## Hot Channel (Peaking) Factors

## Heat Flux Hot Channel Factor – F_{Q}(z)

The Heat Flux Hot Channel Factor – F_{Q}(z) is defined as:

- The ratio of the maximum local linear power density, where there is a minimal margin to limiting fuel temperature (during AOOs), to the average local linear power density in the core.
- The maximum local linear power density [kW/ft] in the core divided by the core average fuel rod linear power density [kW/ft].

Operation within the Heat Flux Hot Channel Factor – F_{Q}(z) limits prevents power peaks that exceed the loss of coolant accident (LOCA) limits derived from the analysis of the Emergency Core Cooling Systems (ECCS). In this analysis, fuel cladding failure during a postulated LOCA is limited by restricting the maximum linear heat rate (LHR) so that the peak cladding temperature does not exceed the acceptance criterion (e.g. 2200°F or 1204°C). Cladding temperatures below this criterion exclude severe cladding failure by oxidation due to a cladding-steam reaction. The Heat Flux Hot Channel Factor – F_{Q}(z) is an assumption in these and other analyses as well as it is an assumption for Safety Limits (SLs) calculations. Operation beyond the Heat Flux Hot Channel Factor – F_{Q}(z) could invalidate core power distribution assumptions used in these analyses (Safety Analyses and Safety Limits derivation).

Now, consider a case where power distribution is limited only by the **F**_{Q}**(z). **But **F**_{Q}**(z) **can be limiting at each elevation of the core (axially flat distribution). The maximum heat flux at several core elevations can occur in the same channel. In this case the coolant enthalpy rise would be very high, most probably over-limit. In this case, DNB is more likely to occur, because the critical heat flux is significantly lower when coolant enthalpy is higher. Therefore, the **F**_{Q}**(z) **itself cannot be used to prevent DNB occurrence and the enthalpy rise hot channel factor must be introduced.

## Nuclear Enthalpy Rise Hot Channel Factor – F^{N}_{ΔH}

The Nuclear Enthalpy Rise Hot Channel Factor – F^{N}_{ΔH} 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 – F^{N}_{ΔH} 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 F^{N}_{ΔH} is an assumption in these and other analyses as well as it is an assumption for Safety Limits (SLs) calculations. Its merit is that F^{N}_{ΔH} 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 – F^{N}_{ΔH} could invalidate core power distribution assumptions used in these analyses (Safety Analyses and Safety Limits derivation).

DNB occurs when a fuel rod cladding surface is overheated, which causes the formation of a** local vapor layer**, causing a dramatic reduction in heat transfer capability. Proximity to the DNB condition is expressed by the departure from nucleate boiling ratio (DNBR), defined as the ratio of the cladding surface heat flux (known as the critical heat flux) required to cause DNB to the actual cladding surface heat flux. The minimum DNBR value during both normal operation and anticipated transients is limited to the DNBR correlation limit for the particular fuel design in use, and is accepted as an appropriate margin to DNB. The DNB acceptance criterion for an anticipated operational occurrence (AOO) is met when there is a 95 percent probability at a 95 percent confidence level (the 95/95 DNB criterion) that DNB will not occur, and the fuel centerline temperature stays below the melting temperature.

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