Solution of heat removal from nuclear reactors by natural convection

This paper summarizes the basis for the solution of heat removal by natural convection from both conventional nuclear reactors and reactors with fuel flowing coolant (such as reactors with molten fluoride salts MSR).The possibility of intensification of heat removal through gas lift is focused on. It might be used in an MSR (Molten Salt Reactor) for cleaning the salt mixture of degassed fission products and therefore eliminating problems with iodine pitting. Heat removal by natural convection and its intensification increases significantly the safety of nuclear reactors. Simultaneously the heat removal also solves problems with lifetime of pumps in the primary circuit of high-temperature reactors.


Introduction
Natural convection and its intensification using gas-lift is one of the inherent and passive safety devices discussed in [3].They are required for new types of 4th generation nuclear reactors.[1].Documentation for designs of natural convection and gas-lift systems for conventional nuclear reactors is missing from Czech literature and for the selected type of MSR with flowing fuel-coolant mixture of fluoride salts the methodology is not even elaborated in the English literature.

Model of calculation of primary circuit for natural convection
First, we derive formulas for a simplified diagram of the primary circuit of a conventional reactor, where the coolant passes through the primary circuit and heat is produced only in fuel cells in the active core.Our model will comprise section i: i = 1 core (index C) i = 2hot loop (index HL) i = 3 heat exchanger (index E) i = 4 cold loop (index CL) out index O in index I For individual parts we can write the equations: where: M T [kg] total weight of the primary coolant under steady operation (ignoring weight of coolant in the pressurizer, and in steady operation is not involved in heat transfer) where: flow section in section i Assuming steady flow and heat transfer in exchanger Equations ( 1) and ( 3) remain for the solution.

Derived formulae for natural convection of coolant in conventional nuclear reactors with fuel cells
Natural convection occurs when the forces of buoyancy overcome resistance forces (loss forces), inertia and gravity.For incompressible fluids it is based on the solution of the continuity equation where And the Bernoulli equation, modified to a form suitable for individual sections of the model.
where g [m/s 2 ] gravitational acceleration the sum of all local and frictional pressure losses in section i For local pressure losses the following relation applies: where j ξ is loss coefficient j-th type.
For friction pressure losses the following relation applies : where i λ [1] is friction coefficient dependant on surface roughness in section i L i [m] is length of piping in section i D ei [m] is equivalent diameter o [m] is wetted perimeter For closed circuit (e.g.primary circuit) is valid: From equations for natural convection of coolant in the primary circuit we easily obtain the equation for balanced flow of coolant Wλ. where For balanced flow is valid: ρ is the mean specific density is vertical change in primary For expressing loss we must determine positional changes and density of coolant in each segment i for coolant ߩ ሺܶሻ.
z are vertical coordinates in segments (z O at outputs and z I at inputs of coolant to segment) First, we make the assumption that changes in heat and thus in the temperature only occur in the core and the exchanger and there the density changes linearly.
Relation (19) we re-write in the form: If we consider the height of the input of coolant into the segment is the same as the output from the previous segment, is valid: where is mean density of coolant in core is temperature difference of coolant when passing through zone ȟܶ ൌ ሺܶ ூ െ ܶ ை ሻ ‫ݖ‬ҧ ா ǡ ‫ݖ‬ҧ [m] the mean height of the heat exchanger and zones After inserting into (13) we obtain: where P [W] is the total thermal power of core.After substitution and modifications we get: From relations (26) to (28) it can be seen that the exchanger must be located above the active core to achieve natural convection and divert power from the core, including the residual power (up to about 7% of the area) from the shutdown reactor.
The basic problem is the accuracy of the determination of total losses in the primary.One of the components is friction loss, which strongly depends on the Reynolds similarity number and roughness of piping.
Here we prepare the dependence of the Reynolds number on the characteristics of natural convection Wλ.
To determine the Reynolds number in individual parts of the primary we must take into account that dynamic viscosity η is heat dependent (η = η (T i )) and refine individual parts of total losses in the primary.
When using H 2 O as a coolant, it is necessary to consider the possibility of the coolant boiling during natural convection.A two-phase flow arises (water + steam) and it is necessary to determine the loss in this case.This is common for BWR (Boiling Water Reactors).
Extending the methodology derived here to other sections such as e.g. the primary coolant inlet chamber below the active zone and the outlet chamber above it and the transition to chimney draft, etc. does not constitute a problem, as relations (25) to (28) remain valid.It is only necessary to include the loss of these sections in the total loss coefficient.

Natural convection in systems with flowing fuel
The above method is unsuitable for shut down reactors with a flowing fuel mix because of the evolution of residual heat in the whole volume of the primary.For this type of reactor, the neglected heat evolution in other parts of the primary is a very rough approximation.
In conventional reactors with solid fuel residual power is concentrated in fuel cells.The main advantage of reactors with molten fluoride salts (MSR -Molten Salt Reactor) is the ability to clean the mix from fission products (FP) during operation.This is done in two ways: a) By bubbling the mixture with He and the removal of gaseous FP such as Kr, Xe and tritium and removing the He by cleaning.This method virtually eliminates the so called "iodine pit".b) Removal of part of the fuel mix and chemical cleaning done at the nuclear power plant.Depending on frequency and quantity it is possible to substantially reduce residual evolution of heat from FP.
The method for solving the balance of FP during cleaning can be found in the works [6,7].
The presence of actinides in the fuel-coolant mix causes the formation of an independent source of neutrons (from spontaneous fission and from (α,n) reactions on the salt elements).Other neutrons originate from FP as so-called 'delayed neutrons'.
This independent source of neutrons in the fuel mix causes additional heat generation in all parts of the primary outside the core due to fission in its otherwise subcritical parts.
This means that the design of the primary must be tested at sub-criticality in its individual sections.The source of neutrons is according to size k ef further multiplied and causes heat generation (similar to the case in the active core) in every part of the primary.It is EFM 2013 therefore necessary to expand the formulation of the previously solved problem.
First we modify relations(1) to (4): where For reactors with flowing fuel the power produced in individual parts of the primary i will generally be varied and determined by the sum where ܲ ி ሾ ሿ is given by the energy from decay of β and γ FP and depends on the mode of cleaning the fuel mixture from FP ܲ ௧ ሾ ሿ is given by the energy from decay of β and γ actinide and its spontaneous fission is determined by actinide fission from an external source of neutrons (which has three components) in different subcritical parts of the primary s ݇ ൏ ͳ where ܳ ௦ ሾȀሿ is source of neutrons from spontaneous fission of actinide ܳ ሺఈǡሻ ሾȀሿ is source of neutrons arising with the help of (ߙǡ ݊ሻ reactions, where α are emitted during α decay of actinide and their reaction with elements in the fluoride salts.ܳ ௗ௬ ሾȀሿ is source of neutrons from FP (delayed neutrons), here there is a strong dependency on time of leaving the core and power For subcritical area is also valid: where We break down the balance ο‫‬ for each part of the primary.We assume that we will use identical exchangers arranged in parallel in the integral layout N.