens inside the evaporator and
the condenser remains to be fixed to complete the qualitative description of
the possible instantaneous thermodynamic cycle of the loop. The simultaneous
heating up and pressurizing of the fluid in the evaporator is a rather complex
process. For analysis it may be conveniently subdivided into two thermodynamic
processes, constant pressure heat addition and isentropic pumping up by the
bubbles. Similarly, in the condenser, constant pressure condensation is
coupled with negative isentropic work. How these complex processes are linked
so as to join the dashed lines in Figure 5 is yet to be determined.
The fact that the overall system volume is fixed, provides another interesting
thermodynamic aspect. Operating the device at any temperature (within
reasonable limits and avoiding near critical operation), necessarily does not
alter the volumetric fill ratio; only the vapor density varies with the
operating temperature. So, if Te and Tc are fixed (thereby fixing the
respective working pressures), a given system with a fixed volumetric fill
ratio will have a fixed corresponding mass quality at the two respective
temperatures. Figure 6 plots the volumetric ratio of vapor against the mass
quality of vapor for ethanol at 25°C and 100°C. It is clearly seen that the
overall mass quality of vapor phase is extremely low for the range of
applicable volumetric ratios of vapor. This also explains the minuscule role
of latent heat in the overall heat transfer.
2.4 Effect of number of turns
2.4.1 Level of perturbations
A complete stop-over of all macro movements inside the loop has been observed
many times in the present range of experiments. This happened more frequently
for FR < 50% coupled with low input power. Sometimes the stop-over has also
been observed for higher filling ratios. The 'self-sustained' oscillating
character is then lost. Such a behavior has never been reported for multi-turn
PHPs, under comparable boundary conditions. Although, in a multi-turn PHP
having a working fluid with low
 , like water, and at comparatively low heat
input fluxes, flow visualization has indicated that there are alternating
periods in which bubble/slugs are moving rapidly (activity phase) and 'stopping'
for a while (static phase). In the latter there is only micro movement of
bubbles with high frequency/low amplitude about a mean position whereas in the
activity phase the bubbles vigorously move with higher amplitudes along the
tube length. As the input heat flux increases it becomes more and more
difficult to distinguish between these two phases since the time period of 'static'
phase reduces drastically [8].
Typical behavior of the loop under the conditions leading to a stop-over is as
follows: The initial partial filling of the loop leads to a natural volumetric
(mis-)distribution of phases in the two tube sections. As the heating is
switched on, the system starts to oscillate in the usual manner. If the
combination of boundary conditions is favorable for a stop-over, bubble
agglomeration takes place leading to the formation of a single large bubble
which envelopes the entire evaporator section. Then oscillations die down
completely and all macro motion of fluid inside the tube stops leading to an
increase of the evaporator temperature. As the number of turns keeps
increasing, the probability of such a tendency towards complete stop-over
should essentially diminish.
2.4.2 Optimum turns
Consider that bare cooper rods of a fixed size are fitted to cool a heater
with a fixed input power. If only one rod is used, after the initial transient
phase, the heater will come to a steady state temperature. As the number of
rods is increased, since the net heater power is fixed, its final steady state
temperature will come down. Net heat handled per rod will decrease and so the
overall system thermal resistance keeps decreasing as the number of rods
increases. The limit is reached when all the copper rods together consume the
entire available space. If the same system is cooled by a pulsating heat pipe
then, in this case, instead of bare copper rods there are copper pipes
partially filled with a working fluid. Since a lot of conductive material is
removed, the intention is to augment the heat transfer by internal convective
flow. In a PHP, the heat transfer primarily takes place due to liquid
convection (latent heat transfer through the vapor helps the bubble pumping
action, and thereby the sensible heat transfer), provided the PHP is optimally
operating in the true pulsating regime.
If the number of turns of the PHP is small, then the heat handled by each turn
will be quite high. The overall thermal resistance will be high since there is
not enough effective heat transfer cross sectional area available.
Extrapolating the previous analogy, provided the heater power is fixed, the
net heat handled by each PHP turn reduces as the number of turns is increased.
If the effective thermal conductance of the PHP is constant, then, as for the
previous case of bare copper rods, the overall thermal resistance should come
down. But the effective thermal conductance of a PHP is not really constant.
In fact, it is dependent on the pressure fluctuations in the system which in
turn depend on the existing temperature gradients. Any decrease in the
evaporator temperature actually reduces the local saturation pressure. If the
condenser temperature is maintained constant then this primarily causes a
reduction in overall existing pressure differential thereby reducing the
driving potential. Thus a monotonous increase in number of turns will not have
the same effects as in the case of bare copper rods. The effective thermal
conductance of a PHP is a strong function of the temperature differential
existing between the evaporator and the condenser. Therefore for a prescribed
heat throughput, an optimum number of turns must exist after which the
pulsating effect of the fluid, and the thermal advantage thereof, will start
to diminish. |
3. Summary and Conclusions |
A two-phase loop, primary building
block of a CLPHP, was constructed to phenomenologically study the internal
thermo-hydraulics of the system. Two-phase dynamic instabilities, as observed
in multi-turn closed loop pulsating heat pipes are also observed in the
two-phase loop. Strong thermo-hydraulic coupling leads to metastable
conditions inside the system. Gravity does affect the performance, at least
for systems with low number of turns. A complete stop-over is observed in a
single loop but has never been reported in a multi-turn PHP device suggesting
that the number of turns increase the level of perturbations. Also, for a
given heat throughput requirement, an optimum number of turns exists. Apart
from a multitude of geometrical, physical and operational variables which
affect the system, the performance is also strongly linked with the flow
patterns existing inside. The contribution of latent heat to the overall heat
transfer has to be judged in the background of this new fact. [1] Akachi, H., Polášek, F. and Štulc, P., Pulsating Heat Pipes, Proc. 5th Int.
Heat Pipe Symp., Melbourne, Australia, pp. 208-217. 1996.
[2] Akachi, H. and Miyazaki, Y., Stereo-Type Heat Lane Heat Sink, Proc. 10th
Int. Heat Pipe Conf., Stuttgart, Germany, 1997.
[3] Tong B., Wong T. and Ooi K., Closed-Loop Pulsating Heat Pipe, Applied
Thermal Engineering, ISSN 1359-4311, Vol. 21, pp. 1845-1862, 2001.
[4] Groll M. and Khandekar S., Pulsating Heat Pipes: A Challenge and still
unsolved problem in Heat Pipe Science, Proc. 3rd Int. Conf. on Transport
Phenomenon in Multiphase Systems, ISBN 83-88906-03-8, pp. 35-43, Kielce,
Poland, 2002.
[5] Gi. K., Sato F. and Maezawa S., Flow Visualization Experiment on
Oscillating Heat Pipe, Proc. 11th Int. Heat Pipe Conf., pp. 149-153, Tokyo,
Japan, 1999.
[6] Khandekar S., Groll M., Charoensawan P. and Terdtoon P. Pulsating Heat
Pipes: Thermo-fluidic Characteristics and Comparative Study with Single Phase
Thermosyphon, Proc. 12th Int. Heat Transfer Conf., ISBN-2-84299-307-1,
Grenoble, France 2002.
[7] Shafii M. B., Faghri A. and Zhang Y. Thermal Modeling of Unlooped and
Looped Pulsating Heat Pipes, ASME J. Heat Transfer, Vol. 123, pp.1159-1172,
2001.
[8] Khandekar S., Schneider M., Schäfer P., Kulenovic R. and Groll M.,
Thermofluid-dynamic Study of Flat Plate Closed Loop Pulsating Heat Pipes,
Microscale Thermophysical Engineering, ISSN-1089-3954, Vol.6, No.4, 2002.
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