# NUCLEATE BOILING REGIME

As demonstrated in the literature, the nucleate boiling is said to begin for heat fluxes higher than 5000 W/m2. This is manifested by a sudden decrease in temperature after having remained constant, for a certain range of heat flux, as shown in the pool boiling curve for propane (Figure 3 presented in 'BIBLIOGRAPHIC RESEARCH - Boiling Regime').

Diphasic simulations were launched using Neptune_CFD with the same mesh as the monophasic simulation at first. As the nucleate boiling model was activated, the values of the wall temperature and different heat fluxes were provided by Neptune CFD by doing small modifications in the FORTRAN files defined in ‘SRC’ directory.

It should be remarked that there are some compromises to be considered, when defining the quality of mesh, between the average wall temperature, average wall heat fluxes, size of the wall adjacent cells and time of simulation. Besides, the ability of Neptune CFD to provide reliable results for boiling regime with high gas volume fraction, due to some difficulties in convergence of the solution, will be discussed in the 'Discussion' section.

# Neptune CFD : Diphasic Simulation

For diphasic simulation, minor modifications are required in edamox compared to monophasic simulation. Simulations were launched by imposing a heat flux ranges between 2000 - 30000 W/m2 as demanded by Technip.

The special module - ‘water and steam’ was selected for liquid - gas phase simulation.

Figure 17: Neptune Special Modules panel for nucleate boiling

In the ‘fluid & flow prop’ windows, the setting remains very similar to the single phase simulation. Number of phases should be set automatically to 2, with phase 1 considered as liquid and phase 2 as gas phase by default. No turbulence models were selected as turbulence was not expected. It is remarkable that there is a new windows ‘INTER-PHASE FORCES’ to define the different inter-phase forces (Figure 18). The bubbly flow is likely to be produced for the heat fluxes range, therefore the following laws were considered for the simulations:

Figure 18: Neptune Fluid&Flow props panel, definition of interphase forces for nucleate boiling

In the ‘Generalities’ panel, the ‘CATHARE functions’ option is selected by default. CATHARE functions are predefined to model H20 and Freon 12 properties. Hence, the option has to be deselected and propane properties such as superficial tension and latent heat have to be defined in USPHY.F.

Besides, the nucleate boiling option was chosen as wall transfer model. The wall temperature and different heat fluxes were calculated by PREVAP.F and ALGO_EV.F. In the ‘Boiling Parameters’ corner, there are two models, 3-flux model (known as GRE model) and 4-flux model (developed by EDF), proposed for fluid/wall heat transfer model. The 4-flux model is developed for higher heat flux, close to critical heat flux by taking into account the contribution by convection of the gas phase to the total heat flux.The detail of these two models can be found in ‘Bibliographic research’ section. The ‘Solid Wall properties’ was deactivated because there was no wall thickness to take into consideration.

Figure 19:Neptune Generalities panel for nucleate boiling

Two scalars were defined in ‘Scalars’ module for liquid phase and gas phase and the wall boundary condition was modified accordingly.

In order to access the wall temperature and different heat fluxes for data analysis, User arrays can be defined in ‘Input-Output Control – USER’ panel and modifications have to be made in PREVAP.F to register the interesting parameters in all the cells. 6 users were registered to access :

• TW = Wall temperature
• PHI = Total heat flux,
• PHIC = Monophasic convective heat flux in the liquid phase
• PHIC2 = Convective heat transfer between the wall and the vapour phase,
• PHIQ = Transient conductive heat ﬂux, called quenching heat flux,
• PHIE = Vaporization heat flux.

# Discussion

The simulations were launched at the first place with the 3 flux model for several values of heat flux desity [Q=2000, 3500, 5000, 10000, 20000 30000] W/m2. The simulations had been ran to represent the boiling process for 5s. Nonetheless, there were errors in the simulations which were found to be caused by high gas volume fraction due to an important heat flux density, imposed as wall boundary condition in static propane. This is because the liquid phase cannot dissipate the heat fast enough, and some small peaks of wall temperature appeared when the cells around the wall are filled with vapour.

A progressive heat flux density was, then, implemented, using the USCLIM.F, so as to create movement in the flow with natural convection (renew the liquid around the tube) that helps to evacuate gas phase. This could prevent the phenomena where the cells around the tube become saturated with gas phase. However, this was found to work for a limited heat flux density up to 6000 W/m².

Animation 1: Evolution of gas volume fraction for a heat flux Q=3000W/m2

Animation 2: Evolution of gas volume fraction for a heat flux Q=5000W/m2

When 3-flux model is used, it is considered that the liquid on the wall, to be used for evaporation, is sufficient to remove the heat from the tube. Superheating of vapour phase is not modelled, which may be the responsible for the errors in the cases with higher heat flux density (high gas void fraction). EDF is developing 4 flux model that models the heat flux absorbed by the steam phase (for more information, please refer to section ' NEPTUNE_CFD - Nucleate Boiling'). Hence, 4 flux model is designed to be more 'robust' than 3 flux as demonstrated in the study performed by Pérez Mañes et al, 2014 [12], in which 4 flux model was used for a heat flux close to critical heat flux with a gas volume fraction that can reach up to 80 % in the near wall region. Below are displayed some simulations launched with a heat flux density of [5000 6000 10000] W/m².

Animation 3: Evolution of gas volume fraction for a heat flux Q=5000W/m2 with 4 flux model

Animation 4: Evolution of gas volume fraction for a heat flux Q=6000W/m2 with 4 flux model

Animation 5: Evolution of gas volume fraction for a heat flux Q=10000W/m2 with 4 flux model

By comparing the simulations for 5000 W/m², the two models are in good agreement for the instance when the boiling started to take place and also gas volume fraction was produced at the bottom of cylinder, then the bubble plume started to glide upward and activated the other nucleate cavity sites. However, the magnitude of gas volume fraction estimated by 4 flux was higher than 3 flux model. On the other hand, by using 4 flux model, it does not seem to resolve the numerical error that was provoked in the previous discussion. Moreover, it is observed, with listing file, that the error occurred around 6000 W/m² which was the same heat flux density for 3 flux model.

Furthermore, the results obtained, with 3 flux model and 4 flux model, were not very satisfying as the average Tw obtained from NEPTUNE_CFD were overestimated, compare to the experimental result proposed in the literature, due to the presence of stagnation points on the tube. The $T_w$ at the stagnation points could be several hundred Kelvin [K] above the saturation temperature and as a consequence, the average $T_w$ obtained by the integration around the tube is not comparable with the experimental results.

Figure 20: Wall temperature for a heat flux Q=20000W/m2

In addition, it was observed that the flow could be turbulent as shown in the velocity map below, Figure 21. However, backflow was observed throughout the simulation (when heated with 2000W/m²) which might be the major cause of turbulent flow (backflow velocity magnitude could reach approximately 12 m/s) and also it might be the agent that prevented the gas to quit the studied domain, thus paralysed the cooling mechanisms. This backflow was caused by the pressure boundary condition at outlet, as the pressure gradient is fixed at zero. Hence, a depression was produced when the gas volume fraction increased in the studied domain.

Figure 21: Velocity map for a heat flux Q=2000W/m2 .Evidence of backflow