Roberta Visentini
email: rvisenti@imft.fr

Catherine Colin
email: colin@imft.fr

Pierre Ruyer
email: pierre.ruyer@irsn.fraller

EXPERIMENTAL INVESTIGATIONS ON HEAT TRANSFER IN TRANSIENT BOILING ABSTRACT

During reactivity initiated accidents in a core of a nuclear reactor, a power excursion occurs on some fuel rods. The consequent rapid boiling is a matter of study for the nuclear power plants safety evaluation, because of the risk for rod-clad failure. In order to better understand the influence of power excursions and to characterise the phases of the rapid boiling phenomenon, an experimental set-up has been built at the Institut de Mécanique des Fluides de Toulouse (IMFT). The test section is a semi annulus. The inner half cylinder is made of a stainless steel foil, heated by Joule effect. Its temperature is measured by an infrared camera filming the backside of the foil, coupled with a high speed camera for the visualization of the phenomena. Measurements were made when a square current signal is applied to the foil. They showed the influence of the supplied power and of the wall temperature increase rate during boiling.

NOMENCLATURE

dT /dt Temperature rate over time [Kjs]. TL Liquid temperature [ 0 C]. ToNB Temperature at the onset of nucleate boiling [ 0 C]. TNB Nucleate boiling temperature [ 0 C]. T.at Saturation temperature [ 0 C]. Tw Wall temperature [ 0 C].

INTRODUCTION

In the core of a nuclear reactor, sorne control rods are located between the rods containing the nuclear fuel, see figure 1. These rods contain a neutron absorbing material which provides the control over the chain reaction. The design basis reactivity accident in pressurised water reactors is the rod ejection accident. This hypothetical accident consists of the failure of the control rod mechanisms housing. The consequences are a local fast rise in generated power and temperature of the nuclear fuel rods. It is called "Reactivity Initiated Accident" (RIA). The resulting power peak duration is only sorne milliseconds but it can lead to failure of the clad containing the nuclear fuel and release of radioactive material into the primary loop coolant. As a result the French "Institut de Radioprotection et de Sûreté Nucléaire" (IRSN), has been studying Reactivity Initiated Accidents (RIAs) for several years.

Clad to coolant beat transfer is a key phenomenon during RIA as it influences the clad temperature and, therefore, its mechanical resistance. Past research programs [START_REF] Bessiron | Clad to coolant heat transfer in NSRR experiments[END_REF][START_REF] Sugiyama | Effect of cladding surface pre oxidation on rod coolability under reactivity initiated accident conditions[END_REF][START_REF] Beloeil | Etude d' un accident de criticité mettant en présence des crayons combustibles et de 1' eau hors réacteur de puissance[END_REF] have shown that the transient clad to coolant beat transfer in these accidentai conditions highly differs from classical steady-state heat transfer correlations. Auracher and Marquardt [START_REF] Auracher | Experimental studies of boiling mechanisms in all boiling regimes un der steady state and transient conditions[END_REF] found that the critical beat flux becomes four-time higher than in the stationary case when the heating rate attains 50K /s. In fast power transients, before the onset of boiling, the main mechanism appears to be conduction [START_REF] Deev | Critical beat flux modeling in water pool boiling during power transients[END_REF][START_REF] Wang | Preliminary analysis of rapid boiling heat transfer[END_REF], as this phase is too short to allow convective beat transfer. As the wall temperature increase is steep, boiling starts on a lot of nucleation sites at the same time which may explains the high value of critical beat fluxes. It has also been shown that oxidation of the fuel rods can contribute to an enhancement of the critical beat flux [START_REF] Sugiyama | Effect of cladding surface pre oxidation on rod coolability under reactivity initiated accident conditions[END_REF].

It is possible to classify [START_REF] Sakurai | Transient boiling caused by vapor film collapse at minimum beat flux in film boiling[END_REF][START_REF] Derewnicki | Experimental studies of heat transfer and va pour formation in fast transient boiling[END_REF] the boiling transients based on the time spent in the nucleate boiling regime. While steady state boiling occurs for a nucleate boiling period of at least 500ms, rapid transient boiling has a nucleate phase that lasts less than lOOms. Once the boiling onset is reached, in rapid transient boiling, a vapor film covers the wall instantly. The nucleate boiling regime does not have time to be established. The boiling phenomenon becomes explosive when the nucleate boiling phase duration is around a hundred micro-seconds. Between the boiling onset and the film boiling onset in RIA conditions, only 20 to 50ms go by. The time needed for boiling bubbles to leave the wall is 4-20ms and sorne tens of bubbles are necessary to talk: about fully developed nucleate boiling [START_REF] Sakurai | Photographie study on transitions from non boiling and nucleate boiling regime to film boiling due to increasing heat inputs in liquid nitrogen and water[END_REF]. Thus, in the RIA boil-ing case, the nucleate boiling phase does not have enough time to be established. The film boiling phase is reached in a very short time. Currently there is no knowledge on the film development during rapid transient boiling. Sorne studies have shown that the wall surface conditions influences the re-wetting regime, and that they have more influence in this phase than in the boiling onset. Hysteresis appears and the critical beat flux is rouch lower in re-wetting than in heating. The re-wetting can be considered stationary, as the fuel rods have a considerable inertia and they do not cool quickly.

Sharp temperature increase is challenging experimentally. We could not find in literature analytical studies done at faster heating rates, except those on Joule heating, but they are affected by very high experimental uncertainties, and sorne experiences directly based on the RIA case [START_REF] Bessiron | Clad to coolant heat transfer in NSRR experiments[END_REF], for the rod geometry. Hence, there is a great interest of building a rapid-heating experience that keeps the rod geometry and that gives more accurate results than previous tests.

In view of the absence of analytical experiments that investigate high heating rates, with a representative geometry and accurate measurement deviees, and of the lack of knowledge on rapid transient boiling, an experimental set-up has been built at the "In- stitut de Mecanique des Fluides de Toulouse". In this article, the experimental apparatus and the measurement techniques are fust described. Then, the evolution of the wall temperature is plotted, for the tests where the nucleate regime was established and for those where the film boiling was reached. The tendency of the boiling onset temperature, TONB, the mean nucleate boilingregime temperature TNB and the film boiling thermal evolution are shown.

EXPERIMENTAL SET•UP AND MEASURMENT TECH• NIQUES

The experimental set-up consists of a metal half-cylinder heated by Joule effect, placed in a half-annulus section. The inner half cylinder is made of a 50 microns thick stainless steel foil. Its diameter is 8.4mm, and its length 200mm. The outer part consists of a 34mm internai diameter glass half cylinder (fig. 2). The semi-annular section is filled with a coolant, named HFE7000. HFE7000 bas been chosen because of its low saturation temperature (34°C at atmospheric pressure}, its latent beat of vaporisation (ten times smaller than the water one), and the reduction in the critical beat flux that it induces (for atrnospheric pressure, the critical beat flux given by Zuber's correlation is l .llMW / m 2 for water and 0.17MW jm 2 for HFE7000). It allows to reduce the required power to reach the transient boiling conditions.

The stainless steel bas been chosen for its high resistivity (72JLD.m). The resistivity and the reduced foil thickness allow to have a high electrical resistance and thus an elevated Joule power. The thickness homogeneity was verified by checking the homogeneity of the heated foil temperature by means of an infra-red camera. The small thickness permits to consider that there is no temperature gradient across the foil (its Biot number is 0.018). The foil-thickness diffusion time, 0.6ms, is actually small enough to assume that there is no time lag between the thermal evolution of the outer and inner wall. Thus, it is possible to measure the temperature of the wall that is in contact with the air, in order to know the temperature of the wall that is wetted. The metal half-cylinder is glued to two lateral quartz glass plates (3mm thickness, 42mm width, 200mm length). The plates, together with the foi!, are placed in an aluminum cel!. In this cell, a visualization box is created in arder to redu ce op ti cal dis tortions. There are windows on the back of the aluminum cel!; they allow the electrical connections and the visual access to the metal foil. A special attention is paid to the electrical connections, as the contact resistance must be reduced. The electrical power that is dissipated in the foil is in average 85% of that of the wh ole system, including also electrical connections and connection cables. The electrical power is provided by a power supply SORENSEN SGA. It covers the 0 -40V voltage range and the 0 -250A current range. It can be used even at very low power, since it can supply even tension and current close to zero. The power supply is driven by an arbitrary generator where all kind of curves can be programmed. Th us, power peaks or graduai power ramps can be realised. The power supply can provide a current increase up to 45Aj s. Moreover, the thermal inertia of a fuel rod can be simulated by a smooth descent in the supplied power .

The metal foil is painted in black in order to increase its emissivity (the paint emissivity is 0.94). The thermal measurements are realized by means of an infra-red camera that looks at the foil from backward (see figure 2). It is a CEDIP JADE III camera and its sensitivity range is 3.5 -5.1 J.lm. It bas a focal plane array type and it bas a Stirling-cooled MCT detector of 240 x 320pixels 2 . An acquisition frequency of lOOOim/s can be reached on small window of 64 x l20pixels 2 while, without windowing, its highest frequency is 350imj s. The lOOOimj s acquisition guarantees that the thermal dynamic is correct! y followed, as the fastest heating tests have a O.ls power rising time, and the diffusion time in the foil thickness is only 0.6ms. The infrared camera is calibrated thanks to a DCN 1000 N4 black body. It is possible to regulate a temperature leve! on this body and to film it by the camera. The uniformity of the black body surface with respect to the required temperature is guaranteed to be 0.3°C by the constructor, at 50°C. Moreover, the declared temperature measurement accuracy is ±0.01 °C and the display resolution is 0.001°C.

In the experiment th at will be presented, a 50im/ s frequency was chosen, with a 240 x 320pixels 2 window size. The metal foil area that was investigated was a 5 x 25mm 2 rectangle.

The thermal measurements are coupled with high speed camera visualizations. The high speed camera, a PHOTRON RS 3000, is directed toward one side of the half cylinder. The used acquisition rate of the experiments was 500im/ s, with an image

ALUMINIUM CELL QUARTZ PLATES HIGH SPEED CAI\IERA LASS HALF CYLINDER VISUALISATION BOX <•••••••••••••••::• ,, . .. VISUALISATION .. •• WINDOWS FIGURE 2. EXPERIMENTAL SET-UP.
size of 1024 x 1024pixels 2 . Before the experimental tests, it is checked that the high speed camera visualization area is at the same height on the half cylinder that the infrared camera visualization zone (25mm). The output signal of the high speed camera is recorded by means of a National Instruments box. By the same box, the tension and current signais are picked up and this permits to synchronize the camera images to the recording of the other measurement signais.

The current signal is acquired by a /TB 300-S LEM sensor. It can measure up to 300A with a ±0.05% accuracy. It can follow current variations up to 1 OOA/ ,us and its response time is lower than l,us at 300A. The sensor was calibrated by means of a 0.02% accuracy calibration instrument. The tension is measured by means of a MY-64 multimeter whose accuracy is 0.5% + ldigit of the read value. lts calibration was done by means of a 0.02% precision sensor. The multimeter flexible cables allow a local voltage measurement, and thus the knowledge of the local electrical resistance of the metal foil. This measurement is done before the experiments. During the tests, the whole system tension is recorded, but it is possible to know the power that really passes through the foil by comparing the foil and the system resistances. The error on the power value is only 0.07%.

The National Instruments box is also used to acquire the thermocouples signais. There are three K-type thermocouples and they measure the HFE7000 temperature, the air temperature and the infrared camera temperature as weil. The K-type thermocouples have a standard error between 2.2% and 0.75% and a l .5°C tolerance in the investigated temperature range. Quantitative infrared measurements are possible only if the surroundings and the camera keep a constant temperature during the tests. The calibration of the infrared camera was made every time the surrounding temperature changed. This ensured to reduce the error on the thermal measurements. Figure 3 presents a scheme of the experimental set-up and measurement techniques.

RESULTS

ln the experiments that will be presented in this article, a current square signal is employed. By means of the arbitrary generator, a current value is chosen and applied. The current signal is shown in figure 4. lt is possible to see that the current value is reached very rapidly and does not change intime. lt is worth noting that it is not the power that is directly controlled. When the current is high and the experiment duration is short, the voltage value cannot stabilize. Moreover, as the applied voltage depends on the foil resistance, the foil temperature changes affect the provided power. This means that squared power signais are obtained only for low currents. This is the case of the blue curve in figure 5. Otherwise, the power curve tends to increase during the test. This can be seen in figure 5, green curve.

The lowest applied current value is 25A. Under this minimum threshold nucleate boiling does not develop. This corresponds to a power of 70W , measured at the exit of the power supply. By means of resistance measurements, it is possible to verify that 85% of the Joule power passes into the metal foils. The rest is lost into the electrical connections. This means that the power density is 2.25W / cm 2 if the lateral heat !osses are not taken into account. The highest imposed current value is 75A, which corresponds to a mean power of 613W (that is 20W / cm 2 on the foil surface without considering the laterallosses).

lt is possible to identify two groups of experiments, that is, experiments whose power is lower than 300W and whose current is below 50A, and experiments whose power and current values are higher than these two thresholds. For the first group, the output power signal can be considered squared, as the blue curve in figure 5. For the second one, the power cannot stabilize; this is the green curve case in the same figure. Considering the experiment duration, the first group experiments last 9s, while the second group one are 4 or 5s long.

Three tests belong to the first group, and two to the second one. This division is due to the fact that each of these five tests was performed for a new IR camera calibration.

Considering the boiling phenomenon, in tests 1 to 3, that is the low power orres, a steady-state nucleate boiling is reached, with a constant or slightly increasing wall temperature. During the experiments that correspond to the tests 4 and 5, whose applied power is higher, a transition to film boiling occurs. Moreover, the nucleate boiling regime is transient. As the provided power is elevated, the boiling phenomenon evolves rapidly from nucleate boiling into film boiling. A transition to the film boiling condition is clearly observed in test five.

The difference between the two groups of experiments is clearly visible in figure 6 and figure 7. There, the power curve is plotted together with the resulting foil wall temperature. The temperature information cornes from the infrared measurements. In fact, it is possible to plot the temperature time evolution by means of the infrared measurements.

On the infrared pictures, a homogeneous area which covers the metal foil surface is considered. It is important not to take into account the borders of the metal foil and to focalise on the central part. Border temperatures are very high, while the curvature effect may alter the measurements far from the center of the half cylinder. The considered window is 3mm large and 10mm long (vertical direction). Its size is big enough to allow a mean spatial temperature evaluation. When the fluid is boiling, the average temperature gradient in the considered area is Jess than 4°C. This is due to the fact that the nucleation sites have a lower temperature than the surrounding points. The temperature inhomogeneity in the considered area of the infrared images is 1 oc during the first liquid phase.

Actually, these figures 6 and 7 present the wall-liquid temperature difference Tw -TL. The mean fluid sub cooling during these experiments, Tsar -TL, is 7°C for the low power case (fig. 6 ) and 6 -7°C for the high power one (fig. 7).

Figure 6 presents the low power case. lt is possible to see that there is a high increase in the temperature value during the first 0.5s. The power passes from zero to the peak value in 30ms. The metal foil follows this rapid increase and gets 20K in less than a second. This corresponds to the single-phase heat transfer regime, before the boiling onset. Infrared measurements and high speed camera images confirm that there are thermal plumes into the fluid. The infrared camera frequency, that is 50Hz, allows to follow the temperature increase. Figure 8 shows a high speed camera image and an infrared image where thermal spirals cl earl y appear.

The highest temperature of the wall temperature plot (fig. fig.PTLOW), corresponds to the boiling onset (ToN8 ). As boiling begins, the heat transfer is enhanced, so the wall temperature decreases considerably. The following part of the boiling temperature evolution intime curve corresponds to an almost constant temperature. It is the nucleate boiling heat trans- fer that avoids the increase of the wall temperature. Figure 9 shows an infrared image where nucleation sites appear. The second image of the same figure presents nucleate boiling as seen by the high speed camera. The small augmentation that can be seen in the temperature evolution corresponds to the power small increase. Finally, as the power is switched off, the temperature decreases rapidly. Once again, the small inertia of the metal foil makes it respond instantaneously to the power signal.

Figure 7 shows the case of a higher power that leads to film boiling. The single-phase heat transfer, that is, before the boiling onset, and the nucleate boiling regime last less than in the previous tests. The nucleate boiling regime is not established. Temperature grows ali the test long, even during nucleate boiling. The film boiling set-up corresponds to a change in the slope. The point of slope change should correspond to the onset of a film boiling regime.

Infrared camera images show that the film begins to develop from the top of the metal foil. This is what can be seen in figure 10.

The experiments are interrupted before that the high temperature damages the metal foil. It is possible to see that there is a delay in the cooling process. This is due to the high temperature reached and probably to the fact that the quartz plates are heated as weiL They have a higher inertia than the metal foil, and they i ~ 6o ltL: . • "" ~-""' • -"" --"""" .... . ~ ... --""_ "" _=,..,.._..., :'1 ~~55 \-' 50 \ •. .. .. : . : . . , .. . ,. : :. ,. , : ' ' need more time to cool down. The temperature enhancement is still parti y caused by the power increment, but it is mainly due to the heat transfer worsening. The vapor film deteriorates the heat trans fer between the wall and the fluid. Repeatability of the tests is shown in figure 11. Two sets of curves are presented: they belong to tests one and two. Figure 12 presents two experiments, having the same power, and belonging to the fifth series. The repeatability of the experiments guarantees that data are consistent.

It is worth noting that a numerical simulation model has been developed in order to evaluate the amount of the heat losses and to know the heat flux transmitted to the fluid. The Fourier equation is solved for the metal foil and quartz plates, using the Comsol Multiphysics software. This allows a more quantitative data treatment. The numerical simulations are under development.

Result Analysis

In the following part, tests are compared in arder to highlight the most significant tendencies. When one of the plotted parameter is the power, it means the power that is produced by the electrical supply. The current and voltage output measurements allow the supplied power evaluation. In arder to know the real heat flux that is passed from the metal foil to the fluid, it is necessary to take into account the thermallosses. The metal foil support is also heated by the Joule power, so this amount of energy that does not go to the fluid, has to be subtracted from the whole power, in arder to evaluate the heat flux. Simulations of the experimental set-up are thus needed and planned for the near future.

The first interesting point is the boiling onset. The boiling onset temperature, ToNB• is the highest temperature that is reached before the nucleate boiling regime begins. This temperature is referred as ToNB in figure 6. As nucleate boiling starts, bubbles appear and they allow a more efficient heat transfer mechanism, because of the phase change, so the wall is cooled down. The boiling onset temperature, ToNB, is plotted in figure 13, figure 14 and figure 15. Since the liquid temperature varies during the tests, the difference ToNB -TL is plotted.

Figure 13, shows how the onset boiling temperature, ToNB• is influenced by the temperature increase slope, dTw /dt. The dTw /dt value is evaluated for the single-phase heat transfer regime, taking into account the beginning temperature and the ToNB value. It is possible to see that the two main groups (that is, test 1, 2 and 3 against 4 and 5) behave differently. Tests 1 to 3 present a linear increase of the ToNB as a function of the dTw/dt. The single-phase heat transfer is enhanced when the temperature increase rate dTw /dt grows. Th us, the beginning of boiling is delayed. The fourth and fifth tests do not follow the same tendency. It seems that ToNB-TL reaches an asymptotic value, independent of the temperature increase rate. The fitting line is almost horizontal. The two groups division occurs at 60K / s heating rate. It is possible to estimate the nucleation site radius [START_REF] Carey | Liquid Vapor Phase Change Phenomena, An introduction to the thermophysics of Vaporization and Condensation Processes in heat Transfer Equipment[END_REF] for a ToNB-TL value of 31K, that is, the asymptotic value. This gives 2 •10-2 p,m. Probably ali the nucleation sites, even the smaller ones, are activated, which explains the asymptotic behavior.

The same behavior can be seen on figure 15. There, the temperature is plotted versus the Joule power. The two groups are clearly divided. Figure 14 is a zoom on the first three tests. The asymptotic tendency is kept by tests 4 and 5. This is due to the proportionality between the Joule power and the temperature increase rate dTw /dt. The curve that fits the data has the following form:

dTw/dt[°C] = 0.3 • power[W] -13.79 (1)
Let us consider the nucleate boiling part. The mean temperature of the nucleate boiling phenomenon is plotted versus the mean power on the same time lap, in figure 16 parallel to that of the second group. In fact the fitting line slope is 0.0152W /K for tests 1 to 3 and 0.0170W /K for tests 4 and 5.

A deeper analysis is needed to make a qualitative comparison to the data of Auracher and Marquardt [START_REF] Auracher | Experimental studies of boiling mechanisms in all boiling regimes un der steady state and transient conditions[END_REF].

It is in fact necessary to calcula te the slope of the nucleate holling temperature. The first test group slope is between 5 • 10-2 K/s and 0.5K /s. Th us, the temperature can be considered constant.

For the fourth test the slope passes from 1, for the lower power belonging to this test, to 4K /s. 16 ). The temperature increase rate being higher than for the first group tests, the slope is steeper. This is consistent with Auracher and Marquardt's results.

Auracher and Marquardt controlled the temperature increase and went up to 50K / s, but the lowest curves correspond to the temperature rates that are present in tests 4 and 5. A quantitative comparison will be possible when the numerical heat transfer simulation will allow to know the heat flux density. In fact it is possible to know the Joule power by means of the tension and current measurements, but the flux that passes from the heated wall to the fluid is still unknown. The quartz plates do not have an elevated thermal conductivity but there is a part of the supplied power that is transmitted through them. In a first evaluation, it seems that around 30% of the total heat flux may be lost into the quartz plate, but it is necessary to throw light on In figure 17 the mean boiling temperature is plotted versus the temperature of boiling onset. The two test groups are still separated. Tests 1 to 3 present a linear proportionality between the two temperature. That is, as the ToNB-TL value grows, the TNB value grows as well. Considering figure 14, it is possible to see that the same tendency that can be found plotting ToNB-TL versus power, is present when TNB is plotted versus ToNB -TL. This is consistent with the proportionality between power and mean nucleate boiling temperature.

Tests 4 and 5, on the contrary, show a vertical asymptote. That is, the boiling temperature TNB keeps growing whlle the ToNB does not. The asymptote is at ToNB-TL~ 37°C. This behavior is understandable taking into account the fact that the boiling onset is not affected by a power increment, whlle the nucleate boiling temperature is. Once again, the effect of power on the nucleate boiling temperature is reproduced in this figure as well.

CONCLUSION

An experimental set-up has been bullt to investigate fast transient holling regimes that can be encountered in the case of an hypothetical reactivity-initiated nuclear accidents. A semi annular metallic foll is heated by Joule effect. The foll temperature evolution is recorded with an infrared camera. Different power steps are applied to the foil. A rapid increase in the wall temperature is observed until the onset of nucleate boiling occurs. Then the wall temperature quickly decreases and stabilizes around a steady value in the nucleate boiling regime. At high power steady nucleate boiling is not observed, the wall temperature always increases and it is possible to see a transition to film boiling. Since the metallic foil is glued to quartz plates, a part of the power could be lost by conduction toward the plates and the heat flux transmitted to the liquid cannot be directly evaluated. Thus the unsteady Fourier equation has to be solved numerically to quantify this beat flux.

The first results are presented in this paper versus the Joule power that is supplied by the electric supplier. The more the power increases, the more the wall temperature increase dTw 1 dt augments. The temperature at the onset of nucleate boiling directly increases with dTw 1 dt until it reaches a maximum value associated to the activation of the smallest nucleation sites on the foil. The evolution of the wall temperature during nucleate boiling is also plotted, versus the mean power for steady and transient nucleate boiling regimes. The beat transfer is much larger in transient regime as already observed by other authors.

In the near future, a numerical simulation of the heat transfer within the metal foil and toward the quartz plates, will be ran. Thus, a quantitative comparison with literature results will be possible. Moreover, different test cases, like linear power increase tests or tests where the film boiling is instantaneously reached will be performed. This last type of experiments will hopefully clarify the mechanism ofboiling when rapid power increase is supplied to the wall.

FIGURE 1 .

 1 FIGURE 1. SCHEME OF TIIE CONTROL ROD SYSTEM.

FIGURE 3 .

 3 FIGURE 3 . SCHEME OF THE MEASUREMENTS.

FIGURE 4 .

 4 FIGURE 4. PROVIDED CURRENT SQUARE SIGNAL.

FIGURE 5 .

 5 FIGURE 5 . HIGHEST (GREEN, TEST 5) AND LOWEST (BLUE, TEST 1) POWER COMPARISON.

FIGURE 6 .

 6 FIGURE 6. POWER AND TEMPERATURE TIME EVOLUTION; TEST 1, FIRST GROUP.

FIGURE 7 .

 7 FIGURE 7. POWER AND TEMPERATURE TIME EVOLUTION; TEST 5, SECOND GROUP.

  (a) IR CAMERA (b) HIGH SPEED CAMERA lM-IMAGE AGE.

FIGURE 8 .

 8 FIGURE 8. THERMAL PLUMES ON THE METAL FOIL.

  (a) IR CAMERA IMAGE (b) HIGH SPEED CAM-ERA/MAGE.

FIGURE 9 .

 9 FIGURE 9. NUCLEATE BOILING ON THE METAL FOIL.

FIGURE 10 .

 10 FIGURE 10. FILM BOILING ON THE METAL FOIL, IR CAM-ERA IMAGE. THE VAPOUR FILM APPEARS FROM THE RIGHT CORNER.

FIGURE 11 .

 11 FIGURE 11. MEASUREMENTS REPEATABILITY, TEST 1 AND 2.

FIGURE 12 .

 12 FIGURE 12. MEASUREMENTS REPEATABILITY, TEST 5. THE EXPERIMENT DURATIONS ARE 5s AND 5.5s AND THE SAME POWER IS APPLIED.

FIGURE 13 .

 13 FIGURE 13. ToNB-n VERSUS TEMPERATURE INCREASE RATE.

FIGURE 14 .

 14 FIGURE 14. ToNB-n VERSUS SUPPLIED POWER, ZOOM ON TESTS 1 TO 3.

FIGURE 15 .

 15 FIGURE 15. ToNB-n VERSUS SUPPLIED POWER.

FIGURE 17 .

 17 FIGURE 17. TNB VERSUS ToNB•

  . The two groups still have different behaviors. The tests belonging to the first category, that is, those where the nucleate boiling phase is well established, can be described by a tendency line which is ..... test 1 500 *test 2

	~400 Q) ~ 300 Cl.. c m 2oo	*test 3 *test +test 5		*		* * *
	E
	100
	94	26	28	30	32	34	36	38
				T NB-TL [oC]
	FIGURE 16.

TNB VERSUS SUPPLIED MEAN POWER.

  The fifth test presents a slop from 4. 7 to 9K /s. Auracher and Marquardt plotted the heat flux density versus the wall superheat using the temperature increase rate as parameter. It means that the variation of the temperature increase rate leads to different boiling curves. According to this statement, the points belonging to tests 1 to 3 can be considered on the same boiling curve. This curve is not very steep as the temperature increase rate is almost zero. The holling regime can thus be considered steady. This is consistent with what is found by Auracher and Marquardt[START_REF] Auracher | Experimental studies of boiling mechanisms in all boiling regimes un der steady state and transient conditions[END_REF]. Points belonging to tests 4 and 5 cannot be collected on the same curve, because of the variation of the temperature increase rate. It is possible to plot a curve for sorne experiments of the fourth test (fig.

time [s]

ACKNOWLEDGMENT

The authors would like to acknowledge the technical staff of IMFT, especially Laurent Mouneix, for building the experimental set-up. Sebastien Cazin is also greatly thanked for his support in the infrared measurements and the flow visualizations.


Quentin Guimard
email: quentin.guimard@univ-cotedazur.fr

SMART360: Simulating Motion prediction and Adaptive bitRate sTrategies for 360°video streaming

Keywords: Information systems → Multimedia streaming, • Computing methodologies → Simulation environments, • Human-centered computing → Virtual reality, • Networks → Network simulations 360°videos, bitrate adaptation, streaming simulations

Adaptive bitrate (ABR) algorithms are used in streaming media to adjust video or audio quality based on the viewer's network conditions to provide a smooth playback experience. With the rise of virtual reality (VR) headsets, 360°video streaming is growing rapidly and requires efficient ABR strategies to also adapt the video quality to the user's head position. However, research in this field is often difficult to compare due to a lack of reproducible simulations. To address this problem, we provide SMART360, a 360°streaming simulation environment to compare motion prediction and adaptive bitrates strategies. We provide sample inputs and baseline algorithms along with the simulator, as well as examples of results and visualizations that can be obtained with SMART360. The code and data are made publicly available.

INTRODUCTION

Adaptive bitrate (ABR) algorithms are used in streaming media to adjust the quality of a video or audio stream in real time based on the viewer's network conditions. The goal of ABR streaming is to provide a smooth playback experience by adapting the bitrate of the stream to match the viewer's available bandwidth.

With the recent rise in popularity and increasing affordability of virtual reality (VR) headsets, 360°video streaming is growing rapidly, but requires even higher bitrates, which makes the use of efficient streaming algorithms even more critical. ABR algorithms for 360°video streaming can even go one step further than regular ABR algorithms, as the video quality can be dynamically adapted to send higher quality content inside the user's viewport. This involves predicting the head and gaze movements of the user several seconds in advance to build a buffer that can be resilient to bandwidth variations.

Adaptive streaming of 360°videos has been the subject of many research works in the past few years [START_REF] Xavier Corbillon | Viewport-adaptive navigable 360-degree video delivery[END_REF][START_REF] Park | Adaptive Streaming of 360-Degree Videos With Reinforcement Learning[END_REF][START_REF] Qian | Optimizing 360 Video Delivery over Cellular Networks[END_REF]. While these works present new approaches and methods to improve the quality of experience (QoE) or bandwidth usage of adaptive streaming systems, it is often difficult to compare them fairly, as the code for simulating them is not always provided.

We present SMART360, a 360°streaming simulation environment that can be used to compare head motion prediction and ABR algorithms. Our contributions are the following:

• we provide a new simulator 1 , equipped with large datasets and baseline algorithms that builds upon the existing solutions, with explanations about the code structure and logic; • we also make the preprocessing pipeline available 2 for transparency and to give the ability to easily create new input configurations for the simulator; • we explain in detail how SMART360 can be used by researchers to implement and compare existing and new motion prediction and adaptive bitrate strategies and show examples of metrics and visualizations that can readily be used to evaluate their algorithms.

RELATED WORK

As a result of the lack of reproducible simulations for most of the 360°adaptive streaming research, several tools have been made available in recent years in an effort to improve reproducibility in this field. Ribezzo et al. [START_REF] Ribezzo | TAPAS-360°: A Tool for the Design and Experimental Evaluation of 360°Video Streaming Systems[END_REF] released TAPAS-360°3, an open-source emulator that enables designing and experimenting omnidirectional video streaming algorithms. Unfortunately, TAPAS-360°does not support tile-based streaming, but works with a set of pre-defined "views". This makes it impossible to use with tile-based bitrate adaptation algorithms, which are the most common type of bitrate adaptation algorithms for 360°video streaming.

Spiteri [START_REF] Spiteri | Video Adaptation for High-Quality Content Delivery[END_REF] released Sabre3604 , a simulation testbed for 360°v ideos as an extension of Sabre5 [START_REF] Spiteri | From Theory to Practice: Improving Bitrate Adaptation in the DASH Reference Player[END_REF], an open-source simulation environment for ABR algorithms. While Sabre360 can be used to compare adaptive bitrate algorithms, it has some drawbacks: (i) it does not implement stalls, but plays "blank tiles" instead, (ii) it is built around a "view" system that only supports one kind of tiling layout (4x4 tiles), and (iii) the ABR optimization for quality allocation is done between each tile download, and makes an individual request for each tile of each segment, which is not realistic.

Jiang et al. [START_REF] Jiang | Plato: Learningbased Adaptive Streaming of 360-Degree Videos[END_REF] provide code for simulating 360°bitrate adaptation and motion prediction along with Plato6 , but the lack of documentation and obscure file structure makes it difficult to use, precluding other researchers from using it and test new algorithms.

Finally, Chopra, Chakraborty, et al. [START_REF] Chopra | PARIMA: Viewport Adaptive 360-Degree Video Streaming[END_REF] provide the code for PARIMA 7 , which allows to test and compare their model to some baselines with QoE metrics, but it is not a streaming simulation since it does not consider network aspects.

Our simulator takes a lot of inspiration from Sabre360, which we consider to be the closest solution to the problem we want to solve. Our work aims at rectifying any shortcomings the existing solutions may have for comparing motion prediction and adaptive bitrate strategies in the context of 360°streaming.

DATA PREPROCESSING

The objective of SMART360 is to provide a simulation environment that enables the comparison of ABR and viewport prediction algorithms when streaming 360°videos with network constraints. In this section, we describe the necessary inputs the simulator needs to perform this task, as well as the preprocessing pipeline the data undergoes before being used by the simulator.

Simulator inputs

All the input data for the SMART360 simulator is provided in the config/ directory of the simulator repository. The input data uses the same JSON format as Sabre360 [START_REF] Spiteri | Video Adaptation for High-Quality Content Delivery[END_REF]. The data provided in the SMART360-simulator/config/ directory is split in two types: real and synthetic data. The real data is extracted from multiple public datasets and is described in the following subsections. The synthetic data contains simple cases of network traces with constant bandwidth and manifests describing uniformly-sized 360°videos. The user head motion traces found in the synthetic directory are copied from real data.

Network traces.

The network traces describe the available bandwidth and the latency over time in different situations. They allow for realistic simulations where the bandwidth is highly variable. The network traces provided in the real input data are the same as the ones used in Sabre360, and come from the 4G/LTE dataset published by van der Hooft et al. [START_REF] Van Der Hooft | HTTP/2-Based Adaptive Streaming of HEVC Video Over 4G/LTE Networks[END_REF]. They are made of 40 traces of bandwidth measurements along several routes in the city of Ghent, Belgium.

For the comparisons between ABR algorithms to be relevant, we need to be in a situation where the algorithm has to adapt to the network constraints. On the one hand, if the bandwidth is very high relative to the video bitrate, there is no need for ABR streaming, as we can just download everything in the highest quality without any rebuffering (stall) event. On the other hand, if the bandwidth is very low relative to the video bitrate, ABR streaming is not so useful either, as we can only download everything in the lowest quality. To make for a relevant comparison between ABR algorithms, we provide a Jupyter notebook to scale the network traces relatively to the video bitrates, as illustrated in Fig. 1. This notebook is available in the SMART360-simulator/notebooks/ directory. 3.1.2 User head motion traces. The user head motion traces describe the behavior of people watching 360°videos. They contain the coordinates of the head orientation over time. This allows calculating which tiles are visible to the user at any given time during the video. We provide 3518 head motion traces from users watching 94 different videos, extracted from three of the datasets used by Romero et al. [START_REF] Fabián Romero Rondón | A Unified Evaluation Framework for Head Motion Prediction Methods in 360[END_REF] in their framework to evaluate head motion prediction methods in 360°videos 8 . The traces have a 5 Hz sampling rate and use a 3D Cartesian coordinate system, where the orientation of the head is represented as a point on the unit sphere. We provide a Python script, available in the SMART360-preprocessing/ root directory to convert the traces from their original CSV format to a JSON format similar to the one used in Sabre360.

Video manifests.

The video manifests describe the video files to be streamed over the Internet. In the case of 360°tiled videos, the manifests describe the tiling layout and the different quality levels of encoding. The SMART360 simulator uses the video manifest to get the size of each downloaded tile. We provide simplified JSON video manifests for the 94 videos mentioned in Sec. 3.1.2 in the same format as the one used in Sabre360. We detail the preprocessing steps to obtain the video manifests from MP4 video files in the next subsection.

Preprocessing pipeline

The preprocessing pipeline is based on TOUCAN-preprocessing 9 , a Java command line application to convert a regular 360°videos into DASH-SRD described videos, using FFmpeg and MP4Box, released by Dambra et al. [START_REF] Savino Dambra | Film Editing: New Levers to Improve VR Streaming[END_REF]. We have made some changes to simplify the original pipeline, update the encoding parameters, and adapt the input and output formats to our problem. The preprocessing pipeline is described in Fig. 2 and detailed in the following subsections.

3.2.1

Video tiling and re-encoding. First, the MP4 videos are split into tiles using the FFmpeg crop filter. Since cropping the videos requires re-encoding them, we choose to re-encode the video tiles in different quality levels while tiling them. The tiling layouts and quality levels are configurable settings that can be specified in an XML file for each video.

The videos are re-encoded with libx265, using the HEVC compression standard. Different quality levels are achieved using different constant rate factors (CRFs). CRF is a method of video compression that is designed to maintain a constant level of perceived quality, as opposed to constant bitrate (CBR) encoding, but similar to using a constant quantization parameter (CQP). Unlike CQP, CRF adjusts the QP to compress different frames by varying amounts by taking motion into account. For high-motion frames, the QP is increased to compress the frame more, and for low-motion frames, the QP is lowered to reduce compression. This leads to a varying bitrate allocation over time, resulting in a more efficient use of the available bandwidth. While constant bitrate and constrained CRF may be better suited for streaming to avoid bitrate variations, CRF is better suited than CQP (the most popular encoding mode to compare adaptive bitrate strategies in 360°videos [START_REF] Yaqoob | A Survey on Adaptive 360°Video Streaming: Solutions, Challenges and Opportunities[END_REF]), as it results in a more constant bitrate [START_REF] Robitza | CRF Guide (Constant Rate Factor in x264, x265 and libvpx[END_REF]. CRF was chosen as the best compromise between bitrate stability (better than CQP), efficiency (not wasting bits like constant bitrate), and encoding time (not needing multiple passes like constrained CRF).

DASH packaging.

Once the videos are cropped into the desired tiling layouts and encoded in the appropriate quality levels, we use the MP4Box multimedia packager to obtain a DASH-SRD compliant video split in segments. The segment duration is also a configurable parameter that can be specified in the same XML file as mentioned in Sec. 3.2.1. The output files generated by this preprocessing step are MP4 tracks and an XML manifest for each video, which correspond to the files that can be streamed over the Internet.

JSON file generation.

Finally, we provide a Python script, available in the SMART360-preprocessing/ root directory to build the JSON manifests that can be used by the simulator. This script simply reads the files that were previously generated and keeps only the information that is relevant for the simulations to put them in the JSON video manifests described in 3.1.3.

SIMULATOR ARCHITECTURE

The SMART360 simulator architecture is based on the architecture of the Sabre360 simulator, with substantial differences. The changes mainly aim at rectifying the shortcomings formulated in Sec. 2, namely: (i) introducing actual stall events that pause the video playback instead of playing blank tiles, (ii) re-thinking the coordinate system and modifying the headset model to support any rectangular tiling layout, and (iii) re-designing the simulator and ABR logic, enabling the planning of quality allocation for multiple tiles and segments in advance.

File and object structure

We present a simplified class diagram in Fig. 3, where we choose to only keep the relevant attributes and methods of the SMART360 simulator. The classes are separated in multiple files located at SMART360-simulator/simulator/. The classes highlighted in red in the diagram, BandwidthEstimator, TiledABR, and Viewport-Predictor are classes that can be easily extended to implement new algorithms. We detail the file structure and classes of the simulator in the following subsections.

4.1.1 Session. The session.py file contains the Session and SessionInfo classes. The Session class is the main class that contains all the objects necessary to the simulation. The Session::run method is the entry point of the simulator and is described in Algo. 1. The SessionInfo class is mainly used to access information and objects like the buffer, log file, or viewport predictor from other objects.

4.1.2 Buffer. The buffer.py file contains the TiledBuffer class. This class contains the buffer in the form of a two-dimensional NumPy array of size B × T , where B is the buffer size (in number of segments) and T is the number of tiles in the video. This class also provides methods to update the buffer. 4.1.6 Bitrate adaptation. The br_adaptation.py file contains the TiledABR abstract class and its subclasses. This class is responsible for deciding which tiles of which segments will be downloaded in which quality, and in which order. We provide three simple ABR strategies with no buffer replacements. TrivialABR tries to download all tiles in the lowest quality and fills the buffer as quickly as possible. MaxStallABR is provided for experimental purposes to calculate the maximum possible stall ratio for a user, in the case where we only download tiles once they are missing in the viewport and causing a stall event. We also provide BaselineABR, a simple ABR strategy with some rate-based and buffer-based elements.

4.1.7 Viewport prediction. The vp_prediction.py file contains the ViewportPredictor abstract class and its subclasses. This class is used to make predictions about user head movements and the resulting viewports. These predictions can in turn be used by the ABR algorithms. We provide two baseline viewport predictors as well as an implementation of a deep learning predictor. NoPredictor gives equal probabilities for all tiles. StaticPredictor assumes the user will not move and gives higher probabilities to tiles that were inside the viewport. DVMSPredictor uses the DVMS deep learning model from Guimard et al. [START_REF] Guimard | Deep Variational Learning for Multiple Trajectory Prediction of 360°Head Movements[END_REF] to make predictions. 4.1.8 Bandwidth estimation. The bw_estimation.py file contains the BandwidthEstimator abstract class and its EWMA subclass. This class can be used to make estimates of the future bandwidth and latency of the network, useful for ABR planning. The EWMA subclass makes latency and bandwidth estimates following an exponentially weighted moving average model, as done in the dash.js reference player 10 , but in a simplified manner.

4.1.9 Logging. The _logging.py file contains the LogFile class. This class provides methods to add simulation information and measurements to a list of records, that is then written to a JSON log file at the end of the simulation. New methods can easily be implemented to include more information and measurements.

4.1.10 Log parsing. The parse_session_logs.py file, located in the log_parsing/ directory, consists of a post-processing pipeline that reads the JSON log file and builds data frames stored in Feather files. This file format produces very lightweight files that are quick to read and write compared to the raw log files.

Simulator logic

In this section, we describe the algorithmic flow of the SMART360 simulator. As mentioned in Sec. 4.1.1, the Session::run method is the entry point to the simulator. We describe the logic behind this method in Algo. 1. For the sake of readability, the algorithms described in Algo. 1 and Algo. 2 are simplified versions of the methods, where only the most relevant steps are shown.

The three ABR functions that appear on lines 3 and 9 of Algo. 1, and line 11 of Algo. 2 refer to the three methods of the TiledABR abstract class that have to be implemented by subclasses, as explained in Sec. 5.1. These functions return download schedules, noted skd. A download schedule is an ordered list of elements that each contain s, the segment number, t, the tile number, and q, the quality level. In the case of startup and stall (lines 3 of Algo. 1 and line 11 of Algo. 2), the full schedule must be downloaded before the video playback can be resumed. In the case of the regular ABR decision function (line 9 of Algo. 1), elements are downloaded in the same order as given by the schedule during ∆ DL seconds.

On line 5 of Algo. 1 and lines 13 and 17 of Algo. 2, "download" implies using the NetworkModel with the appropriate latency and bandwidth, as well as putting the downloaded tiles in the buffer.

In Algo. 2, we give some detail behind the logic of one the most complex methods of the simulator, Session::play_and_download. This method enables the simulation of video playback and tile download at the same time, while also making sure that the NetworkModel and the UserModel stay synchronized. This method brings two improvements over Sabre360:

• the ABR algorithm has to plan and make individual requests for downloading groups of tiles every ∆ DL seconds, which is Algorithm 1 Simplified run method 1: l ← video length 2: p ← 0 ▷ video play head 3: skd st ar tup ← ABR_STARTUP ▷ startup schedule 4: for all s, t, q in skd st ar tup do 5: download tile t from segment s in quality q 6: end for 7: while p < l do • stall events can happen and stall periods can be measured, which we also consider more realistic than the video not pausing and showing blank tiles in Sabre360. We have chosen for stall events to happen in SMART360 only if a tile that should be visible to the user is not present in the buffer. This means that the video does not stop if tiles are missing from the buffer but are not in the user's field of view.

Algorithm 2 Simplified play_and_download method 1: procedure PLAY_AND_DOWNLOAD(skd, ∆ DL )

∆ l e f t ← ∆ DL 3:

while ∆ l e f t > 0 do τ ← min(∆ l e f t , τ coor d , τ seдment )

T buf ← set of tiles in buffer for current segment 8:

T visibl e ← set of visible tiles calculated from coord.

9:

T missinд ← T visibl e -T buf ∩ T visibl e for all s, t, q in skd st ar tup do end while 22: end procedure

USING SMART360 TO COMPARE MOTION PREDICTORS AND ADAPTIVE BITRATE ALGORITHMS

In this section, we explain how researchers can use the SMART360 simulation environment to implement new ABR strategies and motion prediction algorithms for 360°video streaming and compare them.

Implementing an ABR strategy within SMART360

To implement a new ABR strategy, one only needs to create a new subclass of TiledABR (see Sec. 4.1.6) that implements three methods. Each one of these methods returns a download schedule containing elements composed of s, the segment number, t, the tile number, and q, the quality level. In addition to the method parameters, the ABR class can access other information such as the buffer content, the video manifest, or a viewport predictor.

•

Implementing a motion predictor within SMART360

SMART360 also allows the implementation of head motion prediction algorithms, in the form of a viewport predictor that can in turn be used by the ABR algorithm. To implement a new motion predictor, one only needs to create a new subclass of ViewportPredictor (see Sec. 4.1.7) that can implement two methods:

• predict_tiles(s) has to be implemented by the subclass. The parameter s corresponds to the segment number for which we want to make predictions. This method returns a list of length T , where each element corresponds to the score given to each tile. A higher score means a higher probability of being present in the user's viewport during segment s; • update_coord(coord) can be implemented, but is not mandatory. This method allows updating the motion predictor with new head coordinates that can be used to make predictions.

As of right now, the only information that can be used for predictions is the past head coordinates of the user. However, SMART360 could easily be extended to include video information such as saliency maps for head motion prediction.

SMART360 output metrics

SMART360 brings many QoE-related metrics and visualizations, as well as some network-related metrics. The logs that we provide already enable numerous types of insightful visualizations, as shown in Fig. 4, and can easily be extended to include more information and measurements. In this section, we show examples of figures that can be produced with SMART360 to compare ABR and head motion prediction algorithms. The figures presented in this section are extracted from the output_metrics.ipynb notebook, and new visualizations can readily be generated from the same data frames without needing to extend the logs.

• Fig. 4a compares the average visible quality when using two different viewport predictors over one video for all users who have watched this video. In this example, there are five quality levels ranging from 1 to 5, and more details about the simulation settings can be found in the notebook. Here, we can see that the StaticPredictor gives higher average visible quality than NoPredictor.

• Fig. 4b compares the average visible quality when using two different viewport predictors against the video timestamp for all users who have watched this video. The quality levels and simulation settings are the same as in Fig. 4a. Here, we can see with more detail when, in the video, StaticPredictor gives higher average visible quality than NoPredictor.

• Fig. 4c compares the sum of stall periods when using two different viewport predictors against the video timestamp for all users who have watched this video. The simulation settings are the same as in Fig. 4a. Here, we can see with precision exactly when, in the video, the stalls are happening, and that StaticPredictor gives fewer stall periods than NoPredictor.

• Fig. 4d compares the average quality of downloaded tiles that end up in the user's viewport when using two different viewport predictors against the "download offset" for all users who have watched this video. The download offset is inversely proportional to the buffer level: a download offset of -6 means that the tile was downloaded 6 seconds before it was played. The quality levels and simulation settings are the same as in Fig. 4a. Here, we can understand better how the ABR strategy works and how the prediction impacts its behavior regarding the buffer level, and that StaticPredictor gives higher average visible quality than NoPredictor, regardless of the buffer level.

• Fig. 4e compares the distribution of the "hit rate" when using two different viewport predictors over one video for all users who have watched this video. The hit rate is calculated by dividing the number of bits that appeared in the user's viewport by the total number of bits that were downloaded, it can be seen as a form of bandwidth efficiency. The simulation settings are the same as in Fig. 4a. Here, we can see that StaticPredictor is more efficient than NoPredictor and wastes less bandwidth.

The notebook also includes metrics on the spatial and temporal quality variance of 360°videos, as well fairness metrics based on the QoE fairness index described by Hoßfeld et al. [START_REF] Hoßfeld | Definition of QoE Fairness in Shared Systems[END_REF].

DISCUSSION

We believe that SMART360 successfully addresses the shortcomings of the existing solutions to realistically simulate 360°streaming systems and efficiently compare ABR and head motion prediction algorithms. With SMART360, we yearn to encourage reproducible research by providing transparent code that can be adapted and improved.

Possible improvements include but are not limited to: considering the percentage of each tile actually in the viewport for more accurate measurements of the visible quality, instead of counting them as inside the viewport regardless of the proportion of the tile actually in the viewport; giving the ability to the viewport predictor to use more information than the past head coordinates, such as video saliency maps; using multiple threads and communication between threads when events occur during the simulation instead of the monolithic structure of the Session::play_and_download method.

CONCLUSION

In this article, we have presented SMART360, a new simulation environment for 360°video streaming that allows comparing different motion prediction and adaptive bitrate strategies with numerous metrics and graphical visualizations. SMART360 overcomes the drawbacks of the few existing alternative tools by providing highly-configurable code, with many inputs and settings, as well as offering a realistic streaming behavior, with stall events and ABR planning.

We have described the inputs and outputs of the simulator, as well as its internal structure. We have explained how new motion predictors and adaptive bitrate algorithms can be implemented inside the simulation environment to be evaluated and compared.

We believe that SMART360 can improve the reproducibility of research regarding 360°video motion prediction and adaptive streaming algorithms, and make future comparisons of new strategies easier for researchers.

Figure 1 :

 1 Figure 1: Network trace scaling principle.

  video manifests in JSON format ready for simulations

Figure 2 :

 2 Figure 2: SMART360 video preprocessing pipeline.

4. 1 . 3

 13 Headset. The headset.py file contains the Headset-Model and HeadsetConfig classes. These classes contain information about the headset configuration (tile layout, FoV size) and provide methods to calculate which tiles are visible, given the user's head coordinates. Unlike most existing tools, the tile calculation considers the distortion produced by the equirectangular projection. The headset configuration is loaded from JSON file located in the SMART360-simulator/config/ directory. 4.1.4 User. The user.py file contains the UserModel class. This class handles the user head motion trace and is used to get head motion coordinates updates. 4.1.5 Network. The network.py file contains the Network-Model class. This class handles the network trace and provides methods to download groups of tiles in compliance with the bandwidth and latency information present in the network trace.

Figure 3 :

 3 Figure 3: UML class diagram of the SMART360 simulator. All aggregation relationships are one-to-one.

4. 1 .

 1 11 Notebooks. There are two notebooks in the notebooks/ directory. The network_traces_scaling.ipynb notebook is described in Sec. 3.1.1, and the output_metrics.ipynb notebook gives examples of possible visualizations of the SMART360 output metrics, as shown in Sec. 5.3.

8 :

 8 bw est ← network bandwidth estimation 9: skd ← ABR_DECIDE(bw est , ∆ DL ) ▷ download schedule 10: PLAY_AND_DOWNLOAD(skd, ∆ DL ) ▷ see Algo. 2 11: end while more realistic than the very frequent ABR optimizations and requests in Sabre360;

4 :τ

 4 coor d ← time until next user coord. update 5: τ seдment ← time until next video segment 6:

Figure 4 :

 4 Figure 4: Some examples of visualizations from SMART360 simulation output metrics. From left to right: (a) average visible quality, (b) average visible quality against video timestamp, (c) sum of all user stalls against video timestamp, (d) average downloaded quality against download offset, (e) bandwidth efficiency. Colors have the same meaning across all subfigures.

  startup_dl_schedule() is called at the beginning of the simulation. It must return a schedule of what to download before the video playback starts; • decide_dl_schedule(bw est , ∆ DL ) is the main ABR decision method. It is called every ∆ DL seconds and must return a schedule of what to download in the next ∆ DL seconds, given the estimated bandwidth; • stall_dl_schedule(T missinд ) is called whenever a stall event happens. When the video playback is paused during this event, the list of missing tiles in the user's field of view is passed as a parameter and the method must return a schedule of what to download. The video playback can only resume if all the missing tiles and everything in the stall schedule has been downloaded.

https://gitlab.com/SMART360/SMART360-simulator

https://gitlab.com/SMART360/SMART360-preprocessing

https://github.com/c3lab/tapas360

https://github.com/UMass-LIDS/sabre360

https://github.com/UMass-LIDS/sabre

https://github.com/federerjiang/Plato

https://github.com/sarthak-chakraborty/PARIMA

https://gitlab.com/miguelfromeror/head-motion-prediction

https://github.com/UCA4SVR/TOUCAN-preprocessing

https://github.com/Dash-Industry-Forum/dash.js

ACKNOWLEDGMENTS

This work has been partly supported by the French government, through the UCA JEDI and EUR DS4H Investments in the Future projects ANR-15-IDEX-0001 and ANR-17-EURE-0004. This work was partly supported by EU Horizon 2020 project AI4Media, under contract no. 951911 (https://ai4media.eu/).


Roberta Visentini
email: rvisenti@imft.frcolin@imft.fr

Catherine Colin

Pierre Ruyer
email: pierre.ruyer@irsn.fr

EXPERIMENTAL INVESTIGATION ON HEAT TRANSFER IN TRANSIENT BOILING ABSTRACT

During reactivity initiated accidents in a core of a nuclear reactor, a power excursion occurs on some fuel rods. The consequent rapid boiling is a matter of study for the nuclear power plants safety evaluation, because of the risk for rod-clad failure. In order to better understand the influence of power excursions and to characterise the phases of the rapid boiling phenomenon, an experimental set-up has been built at IMFT. The test section is a setni annulus. The inner half cylinder is made of a stainless steel foil, heated by Joule effect. Its temperature is measured by an infrared camera filming the backside of the foil, coupled with a high-speed camera for the visualisation of the phenomena. Measurements were made for two types of tests: when a square current signal is applied to the foil and when the current output follows a triangular shape. These measurements showed the influence ofboth shape and value of the supplied power and of the temperature increase rate on the wall temperature during boiling.

INTRODUCTION

In the core of a nuclear reactor, some control rods are located between the bars ( or rods) containing the nuclear fuel. These rods help controlling the reactions chain. It may occur that one of these control rods is ejected leading to a local fast rise in generated power and temperature of the nuclear fuel bars. It is called "Reactivity Initiated Accident" (RIA). The power peak duration is only some milliseconds but it can lead to failure of the clad containing the nuclear fuel and release of radioactive material into the primary reactor coolant. Thus, the RIA is taken into account for the nuclear power plants safety evaluation.

Clad to coolant heat transfer is a key phenomenon during RIA. Clad temperature and its mechanical resistance depend on it. Past research programs [START_REF] Bessiron | Clad to coolant heat transfer in NSRR experiments[END_REF]; [START_REF] Sugiyama | Effect of cladding surface pre oxidation on rod coolability under reactivity initiated accident conditions[END_REF]; [START_REF] Beloeil | Etude d'un accident de criticité mettant en présence des crayons combustibles et de l'eau hors réacteur de puissance[END_REF]) showed that the transient clad to coolant heat transfer in these accidenta! conditions highly differs from classical heat transfer correlations for established regimes. These experiments pertnitted to plot the boiling curve but they had uncertainties due to difficulties in temperature measurements. The boiling phenomenon is too rapid to be followed accurately by thermocouples. Despite this uncertainty, some characteristics of the fast transient boiling phenomenon were identified.

In the phase of thermal convection before the onset of boiling, the main heat transfer mechanism appears to be conduction: this phase duration is too short to allow convective heat transfer. Then, when the wall temperature increase is steep, it seems that boiling starts on a lot of nucleation sites at the same time. The presence of a great number of bubbles, that permit to dissipate a lot of heat, may explain the fact that the boiling crisis occurs at a higher heat flux. Heterogeneous nucleation at the wall or homogeneous nucleation in an area near the wall, may contribute to the boiling onset [START_REF] Sakurai | Mechanisms of transitions to film boiling at CHFs in subcooled and pressurized liquids due to steady and increasing heat inputs[END_REF]; [START_REF] Sakurai | Photographie study on transitions from non boiling and nucleate boiling regime to film boiling due to increasing heat inputs in liquid nitrogen and water[END_REF], [START_REF] Ciampi | Heterogeneous boiling inception in rapid surface temperature transient state[END_REF]). These mechanisms seem to become more important as the pressure and the sub cooling are high.

It is observed in fast transient boiling studies that, as the heating rate gets higher, the heat flux is more important. For example, [START_REF] Auracher | Experimental studies ofboiling mechanisms in all boiling regimes under steady state and transient conditions, !nt[END_REF] found that the critical heat flux becomes four-time higher than in the stationary case when the heating rate reaches 50K/s. Also the oxidation of the wall can contribute to an enhancement of the critical heat flux. Unfortunately there is not a lot of information on the effect of the wall surface conditions. Moreover, as it is very difficult to get high temperatures in a very short time, it is not possible to find in literature studies done at faster heating rates, except those on Joule heating on wires. But this geometry is far from the geometry of a fuel rod. Hence, there is a great interest of building a rapid-heating experimental device that keeps the rod geometry.

Once the boiling onset is reached, in sufficiently rapid transient boiling a vapour film covers the wall instantly. It is possible to talk about transient boiling when the nucleate boiling regime lasts less than 1 00ms. Actually, if the phase between the boiling onset and the film creation lasts only a few milliseconds, the boiling onset is explosive. The vapour film appears rapidly and violently. For longer times, there is no explosion but the nucleate boiling phase does not have time to develop. This is the case of RIA boiling phenomena. Between the boiling onset and the crisis in RIA conditions, only 20 to 50ms go by. The time needed for boiling bubbles to leave the wall is 4-20ms and some tens of bubbles are necessary to talk about fully developed nucleate boiling [START_REF] Sakurai | Photographie study on transitions from non boiling and nucleate boiling regime to film boiling due to increasing heat inputs in liquid nitrogen and water[END_REF]). The film-boiling phase is reached in a very short time. There is no knowledge on the film development during rapid transient boiling. The following rewetting phase is also unstudied, because of the difficulties in representing the fuel rod real inertia. It seems that the wall surface conditions are quite important in the rewetting regime, and that they have more influence in this phase than in the boiling onset. Hysteresis appears and the critical peak heat flux is much lower in rewetting than in heating. The rewetting can be considered stationary, as the fuel rods have a considerable inertia and they do not cool quickly.

In view of the absence of experiments that investigate high heating rates and of the lack of knowledge on rapid transient boiling, an experimental set-up has been built at IMFT. Its main aim is to permit to understand the effect ofhigh heating rates on the boiling curve.

In this article, the experimental apparatus and the measurement techniques are first described. Then, the evolution of the wall temperature is plotted. Tests where a square power is applied are presented separately from those where a triangular power is used. Moreover, for the first group of experiments, tests where the nucleate regime was established and for those where the film boiling was reached are also distinguished. The tendency on the boiling onset temperature, T ONB, the mean nucleate boilingregime temperature T NB and the film boiling temperature evolution are shown. A simulation mo del with the Comsol software has been developed in order to evaluate the amount of the heat losses and to obtain a quantitative evaluation of the heat flux transmitted to the fluid. It will be used in the near future to evaluate data.

EXPERIMENTAL TEST SETUP

The experimental set-up consists of a metal half-cylinder heated by Joule effect, placed in a half-annulus section. The inner half cylinder is made of a 50 microns thick stainless steel foil. Its diameter is 8.4mm, and its length 200mm. The outer part consists of a 34mm internai diameter glass half cylinder (fig. 1). The semi-annular section is filled with a refrigerant, 1methoxyheptafluoropropane (C 3 F 7 0CH 3 ), named HFE7000. It is chosen because of its low saturation temperature (34°C at atmospheric pressure), its latent heat of vaporisation (ten times smaller than the water one), and the reduction in the critical heat flux that it involves (for atmospheric pressure, the critical heat flux given by Zuber's correlation is 1.11MW/m 2 for water and 0.17 MW/m 2 for HFE7000). Shortly, it allows reducing the needed power.

The stainless steel has been chosen for its high resistivity (72 J..l!lm) in order to have a high electrical resistance and thus an elevated Joule power. The thickness homogeneity was verified by checking the homogeneity of the heated foil temperature by means of an infrared camera. The small thickness permits to consider that there is no temperature gradient inside the foil (its Biot number is 0.018). The diffusion time, 0.6ms, is also small enough to assume that there is no time lag between the thermal evolution of the outer and inner wall. Thus, it is possible to measure the temperature of the wall that is in contact with air, in order to know the temperature of the wall that is wetted. The metal half-cylinder is glued to two lateral quartz glass plates (3mm thick, 42 mm wide, 200 mm long). The plates, together with the foil, are placed in an aluminium cell. In this cell, a visualisation box is created in order to reduce optical distortions. There are windows on the back of the aluminium cell; they allow the electrical connections and the visual access to the metal foil. A special attention is paid to the electrical connections, as the contact resistance must be reduced.

v / ALUMINIUM CELL •••••••• .... QUARTZ PLATES LASS HALF CYLINDER VISUALISATION BOX ••••••••••••• .... <•••••••••••••••::•:\ . ... •• .. VISUALISATION ...... •••• WINDOWS METAL FOIL Figure 1 Test cell.
The electrical power that is dissipated in the foil is in average 85% of that of the whole system, including also electrical connections and connection cables. The electrical power is provided by a SORENSEN SGA power supply. lt covers the 0-40V voltage range and the 0-250A current range. lt can be used even at very low power, since it can supply even tension and current close to zero. The power supply is driven by an arbitrary generator, where all kind of curves can be programmed. Thus, power peaks or graduai power ramps can be imposed. The power supply can provide a current increase up to 45A/s. Moreover, the thermal inertia of a fuel rod can be simulated by a smooth descent in the supplied power.

The metal foil is painted in black in order to increase its emissivity (the paint emissivity is 0.94). In fact, the thermal measurements are realised by means of an infrared camera that looks at the back face of the foil (see figure 1 ). lt is a CEDIP JADE III camera and its sensitivity range is 3.5-5.1 J.lm. lt has a focal plane array type and it has a Stirling-cooled MCT detector of 240 x 320 pixels 2 • An acquisition frequency of 1000 im/s can be reached on small window of 64 x 120 pixels 2 while, without windowing, its highest frequency is 350 im/s. The 1000 im/s acquisition rate guarantees that the thermal dynamic is correctly followed, as the fastest heating tests have a power rising time of 0.1 s, and the diffusion time is only 0.6ms. The infrared camera is calibrated thanks to a DCN 1000 N4 black body. In the experiment that will be presented, a 50 im/s frequency was chosen, with 240 x 320 pixels 2 • The metal foil area that was investigated was a 5 x 25 mm 2 rectangle.

The thermal measurements are coupled with high-speed camera visualisations. The high-speed camera, a PHOTRON RS 3000, looks at the half-cylinder from one side. The used acquisition rate of the experiments was 500 im/s, with an image size of 1024 x 1024 pixels 2 • Before the experimental tests, it was checked that the high-speed camera visualisation area was at the same height on the half cylinder that the infrared camera visualisation zone (25mm). The output signal of the high-speed camera is recorded by means of a National Instruments box. By the same box, the tension and current signais are picked up and this permits to synchronise the camera images to the recording of the other measurement signais.

The current signal is acquired by a !TB 300-S LEM sensor. lt can measure up to 300A with a ±0.05% accuracy. lt can follow current variations up to 100 A/f.ls and its response time is lower than 1 J.lS at 300A. The voltage is measured by means of a MY-64 multimeter whose accuracy is 0.5% + 1 digit of the read value. The multi-meter connected with two cables allows a local voltage measurement. This permits to know the local electrical resistance of the metal foil. This measurement is done before the experiments. During the tests, the whole system tension is recorded, but it is possible to know the power that really passes through the foil by comparing the foil and the system resistances.

The National Instruments box is also used to acquire the thermocouples signais. There are three K-type thermocouples and they measure the HFE7000 temperature, the air temperature and the infrared camera temperature as well. Quantitative infrared measurements are possible only if the surroundings and the camera keep a constant temperature during the tests. Figure 2 presents a scheme of the experimental set-up and measurement techniques.

CAMERA Figure 2: Measurements techniques

RESULTS

In this article, three tests are presented. The first two correspond to the experiments where the supplied power is squared: a current value is fixed by means of the arbitrary generator, and reached almost instantly a constant value. It is important to underline that it is possible to obtain a square power signal only for low current values and long-lasting steps. This is the first test case. Figure 3 shows the shape of the power curve. Voltage cannot stabilize if the current to be provided is too high or the time too short. Moreover, the temperature tends to change the system resistance, thus involving a voltage change during the test duration. Test two includes experiments where the current imposed signal was square, but not the resulting power. Figure 6 presents the power curve in this case. The last test corresponds to a transient power case where the desired current value is reached by following a triangular signal. The resulting power is not exactly triangular, because the voltage does not increase linearly with time. This can be seen in figure 8.

Considering the square-power tests, the lowest current value that allows nucleate boiling is 25A, which correspond to 70W power measuredjust at the exit of the power supply. By means ofresistance measurements, it is possible to verify that 85% of the Joule power is dissipated into the metal foil. The rest is tost into the electrical connections. This means that the power density is 2.25 W/cm 2 if the lateral heat losses are not taken into account. The 25A current value corresponds to the lowest current value employed in these tests. The highest imposed current value is 75A, which corresponds to a mean power of 613W (that is 19.7 W/cm 2 on the foil surface without considering the laterallosses). As explained, it is possible to divide the tests into two categories. Each pulse given during the frrst test lasts 9s and the output power signal can be considered squared. During these experiments, the nucleate boiling regime is reached and stabilized. The second group corresponds to higher power values. In fact, the supplied power is more than 300W and the current is more than 50A. This value is high enough to avoid a square power to be delivered by the power supply.

In test two, during sorne experiments, the film boiling condition was reached (these cases will be called 'b'). As the provided power is elevated, the boiling phenomenon rapidly evolves from nucleate boiling to film boiling. Thus, white the frrst test presents an established nucleate boiling curve, the second one shows a transient boiling curve. It is possible to plot the temperature evolution in time by means of the infrared measurements. On the infrared pictures, an area with an homogeneous temperature field, which covers the metal foil surface, is considered to average the temperature measurements. It is important not to take into account the borders of the metal foil and to focalise on the central part. Border temperatures are very high, white the curvature effect may alter the measurements far from the centre of the half cylinder. The considered window is 3mm large and 10mm long (vertical direction). Its size is big enough to permit a meaningful mean spatial temperature evaluation.

Figure 3 shows the temperature time-evolution for a low-power case (test 1). Power is also plotted in this figure. It is possible to see that there is a high increase in the temperature value during the fust 50ms. The power passes from zero to the peak value in 30ms. The metal foil follows this rapid increase and gets 20 K in a few tens of milliseconds. This corresponds to the thermal convection regime. lnfrared measurements and high-speed camera images confirm that there are thermal plumes into the fluid (fig. 4). The highest temperature corresponds to the boiling onset. As boiling begins, the heat transfer is enhanced, so the wall temperature decreases considerably. The following part of the boiling curve corresponds to an almost constant temperature. It is the nucleate boiling heat transfer that avoids the increase of the wall temperature. ---------~--------------~------------ The small augmentation that can be seen in the temperature evolution corresponds to the power small increase. Finally, as the power is switched off, the temperature decreases to its initial value. Once again, the small inertia of the metal foil makes it respond instantaneously to the power signal.

~~~-

Figure 6 shows the case of a higher power that leads to film boiling (series 2b ).

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The experiments are interrupted before that the high temperature damages the metal foil. It is possible to see that there is a delay, in the cooling process, between the power and the temperature decreases. Once the film boiling regime is reached, the beat transfer is reduced. The amount of heat that passes to the quartz plates is increased, because the transfer toward the fluid is worse than during nucleate boiling. The vapour film deteriorates the beat transfer. Quartz plates have a higher inertia than the metal foil, and they need more time to cool down. The temperature enhancement is still partly caused by the power augmentation, but it is mainly due to the beat transfer worsening. It is possible to see that the tests are repeatable. Figure 7 shows three sets of curves: the two that represent the low power cases belong to tests one, the other two to test 2b. The repeatability of the experiments guarantees that data are consistent.

The third series of data is associated to a triangular signal. The fact that the power is continuously increasing affects the wall temperature behaviour. The lowest transient power curve has a 35A maximum current and lasts 9 seconds, while the highest one has a 65A maximum current and lasts Il seconds. In terms of power, the lowest test ends at 230W (7.4W/cm 2 ) peak power, while the highest at 500W (16W/cm 2 ). Up to now we did not evaluate if the beat tosses are higher in this case than in the square power one. Simulations are needed to shed light on this point. This test reaches the nucleate boiling regime but never passes to film boiling.

The experiments belonging to test 3 can be analysed in two ways. The fust one consists of taking into account the cases where the power ramp is constant while the test duration changes (fig. 8). The second one is considering the cases that have the same peak power but different durations that is, different power ramps (fig. 9).

When the power ramp is constant, the boiling onset always occurs at the same point. The curves are well superimposed till the boiling onset. There is only a small difference in the onset boiling temperature between the tests that have the same power ramp. The nucleate boiling regime needs sorne time to establish. This behaviour did not appear for the square power cases. This is probably due to the fact that the heated system receives progressively the power and thus needs more time to reach a stable condition. There is a slope change in the nucleate boiling part that is associated to the beginning of a nucleate boiling stable regime. Once the nucleate boiling phase is reached, the nucleate boiling temperature increase rate is the same for the tests that have the same power ramp. The final temperature depends on the experiment duration.

When the power ramp changes, there are sorne differences that are worth to be underlined (fig. 9). First of all, the boiling onset is delayed when the power is low. The lack of energy prevents the boiling phenomenon to start. Thus, the convective phase is longer. The boiling onset temperature is not considerably affected by the difference in the power ramps. The boiling curves present a phase of stabilisation before the nucleate boiling regime. The slope change that corresponds to the beginning of the established nucleate boiling phase becomes less significant when the power grows. The system has more energy and needs less time to get to the established nucleate boiling regime. This is consistent with data coming from the square power tests, where this initial phase is not visible at all. If the nucleate boiling part is considered, it is possible to see that a change in the power ramp corresponds to a change in the temperature increase rate. The nucleate boiling regime is longer for the highest power cases, because of the limited duration of the transitional phase of establishment of nucleate boiling and because of the shorter convection phase. Then, it ends at a higher temperature, because of the enhanced temperature increase rate. 40 ,-~-------------,--------------r------------- The good correspondence of the boiling curves that can be seen in figures 8 and 9 proves the consistency of the third test data.

" . ~ • • •• •• •~• • • • • ~• • • •• •• •• ~ 200 1 \ 1 ' 1 '~~ .........

RESULTANALYSIS

In the following part, tests are compared in order to highlight the most significant tendencies.

The first interesting point is the boiling onset. The corresponding temperature, T oNB, is plotted in figure 11. Since the liquid temperature varies during the tests, the difference T oNB-TL is plotted.

This figure shows how the onset boiling temperature is influenced by the temperature increase slope, dT/dt. The dT/dt value is evaluated for the regime of thermal convection, taking into account the beginning temperature and the ToNB-value.

It is possible to see that the two test groups behave differently. Tests 1 presents a linear augmentation of the ToNB-TL as dT/dt increases. The convective heat transfer is enhanced when the temperature increase rate dT/dt grows. Thus, the beginning ofboiling is delayed. The second (and second 'b') test does not follow the same tendency. It seems that ToNB-TL reaches an asymptotic value, which is independent of the temperature increase. There is no difference between the high power experiences that present film boiling and the others. The fitting line is almost horizontal. The two groups division occurs at 60 K/s.

It is possible to estimate the nucleation site radius [START_REF] Carey | Liquid Vapor Phase Change Phenomena, An Introduction to the Thermophysics ofVaporization and Condensation Processes in Heat Transfer Equipment[END_REF]) for a T 0 NB-TL value of 37K, that is, the asymptotic value.

This gives 2 •1 o• 2 1J.m. Probably ail the nucleation sites, even the smaller ones, are activated, that is wh y there is an asymptote. An experiment has been made where a vapour film appears on the wall instantaneously. It corresponds to a case ofrapid boiling. In this experiment, the onset of the nucleate boiling occurs at TONB-TL = 46K, for a dT/dt value of 122 K/s. It is a much higher value than those found in the other tests. This could be due to the presence of other boiling mechanism, which plays a role on the boiling onset. Indeed, a deeper investigation on these rapid boiling test cases is needed.

Figure 11 also presents the third test that is the transient supplied power case. The points can be compared to tests 1. The boiling onset temperature grows for a small temperature increase range. The power is supplied progressively and the thermal convective regime is longer than in the case of power square signais. The boiling onset temperature variation is smaller than for the tests 1. This means that in the case of power ramps, the onset temperature is less affected by the power shape. This is consistent with the fact that square power signais present a very steep beginning, as the power value bas to be reached in a few milliseconds. The initial power ramp is thus more significant in the case of square power.

Then, it is interesting to look at the nucleate boiling part. The mean temperature of the nucleate boiling curve is plotted versus the mean power on the same time lap, in figure 12. The experiences belonging to test 1 in steady nucleate boiling are compared to the transient supplied power case (test 3). In the two cases, the mean temperature grows as the mean power augments. The mean power is evaluated from the nucleate boiling onset to the end of the experiments, for test 1. For test 3, the part where the nucleate boiling phase is not stable, is not considered. The mean temperature and the mean power are evaluated on the part of the curves where nucleate boiling is developed. The power is almost constant.

The two groups have different behaviours. The square power experiences present a well-established nucleate boiling phase and the temperature increase slope is between 5 •10• 2 K/s and 0.5 K/s. Test 3 presents a temperature increase rate around 2K/s.

A deeper analysis is needed to make a quantitative comparison to the data of [START_REF] Auracher | Experimental studies ofboiling mechanisms in all boiling regimes under steady state and transient conditions, !nt[END_REF]. These authors plotted the heat flux density versus the wall superheat for different temperature increase rate dT/dt up to 50 Kls. They found that the variation of the temperature increase rate leads to different boiling curves. As dT/dt increases, the boiling curve becomes steeper and the critical heat flux is increased. The effect of the temperature increase rates on our experimental data is also pointed out in Figure 12. According to the analysis of Auracher and Marquardt, the points belonging to tests 1 can be considered on the same boiling curve with dT/dt close to zero, corresponding to a steady boiling regime. This curve is not very steep as the temperature increase rate is almost zero. Test 3, which corresponds to transient experiments, can be gathered on another boiling curve, whose slope is around 2K/s. The temperature increase rate is higher than for the first group tests, thus the slope is steeper. This is consistent with Auracher and Marquardt's results. However a quantitative comparison with the results of Auracher and Marquardt is not possible because the heat losses toward the lateral quartz plate have still not been precisely evaluated. At a first step, the lateral heat losses into the quartz plate have been roughly estimated around 30% of the total heat flux. Then the heat flux transmitted to the liquid in a steady of transient boiling regimes have been evaluated and are of the same order of magnitude as those found by Auracher and Marquardt's for the same values of dT/dt. The evaluation of the lateral heat losses is necessary to obtain quantitative measurements of the heat flux transmitted to the fluid. Thus, a 2D numerical model will be used in order to know the heat flux that is really passed from the wall to the fluid. The software that has been chosen in order to calculate this flux is Comsol Multiphysics. By means of the resolution of the Fourier equation in both the metal foil and in the quartz plates, it will be possible from an energy balance to quantify the heat flux transmitted from the metal foil to the fluid. The heat flux transmitted to the fluid will be obtained from the difference between the heat flux dissipated by Joule effect in the foil and the heat flux lost into the quartz plates. It is not possible to estimate it a priori, since the time duration of the experiments has a strong influence on the heating rate into the quartz plate and on the borders of the metal foil.

CONCLUSIONS

An experimental set-up has been built to investigate fast transient boiling regimes that can be encountered in the case of reactivity initiated accidents in nuclear reactors. A semi annular metallic foil is heated by Joule effect. The foil temperature evolution is recorded with an infrared camera. An electrical power supply allows delivering a constant or variable value of the current use to heat the foil by Joule effect. Two types of experiments were performed. The first one correspond to the cases where a constant current signal was used, whose duration varied between 9s (test 1) and 4/5s (test 2). The second type corresponds to a linear increase of the current with different slopes and durations (from 7s to 11.5s).

With a constant current, a rapid increase in the wall temperature is observed until the onset of nucleate boiling. Then the wall temperature quickly decreases and stabilizes around a steady value in the nucleate boiling regime. At high power steady nucleate boiling is not observed, the wall temperature always increases and it is possible to see a transition to film boiling. For transient tests the effect of the slope is pointed out.

The first results are presented in this paper versus the Joule power the wall temperature increase rate dT/dt. For the tests at constant current, the more the power increases, the more the wall temperature increase rate dT/dt augments. The temperature at the onset ofnucleate boiling directly increases with dT/dt until it reaches a maximum value corresponding to activation of the smallest nucleation sites on the foil. In transient regime, the value of dT/dt before the onset ofnucleate boiling is small. The temperature required for the onset of nucleate boiling is larger than with a step of current for which energy is instantaneously transmitted into the foil. The evolution of the wall temperature during nucleate boiling is also plotted, versus the mean power for steady and transient nucleate boiling regimes. The heat transfer is larger in transient nucleate boiling regime, than in steady nucleate boiling regime, as already observed by other authors. Since the metallic foil is glued to quartz plates, a significant part of the power is lost by conduction toward the plates and the heat flux transmitted to the liquid cannot be directly evaluated. Thus the unsteady Fourier equation will be solved numerically with the software Comsol Multiphysics to quantify this heat flux. In the near future, Comsol simulation will be run. Thus, a quantitative comparison with literature results will be possible. Moreover, different test cases, like linear growing power tests or tests where the film boiling is instantaneously reached will be performed. This last type of experiments will hopefully clarify the mechanism ofboiling when rapid boiling occurs.

Figure 3

 3 Figure 3 Power and temperature evolution, test 1

Figure 4 :

 4 Figure 4: Convective plumes on the metal foil. From the left, high-speed camera and IR images (Test 1) Figure 5 (right) shows an infrared image where nucleation sites appear. The left image presents nucleate boiling as seen by the high-speed camera.

Figure 5 :

 5 Figure 5: Nucleate boiling on the metal foil. High speed camera and IR images (Test 1)

  10 0 ~~------~------~------~------~--....llol1o'K,ao'l__,_. ...... ...-~~~

Figure 6 :Figure 7 :

 67 Figure 6: Power and temperature evolution, test 2b

Figure 8 :

 8 Figure 8: Comparison of experiments having the same power ramp (Test 3)

Figure 3 :

 3 Figure 3: comparison of experiments having different power ramps (Test 3)

Figure 4 :

 4 Figure 4: ToNB-TL versus temperature increase rate before the onset ofnucleate boiling

Figure 12 :

 12 Figure 12: supplied mean power versus T NB-TL

ACKNOWLEDGMENT

The authors would like to acknowledge the technical staff ofiMFT, especially Laurent Mouneix for the help in designing and building the experimental set-up. Sebastien Cazin is also greatly thanked for his support in the infrared measurements and the flow visualisations.