Multi-parametric experimental validation of a numerical model for the Pulsating Heat Pipe transient simulation

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Dipartimento Di Ingegneria Civile e Industriale Master of Science in Aerospace Engineering

Multi-parametric experimental validation of a

numerical model for the Pulsating Heat Pipe

Transient Simulation

Thesis advisor:

Prof. Sauro Filippeschi

Research supervisors:

Dr. Mauro Mameli

Dr. Vadim Nikolayev

Candidate:

Mauro Abela

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List of Figures

1 Typical heat loads for an Earth orbiting satellite . . . 2

2 Solar and Room Temperature Body Spectral Distribution . . . 3

3 International Space Station deployable radiators . . . 7

4 a) Patch heaters made in custom shapes; b) Cartridge heater . 7 5 NASA Parker Solar Probe louvers . . . 8

6 Wick heat pipe scheme . . . 10

7 Common wick cross-sectional geometries: (a) screen mesh, (b) porous sintered metal, (c) axial grooves, (d) artery, (e) com-posite and (f) screen covered axial grooves-Adapted . . . 11

8 Variable conductance heat pipe . . . 12

9 Loop heat pipe . . . 13

10 Pulsating heat pipe . . . 14

1.1 PHP prototype . . . 24

1.2 PHP representation and sensors locations . . . 25

1.3 Calibration test rig . . . 27

1.4 Calibration Curve . . . 28

1.5 Example of temperature distribution along the tube during micro-gravity . . . 28

1.6 Pinhole camera . . . 29

1.7 Calibration transformations . . . 31

1.8 Pincushion distortion on left, barrel distortion on the right . . 31

1.9 Sapphire tube infrared image before (top) and after (bottom) distortion correction . . . 32

1.10 Re-projection errors and average re-projection error . . . 33

2.1 Algorithm block diagram . . . 35

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2.3 Tube infrared image on top; in the bottom, temperature dis-tribution along tube axis T (x) (orange); the T (x) first deriva-tive DT (x)(blue); filtered DT (x) in black, local maxima (yel-low), local minima (green), liquid plugs left ends(vertical green

lines),liquid plugs right ends(vertical violet lines). . . 36

2.4 From empMtrx to SlugMtrx . . . 36

2.5 manualPlug user interface . . . 38

3.1 Two consecutive frames . . . 39

3.2 SlugIDMtrx k-1 and k columns . . . 40

3.3 SlugIDMtrx k-1 and k columns after ID assignment . . . 41

3.4 k-1 and k frames and SlugIDMtrx columns before ID re-assignment 41 3.5 k-1 and k frames and SlugIDMtrx columns after ID re-assignment 42 3.9 Evolution of temperature and position of a specif liquid plug. 44 3.10 Lengths of liquid plugs visible in the IR window. . . 45

3.6 getID function block diagram. Executed for each frame . . . . 46

3.7 Liquid plugs velocities (Parabola 9 day 3) . . . 47

3.8 Liquid plugs lengths discrepancies (Parabola 9 day 3) . . . 47

4.1 Sketch of the closed loop PHP and topological transformation 49 4.2 PHP basic elements . . . 50

4.3 Geometry of effective evaporators and condensers . . . 52

4.4 General scheme of the C++ program . . . 56

4.5 Computer representation of the instantaneous state of the PHP as a doubly connected list. . . 57

4.6 The PHP geometry pictured by the PHP_Viewer post-processor of the CASCO software. . . 59

5.1 Tested device topology . . . 60

5.2 Tested device on its mounting and an example of liquid initial distribution . . . 61

5.3 Side view of the tested device. In rose, the evaporator spreader; in blue the condensers. . . 62

5.4 Evaporator spreader thermocouples temperature evolution . . 63

5.5 Model of one tube of the empty PHP . . . 64

5.6 Overall scheme of the empty PHP model . . . 65

5.7 Average difference between empty PHP test temperature and model as function of Us . . . 66

5.8 Experimental vs modeled empty PHP evaporator spreader tem-perature . . . 66

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6.1 Effects of different initial distribution. In the up left corner, two graphic representations of initial distributions inside PHP tubes. in blue the liquid plugs, in purple the bubbles . . . 69 6.2 Temporal evolution of temperatures experimental vs simulation 71 6.3 Thermocouples locations on PHP . . . 71 6.4 Liquid plug velocity comparison, experimental (blue) and

sim-ulation (orange) . . . 73 6.5 Liquid plug lengths comparison, experimental (red) and

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List of Tables

1 Typical thermal requirements for spacecraft components . . . 4 2 Wick Heat Pipe vs Pulsating Heat Pipe performances . . . 16 1.1 Measured quantities and uncertainties . . . 25 6.1 Simulation input parameters . . . 69 6.2 Max differences between experimental and simulation

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Abstract

The Thermal Control Subsystem (TCS) has always played a key role in space-craft design. Its primary objective is to maintain all the spacespace-craft components (i.e. payload, subsystems etc.) within their required temperature constraint during each mission phase. Moreover, the continuous miniaturization of elec-tronic components along with the complexity rising of mission requirements are pushing towards the research of new solutions.

An emerging technology, the Pulsating or oscillating Heat Pipes (PHP), is one of the cheapest and most reliable thermal management systems. For these reasons is one of the most promising not only for space applications but also for ground ones. However, since its governing phenomena are not well understood, its large application is still far from being reality. In the last two decades many significant efforts have been done to develop numerical models of such devices, but just few of them are able to mimic a complete thermo-hydraulic response. The validation attempts in literature, are based on the evaluation of the overall performance (i.e equivalent thermal resis-tance) by varying a single parameter such as the filling ratio or the heat load. This is one of the reasons why these model are not thoroughly validated. A multi-parametric validation, in transient conditions, is needed to really assess whether a model is able to provide a fair physical interpretation of the phys-ical involved phenomena. One of the most sophisticated models present in literature is the one developed by V. Nikolayev, which is able to reproduce many physical phenomena observed in PHPs transients. However, it has not been validated yet due to the lack of experimental data.

This thesis represents a first step towards a complete validation of Nikolayev’s model using experimental data provided by the University of Pisa. First, an experimental data post-processing has been performed to obtain all the rele-vant quantities for the validation. Then, Nikolayev’s model has been updated in order to represent as closely as possible the real device with all its fea-tures. Startup simulation results, carried out on multiple parameters, show a remarkable agreement from both qualitative and quantitative point of view.

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Introduction

In this chapter, starting from a general description of the space environment and its peculiarities from a thermal point of view, some common thermal management solutions are presented, giving a particular emphasis to the Heat Pipe technology. A qualitative description of their working principle is pro-vided along with a digression on Heat Pipes employment in past space mis-sions [42]. To follow, it is provided a description of the emerging Pulsating Heat Pipe technology with its strengths and weaknesses as well as a discus-sion about the lack of a model able to predict its behavior which makes the Pulsating Heat Pipes not ready for a large scale application. Finally, after a review of some of the most remarkable models present in literature so far, the objective of this thesis is presented.

I.1 Thermal Control Subsystem

The main objective of the Thermal Control Subsystem (TCS) is to maintain all spacecraft, payload, subsystems between temperature constraints, i.e. be-tween the maximum and minimum operating temperatures [21]. This task is not easy to be performed since the spacecraft is usually in a strongly varying thermal environment. Another key task of the Thermal Control Subsystem is to mitigate spacecraft structures thermal gradients, that can cause high me-chanical stresses and consequently a lifetime reduction. For all these reasons, a good design of the Thermal Control Subsystem is mandatory for ensuring high performances and survival of the spacecraft.

I.1.1 Environmental Heat Sources

During the development and operational life cycle, the spacecraft is exposed to various environmental influences (1). Launch phase environment is dominated by radiant heating from internal surface of booster fairing and free molecular heating due to friction with atmosphere. Outside atmosphere, direct sunlight, reflected sunlight (Albedo), celestial bodies Infrared energy, represent main

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heat sources. Usually the Thermal Control Subsystem is designed to meet in-orbit requirements, while thermal control during ground operations and launch ascent phase is performed acting on the environment rather than the spacecraft. For example, in the latter situation, a common solution is to blow cold or warm air on the spacecraft. In orbit, because of the atmospheric con-vection absence, the overall thermal control consists in balancing the energy absorbed by the environment and the one generated by the spacecraft internal component, against the energy re-emitted as infrared radiation.

Figure 1: Typical heat loads for an Earth orbiting satellite Direct Solar

Sunlight is the main heat source in space, its intensity is not only a function of the distance from the sun ( 1367W/m2 _{at ∼ 1AU, Earth mean distance from} the sun), but depends also on the wavelength. Its energy distribution is, in fact, approximately 7% ultraviolet, 46% visible and 47% near Infrared. Since the Infrared is of a shorter wavelength than that emitted at room temperature, it is possible to select thermal-control finishes that are reflective in the sunlight spectrum but high emissive in long-wavelength Infrared (see Fig. 2, where continuous lines identify the wavelength of peak emission for solar energy and a body at room temperature. Note that solar energy wavelength Is much shorter than that of a body at room temperature. The dashed line represents the absorptance or emittance of a quartz mirror radiator).

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Figure 2: Solar and Room Temperature Body Spectral Distribution

Albedo

Albedo is nothing but the sunlight reflected off by an astronomical body. Be-ing dependent on reflectBe-ing surface conditions, its intensity is highly variable. For example, Albedo tends to increase with clouds coverage and decreases with solar elevation; reflectivity is greater over land rather than over oceans. For these reasons, Earth Albedo usually increases with increasing latitude. However, this variability makes the selection of the best Albedo uncertain.

Astronomical bodies Infrared emission

The sunlight fraction not reflected as Albedo, is absorbed and eventually re-emitted as infrared energy. The sunlight intensity variation, while less sig-nificant with respect to the Albedo ones, are still considerable. Since the heat radiated is proportional to the fourth power of the absolute temperature, it is clear that the surface temperature of the emitting body has a strong influ-ence, in particular, a warmer surface region will emit more than a colder one. Moreover, clouds coverage has an influence, not only because their top is cold but also because they block the radiation from the warm region below. The Earth, for example, having an average temperature of -18°C, emits energy approximately in the same wavelength as spacecraft. In this case is not pos-sible to adopt the same loophole as in the case of the solar short-wavelength infrared energy, i.e. using thermal control coatings to reduce absorption since it would impact on the spacecraft capability of wasting heat. For this reason

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Earth infrared can be a particularly heavy backload on spacecraft in low-altitude orbits.

Free molecular heating and charged particle heating

This form of heating is due to the bombardment of spacecraft surfaces by molecules present in the outer layers of atmosphere. Usually it is encoun-tered during the launch ascent just after the payload fairing separation. In few cases, a spacecraft can experience in orbits with altitude less than 180 km. Generally, the free molecular heating effects can be tolerated without a particular thermal control.

Charged particle heating is due to bombardment by charged particles, coming mainly from the sun and trapped by Van Allen belts. Even if the heating contribution due to this phenomenon is usually small, it can be relevant in those cases in which the equipment operates at cryogenic temperatures.

I.1.2 Typical Thermal Requirements

In this section, a general overview of common spacecraft components thermal requirements is provided.

Component Typical Temperature Ranges [°C]_Operational _Survival

Batteries 0 to 20 - 10 to 25

Solar Panels -150 to 110 -200 to 130

Antennas -100 to 100 -120 to 130

Star Tracker 0 to 30 -10 to 40

Hydrazine Tanks and Lines 15 to 40 5 to 50

Table 1: Typical thermal requirements for spacecraft components

Batteries

Batteries are one of the most thermally sensitive component of a spacecraft. Usually choice falls in two type of batteries: NiCd batteries and NiH2 with operational temperature ranges respectively of 0°C-10°C and 0°C-20°C. In the case of NiH2, Thermal Control Subsystem does not only keep temperature within operational ranges but provides a minimal temperature difference be-tween each cell and also within the cell for efficient charging.

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Solar Arrays and Antennas

Solar array, along with Antennas, belong to the category of external spacecraft devices exposed to the most sever thermal environment.

Solar arrays are employed to convert solar energy into electricity. The solar cell efficiency, the ratio of the output electrical power to the incident radiation, is inversely proportional to its temperature; then, a correct thermal management guarantees the cells to operate into acceptable efficiency ranges. White paint coatings or multi-layer insulation system are employed to minimize the heat contribution coming from Earth (Albedo and Infrared radiation).

Moreover, for both Antennas and solar arrays, temperature control is needed to avoid heavy thermal cycles that eventually result in a lifetime reduction. Sensors

Some sensors, such as infrared detectors, operate at cryogenic temperatures (125° K and below) in order to avoid disturbances due to infrared emission of the device itself. In these scenarios, advanced thermal technology are adopted include constant and variable conductance heat pipes, phase change materials, capillary loops, loop heat pipes and louver systems.

Optical sensors are highly sensitive to thermal gradients because of different thermal expansion coefficients between lens and mounting substrate. Thermal control is therefore needed to maintain thermal gradients within limits, pre-venting distortions that can lead to optical path misalignments and eventually optics cracks.

I.1.3 Thermal Control Subsystem Components

Thermal control techniques are usually divided into two categories: Passive Thermal Control and Active Thermal Control . The first makes use of coat-ings, surface finishes to maintain temperatures in required limits; the latter, makes use of more complex systems such as heaters and thermo-electric cool-ers to fulfill the same objective.

Surface Finishes

In spacecraft thermal design, a wide variety of thermal coatings have been em-ployed for various purposes. Solar reflectors such as white paints, aluminum-backed teflon or silver-aluminum-backed teflon are used to minimize absorption of solar energy while emitting energy almost like an ideal blackbody; polished alu-minum foil or gold plating are used to minimize both absorbed solar energy

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and infrared emission.Black paint is commonly used in the interior of the vehicle if it is desired to exchange energy with the compartment or other equipment.

Thermal control finishes effectiveness in orbit is decreased by charged parti-cles bombardment, ultraviolet radiation, high vacuum and contaminant film deposit with the result of increasing solar absorptivity and a little effect on infrared emissivity.

Insulation

Multilayer Insulation (MLI) is one of the most common thermal control ele-ment on spacecraft, it is composed of multiple layers of low-emittance films with low conductivity between layers. The simplest construction is a layered blanket assembled from embossed, thin mylar sheets with a vacuum-deposited aluminum finish on one side of each sheet. The embossing results in the sheets touching only at a few points, thereby minimizing conductive heat paths be-tween layers. The layers are aluminized on one side only, so that the mylar can act as a low-conductivity spacer. It is used to prevent excessive heat loss from a component or excessive heating from the environment or rocket plumes. It is also used to protect internal propellant tanks, propellant lines, solid rocket motors, and cryogenic dewars.

Radiators

Spacecraft waste heat is mostly rejected to space by radiators as IR radiation. They can be made in different forms, such as structural panels, deployable panels (Fig. 3), flat plate radiators on the side of the spacecraft etc. Radiators reject both satellite waste heat and any other radiant-heat loads absorbed from environment or from other spacecraft surfaces. For these reasons, they usually have a high IR emissivity (> 0.8) and low solar absorptivity (< 0.2).

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Figure 3: International Space Station deployable radiators Heaters

Seasonal environmental conditions, internal heat generation, degradation of passive thermal control element (surface finishes), make temperature varia-tions higher than what passive components can manage. For this reason, sometimes, it is necessary to equip the spacecraft with heaters which ensure components temperature not to go below survival limit. The most common

Figure 4: a) Patch heaters made in custom shapes; b) Cartridge heater type of heater used on spacecrafts is the patch heater (see Fig.4 a)). It consists of an electrical-resistance element sandwiched between two sheets of an insu-lating and flexible material. Another type of heater is the cartridge heater (see Fig.4 b)). It is usually used to heat blocks of material or high-temperature components. It consists of a resistor enclosed in a cylindrical metallic case.

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Usually an hole is drilled in the component to be heated and the cartridge is potted in the hole.

Louvers

Louvers (Fig. 5) are active thermal control elements which modulate radiant heat transfer not only of external radiators but also between internal space-craft surfaces or directly from internal to space. Typically, a louver in its fully open state can reject six times as much heat it rejects when it is in fully closed state so it finds application in those cases in which the heat to be rejected varies widely.

Figure 5: NASA Parker Solar Probe louvers

Heat Pipes

Heat Pipes are passive devices which use a closed two-phase fluid-flow cycle to transport large quantities of heat from one location to another without the use of electrical power, are presented in more details in the next section.

I.2 Heat Pipes

A typical heat pipe consists of an evacuated tube, partially filled with a work-ing fluid and then sealed. The tube material must be compatible with the working fluid such as Copper for water heat pipes, or aluminum for ammo-nia heat pipes.This technologically simple device makes it possible to transfer

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high heat rates over considerable distances, with minimum temperature drops, exceptional flexibility, see fig. 6. For a heat pipe to operate, the working fluid must be at saturated conditions, where the heat pipe contains both liquid and vapor. Because of this, fluids can only operate (theoretically) between the triple (freezing) point and the critical point, where vapor and liquid phases have the same properties. In reality, the operating temperature range for any given fluid is smaller, since the power that the heat pipe can carry drops off sharply near the freezing and critical temperatures. In 1963, Los Alamos physicist George Grover successfully tested a capillary-based heat transfer de-vice, which he patented in the same year with the name heat pipe. Grover’s inspiration for the heat pipe came from rudimentary heat pipes used by British bakers in 19th century. The development of such pipes began in 1839, when American inventor Jacob Perkins patented the hermetic tube boiler. In 1936 Angier March Perkins (Jacob’s son), patented a the tube boiler modified ver-sion called Perkins Tube, which saw widespread use in locomotive boilers and working ovens (including a mobile oven for the British Army). The Perkins Tube served as a the base for Grover’s development of modern heat pipes[10]. Although the capillary-based heat pipes were suggested for the first time by R. S. Gaugler of General Motors in 1942, only in early 1960s, the heat pipe technology has evolved into many different shapes and forms and used in numerous applications from computer cooling to spacecraft thermal control. Grover’s suggestion was taken up by NASA, which played a key role in heat pipe development in the 1960s, particularly regarding applications and relia-bility in space flight. NASA interest was due to the low weight, high heat flux, zero power draw and zero gravity environment adaptability that characterize heat pipes. The first application of heat pipes in the space program was the thermal equilibration of satellite transponders. The heat pipe cooling system managed the high heat fluxes and demonstrated flawless operation in micro-gravity. The cooling system developed was the first variable conductance heat pipe (VCHP), which actively regulates heat flow or evaporator temperature. Early experiments of heat pipes for aerospace applications were conducted in sounding rockets which provided six to eight minutes of zero-g conditions. In 1974, ten separate heat pipe experiments were flown in the International Heat Pipe Experiment [30]. Also heat pipe experiments were conducted aboard the Applications Technology Satellite-6, in which an ammonia heat pipe with a spiral artery wick was used as a thermal diode [18]. With the use of the space shuttle, flight testing of prototype heat pipe designs continued at a much larger scale. A 6-ft. mono groove heat pipe radiator with Freon 21 as the working fluid was flight tested on the eighth space shuttle flight [38]. The Space Station Heat Pipe Advanced Radiator Element consisting of a 50-ft.

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Figure 6: Wick heat pipe scheme

long high capacity mono groove heat pipe encased in a radiator panel, was flown on the space shuttle during 1989 and also, two heat pipe radiator panels were separately flight tested in a shuttle flight of 1991 [6] [7]. In 1992, two dif-ferent axially grooved oxygen heat pipes were tested in a Hitchhiker Canister experiment that was flown aboard the Shuttle Discovery (STS-53) by NASA and the Air Force to determine startup behavior and transport capabilities in micro-gravity [5]. An advanced capillary structure which combined re-entrant and a large number of micro grooves for the heat pipe evaporator was investi-gated in micro-gravity conditions during the 2005 FOTON-M2 mission of the European space agency [39]. In 2007 Swanson presented the NASA thermal technical challenges and opportunities for the new age of space exploration with emphasis on heat pipes and two phase thermal loops [45].

I.2.1 Wick Heat Pipes

Starting from the left of fig. 6, the three main sections can be distinguished: evaporator, adiabatic section and condenser. To understand the working prin-ciple of such heat pipe, let’s consider a starting situation in which the liquid in the wick (Fig. 7) and the vapor are at saturation. In this situation, if heat is injected at the evaporator section, the liquid in the evaporator boils to vapor and moves to the condenser through the adiabatic section; once in the condenser, the vapor condenses and the liquid moves back to the evaporator under the effect of the capillary pressure.

Variable Conductance Heat Pipes

Variable conductance heat pipe (VCHP) Fig. 8 is a capillary driven heat pipe filled with a working fluid and, in addition, with a non-condensable gas (NCG). This type of heat pipe works by varying the condenser section surface

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avail-Figure 7: Common wick cross-sectional geometries: (a) screen mesh, (b) porous sintered metal, (c) axial grooves, (d) artery, (e) composite and (f) screen covered axial grooves-Adapted

able to the working fluid as function of the evaporator temperature. When heat is injected, the NCG is pushed toward the condenser by the working fluid until the NCG pressure is high enough to prevent the working fluid from covering all the condenser surface. As the evaporator temperature increases, the vapor temperature (and pressure) rises, the NCG is compressed, see the lower portion of Fig. 8 and thus the condenser is more exposed to the working fluid. This increases the conductivity of the heat pipe and drives the temper-ature of the evaporator down. Conversely, if the evaporator cools, the vapor pressure drops and the NCG expand as seen in the upper portion of Fig. 8 where condenser is partially active. This reduces the portion of the condenser available for condensation and thus decreases the heat pipe conductivity.

Cryogenic Heat Pipe

Some sensors and communication systems must operate at cryogenic temper-atures and therefore a thermal management is needed in low tempertemper-atures environment. A Copper heat pipe with Acetone as a working fluid was tested on the Space Shuttle Discovery (STS-60) for the Stirling Orbital Refrigerator/ Freezer Experimentation. The heat pipe was proved capable of removing up to 10 W between a temperature range of 213 K - 243 K. Other applications of cryogenic heat pipes have been reviewed elsewhere[37].

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Figure 8: Variable conductance heat pipe

Nano Fluids Heat Pipe

Recent development of nanofluids, i.e. conventional heat transfer fluids with suspended nanometer-sized oxide or metallic particles suspension, increased heat transfer rates of more than 20%. In references[43] [44] it has been demon-strated that is possible to obtain a significant improvement of heat transfer rates by dispersing copper, alumina-and silver colloid suspensions in water. A similar enhancement of thermal conductivity was observed with copper oxide dispersed in water and ethylene glycol[46]. Moreover, the magnetic affinity of the solid particles in metallic suspensions allows for their manipula-tion by electromagnets, thereby eliminating the need for convenmanipula-tional pumps and controls and allows for enhanced heat transfer. This has created inter-est in the application of a novel nanofluid-based actively controlled thermal management system for small satellite applications[22]. The advantages of such a system include improved heat transfer performance, oil-less operation, compact size, reduced weight, and low power consumption, all of which are especially important for space, air, and even naval operations. NASA has set a road map for the development of high temperature heat pipes which will be a solution for the high heat flux encountered during ascent and reentry of the space vehicle[12]. The fluid with ultra fine suspended nano-particles will be the advanced fluid for satellite applications of the heat pipe.

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Loop Heat Pipe

The loop heat pipe (LHP) Fig. 9 is a two-phase heat transfer device which removes heat from a source and passively transfers it to a condenser. LHP’s have the advantage of being able to provide reliable operations over long distance with a small temperature difference. Main components of LHP are an evaporator, a condenser, a vapor line and a compensation chamber. The wick structure is only in the evaporator and in the compensation chamber; rest of the loop is a wickless tube. The working principle of LHP is that liquid in the evaporator section evaporates due to applied heat load, a meniscus is formed at vapor-liquid interface in the wick, a pressure gradient developed as result of the temperature difference between evaporator and condenser pushes the vapor towards the condenser where it condenses. The liquid is pushed back to the evaporator by surface tension force. The compensation chamber is an integral part of the evaporator and is connected to the evaporator by a secondary wick.

Figure 9: Loop heat pipe

Different designs of LHPs ranging from powerful, large size LHPs to minia-ture LHPs (micro loop heat pipe) have been developed and successfully em-ployed in a wide sphere of applications both ground based as well as space applications[19][20]. LHPs operating with ammonia as working fluid are cur-rently the most popular thermal control device for high powered telecom-munication satellites. The first space application of LHP occurred aboard a Russian spacecraft in 1989. LHPs are now commonly used in space aboard satellites including; Russian Granat, Obzor spacecraft, Boeing’s (Hughes) HS 702 communication satellites, Chinese FY-1 Meteorological satellite, NASA space shuttle in 1997 with STS-83 and STS-94. Existing LHPs and CPLs have only one evaporator and one condenser/radiator.

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I.2.2 Pulsating Heat Pipes

Figure 10: Pulsating heat pipe

Fig. 10 shows the basic working scheme of a Pulsating Heat Pipe (PHP). It a wickless, two-phase loop, proposed for the first time by Akachi[3] [2] in early 90’s. Since the wick is the most complex and expensive element of HP, its absence in PHP makes this technology reliable and cheap. The pipe is evacuated and partially filled with a working fluid that resides in the form of liquid plugs and vapor plugs train. The heated vapor plugs expand and push the adjacent fluid towards the condenser where heat is rejected and va-por condenses, recalling the adjacent fluid back to the evava-porator zone. This process results in an oscillating fluid motion. It is worth noting that the heat is transferred not only by the latent heat transfer like in other types of heat pipes, but also by sweeping of the hot walls by the colder moving fluid and vice versa. For comparison, 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.

In order to better understand the reasons of the growing interest on PHP technology in space field, it is useful introduce the Bond number, a

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dimen-sionless parameter that characterizes the ratio of gravitational forces to surface tension forces

Bo = (ρl− ρv)gL 2

σ (1)

where ρl is the liquid phase, ρv is the vapor phase density, g is the accel-eration of gravity, L is the characteristic length and σ is the surface tension. A value of Bo << 1 implies the flow in question is only weakly dependent on gravitational forces, whereas Bo >> 1 implies gravitational forces dominate over surface tension forces and the working fluid will stratify by gravity and oscillations will cease. From eq. 1, it is possible to estimate the critical diam-eter (dcri), i.e the theoretical maximum inner diameter of capillary tube, by posing dcri = 2L.

dcri = 2 p

σ/g(ρl− ρv) (2)

From eq. ??, it is clear that as g decreases, the dcri increases and, since the mass of the thermal fluid per unit length is proportional to the square of the inner diameter, the total heat exchanged increases. Theoretically for g = 0 m/s2 _{,the capillary diameter tends to infinite, in reality, the increase of the} inner diameter is also limited by inertial and viscous effects, in the sense that when the fluid velocity is high, the menisci are unstable and the liquid plug-vapor plug condition is only possible for smaller diameter with respect to dcri. In particular, taking into account inertial and viscous effects, the critical di-ameter can be expressed as

dcr,Ga = s 160µl ρlUl r _σ (ρl− ρv)g (3) where it is again evident that a decrease of g implies an increase of the critical diameter. This is the reason that makes the PHP technology suitable for high power heat transfer in space applications.

However, PHP application is still far from being a reality because, aside the technological simplicity, high reliability and high heat fluxes, there is a com-plexity of the phenomena that govern PHP functioning that is, in fact, not well understood yet.

By the time being, no model in the literature is able to describe the interplay of different hydrodynamic and phase-exchange phenomena and the intrinsically non-stationary operation to predict important design parameters, such as the

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oscillation threshold, heat transfer coefficient and maximum heat load. In the last two decades many significant efforts have been done by researchers who used different approaches to develop PHP numerical models. An overview of such attempts is provided in the next section.

Wick Heat Pipe Pulsating Heat Pipe Radial Heat Flux _{up to 250 W/cm}Very High 2 Medium

Axial Heat Flux High up to 600 W/cm2 High

up to 1200W/cm2 Total Power

(strong dependence on geometry)

Medium

up to 200W per unit up to 10000WHigh Thermal Resistance _{down to 0.01 degC/W}Very Low _{down to 0.02 degC/W}Very Low Equivalent Thermal

Conductivity up to 200000 W/(m K)Very High up to 10000 W/(m K)Medium Start-up time _{few seconds}Fast _{2-3 minutes}medium

Effects of inclination angle

Medium Sintered heat pipe can suffer in the top

heating mode.Very efficient in bottom

heating mode

Critical A proper design may avoid strong effects, top heating

mode is difficult

3D Space Adaptability Low High

Thermally Controlled

Surface medium Large

cost _{(wick structure)}Medium _{(capillary tube)}Low Table 2: Wick Heat Pipe vs Pulsating Heat Pipe performances

I.2.3 Pulsating Heat Pipes numerical models

Most of the models in literature can be grouped in five categories:

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1. Continuum wave propagation approach, in which pressure oscillations are fundamental to induce vapor-liquid circulation;

2. Spring- mass- damper approach, in which the PHP is modeled as a single or multiple spring-mass-damper system;

3. 1D in-house codes, which use mass, momentum and energy conservation equations;

tem Artificial Neural Networks (ANN), a statistical data modelling in-spired by learning processes of human brain;

4. 2D, 3D Volume of Fluid approach (VOF), one of the Computational Fluid Dynamicas (CFD) methods.

The simple analytical model of Miyazaki and Akachi [31] [2] belongs to the (1) approach. The results showed that an optimal filling ratio exists for each PHP: high filling ratios produce a gradual pressure increase followed by a sudden drop; low filling ratios lead to chaotic pressure fluctuations. The same approach has been used by Miyazaki and Arikawa[32] who experimen-tally investigated the oscillatory flow in PHPs measuring the wave velocity, which resulted in fairly agreement with the previous predictions. Wong et al.[47] used the approach (2) modelling a Pulsating Heat Pipe as spring-mass- damper system (liquid slugs are represented by masses, vapor plugs by non-linear springs, friction and the capillary forces by non-linear dampers) in which a sudden pressure pulse was applied to simulate the heat input in vapor plugs. Moreover, minor friction losses, gravity and capillary effects have been neglected. These oversimplifications limit the model applicability. Ma et al.[25][24] using the same approach demonstrated that capillary tube diameter and bubble size determine oscillation occurrence and that their amplitude and frequency are influenced by fluid initial distribution and gravitational forces. In addition, their results indicated that the isentropic bulk modulus generates stronger oscillations than the isothermal bulk modulus. However, their model under-predicted the temperature difference between evaporator and condenser when compared with experimental results. Approach (4) is a novelty with re-spect to others. The first model of this category is the one proposed in 2002 by Khandekar et al.[17] [15] who trained an Artificial Neural Network with 52 sets of experimental data from a closed loop PHP. The model, fed with heat input and filling ratio, calculates the equivalent thermal resistance. The drawback of this kind of approach is the lack of a physical base; this limits the predicting power of the approach to the training experimental data. Several models using the (v) approach appear in literature [48][23][16][11][33] but, in general lack of experimental validation. Moreover, the computational costs of this approach

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are still high compared to others. The approach (3) is the most adopted and promising among the others being the one that gives more insights on PHP behavior with reduced computational costs. Hosoda et al.[14] proposed one of the first model that exploit the resolution of conservation equations; in their model they solved liquid momentum and energy balance neglecting the film presence, friction between working fluid and phase changes. The model over-predicted vapor pressure but showed that propagation of vapor plugs induced fluid flow in capillary tubes. Zhang et al. analytically investigated oscillatory flow in both U-shaped miniature channels[50] and closed-end PHP with an arbitrary number of turns, later they proposed models for heat transfer in the evaporator and condenser sections of PHPs with one open end by analyzing the film evaporation and condensation which drive oscillatory flow in PHP [49]. It was found that the overall heat transfer is dominated by the exchange of sensible heat, not by the exchange of latent heat. Similar results have been achieved by Shafii et al.[40] who developed a Lagrangian theoretical model to simulate the behaviour of plugs in both closed- and open-loop PHPs later improved including an analysis of boiling and condensing heat transfer in the thin liquid film separating the liquid and vapor elements[41]. One of the first most comprehensive model has been proposed only in 2005 by Holley and Faghri[13]. It was a model of a water PHP with sintered wick in which the momentum equation was solved for liquid plugs and energy equation taken into account for liquid phase, vapor phase and external tube wall. The model has been later improved by Mameli et al. [26][29][28] introducing effects of tube bends on the liquid plugs dynamics and the calculation of the two-phase heat transfer coefficient for liquid and vapour sections as function of the heat-ing regime. Das et al. [9] startheat-ing from Shafii’s et al. work [40], developed an evaporation/condensation model of single liquid/vapor couple able to explain the large amplitude oscillations observed experimentally.

Later Nikolayev[35] updated the same model to treat an arbitrary number of bubbles and branches proposing the use of an object oriented implementation which represented a step forward with respect to previous codes. The software that implements his algorithm is called CASCO (Code Avancè de Simulation de Caloduc Oscillant: Advanced PHP simulation code). Several phenomena occurring inside PHPs have been taken into account, such as coalescence of liquid plugs and film junction or rupture; in addition, the liquid film dynam-ics was accounted to correctly represent the vapor heat exchange. Few years later [36], Nikolayev revealed a mechanism of oscillation sustainment by bub-ble generation. The latter is essential for the PHP start-up in the presence of tube heat conduction; without bubble generation, whatever is the power input, the oscillation starts initially but chain bubble coalescence occurs and,

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eventually, all the liquid collapses into a single plug; PHP oscillations decline quickly. The simulations reproduced, at least qualitatively, many physical phenomena observed in PHPs but, as every model in the literature, still lack a thorough experimental validation. Nikolayev’s model is discussed in more details in part II.

I.3 Objective: a thermo-fluidic model

prelimi-nary validation

As is evident from what it has been said so far, there is a need of a proper val-idation of a PHP model. With proper validation, it is meant a simultaneous comparison of multiple parameters characterizing the PHP start-up behavior rather than a comparison of the overall performances. This is especially true at the present stage of research, in which, there is not a thorough understand-ing of all the phenomena involved in the PHP transients. This is where the present work comes in, showing all the steps done to achieve an experimental validation of Nikolayev’s model which is, so far, one of the most comprehen-sive (as it is discussed in more details in chapter 5). Starting from the data collected during the 67th _{European Space Agency parabolic flight campaign} by the University of Pisa [27], it was possible to obtain many parameters char-acteristic of the PHP. In particular, using infrared images framed through a sapphire section of the PHP tube, after a post-processing activity consisting in:

• correction of lens distortion ;

• Liquid plugs recognition and tracking;

it was possible to obtain informations of fluid motion inside the tube such as velocity, length and temperature distribution of liquid plugs. Moreover the tested PHP was equipped with numerous thermocouples which allow to have a wide view of the temperature temporal evolution of the device.

After an update of the Nikolayev’s model made to reproduce as faithfully as possible the tested device, simulations have been run and all the quantities above compared, showing remarkable results.

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Part I

Experimental data computer

vision analysis

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Chapter 1 Parabolic Flight Campaign

A parabolic flight is a mean to achieve micro-gravity environment in which to conduct an experiment. Twice per year ESA gives the opportunity to researchers who want to test their experiment in micro-gravity environment, to take part to the parabolic flight campaigns performed by Novespace (only provider of this kind of flight in Europe).

Among others ESA selected the University of Pisa’s concept of a pulsating heat pipe, especially designed for a future implementation on the heat transfer host module (HTH) of the International Space Station, for the 67th ESA Parabolic Flight Campaign.

The primary objectives of the experiment were:

• To prove that in micro-gravity condition, the operation of the device is purely thermally induced;

• To characterize the fluid local thermodynamic states close to the evap-orator and the condenser zones

• To unveil new insights on the Pulsating heat Pipes.

• To provide data for the validation of actual numerical model.

The tested device (Fig. 1.1 and Fig. 1.2) is a closed loop aluminum tube with an inner and outer diameter of 3mm and 5mm respectively, folded in a 14 turns configuration and partially filled with 22ml of perfluorohexane (50% volumetric filling ratio). An heat spreader made of two aluminum bars brazed on the tube in the evaporator zone and two on the tube in the condenser zone. The evaporator heat spreader is heated up by means of two ceramic ohmic heaters, the condenser heat spreaders are cooled down by means of a Peltier cell system coupled with a cold plate temperature control loop. An external

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Figure 1.1: PHP prototype

tube branch (total length 126 mm) made of sapphire glass, allows to investi-gate the fluid motion, patterns and temperature by means of infrared camera and a high-speed greyscale camera. In particular, the two cameras frame a 65.8 mm portion of the sapphire tube (see Fig.1.2). Before and after the sap-phire tube, the device is equipped with miniature pressure transducers (P1, P2 in Fig.1.2) and K-type micro-thermocouples that allow fluid’s temperature measurements (TC8_2, TC9_2 in Fig. 1.2. Five T-type thermocouples are located between the evaporator spreader and heater; six are located between the Peltier cold side and the condenser spreader; two on top of the condenser spreader; seven are located on the tube external wall: the labels TC 5-TC10 in figure 1, refer to the thermocouples used for the code validation. The heating power is provided by a programmable power supply. The main characteristics and uncertainties of the probes and peripherals are resumed in table 1.1.

The parabolic flight campaign lasted three days, during each day thirty-one parabolic maneuverer have been performed: the first parabola was followed by six sequences of five consecutive parabolas; after each sequence a five minutes break of steady flight was taken. Each parabola is a series of hyper-gravity period (20s±2s at 1.8g), micro-gravity period (20s±2s at 0g), hyper-gravity period with same duration and same acceleration as the first. During the first two days, devoted to the thermal characterization, the device has been heated up at the desired temperature before the micro-gravity occurrence and the

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Figure 1.2: PHP representation and sensors locations

Parameter Specs. Max. error

Tube wall temperature T-Type thermocouples (0.5mm bead diameter) ± 0.1 °C Fluid temperature Omega_{thermocouples (0.25 mm bead diameter)}® KMTSS-IM025E-150 K-Type ± 0.2 °C

Fluid Pressure Keller® _{PAA-M5-HB, 1bar abs} _{± 500 Pa}

Fluid temperature in

sapphire section AIM® infrared camera, (wavelength 3-5µm) ± 2 °C

Power Input GW-Instek®, PSH-6006A ± 3 W

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power was kept constant throughout each sequence. During the third day, devoted to the characterization of startup phenomena, the device, in some cases, has been heated up just after the occurrence of micro-gravity in order to prove that the fluid motion is not primed by inertial effects. In these cases, in order to start the tests from a thermal equilibrium condition, some parabolas have not been exploited allowing the whole system to cool down to the target temperature of the Peltier cold side, set at 20°C [27][8].

1.1 Infrared Analysis

Since in the recent years the IR sensors have become more accurate and re-liable, the IR analysis represents a breakthrough for the non-intrusive mea-surement of the fluid temperature distribution evolution with respect to other recent methods such as the laser-induced fluorescence. The main advantages of the IR technique are the high sensitivity, the low response time and the fact that the measurements are non-intrusive. On the other hand, an in-situ calibration is mandatory and the accuracy is still relatively low depending very much indeed on the procedure and the actual experimental conditions which may differ from the one adopted during calibration.

1.1.1 Calibration

The calibration is obtained by recreating in a controlled environment similar conditions to the flight ones. A devoted liquid loop has been devised (Fig. 1.3), with the same sapphire tube segment of the experiment (I.D./O.D. 3/5 mm, L= 140mm , τ ∼ 0.9) connected to a thermal bath (HAAKE K20, C10), a pump (ISMATEC MCP-Z) and a liquid reservoir. The thermal bath is fun-damental to control the fluid temperature and the pump allows to forcibly recirculate the fluid in the loop. The acquisition system (c-RIO 9073, NI-9016) obtains the inner and outlet fluid temperature by means of two Pt-100 (4 wires, accuracy ±0.2◦_{C). All the components of the calibration test rig,} with the exception of the thermal bath, the pump and the computers, are set in a thermal chamber (BINDER) in order to control the ambient temperature. The thermal camera (AIM) is obviously the same from the flight and is bor-rowed from the European Space Agency. It detects radiation between 3 and 5 µm of wavelength, in the medium infrared.

The fluid temperature is varied from 5◦_{C to 45}◦_{C with steps of 5}◦_{C for each} of the five different ambient temperature levels (18, 20, 22, 24, 26 ◦_{C). As} soon as the system reaches the steady state, both the temperature signals

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Figure 1.3: Calibration test rig

coming from the thermal resistances and the IR images (20 s at 50 fps) are recorded. In this way a 3D map is obtained by a 6th order fitting, giving the temperature of the fluid at a certain screen-ambient temperature and digital output of the camera (Fig. 1.4). Note that the camera signal is “negative hot going”, i.e. decreasing voltage with increasing photon flux.

After the procedure described above, images like the one in Fig 1.5 are obtained. Vapor plugs are clearly not detected by the IR camera due to the low emissivity of the vapor and the related temperature is indeed very close to the cold screen just behind the tubes. Between 1 µm and 5 µm, perfluorohexane is a semi-transparent medium, so its global emissivity does not depend only on the temperature, but also on the liquid thickness. Therefore, the IR analysis is potentially able to provide quantitative temperature analysis only if the liquid thickness is known a-priori (for example in case the whole tube is filled by the liquid phase).

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Figure 1.4: Calibration Curve

Figure 1.5: Example of temperature distribution along the tube during micro-gravity

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1.1.2 Correction of lens distortion

Infrared images acquired during the campaign were affected by lens distor-tion, making the development of a post-processing systematic procedure a complex task to accomplish. Therefore an image lens distortion correction was a mandatory first step.

Tools of Matlab Computer Vision ToolboxTM [1] have been used to evalu-ate the camera parameters and then to correct images distortion. In order to evaluate these parameters, it is needed to have 3D-world points and their corresponding 2D-image points; then these correspondences are used to solve for the camera parameters. The Computer Vision ToolboxTM _calibration al-gorithm implements the model proposed by Jean-Yves Bouguet[4] which in-cludes:

• The pinhole camera model; • Lens distortion.

The pinhole camera model does not take into account lens distortion, there-fore, in order to accurately represent a real camera, the model includes radial and tangential distortion.

Pinhole camera model

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In pinhole camera model, (see Fig. 1.6) the camera is treated as a simple device, without lenses and with a small aperture which light rays pass through. The up side down image is projected on the opposite side of the camera. Intrinsic and extrinsic parameters are contained into the camera matrix (M), which maps the 3D object points in the image plane.

w   x y 1  = M     Xw Yw Zw 1     (1.1)

where w is a scale factor; x, yare 2D point position in pixel coordinates ; Xw, Yw, Zw are 3D point position in world coordinates. Camera matrix can be seen as a rigid transformation (rotation R, and translation t) from world coordinates to camera reference frame and a projective transformation (K) from the 3D camera coordinate into the 2D image coordinates 1.7:

M = KR t where K =   αx γ u0 0 αy v0 0 0 1  

The intrinsic matrix K, contains 5 intrinsic parameters:

• u0, v0 optical center (in pixel), which would be ideally in the center of the image;

• αx = f /px; αy = f /py focal length (in pixel); f is the focal length in world units and px, py size of the pixel in world units;

• γ is the skew coefficient.

Lens distortion

As already mentioned above, the pinhole camera model does not include lens distortion. However, real camera, are affected by lens distortions which show approximately the same radial symmetry of optical lenses. These can be classified as either barrel distortions or pincushion distortion (see Fig. 1.8). The radial distortion model is able to treat these kind of distortion. Denoting

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Figure 1.7: Calibration transformations

Figure 1.8: Pincushion distortion on left, barrel distortion on the right

the distorted points coordinates as xdis, ydis: (

xdis= x(1 + k1r2+ k2r4+ k3r6) ydis= y(1 + k1r2+ k2r4+ k3r6) where:

• x, y are the undistorted pixel locations in normalized image coordinates. Normalized image coordinates are calculated from pixel coordinates by translating to the optical center and dividing by the focal length in pixels. Thus, x and y are dimensionless;

• k1, k2 and k3 are the radial distortion coefficients; • r = px2_{+ y}2

In some cases, tangential distortion may occur. This is due to misalignment between image plane and camera lenses. Denoting again the distorted points coordinates as xdis, ydis:

(

xdis= x + (2p1xy + p2(r2+ 2x2)) ydis = y + (p1(r2+ 2y2) + 2p2xy)

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where, x, y, r are defined as above and p1, p2 are the tangential distortion co-efficients of the lens.

Results

Figure 1.9: Sapphire tube infrared image before (top) and after (bottom) distortion correction

The model briefly discussed above is implemented mainly in two Matlab functions:

• estimateCameraParameters which has as input pairs of image points and world points; as output,the camera parameters object in which, intrinsic, extrinsic and lens distortion parameters (re-projection error, key points used etc.) are stored.

• undistortImage which has as input the image to be corrected and cam-era parameters; as output, the corrected image.

Results of the camera calibration and image distortion correction are shown in Fig. 1.9 (bottom). On the top figure, taking the tube middle axis (in orange) as reference, it is possible to see observe the magnitude of distortion. Fig. 1.10 shows the re-projection errors and the average re-projection error which are representative of the accuracy of the estimated camera parameters. In particular, the calibration performed using 3 infrared images, shows an average re-projection error of about 1.72 pixels.

The described procedure, has been adopted to correct all the frames ac-quired by the infrared camera. Dealing with straight images simplified the development of the computer vision analysis tools described in following chap-ters.

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Mean Reprojection Error per Image 1 2 3 Images 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Mean Error in Pixels

Overall Mean Error: 1.72 pixels

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Chapter 2 Liquid plug detection

In this chapter, the algorithm for liquid plugs detection and its implementa-tion in

Matlab, are described in details. A correct liquid plug detection is crucial to extract useful informations such as liquid plug length, velocities and temper-ature distribution. The algorithm that will be discussed in this and following chapters, is displayed schematically in Fig. 2.1 , where the main input/output variables of each block are outlined:

• tempMtrx is a 701 X 1000 matrix in which the ij element corresponds to the temperature of the j pixel along the tube axis (in white in Fig.2.3) in i frame (per each parabola, 1000 frames were acquired);

• SlugMtrx is a logical matrix with same number of rows and columns as tempMtrx, in which the i, j elements equal to 1 if in the position of pixel j in frame i a liquid plug is detected; vice-versa the element is equal to 0;

• SlugIDMtrx is a matrix in which all the informations regarding the liquid plugs are stored; in it, each liquid plug is identified with a unique identi-fication number (ID). As will be discussed in details in next chapters, the identification is crucial for liquid plugs velocity evaluation. Note that in SlugIDMtrx i- column, are stored the informations of liquid plugs detected in i frame.

The sapphire tube portion, framed by the camera at 50 Hz, is 65.8 mm long and results in a 701x54 pixel image. Therefore, each pixel both in direction perpendicular and parallel to tube middle axis corresponds to ≈ 0.093 mm. A representative frame of infrared camera is showed in Fig. 2.2. Higher temper-ature values (in green/yellow) correspond to liquid phase while vapor phase

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Figure 2.1: Algorithm block diagram

Figure 2.2: Sample frame

, having a low infrared emissivity, is characterized by a lower temperature (blue). The transition regions between higher and lower temperature - i.e. between liquid phase and vapor phase - correspond to the menisci. From in-frared images it was possible to retrieve temperature spatial distribution using the infrared camera calibration curves evaluated by Catarsi et al.[8] specifi-cally for this experiment (see Fig. 2.3).Note that only when the liquid phase fills completely the tube (liquid plug), the temperature values are detectable (continuous line). For all the other cases, i.e. vapor bubbles, or dispersed flow, since the vapor phase is almost transparent in the mid wave infrared spectrum, the corresponding temperature is not physically meaningful (dashed line).

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Figure 2.3: Tube infrared image on top; in the bottom, temperature distri-bution along tube axis T (x) (orange); the T (x) first derivative DT (x)(blue); filtered DT (x) in black, local maxima (yellow), local minima (green), liq-uid plugs left ends(vertical green lines),liqliq-uid plugs right ends(vertical violet lines).

Figure 2.4: From empMtrx to SlugMtrx

Temperatures of tube axis points are stored, as already mentioned above, into tempMtrx. It is recalled that, tempMtrx is a 701X1000 matrix, where a

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column correspond to a particular frame and an element to the temperature of a particular pixel of tube axis. As example, T100,500 is the temperature of pixel 500 in frame 100 or, equivalently, the temperature of the point at 46.6 mm from the origin, at 2 seconds from the acquisition start. The liquid plug detection is performed analyzing one tempMtrx column at a time, therefore the temperature is only function of the space coordinate and can be written as T (x), where x is measured in pixel along tube axis. The algorithm, executed for each frame, consists of four main steps:

• evaluation of temperature first derivative, using the central difference method (blue line in Fig. 2.3), see Listing A.1

DT (x) =              T (x + s) − T (x)

s if x is the first first pixel T (x) − T (x − s)

s if x is the last pixel T (x + s) − T (x − s)

2s otherwise

(2.1)

where s is the step, in this case 1 pixel;

• ’band stop’ filtering DT (black line in Fig. 2.3 ), see lines 7-11 in Listing A.4

DT (x) = (

DT (x) if |DT (x)| ≥ threshold

0 otherwise (2.2)

where the threshold has been inferred empirically;

• Searching for DT (x) local maxima and minima locations (respectively, yellow and green dots in Fig. 2.3).This step is implemented in findMax and findMin functions, see Listing A.2 and Listing A.3. As example, for findMax, one has:

M (x) =        1 if DT (x) > DT (x − 1) ∧ DT (x) > DT (x + 1) ∧ ∀a ∈ ]x−in, x+in[ : a 6= x ∧ DT (a) > DT (a− 1) ∧ DT (a) > DT (a + 1), DT (x) > DT (a) 0 otherwise

(2.3)

where in is the minimum interval between two maxima; • Storing of corresponding SlugMtrx column.

A liquid plug is always detected between a maximum and a minimum. Within this region, the exact location of the liquid slug menisci (green vertical

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lines) corresponds respectively to the first local maximum of the temperature signal after the maximum of the temperature first derivative, while the right end (violet vertical lines)is the last local maximum of the temperature signal before the minimum of the temperature derivative as confirmed by the flow IR visualization (on top of Fig. 2.3).

In some cases, especially when the difference between liquid plugs and background is not pronounced, the algorithm may fail and some manual ad-justments may be needed. This can be done calling the manualPlug function (see ListingA.5). By means of a user interface (Fig. 2.5), it is possible to modify the SlugMtrx column of interest, i.e. liquid plugs ends location, by mouse-selecting liquid plugs ends from left to right.

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Chapter 3 Liquid plug tracking

In this chapter, the plug identification algorithm is discussed in details. In particular, the creation of SlugIDMtrx starting from SlugMtrx, see Fig. 2.1. As already stated in previous chapter, liquid plug identification, i.e. assigning an unique identification number (ID) to each plug, is necessary to evaluate quantities like velocity. This is a consequence of the fact that, for each frame, there may be more than one liquid plug.

The solution adopted consists in assigning the same ID to liquid plugs of similar length, detected in adjacent frames. Once the liquid plug exits the camera field of view, the ID is not used anymore. This procedure is usually precise enough, but, when two or more liquid plugs with similar length are present in the same frame, an uncertainty arises and a further step must be done. In particular, the algorithm tries to evaluate the motion direction to overcome the uncertainty.

In order to better understand the working principle, let’s refer to Fig.3.1 and

Figure 3.1: Two consecutive frames to and to Fig. 3.6. During getID kth iteration:

• (lines 9-46 listing B.1) Liquid plugs are searched browsing k SlugMtrx column elements from 1 to 701 (i.e. from left to right along the tube

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axis); when a nonzero element, following a zero element, is found, this becomes a possible plug left end. Then, when a nonzero element followed by a zero element is found, this becomes a possible plug right end. If the elements between left and right ends are more than 10 (≈ 1mm) the liquid plug informations are stored in SlugIDMtrx k column. Note that, since left end and right end are respectively preceded and followed by a zero elements, liquid plugs information are stored only when they are completely visible.

In this case, two liquid plugs are detected, their lengths li,k = xi,r− xi,l, middle points coordinates pi,k = xi,l+ 0.5li,k are stored into SlugIDMtrx, whose k column is shown in the figure below (Fig. 3.2). The IDs, set to zero at this step, are evaluated in the next one.

Figure 3.2: SlugIDMtrx k-1 and k columns

• (lines 50-51, 158-202 listing B.1) If one or more liquid plug detected in k frame, an ID is assigned by calling giveID function. For each plug detected, its length is compared with the length of each plug of previous frame (k − 1). If lengths are equal ±5 pixel, the liquid plug ID of frame k − 1 is assigned to the liquid plug of frame k. Note that, since sap-phire tube is an adiabatic zone, no evaporation or condensation occurs while the liquid plugs travel through the sapphire tube, thus they are ex-pected to maintain the same length throughout all the recorded frames. In figure below (Fig. 3.3), the matching lengths and the consequently assigned IDs are highlighted.

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Figure 3.3: SlugIDMtrx k-1 and k columns after ID assignment

• (lines 53, 140-154 listing B.1) Once IDs are assigned, uncer function is called to check if there are recurring IDs in the SlugIDMtrx k column. If all IDs are different, uncer returns 0, the liquid plugs informations are stored and getID function passes control to the next iteration. This is the most common scenario but, as already mentioned above, in some cases the ID assignment fails because of the presence of two or more liquid plugs, in the same frame, with lengths that differ by less than 5 pixel.

• (lines 54-134 listing B.1) In this case, the uncer function returns an array with "uncertain" plugs IDs and a while loop is executed until the uncertainties are overcome. First, evalDir function (lines 207-235 listing B.1) is called in order to assess the motion direction: if liquid plugs move from left to right, evalDir returns 1; if liquid plugs move from right to left −1; if it is not possible to assess the motion direction the function returns ’NaN’.

Figure 3.4: k-1 and k frames and SlugIDMtrx columns before ID re-assignment

In order to better explain how evalDir works, let’s refer to Fig. 3.4 where such a situation of uncertainty is shown. As can be seen, the two

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120 pixel liquid plugs in k frame, are identified with the same ID=2. When evalDir is called, it searches for "certain" liquid plugs IDs, i.e. IDs not recurring in frame k; if found, the same ID is searched in frame k − 1, in this example, ID=1. At this point, the difference between selected liquid plug middle point coordinate in frame k and in frame k − 1, is evaluated and its sign returned. So, in this case, one has sgn(265 − 50) = 1 meaning that the plugs are moving from left to right. This information is crucial, because it determines how to re-assign "uncertain" IDs: if the motion is from left to right, rightmost uncertain plug ID in frame k is set equal to the ID rightmost liquid plug with same length in frame k − 1; conversely, if the motion is from right to left. Once the ID is re-assigned, giveID is called again to assign the IDs left. In the example taken into account, the ID of the rightmost liquid plug in frame k ( the one with middle point at 400 pixel) is set equal to 2 and the ID of the remaining liquid plug is set to 3 since in k − 1frame there are no liquid plugs left to compare (the result is shown in the figure below). Once no recurring IDs are left, the k column is saved and the function passes control to the next iteration.

Figure 3.5: k-1 and k frames and SlugIDMtrx columns after ID re-assignment

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Results

Liquid plugs tracking over frames, i.e. over time, allows to visualize the evo-lution of various quantities. Calling the function getVel (see. Listing B.2), it is possible to evaluate the liquid plug velocities over one time step (see Fig. 3.7). In particular, the plug identified with a certain ID, in k frame, has a velocity given by:

vID,k = (pID,k − pID,k−1)facq where facq is the acquisition frequency.

Recalling that two liquid plugs are identified with the same ID if their lengths do not differ of more than5 pixels, it follows that the modulus of the maximum error on velocity is:

= 5 · 0.093 · 10−3· facq ≈ 0.023m/s

Moreover, it has been noted that in less than the 25% of cases the length of a liquid plug changes of more than 2 pixels over one time step (see Fig. 3.8).

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Another useful quantity that is possible to obtain, is the temporal evolu-tion of a liquid plug temperature spatial distribuevolu-tion. Calling getPlugT (see. Listing B.3)function, giving as input a time interval, it is possible to get evo-lution of a temperature spatial distribution of the liquid plugs visible in that interval.

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Finally, calling getLen (see. Listing B.4) it is possible to get the liquid plugs lengths for each time step.

Figure 3.10: Lengths of liquid plugs visible in the IR window.

These quantities along with the ones presented in chapter 1, have been used for Nikolayev’s model validation.

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Figure 3.7: Liquid plugs velocities (Parabola 9 day 3)

0 100 200 300 400 500 600 700 800 900 liquid plugs pairs (same ID)

0 1 2 3 4 5

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Part II

Numerical modeling and

simulations

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Chapter 4 Thermo-fluidic model description

Figure 4.1: Sketch of the closed loop PHP and topological transformation In this chapter, a description of Nikolayev’s model is provided. Basing its work on Das [9] film evaporation/condensation model, Nikolayev [35] devel-oped a model able to treat the PHP with an arbitrary number of bubbles and branches. Moreover several phenomena occurring into PHPs have been taken into account, such as coalescence of liquid plugs, film junction and rupture etc. Later [34] he updated his model, taking into account tube heat conduction. Let’s first recall some PHP basic elements in order to better understand the description provided in the next pages:

• PHP can be divided in three section: evaporator, adiabatic and con-denser. Evaporator section (in red in Fig. 4.1) corresponds to the sec-tion where the heat is injected into the system. Condenser secsec-tion (in blue in Fig. 4.1), corresponds to section where the heat is released. In

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adiabatic section, heat exchanges are only between the fluid and tube wall.

• Main flow pattern inside PHP is the slug flow, i.e. the flow of "Taylor Bubbles" where the gas is surrounded by liquid films;

• Between bubbles are present liquid plugs;

• The the bubbles/liquid plugs interface is called meniscus;

Figure 4.2: PHP basic elements

The approach chosen by Nikolayev is one dimensional since it is a good com-promise between simplicity and ability of describing relevant physical phe-nomena. Similarly to the pioneering approach of Shafii, Zhang and Faghri [40] the PHP meandering tube is opened, unbent 4.1 and projected along a straight axis x which is the only spatial coordinate; the bubbles move along it. Three periodical domains corresponding to the PHP section (evapora-tor, adiabatic and condenser) can be distinguished. One PHP spatial period Lp = Le+ 2La+ Lc contains the three sections in the following order: evapo-rator, adiabatic, condenser and adiabatic. The total PHP length is given by Lt= NpLp+ Lf b,where Np is the number of periods and Lf b is the feedback section length The origin of the spatial coordinate, x = 0 coincides with the beginning of an evaporator. Since the axis is infinite, periodical boundary con-ditions are applied in such a way that local values of variables at coordinate x are equal to those at x + Lt for any x. In this description, the i-bubble left meniscus coordinate Xl

i is always smaller than the right meniscus coordinate X_ir. Bubbles order does not change, while their total number M may vary in time as consequence of bubble generation, coalescence or disappearance. The liquid plug which is in the right neighbor to the i-bubble is identified with the same index i; the left liquid plug end is thus Xl

i and the right is Xi+1l . The main assumption on which the model is based are:

Multi-parametric experimental validation of a numerical model for the Pulsating Heat Pipe transient simulation