Nuclear reactor heat removal

In nuclear engineering there are a number of empirical or semi-empirical relations used for quantifying the process of removing heat from a nuclear reactor core so that the reactor operates in the projected temperature interval that depends on the materials used in the construction of the reactor.

Common liquid coolants for nuclear reactors include: deionized water (with boric acid as a chemical shim during early burnup), heavy water, the lighter alkaline metals (such as sodium and lithium), lead or lead-based eutectic alloys like lead-bismuth, and NaK, a eutectic alloy of sodium and potassium.

Gas cooled reactors operate with coolants like carbon dioxide, helium or nitrogen but some very low powered research reactors have even been air-cooled with Chicago Pile 1 relying on natural convection of the surrounding air to remove the negligible thermal power output.

represents the number of atoms in a cubic meter of fuel, a is the amount of energy released in the fuel in each fission reaction (~181 MeV),

[1] Recovery of this amount of heat is achieved by using cooling fluids whose temperature at the entrance to the reactor channel

Under these conditions, the temperature of the cooling agent at distance z travelled into the cooling channel inside nuclear reactor is obtained by integrating the previous equation:

is the local heat flow on the casing - cooler contact surface unit and

The heat discharge from the PWR and PHWR reactors is made by pressurized water under forced convection.

The general expression for determining the transfer coefficient is given by the Dittus - Boelter equation:

If the flow of the fluid is made under conditions of a great difference between its temperature and the contact surface, the transfer coefficient is determined from the relationship:

is the dynamic viscosity of the coolant at the temperature of the adhering fluid film at the surface of the casing.

The relation presented above is valid in the case of a long channel with

The transfer coefficient for cooling the pipes by natural convection[3] is obtained from:

is the difference between the average wall temperatures of the casing and the cooling agent.

In boiling water cooled reactors (BWR) and partly in pressure water cooled reactors (PWR and PHWR) the heat transfer is made with a vapor phase in the cooling medium, which is why this type of heat transfer is called heat transfer in a biphasic system.

[1] Increasing the flow of heat, reducing the agent flow and lowering the pressure can lead to increased temperature of the cooled surface.

If the temperature of the fluid in the channel section that we consider is lower than the boiling temperature under local pressure conditions, the vaporization is limited to the immediate vicinity of the surface and in this case the boiling is called submerged boiling.

There is no proportionality between the heat flow and the difference between the surface temperature and the coolant temperature that allows the definition of a heat transfer coefficient similar to the one-phase case.

In this situation we can use the equation of Jens and Lottes, which establishes a connection between the difference

If the temperature of the fluid in the channel section considered is slightly higher than the boiling temperature under local pressure conditions, the heat transfer is by boiling with nucleation, forming vapor bubbles trained by the cooling agent (that becomes biphasic throughout its entire volume).

The vapor content of the PHW-CANDU reactor is about 0.03-0.04 kg steam / kg of agent, thus increasing the amount of heat transported by the unit mass of agent by over 10%.

If the cooled surface temperature far exceeds the boiling temperature of the cooling agent in the channel section, the vapor content of the agent increases considerably, the continuous phase becoming the vapor phase and the liquid phase becoming only a suspension between vapors.

The cooled surface remains covered with a liquid film which still provides a very high heat transfer coefficient,

The film of liquid is continuously fed with drops from the agent suspension.

Watering of the surface continues, however, by the drops of liquid in the suspension that are present in the cooling agent as long as the heat flow remains below a value that depends on local conditions (value that is called critical flux).

The heat transfer coefficient in the pre-crisis period can be determined from the relationship:

[1] The heat transfer to the gas-cooled reactors is carried out by forced convection.

For a gaseous thermal agent, the heat transfer coefficient can be deduced from a relation of the type Dittus-Boelter, but taking into account, for the intervening sizes, the values corresponding to the average temperature of the fluid film denoted by the index

which differs in the use of water by a slightly lower value of the coefficient a.

Forced flow relationships established for fluids are also not valid for liquid metals.