Control of coolant temperature in a nuclear reactor

[shrvn]

I am trying to build a model of CANDU reactor core using a software called DYMOLA.For this purpose,I am trying to figure out a mathematical relation between coolant temperature and Power developed in a reactor.I have the following questions:

1.What is the effect of increasing the neutron flux (hence,increasing the power developed in the core) on the coolant exit temperature.Is there a mathematical relation that relates the temperature of coolant coming out of the reactor to the neutron flux.

2.I read that in a CANDU reactor a decrease in coolant temperature increases the reactivity.

But,consider the following scenario:

Coolant temperature decreases---->>Reactivity increases---->>Power developed in the reactor increases---->>resulting in an increase in coolant temperature---->>which decreases the reactivity!

When does the cycle stop??

Hope you understood my question

 

[SmalltownNuke]

I'm not very familiar with CANDU reactors, however with PWRs the coolant temperature is controlled via steam demand and boric acid concentration. By using more steam, the coolant temperature decreases. Due to the steam generator being a saturated system, simply lowering the pressure of the SG will lower its temperature. This is why uncontrolled heat extractions (steam line breaks) are often a driving scenario for shutdown margin.

There are many on this board who are much more knowledgeable than I when it comes to the mathematics, however I do know for light water PWRs, neutron flux is not constant throughout core life (higher at end of life) due to a lower concentration of U235 as the core ages.

 

[Astronuc]

The coolant temperature is related to the enthalpy, or specific enthalpy, and pressure.

h = c_pT.

The coolant enters the core at some inlet temperature/sp. enthalpy (T_i/h_i) and exits with an increase temperature/sp. enthalpy (T_e/h_e).

As the coolant flow along the channel between the fuel rods, heat is transferred from the cladding to the coolant.

$$h_e = h_i + \Big({\int_o^z q''(z){\pi}D_h dz} + {\int_o^z f_c q'(z) dz}\Big)/GA$$

where z = axial elevation, or core height for the exit.
q''(z) is the heat flux at the cladding surface,
q' = linear heat rate = πD_hq''
D_h = heated diameter (cladding OD)
f_c = fraction of heat from fuel that is directly deposited into the coolant rather than conducted through the cladding
G = coolant mass flux (kg/s-m² in SI)
A = flow area of coolant channel.

 

[Astronuc]

But,consider the following scenario:

Coolant temperature decreases---->>Reactivity increases---->>Power developed in the reactor increases---->>resulting in an increase in coolant temperature---->>which decreases the reactivity!

When does the cycle stop??

Don't confuse time dependent with steady-state behavior.

Reactors have several competing reactivity mechanisms. These are in the fuel and moderator, and soluble neutron absorbers, and even integral (in the fuel) burnable absorbers as needed.

Doppler resonance absorption increases with temperature, as does spectral shift when moderator density decreases, which means less moderation. One can also introduce soluble boron into the cooling water or heavy water moderator. In CANDU reactors the coolant and moderator are separate heavy water circuits (Ref: http://www.nuclearfaq.ca/cnf_sectionD.htm#s).

 

[shrvn]

Thank you Astronuc and SmalltownNuke