Departure from Nucleate Boiling Ratio – DNBR
As was written, 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. Note that, even for BWRs, which have a significantly bottom-peaked axial power profile, the DNB-risk have to be taken into account.
DNB occurs, when the local heat flux reaches value of critical heat flux. This phenomenon occurs in the subcooled or low-quality region (approximate quality range: from –5% to +5%). The behaviour 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:
This type of 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.
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. Needless to say, the establishment of a minimum DNB ratio provides a major limitation on the design of water cooled reactors. This phenomenon limits the maximal thermal power of each PWR.
DNB ratio (DNBR – Departure from Nucleate Boiling Ratio) is the measure of 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.
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 correlation were perfect (without uncertainties), the criterion would be simple:
Local heat flux must be lower than critical heat flux (i.e. DNBR must be higher tham one).
But in reality, no correlation is perfect and uncertainties must be involved in this calculation. These uncertainty bands or error bounds establish a minimum acceptable value for the DNB Ratio, which may be significantly greater than one as indicated in the figure. 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 minimal value of DNBR is not necessarily in the center of the core. The Minimum DNB Ratio (MDNBR) occurs at the location where 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 its highest, the heat flux necessary to cause DNB should be at its 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.
See also: Hot Channel Factors
The Nuclear Enthalpy Rise Hot Channel Factor – FNΔH is defined as:
- 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.
- 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, that are 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 with an information about power distribution as well as about the coolant temperature (enthalpy). 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).