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DNB – Departure from Nucleate Boiling

In the 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 nucleate boiling heat flux cannot be increased indefinitely. At some value, we call it the “critical heat flux”, the steam produced can form an insulating layer over the surface, which in turn deteriorates the heat transfer coefficient. Dynamic changes of boiling regime associated with exceeding the critical heat flux are widely known as “boiling crisis”.

The boiling crisis can be classified as:

  • dry-out (will be described below DNB) in the high-quality region
  • departure from nucleate boiling (DNB) in the subcooled or low-quality region (approximate quality range: from –5% to +5%).

But the critical heat flux is used for both regimes.

DNBR - Departure from Nucleate Boiling RatioIn the 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 behavior of the boiling crisis depends on many flow conditions (pressure, temperature, flow rate). Still, the boiling crisis occurs at relatively high heat fluxes and appears to be associated with the cloud of bubbles adjacent to the surface. These bubbles or films of vapor reduce the amount of incoming water. Since this phenomenon deteriorates the heat transfer coefficient and the heat flux remains, heat accumulates in the fuel rod, causing a dramatic rise in cladding and fuel temperature. Simply, a very high-temperature difference is required to transfer the critical heat flux produced from the fuel rod’s surface to the reactor coolant (through the vapor layer).

In the 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-dry-out 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).

One of the key safety requirements of pressurized water reactors 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 the acceptance criteria in safety analyses as well as it constitutes one of the safety limits in technical specifications.

An important duty of the plant operator is to control plant parameters such that a safe margin to DNB (or distance from DNB on the heat transfer curve) is maintained. Any sudden, large change in the following plant parameters/directions will decrease the margin to DNB:

  • Decrease in reactor coolant pressure
  • Decrease in reactor coolant flow rate
  • Increase in reactor power
  • Increase in reactor coolant inlet temperature

Therefore, the function of the operators and the plant design is to prevent a sudden, large change in these plant parameters.

Heat Flux Limitations in Nuclear Reactors
Nuclear reactors produce enormous amount of heat (energy) in a small volume. The density of the energy generation is very large, which puts demands on its heat transfer system (reactor coolant system). For a reactor to operate in a steady-state, all of the heat released in the system must be removed as fast as it is produced. This is accomplished by passing a liquid or gaseous coolant through the core and through other regions where heat is generated. The heat transfer must be equal to or greater than the heat generation rate or overheating, and possible damage to the fuel may occur.

The temperature in an operating reactor varies from point to point within the system. Consequently, there is always one fuel rod and one local volume hotter than all the rest. The peak power limits must be introduced to limit these hot places. The peak power limits are associated with such phenomena as the departure from nucleate boiling and the conditions that could cause fuel pellet melt.

Therefore power distribution within the core must be properly limited. These limitations are usually divided into two basic categories:

Critical Heat Flux

Dryout vs. DNBAs was written, in nuclear reactors, limitations of the local heat flux are of the highest importance for reactor safety. For pressurized water reactors and boiling water reactors, there are thermal-hydraulic phenomena, which cause a sudden decrease in heat transfer efficiency (more precisely in the heat transfer coefficient). These phenomena occur at a certain value of heat flux, known as the “critical heat flux”. The phenomena that cause heat transfer deterioration are different for PWRs and 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, and we call it the “critical heat flux” (CHF) at some value. The steam produced can form an insulating layer over the surface, which deteriorates the heat transfer coefficient. Immediately after the critical heat flux has been reached, boiling becomes 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 heat transfer deterioration are different for PWRs and BWRs.

Boiling Curve - Boiling Modes

Critical Heat Flux for DNB – Correlations

As was written, the boiling crisis can be classified as dry-out (will be described below DNB) in the high-quality region and departure from nucleate boiling (DNB) in the subcooled or low-quality region (approximate quality range: from –5% to +5%). But the critical heat flux is used for both regimes.

DNB – W-3 Correlation

One of the most well-known design correlations for predicting departure from nucleate boiling is the W-3 correlation developed at the Westinghouse Atomic Power Division by Tong. It is applicable for subcooled and low to moderate quality flows. The W-3 correlation is a function of coolant enthalpy (saturated and inlet), pressure, quality, and coolant mass flux:

CHF - Critical Heat Flux - Correlation

The correlation W-3 is for critical heat flux in uniformly heated channels. To account for non-uniform heat fluxes, Tong introduced the correction factor, F.

Special Reference: Tong, L. S., Weisman, Joel. Thermal Analysis of Pressurized Water Reactors. Amer Nuclear Society, 3rd edition, 5/1996. ISBN-13: 978-0894480386.

Cold Wall Factor – CWF

Tong, L. S., and Weisman, Joel also introduce a new factor known as the “cold wall factor”, which corrects CHF in a channel containing an unheated wall (e.g., channel adjacent to control rod guide tube). In these channels, the liquid film builds up along the cold wall, and this fluid is not effective in cooling the heated surface. The fluid cooling the heated surface is at higher enthalpy than calculated without the assumption of a cold wall. Note that there is an assumption that cold wall deteriorates heat transfer compared to channel with all sides heated at the same bulk exit enthalpy.

CHF Look-up Tables

CHF look-up tables are used widely to predict the critical heat flux (CHF). The CHF look-up table is a normalized data bank for a vertical 8 mm water-cooled tube. The 2006 CHF look-up table is based on a database containing more than 30,000 data points, and they cover the ranges of 0.1–21 Mpa pressure, 0–8000 kg.m–2.s-1 (zero flow refers to pool-boiling conditions) mass flux and –0.5 to 1 vapor quality (negative qualities refer to subcooled conditions).

Special Reference: GROENEVELD, D.C. et al., The 2006 look-up table, Nuclear Engineering and Design 237 (2007), 1909–1922.

Departure from Nucleate Boiling Ratio – DNBR

As was written, in the 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. Note that, even for BWRs, which have a significantly bottom-peaked axial power profile, the DNB-risk must be considered.

DNB occurs when the local heat flux reaches the value of critical heat flux. This phenomenon occurs in the subcooled or low-quality region (approximate quality range: from –5% to +5%). The behavior of this type of boiling crisis depends on many flow conditions (pressure, temperature, flow rate) since the critical heat flux is generally a function  of coolant enthalpy (saturated and inlet), pressure, quality, and coolant mass flux:

CHF - Critical Heat Flux - Correlation

This boiling crisis occurs at relatively high heat fluxes and appears to be associated with the cloud of bubbles adjacent to the surface. These bubbles or films of vapor reduce the amount of incoming water. Since this phenomenon deteriorates the heat transfer coefficient and the heat flux remains, heat accumulates in the fuel rod, causing the dramatic rise of cladding and fuel temperature. Simply, a very high-temperature difference is required to transfer the critical heat flux produced from the fuel rod’s surface to the reactor coolant (through the vapor layer). In the case of PWRs, the critical flow is inverted annular flow, while in BWRs, the critical flow is usually annular flow.

One of the key safety requirements of pressurized water reactors 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 the acceptance criteria in safety analyses as well as it constitutes one of the safety limits in technical specifications. The establishment of a minimum DNB ratio provides a major limitation on the design of water-cooled reactors, and this phenomenon limits the maximal thermal power of each PWR.

DNB ratio (DNBR – Departure from Nucleate Boiling Ratio) measures the margin to critical heat flux. DNBR is defined as:

the critical heat flux at a specific location and specific coolant parameters divided by the operating local heat flux at that location.

DNBR - definition

The reactor core must be designed to keep the DNBR larger than the minimum allowable value (known as the correlation limit) during steady-state operation, normal operational transients, and anticipated operational occurrences (AOOs). For predicting departure from nucleate boiling, CHF can be, for example, determined using the W-3 correlation developed at the Westinghouse Atomic Power Division. If these correlations were perfect (without uncertainties), the criterion would be simple:

DNBR - criterion

Local heat flux must be lower than critical heat flux (i.e., DNBR must be higher than one).

DNBR - Departure from Nucleate Boiling RatioBut in reality, no correlation is perfect, and uncertainties must be involved in this calculation. As indicated in the figure, these uncertainty bands or error bounds establish a minimum acceptable value for the DNB Ratio, which may be significantly greater than one. Uncertainties may reach about 20%, and therefore the DNBR must be larger than, for example, DNBRlim = 1,2.

As can be seen from the figure, the CHF significantly decreases with increasing coolant enthalpy. Therefore the minimal value of DNBR is not necessarily in the center of the core. The Minimum DNB Ratio (MDNBR) occurs when the critical heat flux and the operating heat flux are the closest, and it is usually in the upper part of the core. Moreover, at the channel inlet where the coolant subcooling is the highest, we would expect the heat flux necessary to cause DNB at this location to be extremely high. On the other hand, at the channel exit where the coolant enthalpy is highest, the heat flux necessary to cause DNB should be lowest.

Special Reference: Tong, L. S., Weisman, Joel. Thermal Analysis of Pressurized Water Reactors. Amer Nuclear Society, 3rd edition, 5/1996. ISBN-13: 978-0894480386.

critical heat flux vs local heat flux

The Nuclear Enthalpy Rise Hot Channel Factor – FΔH
See also: Hot Channel Factors

The Nuclear Enthalpy Rise Hot Channel Factor – FNΔH is defined as:

  1. The ratio of the integral of linear power along the fuel rod on which minimum departure from nucleate boiling ratio occurs (during AOOs) to the average fuel rod power in the core.
  2. The ratio of the integral of linear power along the fuel rod with the highest integrated power [kW/rod] to the average rod power [kW/rod].

Operation within the Nuclear Enthalpy Rise Hot Channel Factor – FNΔH limits prevents departure from nucleate boiling (DNB) during accidents limiting from DNB point of view. For example, a loss of forced reactor coolant flow accident, a loss of normal feedwater flow, or an inadvertent opening of a pressurizer relief valve. The Nuclear Enthalpy Rise Hot Channel Factor FNΔH is an assumption in these and other analyses, as well as it is an assumption for Safety Limits (SLs) calculations. Its merit is that FNΔH provides information about power distribution as well as about the coolant temperature (enthalpy), and both are crucial for DNB occurrence. Operation beyond the Nuclear Enthalpy Rise Hot Channel Factor – FNΔH could invalidate core power distribution assumptions used in these analyses (Safety Analyses and Safety Limits derivation).

Post-DNB Heat Transfer

The nucleate boiling heat flux cannot be increased indefinitely. We call it the “critical heat flux” (CHF) at some value. The steam produced can form an insulating layer over the surface, which deteriorates the heat transfer coefficient. This is because a large fraction of the surface is covered by a vapor film, which acts as 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 becomes unstable, and transition boiling occurs. The transition from nucleate boiling to film boiling is known as the “boiling crisis”. Since the heat transfer coefficient decreases beyond the CHF point, the transition to film boiling is usually inevitable.

Boiling Curve - Boiling ModesA further increase in the heat flux is not necessary to maintain film boiling. A film of vapor fully covers the surface, significantly reducing the convection coefficient since the vapor layer has a 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 conduction to the vapor. The heated surface stabilizes its temperature at point E (see figure). If the material is not strong enough for withstanding this temperature, the equipment will fail by damage to the material.

 
References:
Heat Transfer:
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Advanced Reactor Physics:

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  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Boiling and Condensation