# Pool Boiling – Boiling Curve

## Pool Boiling – Boiling Curve

As was written, the most common configuration, known as pool boiling is when a pool of liquid is heated from below through a horizontal surface. In pool boiling the liquid is quiescent and its motion near the surface is primarily due to natural convection and to mixing induced by bubble growth and detachment.

The pioneering work on boiling was done in 1934 by S. Nukiyama, who used electrically heated nichrome and platinum wires immersed in liquids in his experiments. Nukiyama was the first to identify different regimes of pool boiling using his apparatus. He noticed that boiling takes different forms, depending on the value of the wall superheat temperature ΔTsat (known also as the excess temperature)which is defined as the difference between the wall temperature, Twall and the saturation temperature, Tsat.

Four different boiling regimes  of pool boiling (based on the excess temperature) are observed:

• Natural Convection Boiling                            ΔTsat < 5°C
• Nucleate Boiling                                   5°C < ΔTsat < 30°C
• Transition Boiling                                 30°C < ΔTsat < 200°C
• Film Boiling                                        200°C < ΔTsat

These regimes are illustrated on the boiling curve in the figure, which is a plot of heat flux versus the excess temperature. Although the boiling curve given in this figure is for water, the general shape of the boiling curve remains the same for different coolants. Note that, the specific shape of the curve depends also on the system parameters such as the pressure and coolant flow rate, but it is practically independent of the geometry of the heating surface.

Boiling and Condesation

In preceding chapters, we have discussed convective heat transfer with very important assumption. We have assumed a single-phase convective heat transfer without any phase change. In this chapter we focus on convective heat transfer associated with the change in phase of a fluid. In particular, we consider processes that can occur at a solid–liquid or solid–vapor interface, namely, boiling (liquid-to-vapor phase change) and condensation (vapor-to-liquid phase change).

For these cases latent heat effects associated with the phase change are significant. Latent heat, known also as the enthalpy of vaporization, is the amount of heat added to or removed from a substance to produce a change in phase. This energy breaks down the intermolecular attractive forces, and also must provide the energy necessary to expand the gas (the pΔV work). When latent heat is added, no temperature change occurs.

The enthalpy of vaporization is a function of the pressure at which that transformation takes place.

Latent heat of vaporization – water at 0.1 MPa (atmospheric pressure)

hlg = 2257 kJ/kg

Latent heat of vaporization – water at 3 MPa

hlg = 1795 kJ/kg

Latent heat of vaporization – water at 16 MPa (pressure inside a pressurizer)

hlg = 931 kJ/kg

The heat of vaporization diminishes with increasing pressure, while the boiling point increases. It vanishes completely at a certain point called the critical point. Above the critical point, the liquid and vapor phases are indistinguishable, and the substance is called a supercritical fluid.

The change from the liquid to the vapor state due to boiling is sustained by heat transfer from the solid surface; conversely, condensation of a vapor to the liquid state results in heat transfer to the solid surface. Boiling and condensation differ from other forms of convection in that they depend on the latent heat of vaporization, which is very high for common pressures, therefore large amounts of heat can be transferred during boiling and condensation essentially at constant temperature. Heat transfer coefficients, h, associated with boiling and condensation are typically much higher than those encountered in other forms of convection processes that involve a single phase.

This is due to the fact, even in turbulent flow, there is a stagnant fluid film layer (laminar sublayer), that isolates the surface of the heat exchanger. This stagnant fluid film layer plays crucial role for the convective heat transfer coefficient. It is observed, that the fluid comes to a complete stop at the surface and assumes a zero velocity relative to the surface. This phenomenon is known as the no-slip condition and therefore, at the surface, energy flow occurs purely by conduction. But in the next layers both conduction and diffusion-mass movement in the molecular level or macroscopic level occurs. Due to the mass movement the rate of energy transfer is higher. As was written, nucleate boiling at the surface effectively disrupts this stagnant layer and therefore nucleate boiling significantly increases the ability of a surface to transfer thermal energy to bulk fluid.

## Nucleate Boiling

The most common type of local boiling encountered in nuclear facilities is nucleate boiling. But in case of nuclear reactors, nucleate boiling occurs at significant flow rates through the reactor. In nucleate boiling, steam bubbles form at the heat transfer surface and then break away and are carried into the main stream of the fluid. Such movement enhances heat transfer because the heat generated at the surface is carried directly into the fluid stream. Once in the main fluid stream, the bubbles collapse because the bulk temperature of the fluid is not as high as the heat transfer surface temperature where the bubbles were created. As was written, nucleate boiling at the surface effectively disrupts this stagnant layer and therefore nucleate boiling significantly improves the ability of a surface to transfer thermal energy to bulk fluid. This heat transfer process is sometimes desirable because the energy created at the heat transfer surface is quickly and efficiently “carried” away.

Close to the wall the situation is complex for several mechanisms increase the heat flux above that for pure conduction through the liquid.

1. Note that, even in turbulent flow, there is a stagnant fluid film layer (laminar sublayer), that isolates the surface of the heat exchanger. The upward flux (due to buoyant forces) of vapor away from the wall must be balanced by an equal mass flux of liquid and this brings cooler liquid into closer proximity to the wall.
2. The formation and movement of the bubbles turbulises the liquid near the wall and thus increases heat transfer from the wall to the liquid.
3. Boiling differ from other forms of convection in that it depends on the latent heat of vaporization, which is very high for common pressures, therefore large amounts of heat can be transferred during boiling essentially at constant temperature.

The nucleate boiling heat flux cannot be increased indefinitely. At some value, we call it the “critical heat flux” (CHF), the steam produced can form an insulating layer over the surface, which in turn deteriorates the heat transfer coefficient. This is because a large fraction of the surface is covered by a vapor film, which acts as an thermal insulation due to the low thermal conductivity of the vapor relative to that of the liquid. Immediately after the critical heat flux has been reached, boiling become unstable and transition boiling occurs. The transition from nucleate boiling to film boiling is known as the “boiling crisis”. Since beyond the CHF point the heat transfer coefficient decreases, the transition to film boiling is usually inevitable.

Nucleate Boiling Correlations - Pool Boiling
Boiling regimes discussed above differ considerably in their character. There are also different correlations that describe the heat transfer. In this section we review some of the more widely used correlations for nucleate and film boiling.

Nucleate Pool Boiling

Rohsenow correlation

The most widely used correlation for the rate of heat transfer in the nucleate pool boiling was proposed in 1952 by Rohsenow:

Rohsenow correlation

where

• q – nucleate pool boiling heat flux [W/m2]
• c1 — specific heat of liquid J/kg K
• ΔT — excess temperature °C or K
• hfg  – enthalpy of vaporization, J/kg
• Pr — Prandtl number of liquid
• n — experimental constant equal to 1 for water and 1.7 for other fluids
• Csf — surface fluid factor, for example, water and nickel have a Csf of 0.006
• μ1 — dynamic viscosity of the liquid kg/m.s
• g – gravitational acceleration m/s2
• g0 — force conversion factor kgm/Ns2
• ρ1 — density of the liquid kg/m3
• ρv — density of vapour kg/m3
• σ — surface tension-liquid-vapour interface N/m

As can be seen, ΔT ∝ (q). This very important proportionality shows increasing ability of interface to transfer heat.

## Boiling Crisis – Critical Heat Flux

As was written, in nuclear reactors, limitations of the local heat flux is of the highest importance for reactor safety. For pressurized water reactors and also for boiling water reactors, there are thermal-hydraulic phenomena, which cause a sudden decrease in the efficiency of heat transfer (more precisely in the heat transfer coefficient). These phenomena occur at certain value of heat flux, known as the “critical heat flux”. The phenomena, that cause the deterioration of heat transfer are different for PWRs and for BWRs.

In both types of reactors, the problem is more or less associated with departure from nucleate boiling. The nucleate boiling heat flux cannot be increased indefinitely. At some value, we call it the “critical heat flux” (CHF), the steam produced can form an insulating layer over the surface, which in turn deteriorates the heat transfer coefficient. Immediately after the critical heat flux has been reached, boiling become unstable and film boiling occurs. The transition from nucleate boiling to film boiling is known as the “boiling crisis”. As was written, the phenomena, that cause the deterioration of heat transfer are different for PWRs and for BWRs.

Critical Heat Flux - Pool Boiling
The nucleate boiling heat flux cannot be increased indefinitely. At some value, we call it the “critical heat flux” (CHF), the steam produced can form an insulating layer over the surface, which in turn deteriorates the heat transfer coefficient. Immediately after the critical heat flux has been reached, boiling become unstable and film boiling occurs. The transition from nucleate boiling to film boiling is known as the “boiling crisis”.

The critical heat flux for pool boiling was determined theoretically by S. S. Kutateladze in Russia in 1948 and N. Zuber in the United States in 1958 using different approaches, and is expressed as:

where

• qmax – critical heat flux [W/m2]
• Ccr — geometry dependent constant
• hfg  – enthalpy of vaporization, J/kg
• g – gravitational acceleration m/s2
• ρl — density of the liquid kg/m3
• ρv — density of vapour kg/m3
• σ — surface tension-liquid-vapour interface N/m

For large horizontal cylinders, spheres and large finite heated surfaces, the value of this constant is Ccr = 0.131. For large horizontal plates, a value is Ccr = 0.149.

It is important to note that the critical heat flux depends strongly on pressure, mainly through the pressure dependence of vapor density, surface tension and the heat of vaporization. Note that ρv increases with increasing pressure but σ and hfg decrease with increasing pressure. Therefore the resulting change in qmax depends on which effect dominates.

At low pressures (including atmospheric pressure), the pressure dependence is mainly through the change in vapor density leading to an increase in the critical heat flux with pressure. However, as pressures approach the critical pressure, both the surface tension and the heat of vaporization converge to zero, making them the dominant sources of pressure dependency. Therefore at high pressures (as in PWRs – 16 MPa), the critical heat flux decreases with pressure.

References:
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