http://www.pmmh.espci.fr/~vnikol/PHP.html
Modeling of pulsating heat pipe (PHP)
by V.S. Nikolayev
Postdoc vacant position 2012 concerning this subject
One of the contemporary technological challenges is a reduction of mass of transportation
means in order to reduce their energy consumption and CO2 emission. This requires replacing
of metals by lighter synthetic materials (composites, ceramics, etc.), which, however, are poor
heat conductors and thus require special thermal management solutions for their cooling
capability to handle heat loads up to several kW. On the other hand, with the increase of
power levels related to the miniaturization of electronics progressing towards multi chip
modules, conventional cooling technologies and thermal management are facing growing
challenges including the cooling heat fluxes of 100 W/cm2, long term reliability, and very low
costs for consumer market products, among others. This necessitates the development and use
of more efficient, nontraditional cooling approaches. Special devices called heat pipes are
used more and more widely to transfer the excessive heat to a colder environment.
What is a heat pipe?
A heat pipe is a container tube filled with the working fluid. One end of this tube (called
evaporator section) is brought in thermal contact with a hot point to be cooled. The other end
(called condenser section) is connected to the cold point where the heat can be dissipated. A
portion of the tube between evaporator and condenser is called adiabatic section.
The working fluid and its pressure are chosen in such a way that the saturation temperature is
between the evaporator temperature Te and condenser temperature Tc. The fluid is thus
vaporized in the evaporator section. The created vapor is transported to the condenser section
and condenses there. The liquid is transported back to the evaporator section. The heat is
transferred mainly due to the latent heat absorption in the evaporator and its release in the
condenser. Since the latent heat is large, the heat pipes are quite efficient. They are capable of
evacuating up to 100-200 W/cm2. There are different kinds of heat pipes. They differ by their
geometry and a mechanism of fluid transport inside the heat pipe.
Pulsating heat pipe
Pulsating (or oscillating) heat pipe, invented in early 1990s present promising alternatives for
the removal of high localized heat fluxes to provide a necessary level of temperature
uniformity across the components that need to be cooled. PHP is a capillary tube (with no
wick structure) bent into many turns and partially filled with a working fluid. Because the
tube is thin, the liquid plugs and vapor bubbles are formed inside it.
Two possible PHP geometries.
When the temperature difference between evaporator and condenser exceeds a certain
threshold, the gas bubbles and liquid plugs begin to oscillate spontaneously back and forth.
The amplitude of oscillations is quite strong and the liquid plugs penetrate into both
condenser and evaporator. The heat is thus transferred not only by the latent heat tansfer like
in other types of heat pipes, but also by sweeping of the hot walls by the colder moving fluid
and vice versa. This phenomenon is the reason of high efficiency of PHPs in comparison with
other types of heat pipes. Compared to other cooling solutions, PHPs are simple and thus
more reliable and cheap. They are capable to transfer several kW to distances of the order of 1
m even when their orientation with respect to gravity is unfavorable. For comparison,
advanced heat pipes used for spatial applications have heat transfer capacity (measured in
W∙m) order of value smaller. The heat transfer capacity of the conventional heat pipes used
for cooling of microelectronic devices like laptop computers is 2 to 3 orders of value smaller
than that of PHPs. These features make PHP extremely promising for the thermal
management of the next generation of electronic and other systems. However, the functioning
of PHPs is not completely understood. A complicated interplay of different hydrodynamic and
phase-exchange phenomena needs to be accounted for in the modeling approaches. Unlike
other heat transfer devices, the functioning of PHPs is non-stationary and thus difficult to
model. A number of PHP studies have been carried out since 1990s. Researchers agree that
the oscillations are driven by an instability that appears due to coupling of the adiabatic vapor
compression and evaporation/condensation mass exchange. However this instability has not
been studied until recently. Such important parameters as oscillation threshold, heat transfer
coefficient, and maximum heat load cannot be predicted from calculations. It is not even clear
whether the oscillations are persistent or not and at which regimes. For these reasons the PHP
applications are very limited. The PHP parameters are adjusted empirically, often without any
certainty. To our knowledge, only a couple of small companies in the world produce them. A
comprehensive introduction to PHPs can be found in PhD theses in English or French.
There are two possible PHP geometries: open loop and closed loop PHP. In the open loop
PHP, the ends may be open or closed. It is however generally recognized that the closed loop
PHP is more efficient. For this reason, we target this type of the PHP in our numerical
multibubble modeling presented below.
Steam toy boat
There is a children's toy that is called "click-click" or "putt-putt" or "pop-pop" boat. Its name
comes from the sound made by this toy while it moves. The sound is made by the cover of the
fluid tank made of the thin metal membrane. The latter deforms when the pressure inside the
tank varies and makes the sound. Web sites in English and in both English and French present
interesting features of the steam boats and how to do it yourself (the toy is sold in traditional
toy shops in France). They also give references to other web pages and to a discussion group
on these wonderful toys.
Steam boat
Scheme of the steam boat
One can mention that the boat engine is similar to the PHP. The tubes play the role of the
condenser and adiabatic sections. The water reservoir (tank) works as the evaporator.
Scheme of the engine of the steam boat
This boat works according to the same principle as the PHP. The water plugs oscillate inside
the open tubes and the water is alternatively expulsed or sucked up. During the expulsion, the
water flow is directed backwards while the suction is nearly isotropic. The created differential
momentum propels the boat forward.
What triggers the oscillations?
Researchers agree that the oscillations are driven by an instability that appears due to coupling
of the adiabatic vapor compression and evaporation/condensation mass exchange. This
instability is not yet understood. What is its principal positive feedback that makes the system
unstable? What provides the instability threshold? Is the stopping threshold (measured by
lowering the heating/cooling power) differs from the oscillation start threshold? These
questions need to be answered. A parametric study of the instability needs to be carried out
(different fluids, temperatures, pressures). The behavior of the physical parameters in the
vapor phase remains to be controversial. In some modeling approaches, the vapor is allowed
to be strongly overheated due to its compression. It is assumed in the others to be at saturation
temperature corresponding to its pressure, which is a behavior analogous to that observed in
bubbles at boiling or in conventional heat pipes. However, the vapor compression is a moving
force of the oscillations and its behavior needs to be clearly understood. We proposed recently
a model that describes the simplest PHP that contains one bubble and one liquid plug. We
have discussed the factors that define its frequency and the threshold of oscillations. The
model shows the importance of the liquid films left on the internal wall of the tube by the
receding liquid plugs. The model agrees with the experimental results obtained in
collaboration with CETHIL.
Multibubble PHP model
To our knowledge, there is only one approach to the bubble-level modeling of the PHP. We
developed a new approach based on the developed recently single bubble model. It is capable
to describe the variable bubble number so that events like bubble coalescence can be
accounted for. The computer code is object oriented and is written with C++. The volume of
its output data might be (and usually is) very large and difficult to process. A special
application, called PHP Viewer, has been developed. It visualizes data files created with the
simulation program. The PHP Viewer allows visualization of the dynamics of gas-liquid
interfaces and of the wetting (liquid) films that envelope the gas. The film dynamics is very
important because their evaporation/condensation is the main moving force of the oscillations.
The wetting films cover the internal tube walls completely when the gas exists in the
condenser and adiabatic sections. The evaporator section may or may not be covered by the
films. The film length in the evaporator changes because the films vaporize. The films are left
on the walls by the receding gas-liquid menisci or "eaten up" by them when they advance.
The next figure shows how the liquid plugs, the vapor and the films are represented by PHP
Viewer. The evaporator area is shown with rose and the condenser with light blue color. Their
temperatures and the simulated time moment are presented at the top.
An example of the PHP modeling (the working fluid: water) is presented on the video. It
shows also some functionality of PHP Viewer 1.5 like animation speed control. Double click
to open the video fullscreen, press Escape to exit.
This simulation is one dimensional. The only space variable x runs along the tube of the PHP.
The modeling is performed by breaking the loop, "unbending" it, and imposing periodic
boundary conditions at its ends as is shown in the figure below. The evaporator, adiabatic and
condenser sections are indicated with the same colors as above and with the letters E,A,C,
respectively.
The time evolution of positions of the gas-liquid interfaces is plotted below. Only a part of the
whole x extension is shown. Several stages of the evolution can be distinguished. First, some
bubbles disappear because the liquid plugs coalesce between them. The coalescence
corresponds to the point where two interfaces meet each other. The instability develops next
and the amplitude of oscillations grow with time. The last stage is that of the developed
oscillations.
Heat transfer
The PHP Viewer 1.6 can display the liquid temperature distribution shown by colors. The
correspondence colors-temperatures are shown with a bar at the top of the screen. Red (blue)
corresponds to the highest (lowest) displayed temperature. An example of the temperature
variation in the liquid is presented in the video below where the gravity is directed to the
right. It shows that the ends of the liquid plugs that enter the evaporator become warmer than
the rest of the plugs. The temperature of the liquid-vapor interfaces is the saturation
temperature that may quickly vary in time (following the pressure of the vapor). An example
of the temperature variation in the regime of developed oscillations is shown in the video
below. Double click to open the video fullscreen, press Escape to exit.
The corresponding heat transfer evolution is shown in the image below. The heat exchange
with evaporator and condenser are shown. In the developed regime, a dynamic equilibrium is
established: the time average of the power taken from evaporator is equal to that average
power given to the condenser.
In this particular case, about 60% of the power given to evaporator is transferred due to the
latent heat during film evaporation. The other part of the heat is taken due to the heating of the
liquid plugs when they are situated inside the evaporator part. Since at any time moment there
is one or several bubbles inside the condenser, the major part (99%) of the condenser heat
exchange is performed via condensation on the films that cover the internal walls of the tube.
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