Modeling of Pulsating Heat Pipe %28PHP%29

Modeling of pulsating heat pipe (PHP)

by V.S. Nikolayev

Postdoc vacant position 2014 concerning this subject

One of the contemporary technological challenges is a reduction of mass of transportation means in order to reducetheir energy consumption and CO

2 emission. This requires replacing of metals by lighter synthetic materials

(composites, ceramics, etc.), which, however, are poor heat conductors and thus require special thermalmanagement solutions for their cooling capability to handle heat loads up to several kW. On the other hand, withthe 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 heatfluxes of 100 W/cm2, long term reliability, and very low costs for consumer market products, among others. Thisnecessitates the development and use of more efficient, nontraditional cooling approaches. Special devices calledheat 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) isbrought in thermal contact with a hot point to be cooled. The other end (called condenser section) is connected tothe cold point where the heat can be dissipated. A portion of the tube between evaporator and condenser is calledadiabatic section.

The working fluid and its pressure are chosen in such a way that the saturation temperature is between theevaporator temperature T

e and condenser temperature T

c. 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 theevaporator section. The heat is transferred mainly due to the latent heat absorption in the evaporator and itsrelease in the condenser. Since the latent heat is large, the heat pipes are quite efficient. They are capable ofevacuating up to 100-200 W/cm2. There are different kinds of heat pipes. They differ by their geometry and amechanism 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 highlocalized heat fluxes to provide a necessary level of temperature uniformity across the components that need to becooled. 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.

Modeling of pulsating heat pipe (PHP) file:///C:/Users/ojn.WIN-NTNU-NO/Documents/ToBackup/Literature...

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Two possible PHP geometries.

When the temperature difference between evaporator and condenser exceeds a certain threshold, the gas bubblesand liquid plugs begin to oscillate spontaneously back and forth. The amplitude of oscillations is quite strong and theliquid plugs penetrate into both condenser and evaporator. The heat is thus transferred not only by the latent heattansfer like in other types of heat pipes, but also by sweeping of the hot walls by the colder moving fluid and viceversa. 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 totransfer several kW to distances of the order of 1 m even when their orientation with respect to gravity isunfavorable. For comparison, advanced heat pipes used for spatial applications have heat transfer capacity(measured in Wm) order of value smaller. The heat transfer capacity of the conventional heat pipes used forcooling of microelectronic devices like laptop computers is 2 to 3 orders of value smaller than that of PHPs. Thesefeatures make PHP extremely promising for the thermal management of the next generation of electronic and othersystems. However, the functioning of PHPs is not completely understood. A complicated interplay of differenthydrodynamic and phase-exchange phenomena needs to be accounted for in the modeling approaches. Unlike otherheat transfer devices, the functioning of PHPs is non-stationary and thus difficult to model. A number of PHPstudies have been carried out since 1990s. Researchers agree that the oscillations are driven by an instability thatappears due to coupling of the adiabatic vapor compression and evaporation/condensation mass exchange. Howeverthis instability has not been studied until recently. Such important parameters as oscillation threshold, heattransfer coefficient, and maximum heat load cannot be predicted from calculations. It is not even clear whether theoscillations are persistent or not and at which regimes. For these reasons the PHP applications are very limited. ThePHP parameters are adjusted empirically, often without any certainty. To our knowledge, only a couple of smallcompanies in the world produce them. A comprehensive introduction to PHPs can be found in PhD theses in Englishor French.

There are two possible PHP geometries: open loop and closed loop PHP. In the open loop PHP, the ends may beopen or closed. It is however generally recognized that the closed loop PHP is more efficient. For this reason, wetarget 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 thesound made by this toy while it moves. The sound is made by the cover of the fluid tank made of the thin metalmembrane. The latter deforms when the pressure inside the tank varies and makes the sound. Web sites in Englishand in both English and French present interesting features of the steam boats and how to do it yourself (the toyis sold in traditional toy shops in France). They also give references to other web pages and to a discussion groupon these wonderful toys.


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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 adiabaticsections. 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 andthe water is alternatively expulsed or sucked up. During the expulsion, the water flow is directed backwards whilethe 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 adiabaticvapor compression and evaporation/condensation mass exchange. This instability is not yet understood. What is itsprincipal positive feedback that makes the system unstable? What provides the instability threshold? Is the stoppingthreshold (measured by lowering the heating/cooling power) differs from the oscillation start threshold? Thesequestions 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 isassumed in the others to be at saturation temperature corresponding to its pressure, which is a behavioranalogous to that observed in bubbles at boiling or in conventional heat pipes. However, the vapor compression is amoving force of the oscillations and its behavior needs to be clearly understood. We proposed recently a model thatdescribes the simplest PHP that contains one bubble and one liquid plug. We have discussed the factors that defineits frequency and the threshold of oscillations. The model shows the importance of the liquid films left on theinternal wall of the tube by the receding liquid plugs. The model agrees with the experimental results obtained incollaboration with CETHIL.

Multibubble PHP model

To our knowledge, there is only one approach to the bubble-level modeling of the PHP. We developed a newapproach based on the developed recently single bubble model. It is capable to describe the variable bubblenumber so that events like bubble coalescence can be accounted for. The computer code is object oriented and iswritten with C++. The volume of its output data might be (and usually is) very large and difficult to process. Aspecial application, called PHP Viewer, has been developed. It visualizes data files created with the simulationprogram. 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 themain moving force of the oscillations. The wetting films cover the internal tube walls completely when the gas existsin the condenser and adiabatic sections. The evaporator section may or may not be covered by the films. The filmlength in the evaporator changes because the films vaporize. The films are left on the walls by the recedinggas-liquid menisci or "eaten up" by them when they advance. The next figure shows how the liquid plugs, the vaporand the films are represented by PHP Viewer. The evaporator area is shown with rose and the condenser with lightblue color. Their temperatures and the simulated time moment are presented at the top.


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An example of the PHP modeling (the working fluid: water) is presented on the video. It shows also somefunctionality of PHP Viewer 1.5 like animation speed control. Double click to open the video fullscreen, press Escapeto exit.

This simulation is one dimensional. The only space variable x runs along the tube of the PHP. The modeling is


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performed by breaking the loop, "unbending" it, and imposing periodic boundary conditions at its ends as is shownin the figure below. The evaporator, adiabatic and condenser sections are indicated with the same colors as aboveand 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 isshown. Several stages of the evolution can be distinguished. First, some bubbles disappear because the liquid plugscoalesce between them. The coalescence corresponds to the point where two interfaces meet each other. Theinstability develops next and the amplitude of oscillations grow with time. The last stage is that of the developedoscillations.

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 wherethe gravity is directed to the right. It shows that the ends of the liquid plugs that enter the evaporator becomewarmer than the rest of the plugs. The temperature of the liquid-vapor interfaces is the saturation temperature thatmay quickly vary in time (following the pressure of the vapor). An example of the temperature variation in theregime of developed oscillations is shown in the video below. Double click to open the video fullscreen, press Escapeto exit.


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The corresponding heat transfer evolution is shown in the image below. The heat exchange with evaporator andcondenser are shown. In the developed regime, a dynamic equilibrium is established: the time average of the powertaken 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 filmevaporation. The other part of the heat is taken due to the heating of the liquid plugs when they are situated insidethe 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 ofthe tube.


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References

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