Thermal Engineering

Boiling in Nuclear Reactors

Boiling in BWRs

In BWRs boiling of coolant occurs at normal operation and it is very desired phenomenon. Typical flow qualities in BWR cores are on the order of 10 to 20 %. A boiling water reactor is cooled and moderated by water like a PWR, but at a lower pressure (7MPa), which allows the water to boil inside the pressure vessel producing the steam that runs the turbines. Evaporation therefore occurs directly in fuel channels. Therefore BWRs are the best example for this area, because evaporation of coolant occurs at normal operation and it is very desired phenomenon.

In BWRs there is a phenomenon, that is of the highest importance in reactor safety. This phenomenon is known as the “dryout” and it is directly associated with changes in flow pattern during evaporation in the high-quality region. At normal the fuel surface is effectively cooled by boiling coolant. However when the heat flux exceeds a critical value (CHF – critical heat flux) the flow pattern may reach the dryout conditions (thin film of liquid disappears). The heat transfer from the fuel surface into the coolant is deteriorated, with the result of a drastically increased fuel surface temperature.

Boiling in PWRs

Although the earliest core designs assumed that surface boiling could not be allowed in PWRs, this assumption was soon rejected and two-phase heat transfer is now one of normal operation heat transfer mechanisms also in PWRs. For PWRs at normal operation, there is a compressed liquid water inside the reactor core, loops and steam generators.  The pressure is maintained at approximately 16MPa. At this pressure water boils at approximately 350°C(662°F). As was calculated in example, the surface temperature T_Zr,1 = 325°C ensures, that even subcooled boiling does not occur. Note that, subcooled boiling requires T_Zr,1 = T_sat. Since the inlet temperatures of the water are usually about 290°C (554°F), it is obvious this example corresponds to the lower part of the core. At higher elevations of the core the bulk temperature may reach up to 330°C. The temperature difference of 29°C causes the subcooled boiling may occur (330°C + 29°C > 350°C). On the other hand, nucleate boiling at the surface effectively disrupts the stagnant layer and therefore nucleate boiling significantly increases the ability of a surface to transfer thermal energy to bulk fluid. As a result, the convective heat transfer coefficient significantly increases and therefore at higher elevations, the temperature difference (T_Zr,1 – T_bulk) significantly decreases.

In case of PWRs, the critical safety issue is named DNB (departure from nucleate boiling), which causes the formation of a local vapor layer, causing a dramatic reduction in heat transfer capability. This phenomenon occurs in the subcooled or low-quality region. The behaviour of the boiling crisis depends on many flow conditions (pressure, temperature, flow rate), but the boiling crisis occurs at a relatively high heat fluxes and appears to be associated with the cloud of bubbles, adjacent to the surface. These bubbles or film of vapor reduces the amount of incoming water. Since this phenomenon deteriorates the heat transfer coefficient and the heat flux remains, heat then accumulates in the fuel rod causing dramatic rise of cladding and fuel temperature.

Saturation in Pressurizer

A pressurizer is a component of a pressurized water reactor. Pressure in the primary circuit of PWRs is maintained by a pressurizer, a separate vessel that is connected to the primary circuit (hot leg) and partially filled with water which is heated to the saturation temperature (boiling point) for the desired pressure by submerged electrical heaters. Temperature in the pressurizer can be maintained at 350 °C (662 °F), which gives a subcooling margin (the difference between the pressurizer temperature and the highest temperature in the reactor core) of 30 °C. Subcooling margin is very important safety parameter of PWRs, since the boiling in the reactor core must be excluded. The basic design of the pressurized water reactor includes such requirement that the coolant (water) in the reactor coolant system must not boil. To achieve this, the coolant in the reactor coolant system is maintained at a pressure sufficiently high that boiling does not occur at the coolant temperatures experienced while the plant is operating or in an analyzed transient.

Functions

Pressure in the pressurizer is controlled by varying the temperature of the coolant in the pressurizer. For these purposes two systems are installed. Water spray system and electrical heaters system. Volume of the pressurizer (tens of cubic meters) is filled with water on saturation parameters and steam. The water spray system (relatively cool water – from cold leg) can decrease the pressure in the vessel by condensing the steam on water droplets sprayed in the vessel. On the other hand the submerged electrical heaters are designed to increase the pressure by evaporation the water in the vessel. Water pressure in a closed system tracks water temperature directly; as the temperature goes up, pressure goes up.

Boiling in Steam Generator

Steam generators are heat exchangers used to convert feedwater into steam from heat produced in a nuclear reactor core. The steam produced drives the turbine. They are used in the most nuclear power plants, but there are many types according to the reactor type.

The hot primary coolant (water 330°C; 626°F; 16MPa) is pumped into the steam generator through primary inlet. High pressure of primary coolant is used to keep the water in the liquid state. Boiling of the primary coolant shall not occur. The liquid water flows through hundreds or thousands of tubes (usually 1.9 cm in diameter) inside the steam generator. The feedwater (secondary circuit) is heated from ~260°C 500°F to the boiling point of that fluid (280°C; 536°F; 6,5MPa). Heat is transferred through the walls of these tubes to the lower pressure secondary coolant located on the secondary side of the exchanger where the coolant evaporates to pressurized steam (saturated steam 280°C; 536°F; 6,5 MPa). The pressurized steam leaves the steam generator through a steam outlet and continues to the steam turbine. The transfer of heat is accomplished without mixing the two fluids to prevent the secondary coolant from becoming radioactive. The primary coolant leaves (water 295°C; 563°F; 16MPa) the steam generator through primary outlet and continues through a cold leg to a reactor coolant pump and then into the reactor.

See also:

Boiling and Condensation

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 ΔT_sat (known also as the excess temperature), which is defined as the difference between the wall temperature, T_wall and the saturation temperature, T_sat.

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

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

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.

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.

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.

See also:

Boiling and Condensation

Natural Convection Boiling – Onset of Nucleate Boiling

Categorization by the wall superheat temperature, ΔT_sat:

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 ΔT_sat (known also as the excess temperature), which is defined as the difference between the wall temperature, T_wall and the saturation temperature, T_sat.

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

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

Natural Convection Boiling

In thermodynamics, the requirement for boiling of pure substances to occur is that T_wall = T_sat. But in real experiments, boiling does not occur until the liquid is heated a few degrees above the saturation temperature. The surface temperature must be somewhat above the saturation temperature in order to sustain vapor formation. Natural convection boiling occurs when ΔTsat < 5°C. In this boiling mode, vapour will be observed over the water surface, but usually no bubbles will be observed. As the superheat temperature is increased, bubble inception will eventually occur, but below point A, fluid motion is determined principally by natural convection currents. The point A is usually referred to as the onset of nucleate boiling – ONB.

Boiling

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)

h_lg = 2257 kJ/kg

Latent heat of vaporization – water at 3 MPa

h_lg = 1795 kJ/kg

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

h_lg = 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.

See also:

Boiling and Condensation

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.

In following section, we will distinguish between:

• nucleate pool boiling
• nucleate flow boiling

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 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
• h_fg  – enthalpy of vaporization, J/kg
• Pr — Prandtl number of liquid
• n — experimental constant equal to 1 for water and 1.7 for other fluids
• C_sf — surface fluid factor, for example, water and nickel have a C_sf 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
• ρ_v — density of vapour kg/m³
• σ — surface tension-liquid-vapour interface N/m

As can be seen, ΔT ∝ (q)^⅓. This very important proportionality shows increasing ability of interface to transfer heat.

Nucleate Boiling – Flow Boiling

In flow boiling (or forced convection boiling), fluid flow is forced over a surface by external means such as a pump, as well as by buoyancy effects. Therefore, flow boiling is always accompanied by other convection effects. Conditions depend strongly on geometry, which may involve external flow over heated plates and cylinders or internal (duct) flow. In nuclear reactors, most of boiling regimes are just forced convection boiling. The flow boiling is also classified as either external and internal flow boiling depending on whether the fluid is forced to flow over a heated surface or inside a heated channel.

Internal flow boiling is much more complicated in nature than external flow boiling because there is no free surface for the vapor to escape, and thus both the liquid and the vapor are forced to flow together. The two-phase flow in a tube exhibits different flow boiling regimes, depending on the relative amounts of the liquid and the vapor phases. Therefore internal forced convection boiling is commonly referred to as two-phase flow.

Nucleate Boiling Correlations – Flow Boiling

McAdams Correlation

In fully developed nucleate boiling with saturated coolant, the wall temperature is determined by local heat flux and pressure and is only slightly dependent on the Reynolds number. For subcooled water at absolute pressures between 0.1 – 0.6 MPa, McAdams correlation gives:

Thom Correlation

The Thom correlation is for the flow boiling (subcooled or saturated at pressures up to about 20 MPa) under conditions where the nucleate boiling contribution predominates over forced convection. This correlation is useful for rough estimation of expected temperature difference given the heat flux:

Chen’s Correlation

In 1963, Chen proposed the first flow boiling correlation for evaporation in vertical tubes to attain widespread use. Chen’s correlation includes both the heat transfer coefficients due to nucleate boiling as well as forced convective mechanisms. It must be noted, at higher vapor fractions, the heat transfer coefficient varies strongly with flow rate. The flow velocity in a core can be very high causing very high turbulences. This heat transfer mechanism has been referred to as “forced convection evaporation”. No adequate criteria has been established to determine the transition from nucleate boiling to forced convection vaporization. However, a single correlation that is valid for both nucleate boiling and forced convection vaporization has been developed by Chen for saturated boiling conditions and extended to include subcooled boiling by others. Chen proposed a correlation where the heat transfer coefficient is the sum of a forced convection component and a nucleate boiling component. It must be noted, the nucleate pool boiling correlation of Forster and Zuber (1955) is used to calculate the nucleate boiling heat transfer coefficient, h_FZ and the turbulent flow correlation of Dittus-Boelter (1930) is used to calculate the liquid-phase convective heat transfer coefficient, h_l.

The nucleate boiling suppression factor, S, is the ratio of the effective superheat to wall superheat. It accounts for decreased boiling heat transfer because the effective superheat across the boundary layer is less than the superheat based on wall temperature. The two-phase multiplier, F, is a function of the Martinelli parameter χ_tt.

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.

Departure From Nucleate Boiling – DNB

In case of PWRs, the critical safety issue is named DNB (departure from nucleate boiling), which causes the formation of a local vapor layer, causing a dramatic reduction in heat transfer capability. This phenomenon occurs in the subcooled or low-quality region. The behaviour of the boiling crisis depends on many flow conditions (pressure, temperature, flow rate), but the boiling crisis occurs at a relatively high heat fluxes and appears to be associated with the cloud of bubbles, adjacent to the surface. These bubbles or film of vapor reduces the amount of incoming water. Since this phenomenon deteriorates the heat transfer coefficient and the heat flux remains, heat then accumulates in the fuel rod causing dramatic rise of cladding and fuel temperature. Simply, a very high temperature difference is required to transfer the critical heat flux being produced from the surface of the fuel rod to the reactor coolant (through vapor layer).

In case of PWRs, the critical flow is inverted annular flow, while in BWRs, the critical flow is usually annular flow. The difference in flow regime between post-dryout flow and post-DNB flow is depicted in the figure. In PWRs at normal operation the flow is considered to be single-phase. But a great deal of study has been performed on the nature of two-phase flow in case of transients and accidents (such as the loss-of-coolant accident – LOCA or trip of RCPs), which are of importance in reactor safety and in must be proved and declared in the Safety Analysis Report (SAR).

In pressurized water reactors, one of key safety requirements is that a departure from nucleate boiling (DNB) will not occur during steady state operation, normal operational transients, and anticipated operational occurrences (AOOs).  Fuel cladding integrity will be maintained if the minimum DNBR remains above the 95/95 DNBR limit for PWRs ( a 95% probability at a 95% confidence level). DNB criterion is one of acceptance criteria in safety analyses as well as it constitutes one of safety limits in technical specifications.

Dryout – BWRs

In BWRs, similar phenomenon is known as “dryout” and it is directly associated with changes in flow pattern during evaporation in the high-quality region. At given combinations of flow rate through a channel, pressure, flow quality, and linear heat rate, the wall liquid film may exhaust and the wall may be dried out. At normal, the fuel surface is effectively cooled by boiling coolant. However when the heat flux exceeds a critical value (CHF – critical heat flux) the flow pattern may reach the dryout conditions (thin film of liquid disappears). The heat transfer from the fuel surface into the coolant is deteriorated, with the result of a drastically increased fuel surface temperature. In the high-quality region, the crisis occurs at a lower heat flux. Since the flow velocity in the vapor core is high, post-CHF heat transfer is much better than for low-quality critical flux (i.e. for PWRs temperature rises are higher and more rapid).

See also:

Boiling and Condensation

Transition Boiling – Partial Film Boiling

Categorization by the wall superheat temperature, ΔT_sat:

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 ΔT_sat (known also as the excess temperature), which is defined as the difference between the wall temperature, T_wall and the saturation temperature, T_sat.

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

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

Transition 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. 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.

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.

Minimum Heat Flux – Leidenfrost Point

The Leidenfrost point, which corresponds to the minimal heat flux, is of practical interest since it represents the lower limit for the heat flux in the film boiling regime. If the heat flux drops below this minimum, the film will collapse, causing the surface to cool and nucleate boiling to be reestablished. Therefore, at this point, return to nucleate boiling (RNB) occurs. The terms quenching, minimum heat flux, return to nucleate boiling, departure from film boiling, film boiling collapse, and Leidenfrost point have been used interchangeably to refer to various forms of rewetting, but they are not exactly synonymous.

Using the stability theory, Zuber derived the following expression for the minimum heat flux (and corresponding Leidenfrost point) for a large horizontal plate:

where

• q_min – minimal heat flux [W/m²]
• h_fg  – enthalpy of vaporization, J/kg
• g – gravitational acceleration m/s²
• ρ_l — density of the liquid kg/m³
• ρ_v — density of vapour kg/m³
• σ — surface tension-liquid-vapour interface N/m

Leidenfrost Effect

The Leidenfrost effect is a physical phenomenon in which a liquid, in near contact with a mass significantly hotter (e.g. a water drop in a hot pan) than the liquid’s boiling point, produces an insulating vapor layer keeping that liquid from boiling rapidly. The fact that a water drop is long lived when deposited on metal that is much hotter than the boiling temperature of water was first reported by Hermann Boerhaave in 1732. It was not investigated extensively until 1756 when a German doctor Johann Gottlob Leidenfrost published ‘‘A Tract About Some Qualities of Common Water.’’

This effect is can be commonly demonstrated during cooking when one sprinkles drops of water in a pan to gauge its temperature: if the pan’s temperature is at or above the Leidenfrost point, the water skitters across the pan and takes longer to evaporate than in a pan below the temperature of the Leidenfrost point (but still above boiling temperature). The Leidenfrost point, which corresponds to the minimal heat flux, is of practical interest since it represents the lower limit for the heat flux in the film boiling regime. If the heat flux drops below this minimum, the film will collapse, causing the surface to cool and nucleate boiling to be reestablished. The Leidenfrost effect is also responsible for the ability of liquid nitrogen to skitter across floors.

See also:

Boiling and Condensation

Leidenfrost Effect

The Leidenfrost effect is a physical phenomenon in which a liquid, in near contact with a mass significantly hotter (e.g. a water drop in a hot pan) than the liquid’s boiling point, produces an insulating vapor layer keeping that liquid from boiling rapidly. The fact that a water drop is long lived when deposited on metal that is much hotter than the boiling temperature of water was first reported by Hermann Boerhaave in 1732. It was not investigated extensively until 1756 when a German doctor Johann Gottlob Leidenfrost published ‘‘A Tract About Some Qualities of Common Water.’’

This effect is can be commonly demonstrated during cooking when one sprinkles drops of water in a pan to gauge its temperature: if the pan’s temperature is at or above the Leidenfrost point, the water skitters across the pan and takes longer to evaporate than in a pan below the temperature of the Leidenfrost point (but still above boiling temperature). The Leidenfrost point, which corresponds to the minimal heat flux, is of practical interest since it represents the lower limit for the heat flux in the film boiling regime. If the heat flux drops below this minimum, the film will collapse, causing the surface to cool and nucleate boiling to be reestablished. The Leidenfrost effect is also responsible for the ability of liquid nitrogen to skitter across floors.

Minimum Heat Flux – Leidenfrost Point

The Leidenfrost point, which corresponds to the minimal heat flux, is of practical interest since it represents the lower limit for the heat flux in the film boiling regime. If the heat flux drops below this minimum, the film will collapse, causing the surface to cool and nucleate boiling to be reestablished. Therefore, at this point, return to nucleate boiling (RNB) occurs. The terms quenching, minimum heat flux, return to nucleate boiling, departure from film boiling, film boiling collapse, and Leidenfrost point have been used interchangeably to refer to various forms of rewetting, but they are not exactly synonymous.

Using the stability theory, Zuber derived the following expression for the minimum heat flux (and corresponding Leidenfrost point) for a large horizontal plate:

where

• q_min – minimal heat flux [W/m²]
• h_fg  – enthalpy of vaporization, J/kg
• g – gravitational acceleration m/s²
• ρ_l — density of the liquid kg/m³
• ρ_v — density of vapour kg/m³
• σ — surface tension-liquid-vapour interface N/m

See also:

Boiling and Condensation

Minimum Heat Flux – Quenching – Departure from Film Boiling

The Leidenfrost point, which corresponds to the minimal heat flux, is of practical interest since it represents the lower limit for the heat flux in the film boiling regime. If the heat flux drops below this minimum, the film will collapse, causing the surface to cool and nucleate boiling to be reestablished. Therefore, at this point, return to nucleate boiling (RNB) occurs. The terms quenching, minimum heat flux, return to nucleate boiling, departure from film boiling, film boiling collapse, and Leidenfrost point have been used interchangeably to refer to various forms of rewetting, but they are not exactly synonymous.

Using the stability theory, Zuber derived the following expression for the minimum heat flux (and corresponding Leidenfrost point) for a large horizontal plate:

where

• q_min – minimal heat flux [W/m²]
• h_fg  – enthalpy of vaporization, J/kg
• g – gravitational acceleration m/s²
• ρ_l — density of the liquid kg/m³
• ρ_v — density of vapour kg/m³
• σ — surface tension-liquid-vapour interface N/m

Leidenfrost Effect

The Leidenfrost effect is a physical phenomenon in which a liquid, in near contact with a mass significantly hotter (e.g. a water drop in a hot pan) than the liquid’s boiling point, produces an insulating vapor layer keeping that liquid from boiling rapidly. The fact that a water drop is long lived when deposited on metal that is much hotter than the boiling temperature of water was first reported by Hermann Boerhaave in 1732. It was not investigated extensively until 1756 when a German doctor Johann Gottlob Leidenfrost published ‘‘A Tract About Some Qualities of Common Water.’’

This effect is can be commonly demonstrated during cooking when one sprinkles drops of water in a pan to gauge its temperature: if the pan’s temperature is at or above the Leidenfrost point, the water skitters across the pan and takes longer to evaporate than in a pan below the temperature of the Leidenfrost point (but still above boiling temperature). The Leidenfrost point, which corresponds to the minimal heat flux, is of practical interest since it represents the lower limit for the heat flux in the film boiling regime. If the heat flux drops below this minimum, the film will collapse, causing the surface to cool and nucleate boiling to be reestablished. The Leidenfrost effect is also responsible for the ability of liquid nitrogen to skitter across floors.

See also:

Boiling and Condensation

Film 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. 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.

A further increase in the heat flux causes a film of vapour to fully cover the surface. This significantly reduces the convection coefficient, since the vapor layer has significantly lower heat transfer ability. As a result the excess temperature shoots up to a very high value. Beyond the Leidenfrost point, a continuous vapor film blankets the surface and there is no contact between the liquid phase and the surface. In this situation the heat transfer is both by radiation and by conduction to the vapour. If the material is not strong enough for withstanding this temperature, the equipment will fail by damage to the material. This phenomenon is also known as burn out. In pressurized water reactors, one of key safety requirements (maybe the most important) is that a departure from nucleate boiling (DNB)  will not occur during steady state operation, normal operational transients, and anticipated operational occurrences (AOOs).  Fuel cladding integrity will be maintained if the minimum DNBR remains above the 95/95 DNBR limit for PWRs ( a 95% probability at a 95% confidence level). Since this phenomenon deteriorates the heat transfer coefficient and the heat flux remains, heat then accumulates in the fuel rod causing dramatic rise of cladding and fuel temperature. Simply, a very high temperature difference is required to transfer the critical heat flux being produced from the surface of the fuel rod to the reactor coolant (through vapor layer).

Film boiling occurs when the pressure of a system drops or the flow decreases In this case the bubbles cannot escape as quickly from the heat transfer surface. Likewise, if the temperature of the heat transfer surface is increased, more bubbles are created. As the temperature continues to increase, more bubbles are formed than can be efficiently carried away. The bubbles grow and group together, covering small areas of the heat transfer surface with a film of steam. This is known as partial film boiling.

Following sections describe:

• Transition to Film Boiling – Critical Heat Flux
• Departure from Film Boiling – Leidenfrost Point

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.

Departure From Nucleate Boiling – DNB

In case of PWRs, the critical safety issue is named DNB (departure from nucleate boiling), which causes the formation of a local vapor layer, causing a dramatic reduction in heat transfer capability. This phenomenon occurs in the subcooled or low-quality region. The behaviour of the boiling crisis depends on many flow conditions (pressure, temperature, flow rate), but the boiling crisis occurs at a relatively high heat fluxes and appears to be associated with the cloud of bubbles, adjacent to the surface. These bubbles or film of vapor reduces the amount of incoming water. Since this phenomenon deteriorates the heat transfer coefficient and the heat flux remains, heat then accumulates in the fuel rod causing dramatic rise of cladding and fuel temperature. Simply, a very high temperature difference is required to transfer the critical heat flux being produced from the surface of the fuel rod to the reactor coolant (through vapor layer).

In case of PWRs, the critical flow is inverted annular flow, while in BWRs, the critical flow is usually annular flow. The difference in flow regime between post-dryout flow and post-DNB flow is depicted in the figure. In PWRs at normal operation the flow is considered to be single-phase. But a great deal of study has been performed on the nature of two-phase flow in case of transients and accidents (such as the loss-of-coolant accident – LOCA or trip of RCPs), which are of importance in reactor safety and in must be proved and declared in the Safety Analysis Report (SAR).

In pressurized water reactors, one of key safety requirements is that a departure from nucleate boiling (DNB) will not occur during steady state operation, normal operational transients, and anticipated operational occurrences (AOOs).  Fuel cladding integrity will be maintained if the minimum DNBR remains above the 95/95 DNBR limit for PWRs ( a 95% probability at a 95% confidence level). DNB criterion is one of acceptance criteria in safety analyses as well as it constitutes one of safety limits in technical specifications.

Dryout – BWRs

In BWRs, similar phenomenon is known as “dryout” and it is directly associated with changes in flow pattern during evaporation in the high-quality region. At given combinations of flow rate through a channel, pressure, flow quality, and linear heat rate, the wall liquid film may exhaust and the wall may be dried out. At normal, the fuel surface is effectively cooled by boiling coolant. However when the heat flux exceeds a critical value (CHF – critical heat flux) the flow pattern may reach the dryout conditions (thin film of liquid disappears). The heat transfer from the fuel surface into the coolant is deteriorated, with the result of a drastically increased fuel surface temperature. In the high-quality region, the crisis occurs at a lower heat flux. Since the flow velocity in the vapor core is high, post-CHF heat transfer is much better than for low-quality critical flux (i.e. for PWRs temperature rises are higher and more rapid).

Departure from Film Boiling – Leidefrost Point

The Leidenfrost point, which corresponds to the minimal heat flux, is of practical interest since it represents the lower limit for the heat flux in the film boiling regime. If the heat flux drops below this minimum, the film will collapse, causing the surface to cool and nucleate boiling to be reestablished. Therefore, at this point, return to nucleate boiling (RNB) occurs. The terms quenching, minimum heat flux, return to nucleate boiling, departure from film boiling, film boiling collapse, and Leidenfrost point have been used interchangeably to refer to various forms of rewetting, but they are not exactly synonymous.

Using the stability theory, Zuber derived the following expression for the minimum heat flux (and corresponding Leidenfrost point) for a large horizontal plate:

where

• q_min – minimal heat flux [W/m²]
• h_fg  – enthalpy of vaporization, J/kg
• g – gravitational acceleration m/s²
• ρ_l — density of the liquid kg/m³
• ρ_v — density of vapour kg/m³
• σ — surface tension-liquid-vapour interface N/m

See also:

Boiling and Condensation

Subcooled Boiling

In subcooled boiling, the temperature of most of the liquid is below the saturation temperature and bubbles formed at the surface may condense in the liquid. This condensation (collapsing) produces a sound of frequency ~ 100Hz – 1 KHz. This is why an electric kettle makes the most noise before the water comes to saturated boiling. The term subcooling refers to a liquid existing at a temperature below its normal boiling point.

Subcooled Boiling in PWRs

Although the earliest core designs assumed that subcooled surface boiling could not be allowed in PWRs, this assumption was soon rejected and two-phase heat transfer is now one of normal operation heat transfer mechanisms also in PWRs. For PWRs at normal operation, there is a compressed liquid water inside the reactor core, loops and steam generators.  The pressure is maintained at approximately 16MPa. At this pressure water boils at approximately 350°C(662°F), which gives a subcooling margin (the difference between the pressurizer temperature and the coolant outlet temperature in the reactor core) of 30 °C. Noteworthy, this subcooling margin concerns the bulk temperature, since bulk boiling is in any case prohibited.

Subcooling margin is very important safety parameter of PWRs, since the bulk boiling in the reactor core must be excluded. The basic design of the pressurized water reactor includes such requirement that the coolant (water) in the reactor coolant system must not boil. To achieve this, the coolant in the reactor coolant system is maintained at a pressure sufficiently high that boiling does not occur at the coolant temperatures experienced while the plant is operating or in an analyzed transient.

As was calculated in example, the surface temperature T_Zr,1 = 325°C ensures, that even subcooled boiling does not occur. Note that, subcooled boiling requires T_Zr,1 = T_sat. Since the inlet temperatures of the water are usually about 290°C (554°F), it is obvious this example corresponds to the lower part of the core. At higher elevations of the core the bulk temperature may reach up to 330°C. The temperature difference of 29°C causes the subcooled surface boiling may occur (330°C + 29°C > 350°C). On the other hand, nucleate boiling at the surface effectively disrupts the stagnant layer and therefore nucleate boiling significantly increases the ability of a surface to transfer thermal energy to bulk fluid. As a result, the convective heat transfer coefficient significantly increases and therefore at higher elevations, the temperature difference (T_Zr,1 – T_bulk) significantly decreases.

In case of PWRs, the critical safety issue is named DNB (departure from nucleate boiling), which causes the formation of a local vapor layer, causing a dramatic reduction in heat transfer capability. This phenomenon occurs in the subcooled or low-quality region. The behaviour of the boiling crisis depends on many flow conditions (pressure, temperature, flow rate), but the boiling crisis occurs at a relatively high heat fluxes and appears to be associated with the cloud of bubbles, adjacent to the surface. These bubbles or film of vapor reduces the amount of incoming water. Since this phenomenon deteriorates the heat transfer coefficient and the heat flux remains, heat then accumulates in the fuel rod causing dramatic rise of cladding and fuel temperature.

Nucleate Boiling – Flow Boiling

In flow boiling (or forced convection boiling), fluid flow is forced over a surface by external means such as a pump, as well as by buoyancy effects. Therefore, flow boiling is always accompanied by other convection effects. Conditions depend strongly on geometry, which may involve external flow over heated plates and cylinders or internal (duct) flow. In nuclear reactors, most of boiling regimes are just forced convection boiling. The flow boiling is also classified as either external and internal flow boiling depending on whether the fluid is forced to flow over a heated surface or inside a heated channel.

Internal flow boiling is much more complicated in nature than external flow boiling because there is no free surface for the vapor to escape, and thus both the liquid and the vapor are forced to flow together. The two-phase flow in a tube exhibits different flow boiling regimes, depending on the relative amounts of the liquid and the vapor phases. Therefore internal forced convection boiling is commonly referred to as two-phase flow.

Nucleate Boiling Correlations – Flow Boiling

McAdams Correlation

In fully developed nucleate boiling with saturated coolant, the wall temperature is determined by local heat flux and pressure and is only slightly dependent on the Reynolds number. For subcooled water at absolute pressures between 0.1 – 0.6 MPa, McAdams correlation gives:

Thom Correlation

The Thom correlation is for the flow boiling (subcooled or saturated at pressures up to about 20 MPa) under conditions where the nucleate boiling contribution predominates over forced convection. This correlation is useful for rough estimation of expected temperature difference given the heat flux:

Chen’s Correlation

In 1963, Chen proposed the first flow boiling correlation for evaporation in vertical tubes to attain widespread use. Chen’s correlation includes both the heat transfer coefficients due to nucleate boiling as well as forced convective mechanisms. It must be noted, at higher vapor fractions, the heat transfer coefficient varies strongly with flow rate. The flow velocity in a core can be very high causing very high turbulences. This heat transfer mechanism has been referred to as “forced convection evaporation”. No adequate criteria has been established to determine the transition from nucleate boiling to forced convection vaporization. However, a single correlation that is valid for both nucleate boiling and forced convection vaporization has been developed by Chen for saturated boiling conditions and extended to include subcooled boiling by others. Chen proposed a correlation where the heat transfer coefficient is the sum of a forced convection component and a nucleate boiling component. It must be noted, the nucleate pool boiling correlation of Forster and Zuber (1955) is used to calculate the nucleate boiling heat transfer coefficient, h_FZ and the turbulent flow correlation of Dittus-Boelter (1930) is used to calculate the liquid-phase convective heat transfer coefficient, h_l.

The nucleate boiling suppression factor, S, is the ratio of the effective superheat to wall superheat. It accounts for decreased boiling heat transfer because the effective superheat across the boundary layer is less than the superheat based on wall temperature. The two-phase multiplier, F, is a function of the Martinelli parameter χ_tt.

See also:

Boiling and Condensation

Saturated Boiling – Bulk Boiling

In saturated boiling (known also as bulk boiling), the temperature of the liquid slightly exceeds the saturation temperature. Bulk boiling may occur, when system temperature increases or system pressure drops to boiling point. At this point, the bubbles entering the coolant channel will not collapse. The bubbles will tend to join together and form bigger steam bubbles. Steam bubbles are then propelled through the liquid by buoyancy forces, eventually escaping from a free surface.

Bulk Boiling in BWRs

In BWRs boiling of coolant occurs at normal operation and it is very desired phenomenon. Typical flow qualities in BWR cores are on the order of 10 to 20 %. A boiling water reactor is cooled and moderated by water like a PWR, but at a lower pressure (7MPa), which allows the water to boil inside the pressure vessel producing the steam that runs the turbines. Evaporation therefore occurs directly in fuel channels. Therefore BWRs are the best example for this area, because evaporation of coolant occurs at normal operation and it is very desired phenomenon.

In BWRs there is a phenomenon, that is of the highest importance in reactor safety. This phenomenon is known as the “dryout” and it is directly associated with changes in flow pattern during evaporation in the high-quality region. At normal the fuel surface is effectively cooled by boiling coolant. However when the heat flux exceeds a critical value (CHF – critical heat flux) the flow pattern may reach the dryout conditions (thin film of liquid disappears). The heat transfer from the fuel surface into the coolant is deteriorated, with the result of a drastically increased fuel surface temperature.

Bulk Boiling in PWRs

For PWRs at normal operation, there is a compressed liquid water inside the reactor core, loops and steam generators.  The pressure is maintained at approximately 16MPa. At this pressure water boils at approximately 350°C(662°F), which gives a subcooling margin (the difference between the pressurizer temperature and the coolant outlet temperature in the reactor core) of 30 °C. Noteworthy, this subcooling margin concerns the bulk temperature, since bulk boiling is in any case prohibited.

Subcooling margin is very important safety parameter of PWRs, since the bulk boiling in the reactor core must be excluded. The basic design of the pressurized water reactor includes such requirement that the coolant (water) in the reactor coolant system must not boil. To achieve this, the coolant in the reactor coolant system is maintained at a pressure sufficiently high that boiling does not occur at the coolant temperatures experienced while the plant is operating or in an analyzed transient.

As was calculated in example, the surface temperature T_Zr,1 = 325°C ensures, that even subcooled boiling does not occur. Note that, subcooled boiling requires T_Zr,1 = T_sat. Since the inlet temperatures of the water are usually about 290°C (554°F), it is obvious this example corresponds to the lower part of the core. At higher elevations of the core the bulk temperature may reach up to 330°C. The temperature difference of 29°C causes the subcooled surface boiling may occur (330°C + 29°C > 350°C). On the other hand, nucleate boiling at the surface effectively disrupts the stagnant layer and therefore nucleate boiling significantly increases the ability of a surface to transfer thermal energy to bulk fluid. As a result, the convective heat transfer coefficient significantly increases and therefore at higher elevations, the temperature difference (T_Zr,1 – T_bulk) significantly decreases.

Nucleate Boiling – Flow Boiling

In flow boiling (or forced convection boiling), fluid flow is forced over a surface by external means such as a pump, as well as by buoyancy effects. Therefore, flow boiling is always accompanied by other convection effects. Conditions depend strongly on geometry, which may involve external flow over heated plates and cylinders or internal (duct) flow. In nuclear reactors, most of boiling regimes are just forced convection boiling. The flow boiling is also classified as either external and internal flow boiling depending on whether the fluid is forced to flow over a heated surface or inside a heated channel.

Internal flow boiling is much more complicated in nature than external flow boiling because there is no free surface for the vapor to escape, and thus both the liquid and the vapor are forced to flow together. The two-phase flow in a tube exhibits different flow boiling regimes, depending on the relative amounts of the liquid and the vapor phases. Therefore internal forced convection boiling is commonly referred to as two-phase flow.

Nucleate Boiling Correlations – Flow Boiling

McAdams Correlation

In fully developed nucleate boiling with saturated coolant, the wall temperature is determined by local heat flux and pressure and is only slightly dependent on the Reynolds number. For subcooled water at absolute pressures between 0.1 – 0.6 MPa, McAdams correlation gives:

Thom Correlation

The Thom correlation is for the flow boiling (subcooled or saturated at pressures up to about 20 MPa) under conditions where the nucleate boiling contribution predominates over forced convection. This correlation is useful for rough estimation of expected temperature difference given the heat flux:

Chen’s Correlation

In 1963, Chen proposed the first flow boiling correlation for evaporation in vertical tubes to attain widespread use. Chen’s correlation includes both the heat transfer coefficients due to nucleate boiling as well as forced convective mechanisms. It must be noted, at higher vapor fractions, the heat transfer coefficient varies strongly with flow rate. The flow velocity in a core can be very high causing very high turbulences. This heat transfer mechanism has been referred to as “forced convection evaporation”. No adequate criteria has been established to determine the transition from nucleate boiling to forced convection vaporization. However, a single correlation that is valid for both nucleate boiling and forced convection vaporization has been developed by Chen for saturated boiling conditions and extended to include subcooled boiling by others. Chen proposed a correlation where the heat transfer coefficient is the sum of a forced convection component and a nucleate boiling component. It must be noted, the nucleate pool boiling correlation of Forster and Zuber (1955) is used to calculate the nucleate boiling heat transfer coefficient, h_FZ and the turbulent flow correlation of Dittus-Boelter (1930) is used to calculate the liquid-phase convective heat transfer coefficient, h_l.

The nucleate boiling suppression factor, S, is the ratio of the effective superheat to wall superheat. It accounts for decreased boiling heat transfer because the effective superheat across the boundary layer is less than the superheat based on wall temperature. The two-phase multiplier, F, is a function of the Martinelli parameter χ_tt.

See also:

Boiling and Condensation