1 Phenomenon.
In this talk we propose an approximation method for using general equations of state (EOS), including tabulated ones, in the numerical simulation of dynamical liquid-vapor phase change in pool **boiling** type flows. This phenomenon concerns various engineering fields such as the study of pressurized water reactors in the nuclear industry. Indeed, understanding the triggering of **boiling** crisis is a critical safety issue for the nuclear industry: when the transition occurs from **nucleate** **boiling** to film **boiling** in the vicinity of heating wall, the vapor acts as a thermal insulator and the wall temperature raises suddenly. If this phenomenon occurs, it may cause serious damages to the facility.

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Several points remain unclear about the physical processes involved in the formation and depletion of micro-layers. In partic- ular, it is not fully understood for which conditions **nucleate** boil- ing occurs in contact line or in micro-layer regime. The main motivation of the present work is to provide detailed informations in order to characterise the transition between the regimes, using fully resolved Direct Numerical Simulations (DNS). The-in house solver DIVA has been used to solve the incompressible Navier- Stokes equations for two phase flows and to account for phase change. Axisymmetric configurations have been employed, with very refined grids allowing the description of a possible micro- layer having a thickness of the order of the micron, beneath a bub- ble having a radius of the order of the millimetre. Simulations of this multi-scale phenomenon are challenging and require using massively parallel supercomputers and suitable numerical tools to verify that the results are not affected by grid dependence effects. Moreover, it is noteworthy that micro-layers involve locally very high heat fluxes in the range of several MW, that could induce stability issues for numerical solvers if the thermal gradients are not sufficiently resolved. To the authors knowledge, there are no other DNS results with phase change available in the literature showing the formation and depletion of a micro-layer and the pre- sent work is the first attempt to carry out a fully resolved DNS of **nucleate** **boiling** in micro-layer regime.

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Numerical solvers based either on fundamental conservation
equations [12,13] or Lattice Boltzmann equations [14,15] can be
used to simulate **nucleate** **boiling**. In the present paper, we will focus on the first class of numerical solvers. From a numerical point of view, varying or suppressing the gravity acceleration does not present any immediate constraint. However, the requirements in terms of resolutions (small grid cells size) in order to achieve con- verged results, the long simulation times and the complexity of the phenomenon strongly impact the cost of the problem (long com-

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reproducing the phenomenon [27,45,48] .
Several points remain unclear about the physical processes involved in the formation and depletion of micro-layers. In partic- ular, it is not fully understood for which conditions **nucleate** boil- ing occurs in contact line or in micro-layer regime. The main motivation of the present work is to provide detailed informations in order to characterise the transition between the regimes, using fully resolved Direct Numerical Simulations (DNS). The-in house solver DIVA has been used to solve the incompressible Navier- Stokes equations for two phase flows and to account for phase change. Axisymmetric configurations have been employed, with very refined grids allowing the description of a possible micro- layer having a thickness of the order of the micron, beneath a bub- ble having a radius of the order of the millimetre. Simulations of this multi-scale phenomenon are challenging and require using massively parallel supercomputers and suitable numerical tools to verify that the results are not affected by grid dependence effects. Moreover, it is noteworthy that micro-layers involve locally very high heat fluxes in the range of several MW, that could induce stability issues for numerical solvers if the thermal gradients are not sufficiently resolved. To the authors knowledge, there are no other DNS results with phase change available in the literature showing the formation and depletion of a micro-layer and the pre- sent work is the first attempt to carry out a fully resolved DNS of **nucleate** **boiling** in micro-layer regime.

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During **boiling**, a steep temperature gradient exists near the heating wall. This thermal gradient is accompanied by an optical index variation. The incident laser light is then nonuniform near the wall. Furthermore, the reflection of the light at vapor bubble surface also contributes to non-uniformity. Therefore, the use of two dyes is essential to avoid the measurement errors due to theses non-uniformities and to get an accurate measurement of the temperature field in **nucleate** **boiling** problem. The two-color LIF

1. Introduction
Cryogenics propellants are stored in a liquid state in space tanks, at a temperature which is only a few degrees smaller than the saturation temperature. Even low heat loads could induce **nucleate** **boiling**. The consequences are an increase in the pressure and the risk of pumping vapour in the feed system. It is thus very important to be able to predict and to control the phenomenon. **Nucleate** **boiling** in micro-gravity conditions is actually a topic of large scientific interest, and a number of questions remain unan- swered. For instance there are open questions on the quantitative impact of the gravity level on the critical heat flux and more in gen- eral on the heat transfer behaviour [1,2] . Moreover, the impact of wall superheat and wetting properties, that have been largely investigated in normal gravity conditions, are not clearly under- stood in micro-gravity conditions [3,4] . Therefore basic studies, dealing with single bubbles, are required to improve our under- standing. As a matter of fact, in terrestrial gravity conditions, com- plex experiments with long observation times are possible. On the other hand, things become much more complicated if micro- gravity conditions are searched. Most of the experiments in

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Fig. 16 a represents the logarithm of the ratio / w=/gen of the same test. Once again, the black lines deduced from the analysis of the vapor front thickness analysis have been reproduced. It is
very close to 0 (i.e. / w ’ /gen ) as soon as the steady **nucleate** boil- ing regime is reached. During the transient convection stage, it indicates that the heat flux is approximately one order of magni- tude less than the power intensity. The boundary of this regime is a short period represented by a rather thin orange line near the black dashed line. The heat flux is for a small fraction of time of the magnitude or larger than the power intensity. Despite this very evanescent step, the transition between those regimes is clearly made of two successive steps. The first one occurs when the first big vapor pocket covers the wall, i.e. between the black solid and the black dashed lines. It corresponds to a quasi-null heat flux toward the fluid (until around 1000 times less than the power dissipated). This corresponds clearly to the inflexion of the wall temperature just before the decrease that has been identified on the temporal local evolution of the wall temperature in Section 3.5 . It is followed by a very rapid increase of the wall to fluid heat flux with maximal values more than 10 times the power dissipated. The transient heat flux during this transition toward **nucleate** **boiling** regime is therefore a very efficient heat transfer.

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Transient **boiling** has been studied since the 1950s and most of these investigations were performed in pool **boiling** condition using ribbon [1] , wire [2–4] or plate [5–7] heaters. Visentini [8]
studied transient pool **boiling** in semi-annular geometry that is clo- ser to the typical geometry encountered in a PWR. These studies point out that the **boiling** incipience, corresponding to the appari- tion of the first vapor bubble and generally denoted as onset of **nucleate** **boiling** (ONB), occurs with a wall superheat (T w ! T sat ) that increases with the heating rate and the subcolling. Sakurai et al. [2] , Jonhson [9] , Su et al. [7] used a modified Hsu’s criterion to predict the superheat at ONB with a good agreement with their experiments. These studies also report different **boiling** regimes during the transition from the ONB to the fully developed **nucleate** **boiling** regime (FDNB) or to the film **boiling** regime. In particular, and depending on the experimental condition, a temperature over- shoot (OV), i.e. a temperature larger than the FDNB temperature, can be observed during this transition. The case of transient **boiling** with forced convection has also been studied on ribbon [9] , wire

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the exit section must become small at high quality, Since the boiling process depends on a liquid covered surface, it is reasonable to expect that the average depth of the liqu[r]

At hibg heat flux, in the nei*hborhood of burnout, the test section is normally almost isothermal, so that, while the magnitude of the test section resistance may [r]

In addition, no general correlation scheme exists, so that it is impossible for .a designer to take burnout data for water, for instance, and use it to calculate[r]

For a fixed coolant mass flow rate, the swirling flow produced by the MSLTTs allows the IPWR to have a higher operating heat flux while maintaining the design criteria of M[r]

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Toulouse, 31400, France
E-mail: msagan@imft.fr, tanguy@imft.fr, colin@imft.fr ABSTRACT
In this work, we study different phenomena that occur during **nucleate** **boiling**. We numerically investigate **boiling** using two phase flow direct numerical simulation based on a level set / Ghost Fluid method. This method allows us to follow the interface and to make accurate geometric calculation as for bubble curvature. **Nucleate** **boiling** on a plate is not only a thermal issue, but also involves multiphase dynamics issues at different scales and at different stages of bubble growth. As a consequence, we divide the whole problem and investigate separately the different phenomena considering their nature and the scale at which they occur.

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a b s t r a c t
In this paper, we present Direct Numerical Simulations of **Nucleate** **Boiling** on a single site in configura- tions involving both a large microscopic contact angle, a moderate Jakob number (less than 50) and a high density ratio between the two phases. A detailed study on the validation of the numerical simulations is presented. Several issues about the numerical modelling of the contact line are addressed in order to define a global strategy to perform accurate and predictive simulations. Benchmarks from pioneering studies (Son et al., 1999) have been reproduced with more recent numerical methods and thinner grids in order to define the most relevant strategy for successful simulations. In particular, the grid sensitivity of the solution is thoroughly investigated by performing simulations with four successive grids. The numerical results are compared favorably with experimental data, since the discrepancy between the numerical solutions and the experimental data is always less than 10% whether the departure diameter or the departure frequency are considered. The influence on the numerical solution of the thermal con- duction in the solid heater is also assessed and we report that this parameter has no influence in the con- figurations of thick and highly conductive materials that have been considered in this study. We also present clarifications about the requirement of a specific modelling in the contact line region in order to account for a possible impact of the micro-region. Finally, based on the results of this analysis of our numerical simulations, we formulate the following unusual conclusion: the implementation of a micro-region model and an additional coupling between the overall solver and such a model is not required to perform well-resolved and accurate numerical simulations in the case of high density ratio, high microscopic contact angle (up to 30 °) and moderate Jakob number. Next, we present some compar- isons on the bubble shape evolution between the numerical simulations and a static force balance model, in order to investigate the mechanisms leading to the bubble detachment. Finally, we conclude this paper by presenting a parametric study, by varying the Jakob number, in order to propose a new correlation on the bubble detachment radius depending on the latter dimensionless number.

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symbols)– comparison with the correlations of Kim & Mudawar [19] and Cioncolini & Thome [20]
CONCLUSION
Experiments on flow **boiling** in a tube of 6 mm diameter are performed both in normal and microgravity conditions. Flow visualizations allow the determination of the flow regimes: bubbly, slug and annular flows. The void fraction is measured by capacitances probes. The liquid film thickness deduced from the void fraction measurements in annular flow regime decreases with the mass flux and is lower in microgravity conditions than on ground. The wall shear stress is well predicted by Lockhart and Martinelli correlation except at low mass fluxes (G < 100 kg/m 2 /s). The interfacial shear stress is typically smaller in microgravity conditions especially at low mass flux. Heat transfer coefficient measurements show that in **nucleate** **boiling** regime at low qualities, the values are smaller than the prediction of classical correlations, and smaller in microgravity than on ground. In convective **boiling** regime at high qualities, The results are in good agreement with the correlation of Cioncolini and Thome [20]. New experiments will be performed in collaboration with University of Maryland to access to the local instantaneous measurements of the heat transfer coefficient by using Infrared Thermography [21].

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Conclusion and perspectives
Clad to coolant heat transfer during transient **boiling**, such as during a reactivity initiated accident, is still unsufficiently understood. The “Institut de Sûreté et de Radioprotection Nucléaire” in collaboration with the “Institut de Mécanique des Fluides de Toulouse” investigates the phenomenon thanks to a dedicated experiment. The facility can simulate rapid and mastered heating of a wall in contact with a refrigerant fluid. A large range of wall heating rates can be achieved from a few K/s till 2000K/s. Space and time evolutions of the wall temperature, wall heat flux and visual observation of **boiling** are recorded. It allows to catch **boiling** regime transition (onset of **nucleate** **boiling** or vapour film establishment) and to deduce the quantitative effect of wall heating rate on the heat flux over the whole range of heat transfer regimes. From the analysis of the first campaign tests, the following conclusions can be drawn. The single-phase heat transfer stage is a mix of transient conduction and convection. For transient cases, the onset of **nucleate** **boiling** is mainly characterized by a threshold of energy transferred to the fluid rather than a wall temperature criterion. For very rapid transient, the spinodal limit is reached after a few milliseconds. Steady **nucleate** **boiling** regime of HFE7000 is well described by Forster and Zuber’s correlation for saturated or subcooled pool **boiling** or by Chen’s correlation for convective case. Transient conditions heat flux increases linearly with wall heating rate in a consistent way with the results obtained by Auracher and Marquadt. The heat flux at departure from **nucleate** **boiling** is close to the Zuber’s correlation and increases with wall heating rates, in agreement with results obtained by Auracher and Marquadt. For very rapid transient tests, the vapour film covers instantaneously the heated wall and heat transfer is one or two orders of magnitude larger than the correlation prediction for the same wall temperature and steady state conditions.

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Conclusion and perspectives
Clad to coolant heat transfer during transient **boiling**, such as during a reactivity initiated accident, is still unsufficiently understood. The “Institut de Sûreté et de Radioprotection Nucléaire” in collaboration with the “Institut de Mécanique des Fluides de Toulouse” investigates the phenomenon thanks to a dedicated experiment. The facility can simulate rapid and mastered heating of a wall in contact with a refrigerant fluid. A large range of wall heating rates can be achieved from a few K/s till 2000K/s. Space and time evolutions of the wall temperature, wall heat flux and visual observation of **boiling** are recorded. It allows to catch **boiling** regime transition (onset of **nucleate** **boiling** or vapour film establishment) and to deduce the quantitative effect of wall heating rate on the heat flux over the whole range of heat transfer regimes. From the analysis of the first campaign tests, the following conclusions can be drawn. The single-phase heat transfer stage is a mix of transient conduction and convection. For transient cases, the onset of **nucleate** **boiling** is mainly characterized by a threshold of energy transferred to the fluid rather than a wall temperature criterion. For very rapid transient, the spinodal limit is reached after a few milliseconds. Steady **nucleate** **boiling** regime of HFE7000 is well described by Forster and Zuber’s correlation for saturated or subcooled pool **boiling** or by Chen’s correlation for convective case. Transient conditions heat flux increases linearly with wall heating rate in a consistent way with the results obtained by Auracher and Marquadt. The heat flux at departure from **nucleate** **boiling** is close to the Zuber’s correlation and increases with wall heating rates, in agreement with results obtained by Auracher and Marquadt. For very rapid transient tests, the vapour film covers instantaneously the heated wall and heat transfer is one or two orders of magnitude larger than the correlation prediction for the same wall temperature and steady state conditions.

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the wall move and condense in the ﬂow core and increase its temperature.
(ii) In saturated **boiling** the ﬂow core has reached saturation. **Nucleate** and convective **boiling** compete. In **nucleate** **boiling** the heat transfer coefﬁcient depends on the heat ﬂux which is the driving force of bubble generation (dashed lines). In convective **boiling** the heat transfer coefﬁcient is independent of the heat ﬂux but depends on the liquid quality and mass velocity which are the driving forces of convection. The combination of both shows almost horizontal and parallel lines at low vapour quality (**nucleate** **boiling**) which merge into a single increasing line at higher vapour quality (convective **boiling**). The smaller the heat ﬂux the sooner (in terms of vapour quality) convective **boiling** will take over from **nucleate** **boiling**. This is further highlighted by ﬁgure 2 which represents experimental results on ﬂow **boiling** regimes in tubes.

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vapor bubbles suddenly form a film which covers the heating surface and insulates the latter from the bulk of the liquid. The temperature of the heating surface grows so rapidly that the heater can fuse unless its power is controlled. This phenomenon is known under the names of “**boiling** crisis,” “burnout,” or “Departure from **Nucleate** **Boiling**” (DNB) [1]. The final state of this transition is called film **boiling**.

5.2.4 Three dimensional film **boiling**-Meso Scale
This computation is performed in a three-dimensional hexahedral domain with a heat source (Figure 5.11). Using the immersed volume method and a stabilized ﬁnite element method for solving conjugate heat transfer, a hot solid is immersed inside a ﬁlled-water tank as shown in (Figure 5.11). The heat source is at a temperature of 700 ∘ C and is made of a nickel-based alloy (inconel718). The water is at a temperature (90 ∘ C) close to the saturation temperature. The time step is equal to 0.0005 s. The vapor interface is initially coincident with the solid boundary. The evolution of the interface during ﬁlm **boiling** is plotted in Figure 5.12. At 𝑡 = 0.2 s, a continuous vapor layer forms between the heated solid and the surrounding liquid. In contrast to the results for small geometry workpieces, where a vapor bubble is periodically detached from the vapor ﬁlm, the results for a heated solid (with width 2 cm, length 2 cm and height 8 cm) shows the interfacial disturbance growing along the upper surface of the solid, as seen at 𝑡 = 0.25 s and 𝑡 = 0.375 s. Then a population of bubbles are released along the upper surface of the solid Figure 5.12(c)-5.12(d). Figure 5.13 shows the evolution of the velocity ﬁeld on a vertical center plane. From this test we can deduce that in the quenching process, the dipped metal provides a natural generator of vapor. This 3D computation has required 10 days on 16 cores. The numerical results are similar to the one performed by Son in [12], where the author simulates the liquid-vapor phase change, and more particularly, the evolution of a vapor ﬁlm on a horizontal cylinder. These numerical results indicate without doubts that the proposed approach is suitable for parallel numerical simulation of industrial quenching process with diﬀerent loads and complex geometries. At a lower solid temperature, wall contact should occur but the study of this eﬀect and the modelling of the **nucleate** **boiling** regimes will be the subject of future work.

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