# Confined boiling on an immersed heated corner: influence of one wall on the other

Antonio Della Volpe, Nicolas Baudin, Stéphane Roux, Robert Yu, Jean-Michel

Fiard, Jérôme Bellettre

► To cite this version:

Antonio Della Volpe, Nicolas Baudin, Stéphane Roux, Robert Yu, Jean-Michel Fiard, et al. Confined boiling on an immersed heated corner: influence of one wall on the other. Journal of Physics: Conference Series, 2024, 2766 (1), pp.012129. 10.1088/1742-6596/2766/1/012129. hal-04623163v2

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Confined boiling on an immersed heated corner:
influence of one wall on the other

To cite this article: Antonio Della Volpe et al 2024 *J. Phys.: Conf. Ser.* **2766** 012129

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# Confined boiling on an immersed heated corner: influence of one wall on the other

Antonio della Volpe¹,², Nicolas Baudin¹*, Stéphane Roux¹, Robert Yu², Jean-Michel Fiard², Jérôme Bellettre¹

¹ LTEN UMR 6607 CNRS, Nantes Université, Nantes, 44300, France

² RENAULT GROUP, Guyancourt, 78280, France

E-mail: nicolas.baudin@univ-nantes.fr

**Abstract.** An experimental test section with horizontal and vertical heated plates forming an inverted L-shape is filled with 3M Novec7000 dielectric fluid at atmospheric pressure. Both plates of 64 × 40 mm² dimensions are heated with wall heat fluxes ranging from 0 to 20 Wcm⁻². There is natural convection for low heat fluxes, medium heat fluxes trigger boiling and for higher power, the critical heat flux is reached. The wall temperature and heat flux are calculated from in-wall thermocouple measurements in steady state. The bubbly flow on the vertical surface is observed with a high-speed camera through a window.

The confinement between the vertical heated surface and the wall is varied from 0.5 to 15 mm. In the range of this study, the heat transfer coefficient in natural convection and nucleate boiling regimes increases when the spacing decreases. However, since the critical heat flux decreases when it is more confined, the film boiling regime is reached faster. From the visualizations and the thermal measurements we try to model these different behaviors.

Depending on which plate is switched on or off we observed different behaviors. The confinement of the vertical plate does not have any influence on the horizontal one since the plate width is much bigger than the gap change. Also, the horizontal plate heating does not influence the heat transfer on the vertical plate in this study. However, there is an influence of the vertical boiling on the horizontal one, stronger when there is a confinement than in free configuration.

## 1. Introduction

Many technologies require both efficient and compact cooling solutions: servers in data centers, electric components in automotive industry, fuel cells in transportation sector, etc. Heat fluxes ranging from 1 to more than 100 Wcm⁻² need to be dissipated at temperatures ranging from 30 to 100 °C. Immersion cooling consists in bathing the heating components in a dielectric fluid with a saturation temperature close to the operating temperature. Thus, the liquid boils in contact with the heated surface, providing high heat transfer coefficients.

Due to the compactness required by the technologies applications, the boiling is confined, which leads to particular behaviors and heat transfers. Many studies in the 90's (Xia et al. [1]; Bonjour et al. [2]) focused on small heated areas with few thermocouple measurements. They allowed to get a first understanding of the phenomenon involved in the boiling confinement, and to get correlations for the Nucleate Boiling (NB) regime and the Critical Heat Flux (CHF) depending on a confinement number. One of the main conclusions are that when the spacing between the heated surface and the wall decreases, there is first an increase of the heat transfer

<figure><img src="image_5.png" /></figure>
<figure><img src="image_6.png" /><figcaption>Figure 1: 2D schematic plan of the main setup components</figcaption></figure>

coefficient during NB regime and then a decrease past a critical confinement number. There is not yet a consensus on the reason behind that. More recent studies (Ait-Ameur [3], Della Volpe et al. [4]), investigated bigger areas instrumented with more thermocouples and gave more insight about the temperature distribution along the heated surface area.

When the heated body is large enough, there are both a vertical and a horizontal surfaces which are heated, forming an inverted L-shape heated shape. One can wonder if the bubbly flow on one wall can influence the other one. This paper first reminds some results from [4] about the thermal influence of one wall on the other, then presents an image analysis methodology to help understanding the thermal behavior.

## 2. Methodology

### 2.1. Testbench

A testbench (figure 1) has been designed to study the boiling around an inverted L-shape heated body immersed in a temperature and pressure controlled bath of 3M Novec 7000, a dielectric fluid. The heating is provided by two Thermocoax SEA 10/75 heating elements for each heated plate. There is a Deltherm thermal insulator piece between the plates, which allows to heat the plates either simultaneously or separately. The Thermocoax elements deliver each up to 250 W homogeneously in copper plates. The heat is transferred from the copper plates to inox 316L steel plates (6 mm thick and 64 × 40 mm² surfaces). The other side of the steel plates is in contact with the dielectric fluid, where the boiling takes place. Deltherm thermal insulator surrounds both the copper and steel plates all around except the boiling surfaces, granting low heat flux losses. The assembled heating element can be moved closer or farther from the glass wall through a 50 mm long micrometer screw, which allows to regulate the confinement *e* in the canal in front of the vertical plate. A condenser is situated 5 mm on top of the horizontal heating plate. The bottom of the system is connected to an expansion tank to help controlling the pressure around 1 atm. A wide glass window is installed in front of the vertical plate to monitor the system at any time. The transparent glass also represents the confining wall.

Before running an experimental test, a vacuum pump is used to remove the air from the test-bench. The fluid is also degassed by boiling it in its storage tank and releasing the vapour for a few seconds by the top vapor outlet. All measurements which will be presented are obtained in steady state regime i.e. when all the temperature measurements do not vary more than 0.2 °C over a 5 minutes period.
## 2.2. Measurements and data reduction

0.5 mm diameter K-type thermocouples are situated at the middle of the heated plates at different depths, plus another thermocouple in front of the plate immersed in the fluid. The surface temperature $T_p$ and the surface wall to fluid heat flux $q''$ are obtained from the thermocouples inside the steel plate, assuming steady state and 1D conduction, and thus without interfering with the boiling. All the thermocouples are connected to a Keysight 34980A acquisition center coupled with a Keysight 34921A isothermal cold box. The superheat is then calculated $\Delta T = T_p - T_{sat}$, $T_{sat}$ being the fluid saturation at the measured pressure, interpolated from Rausch et al. [5] study on HFE fluid properties ($T_{sat} \approx 34$ °C at atmospheric pressure).

The uncertainties are calculated using GUM's methodology [6] assuming a temperature accuracy of 0.2 °C and a position uncertainty of 0.1 mm.

Confinement is measured through the micrometric screw which has a resolution of 0.01 mm and an accuracy of ±0.003 mm. This allows to control the confinement value $e$ of the vertical heated plate in a range of 0.5 mm < $e$ < 15 mm. This corresponds to a Bond number $Bo = \frac{(\rho_l - \rho_v)ge^2}{\sigma}$ ranging from 0,27 to 244 where $\sigma$ is the surface tension of the fluid. A small Bond number ($\ll 1$) means that the confinement has an effect on the boiling.

More details about the experimental setup and its validation can be found in [4].

## 2.3. Image analysis

A FASTCAM SA-X2 type 1080K-M4 camera is placed in front of the vertical heating surface to visualise the boiling process with a frequency ranging from 500 to 2000 Hz depending on the heating power. The camera field allows to see the whole vertical surface. The following image processing methodology had been done to get average bubbles velocity:

* A part of the image is selected (red rectangle on figure 2a).

* An average along x axis of gray intensity on the red rectangle (Average slice) and on the thin vertical slice (blue rectangle on figure 2a, Center slice)) are performed for each frame.

* Figure 2b shows the average slice over the frame number. Since bubbles reflect light and are brighter than the steel plate, their motion is seen as a streak on figure 2b. The orientation of the streak may be assimilated to the velocity of the bubble.

* To obtain the orientation $\theta$ of the streak, and thus an estimated bubble velocity $v_b$, the toolbox `orientationpy` is used. Figure 2c shows the vectors $\vec{s}$ obtained through figure 2b gradients with the toolbox.

* These vectors are filtered: first, all the vectors corresponding to unrealistic values of $v_b$ ($< 0$ and $> 1 \text{ ms}^{-1}$) are discarded. Then, to remove the vectors outside the streaks (low values of $v_b$ or small values of the norm of $\vec{s}$), only values of $\frac{||\vec{s}||v_b}{(||\vec{s}||v_b)_{\text{max}}}$ higher than 1% are kept.

# 3. Results and discussion

## 3.1. Thermal performances

For each plate, two configurations are compared: when the plate is heated solely, and when the two are heated together. Moreover, a juxtaposition of data for both the free case and for the smaller vertical canal width 'e = 0.5 mm' is given to check if it has an impact for both cases. The boiling curves i.e. the wall heat flux as a function of the wall superheat are plotted for each configuration.
<figure><img src="image_7.png" /><figcaption>Figure 2: Images post-processing. a: Image selection; b: Average slice over frame number; c: Vectors obtained from *OrientationPy* toolbox</figcaption></figure>

Figure 3a shows the difference between when both plates are heated simultaneously and when the vertical plate is heated on its own. For the free configuration ($\infty$: $e = 15$ mm i.e. $Bo = 244$), when the vertical plate is heated alone ($V \infty$), several regimes can be recognised, highlighted by red vertical lines and camera pictures. For low heat fluxes, there is mostly natural convection with few bubbles enhancing the heat transfer. For medium heat fluxes, boiling is the main heat transfer mechanism, hence the boiling curve slope is steeper. For higher heat fluxes, the bubbles coalesce, leading to a crowded bubble flow, characterised by a smaller boiling curve slope.

The figure also shows the effect of the strongest confinement ($e = 0.5$ mm i.e. $Bo = 0.27$) on the vertical plate ($V e = 0.5$ mm). The heat flux is higher than in the free configuration, at least for low heat fluxes. Della Volpe et al. [4] explain that there may be a stronger convection due to the bubbles "squeezing". A thinner liquid layer between the flat bubbles and the wall could also induce this heat transfer enhancement. However, the bubble flow becomes easily crowded, which triggers the critical heat flux at low heat fluxes ($\approx 17 W cm^{-2}$) and prevents the occurrence of the different regimes for very low confinement such as $e = 0.5$ mm.

Switching the top horizontal plate could have resulted in a chimney effect and an increase of the convection along the vertical plate, and so an heat transfer increase. However, no such thing was clearly observed in the configurations which were tested, in both confined and free cases.

Figure 3b shows the boiling curves of the horizontal plate, when both plates are heated ($H + V$ configuration) and when only the horizontal is heated ($H$). The confinement ($\infty$ and $e = 0.5$ mm) refers to the vertical plate confinement. Similar regimes can be observed on the boiling curves although not confirmed through visual observations here.

Up to $12 W cm^{-2}$, there is little to no variation between all the data points ($< 1 °C$). This regime corresponding mainly to natural convection along both plates, it is possible that the weak flow coming up from the vertical plate, in a corner of the top chamber, does not disturb much the natural convection over the large horizontal plate.

For higher heat flux, corresponding to the fully developed boiling regime, some differences occur between $V$ and $H + V$ configurations. The heat transfer on the top horizontal plate is
<figure><img src="image_8.png" /><figcaption>Figure 3: Boiling curves. a: in the middle of the vertical heated plate [4]; b: in the middle of the horizontal heated plate [4]</figcaption></figure>

enhanced, possibly due to an additional mixing due to the bubbles coming up from the vertical plate. This enhancement increases when the confinement on the vertical plate decreases. One reason for this behaviour could be the overall size of the bubbles which increases when the vertical plate is confined: they are flat, but very large (≈ *cm*), while for a "free" case all the bubbles tend to have a similar and small size (≈ *mm*). Also, for high confinement, the flow becomes more unsteady, which leads to a kind of bubble puffing which may disturb a lot the boiling occurring on the horizontal plate.

## 3.2. *Bubble velocity analysis*

Figure 4a shows the bubble velocity distribution obtained using the previously explained methodology on the *Average slice* for different filtering. For no or small filtering, a tail appears toward low velocities, which may be an artefact of the methodology (bad vectors or empty vectors obtained from *orientationpy*). A 1% filter seems the best trade off for now, between removing too much information at low velocities and adding too much artefact. Even if the filter changes the average velocity, it does not change the velocity with the highest probability, which may be the most meaningful information then. The same figure can be plotted for the *Center slice*. However, especially for low power, there may be only few bubbles passing through the center slice, and the estimation of the velocity distribution becomes very noisy and difficult to use.

No uncertainty will be given here since verification tests are needed. Preliminary comparison between the results obtained with this image processing and results obtained by tracking bubbles "by hand" showed that the described methodology managed to estimate the velocity within 10% error when using the *Center slice* when possible. Moreover, the order of magnitude of the bubble velocity estimated here is in good agreement with the one given in Scheiff et al. [7] with HFE7000. The estimation based on the *Average slice* is always successful since the averaging smooths the distribution. However it can differ by up to 30% from the velocity measured by tracking bubbles. It would be better to add the velocity distribution of several slices.

Figure 4b shows the estimated bubble velocity for a confined case in *V* and *H + V* configurations. Like with the thermal results, no clear difference is seen.

Figure 4b also shows the estimated bubble velocity for a confined and a free case. At low heat fluxes (below 10 *W*cm⁻²), there seems to be no clear difference between confined and free cases. The heat transfer difference in this regime, shown on figure 3a, should be mainly due to
<figure><img src="image_9.png" /><figcaption>Figure 4: Image analysis. a: Bubble estimated velocity distribution (vertical plate, $e = 0.5 \ mm$, $P = 50 \ W$); b: Bubble estimated velocity along the vertical plate (Cent: Center slice, Av: Average slice, conf: confined with $e = 0.5 \ mm$)</figcaption></figure>

a change in the natural convective flow without incidence on the bubbles. At higher heat fluxes, the free case bubbles seem to have a higher velocity than in the confined case. That is one step forward the understanding of the heat transfer difference during the developed boiling regime.

An estimation of the bubble diameter would be needed too, and future work will try to estimate this diameter from the thickness of the streaks on figure 2b. Also, a rigorous validation of what is estimated will be needed. Indeed, at high heat fluxes, the streaks may correspond to flow patterns other than single bubbles, such as vapour pockets or even waves on a vapour film.

## 4. Conclusions

This article presented results about the immersion cooling performances on a heated inverted L-shape body in a free and confined bath of HFE7000. The focus was here on the effect of one plate on the other one. It seems that switching on the horizontal plate does not have any effect on what happens on the vertical heated plate. On the contrary, switching on the vertical plate can increase the heat transfer between the horizontal plate and the fluid in developed boiling regime. This enhancement is greater at high confinement (low $e$). A possible explanation is the additional mixing brought by bigger puffing bubbles coming up from the vertical plate. A quick and simple image processing methodology was presented to get bubble velocities based on the recognition of streaks in an figure plotting a camera vertical slice versus time. Although more validation is needed, the results seem encouraging and support the thermal results.

## References

[1] Xia C, Guo Z and Hu W 1992 ASME-PUBLICATIONS-HTD **197** 111–111

[2] Bonjour J 1998 *Amelioration des transferts de chaleur en ebullition naturelle convective par effet de confinement*. Ph.D. thesis Lyon, INSA

[3] Ait Ameur M 2006 *Etude expérimentale de l'ébullition naturelle confinée: analyse des instabilités et des transferts thermiques* Ph.D. thesis Lyon, INSA

[4] della Volpe A, Baudin N, Roux S, Yu R, Fiard J M and Bellettre J 2024 *Applied Thermal Engineering* 122498

[5] Rausch M H, Kretschmer L, Will S, Leipertz A and Froba A P 2015 *Density, surface tension, and kinematic viscosity of hydrofluoroethers HFE-7000, HFE-7100, HFE-7200, HFE-7300, and HFE-7500* vol 60 (ACS Publications)

[6] JCGM 2008 JCGM 100:2008

[7] Scheiff V, Bergame F, Sebilleau J, Ruyer P and Colin C 2021 *International Journal of Heat and Mass Transfer* **164** 120548