Modeling of the boiling crisis

Boiling is observed commonly in everyday life. This is why it seems well understood. It is true that boiling has been extensively studied from an empirical point of view for the most common fluids and regimes, for instance for water at atmospheric pressure and moderate heat flux supplied to fluid. However, the basic theory of boiling remains terra incognita in spite of the huge amount of work devoted to it. The main cause of this contradiction originates from the violence of the fluid motion that on the one hand conceals the mechanisms of bubble growth from detailed observation, and on the other hand hugely complicates direct numerical simulations. Most still unanswered questions concern the close vicinity of the heating surface, down to the scale of bubbles growing at the surface of the heater especially during boiling at high heat fluxes common for industrial heat exchangers, e.g. nuclear power plant steam generators.

What is the boiling crisis?

Let us consider the boiling curve (called often Nukiyama curve) presented in the animation below.

The term “pool boiling” means that there is no externally imposed fluid flow, like in a tea pot. It is considered below for simplicity. The curve for the flow boiling, where the boiling fluid flows as a whole, is similar.

We are interested here in the left branch of the boiling curve that can be obtained by making stationary boiling experiments for different values of the imposed heat flux measured in W/m2. For each heat flux the average heater temperature is noted and serves as the abscissa for the corresponding curve point while the flux serves for the ordinate. The rate of the heat transfer from the heater to the liquid can be characterized by the slope of the boiling curve.

When the heat flux is small, only a fluid convection can be observed. At a larger heat flux one can observe the regime of nucleate boiling, that can be commonly observed in a sauce pan. It features separate vapor bubbles that nucleate (i.e. form) and grow at the heater. In this regime the heat transfer rate is very large due to both the phase change (latent heat of evaporation) and the fact that the superheated liquid is carried away from the heating surface by the departing vapor bubbles. Therefore the boiling curve slope is larger than for the convection regime.

The temperature of the heating surface increases with the heat flux. When the latter exceeds a critical value (called Critical Heat Flux, CHF), the vapor bubbles on the heating surface abruptly form a film that thermally insulates the heater from the liquid. In other words, the heater dries out. This is the film boiling regime. It can also be observed in the kitchen by sprinkling water onto a hot frying pan. In spite of the large temperature of the heater (the pan) the water drops survive for a long time precisely due to the thermally insulating vapor film that prevents the liquid from touching the pan. Obviously, the heater-liquid heat transfer is much lower than in the first case. During the transition from nucleate to film boiling, the heat transfer is blocked and the temperature of the heater rapidly grows that can lead to its burnout and thus to an important accident if boiling in an industrial heat exchanger is concerned. This phenomenon is known under the names of “boiling crisis” (BC), “CHF phenomenon”, or “Departure from Nucleate Boiling”. The CHF value is thus very important. It depends on various parameters of the system (pool or flow boiling, degree of underheating of the bulk fluid, system pressure, heater geometry, etc.).

What triggers the boiling crisis?

Correct CHF estimation requires a clear understanding of the physical phenomenon that triggers the boiling crisis. In spite of its importance, the mechanism of the boiling crisis remains poorly studied. Our purpose is to explain why, how, and when the vapor film begins to form. Numerous models were proposed where completely different mechanisms are assumed to be responsible for the different regimes of boiling. The underlying hypotheses for these models are frequently controversial. In addition, many of these hypotheses are hardly justified. This confusion is closely related to the experimental difficulties with the observations of BC. For reasons of industrial importance, the most common boiling experiments are carried out at low (atmospheric) system pressures as compared to the critical pressure of the given fluid. The CHF value is then large, of the order of 1MW/m2. The violence of boiling at large heat fluxes makes observations very difficult. However, several important features of BC that shed some light on the underlying physics have nevertheless been firmly established. The most important among them is its local nature. BC begins in a thin layer of liquid adjacent to the heating surface at a definite spot. This layer is nearly quiescent because the fluid is nearly immobile in the close vicinity of any solid independently of the fluid velocity far from the solid surface. The phenomena at this scale "feel" only the averaged values of macroscopic flow variables and thus do not depend on details of the flow regime which should not thus change the BC mechanism.

On the other hand, the contribution of the microscale hydrodynamic motion (that can change in magnitude with the system pressure) to the BC triggering is still unclear. For instance, "bubble crowding" hypothesis postulates that in the vicinity of the triple contact line the evaporation at some conditions might be faster than the fluid supply. The contact line recedes thus drying the bubble nucleation site. This argument seems to us controversial because of the huge liquid pool that surrounds the bubbles. Once the fluid is lacking near the contact line, the bubble interface changes its curvature thus increasing the pressure drop in the fluid and attracting more liquid towards the contact line. Some other mechanism need to cause the bubble distortion necessary to provide the heater drying. This mechanism should be then unique and independent on the system pressure.

We have made the fundamental hypothesis that the boiling crisis is triggered by the vapor recoil when liquid transforms into vapor. Every fluid molecule evaporated from the liquid interface causes a recoil force analogous to that created by the gas emitted by a rocket engine. It pushes the interface towards the liquid side in the normal direction. This force appears because the fluid necessarily expands while transforming from liquid to gas phase. Obviously, the stronger the evaporation rate, the larger the vapor recoil force.

The inertial confinement fusion presents an example of another manifestation of the vapor recoil. Under the action of heating induced by the multiple laser beams, the shell enveloping the inertial fusion target vaporizes so rapidly that it creates a huge vapor recoil that compresses the target. Its temperature then rises and can attain huge values necessary to initialize the chain fusion nuclear reaction, see also the Laser Megajoule site (in French).

Let us now consider the variation of the evaporation rate along the surface of a bubble growing at the heating surface. Since the fluid is hotter close to the heater than far from it, the evaporation distributed along the bubble surface is strongest in the vicinity of the line of contact of the bubble surface with the heater. The vapor recoil is also strongest at the contact line and therefore tends to pull the contact line outward, thus spreading the dry area or “dry spot” under the bubble as it is illustrated below.

Bubble_rec

Such a localization of the evaporation at the contact line allows to construct a simplified theory by assuming that the evaporation exists at the contact line only. Some results can then be obtained in a simple way. However other important features of the missing in this approach. To capture them, a numerical simulation of bubble growth can be performed. Such a simulation requires solving of extremely delicate thermal and capillary problems. The bubble growth and beginning of its spreading are presented in the animation below.

The calculation has been performed for water at 10 MPa. It can be seen that the dry spot is initially very small and remains so during the initial growth stage. At about 180 ms the dry spot begins to grow suddenly, i.e. the bubble spreads. Such a spreading represents the beginning of formation of the vapor film characteristic for the boiling crisis. This figure also shows formation of a hot spot at the heater surface in the middle of the dry area. This temperature rise illustrates the already discussed blocking of the heat transfer by vapor.

The actual contact angle was imposed to be zero throughout the simulation. However the apparent contact angle grows it time. This effect appears because the bubble curvature is proportional to the vapor recoil force when the latter is large, see the articles dealing with the simplified theory for more details.

Experimental verification

This theoretical approach can be compared to experiments at high pressures close to the critical pressure of the given fluid. The bubble growth is then slow due to the slowness of the thermal diffusion (that becomes infinitely slow in the critical point; this phenomenon is called "critical slowing down"). The slowness of the fluid motion allows the bubble shape to be observed optically in detail. In addition, the CHF value tends to zero at the critical point which means that the boiling crisis can be attained without injecting large heat flux otherwise necessary for the observations. However, near-critical bubble growth experiments have an important drawback. Since the surface tension becomes very low near the critical point, gravity completely flattens the liquid interface. Reduced gravity conditions are thus necessary to preserve the usual convex bubble shape. Some of the results of such an experiment performed on board the Mir space station are presented in the upper row of the figure below.

Mir_Theor_Exp

This experiment was carried out with SF6 fluid near its critical liquid-gas point. The choice of SF6 was made for practical reasons: the critical point of this fluid is at 45.6°C, 38 bar and requires much less severe conditions for the experiment than for example water (374°C, 220 bar). The system was so close to the critical point that the growth of a single vapor bubble could be observed during 45 min thus allowing for a very detailed analysis. The sequential photos of the growing vapor bubble were taken through the transparent bases of the cylindrical cell, the lateral copper walls of which are being heated. Spreading of the dry spot under the bubble similar to that in simulation above can be seen. The bubble shapes all calculated for zero contact angle but for different values of the vapor recoil strength N are presented for comparison in the lower row of the last figure. The vapor and liquid domains are indicated with the letters V and L respectively. The correspondence is good. One notices the growth of the apparent contact angle, a signature of the vapor recoil effect. New experiments are foreseen with the CNES-NASA DECLIC apparatus which will be flying onboard of the International Space Station. See a recent article in English or in French on DECLIC at the CNES web site.

Another means to reach the reduced gravity is the compensation of the gravity by the magnetic forces. It is possible to obtain it not only for the case of magnetic but also for usual fluids. We use the magnetic levitation to study the boiling crisis in cryogenic fluids like oxygen and hydrogen. See this CEA/SBT page in English and a more detailed page in French on the magnetic levitation. See also our review article. Some older documents on magnetic levitation can be found here.

Recent magnetic levitation experiment confirmed the vapor recoil theory. The predicted near critical behavior of the CHF was obtained experimentally.

Generally speaking, the comparison between the results presented above shows the complementarity of theory (basic assumptions), experiment (test of the validity of a model) and simulation (access to parameters not attainable by experiments).

References

More papers can be found in the section of the publication list devoted to the boiling crisis.

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Last change 23/11/2010