How to model transient conditions?

[shakystew]

Hello,

I am graduate student in NE within the US. I am working on a grant that examines a small (10-100 microns) ceramic film region on the outside of the cladding region. I have assessed the neutronic impact, as well as a thermal impact (heat transfer coefficients, etc.) of the additional region will have, but now I am too evaluate the impact during transient conditions (will the region yield more time before fuel melts, etc.). I am completely lost where to begin this evaluation.

I have heard of a licensing code RELAP that could be used for this analysis, but I am unfamiliar with this code.

Any assistance would be much appreciated. Thanks in advance.

 

[Astronuc]

A ceramic coating on the outside of cladding would do much to stop melting of the fuel during a given transient. The goal of that coating would be to simply reduce/mitigate the chemical interaction between coolant and metal cladding, or postpone the interaction long enough to enable coolant to be reintroduced into the system.

The fuel melting would be a function of the thermal inertia in the system and the ability to remove the thermal energy. If the interaction of the cladding with the coolant would cause it to lose integrity sooner, then the coating may serve to delay or mitigate that failure mechanism.

RELAP is a system code and one would need a tranisent case to run. RELAP should provide the thermal boundary conditions on the fuel for a given transient. One would then put those conditions in a fuel modeling code that simulates the thermomechancial behavior of the fuel. The coating would represent a thermal resistance, and it's resistance to oxidation would have to be introduced in a modification of the high temperature corrosion model in the code.

 

[shakystew]

That is my thinking as well, and that is what I am finding, but I am still confused on how to begin to evaluate a pin during a transient. I will not have access to RELAP (Advisor does not want me to 'waste my time'), so I am lost.

 

[gmax137]

Yes, RELAP is like a box of tinkertoys - If you had access to RELAP you would still have to build the model of the system before you could use it. People spend their careers working on such models. So if you are interested in the fuel cladding behavior, getting into RELAP is indeed a waste of your time. So instead, develop a fuel pin model and then pick a transient (or class of transients) that challenges the fuel clad and start with a simple representation of the transient as a boundary condition for your fuel pin model. Say a loss of coolant - the boundary condition is adiabatic (though that's a tough one to fix by adding ceramic layers). Maybe a steam line break (depressurizes the RCS fluid, allowing the pins to exceed critical heat flux). Now you're talking...

 

[Astronuc]

That is my thinking as well, and that is what I am finding, but I am still confused on how to begin to evaluate a pin during a transient. I will not have access to RELAP (Advisor does not want me to 'waste my time'), so I am lost.

What does one know about the oxidation resistance of the coating? One could simply look at the corrosion of the ceramic coating in comparsion with the corrosion of the underlying Zr-alloy - at some temperature(s) representative of a thermal transient.

 

[Hologram0110]

That is my thinking as well, and that is what I am finding, but I am still confused on how to begin to evaluate a pin during a transient. I will not have access to RELAP (Advisor does not want me to 'waste my time'), so I am lost.

I do some fuel modeling work (CANDU fuel, but the principals are the same), so I might be able to help clear some of this up. During a reactor transient, even if the reactor is off, heat is still being deposited in the fuel. If the coolant is disrupted in someway (pipe rupture or pumps lose power) the temperature of the fuel and cladding will begin to rise. At high enough temperatures the coolant water will start to oxidize the cladding and releasing heat (exothermic reaction). Positive feedback can occur as this can increase the temperature, increasing the oxidation rate.

This is bad for a few reasons, a thick oxide layer is bad for the fuel. The oxide is mechanically weak and it thermally insulates the fuel. In addition, hydrogen is produced in the coolant which can be an explosive risk when mixed with the atmosphere.

The goal of a ceramic coating on Zr cladding is to prevent or slow the formation of the oxide layer. If you can prevent the oxidation, you can prevent the positive feedback, and you can maintain the integrity of the fuel. However, this has a downside, it can reduce heat removal from the fuel (particularly if the ceramic has poor thermal conductivity). Thus you would want to perform an analysis, which compares the centerline fuel temperature and the amount of cladding oxidation with and without the ceramic coating.

To do this type of analysis you will need a fuel modeling tool that you can modify. The biggest change should be replacing the correlation used for the cladding oxidation. You might also consider including the ceramic layer in the heat-transfer model (although if it thin or has a high thermal conductivity it may be included in the heat-transfer coefficent).

I actually produced my own fuel modeling code using commercial FEA, which would be extremely easy to modify for this analysis, but it has not been thoroughly validated. You might want to look at some transient fuel model codes like FRAPTRANS, FALCON, Moose/Bison, Transruanus, Femaxi or others to see if they will give you access to the source code to make these changes.

 

[shakystew]

I am now looking into codes that I can use for this analysis, and I have given my advisor some of the names of the codes listed above to see if he wants me to go that track.

In the mean time, I am attempting to obtain a better representation of the heat transfer coefficient. My understanding is that this factor is dependent on the coolant flow conditions. It seems to me that I must make several assumptions (e.g. inlet/outlet temp., coolant flow velocity) to obtain this.

I am looking at a text by Todreas Nuclear Systems, Vol. I (here on p.426), and I am using the analogy that the temperature profile is analogous to an electrical circuit. That is, that the temp. drop (as seen in Todreas bottom of p. 426) can be represented by adding each respective region then multiplying by the linear power.

I think I am confused on how to get about assessing the heat transfer coefficient all together.

 

[Hologram0110]

Hi again,

All the codes I mentioned before are fuel performance codes. The input to these codes are: the heat-transfer coefficent, local bulk coolant temperature and pressure, element/pin linear power history and geometry/manufacting details. They then output fuel temperature, strains and fission gas.

Unfortunately they won't help you calculate any of the fluid parameters outside the element/pin. Calculating the heat transfer coefficent is done by thermal hydraulic codes. This is a very complicated problem, especially for transients, because it involves heat transport and two-phase flow. Thermal hydralics is not my area of expertise (I just take the heat transfer coefficent as input for my model), and I'm actually not very familiar with the theory of how they are calculated. I assumed that they were semi-emperical and relied on experimental correlations of things like this. As a non-fluid dynamics person, I would guess that those curves are specific to the combination of surface material and coolant fluid. I know they are also influenced by the surface texture. You'd best check with a thermal-hydralics person to see if these curves can be calculated or find one for your specific ceramic.

If you wanted to assume that the ceramic to water heat-tranfer was the same as the Zr to water this actually becomes pretty easy. You wouldn't even need to edit the source code for those fuel modeling programs to include the effects of the ceramic (not counting the change in heating due to oxidation). Since it is a surface layer you could just include the thermal resistance in the heat-transfer coeffieent. Then no source code editing would be required.

Heat-transfer coefficents are analogous to electrical conductances (inverse of resistance). In this case, the layers are in series, so you had the thermal resistance like resistors in series.

new_HT_coeff = 1/(ceramic_thickness/k_ceramic + 1/HT_coeff )

If you have any questions about fuel modeling I'd be happy to try and help.

 

[Astronuc]

I am now looking into codes that I can use for this analysis, and I have given my advisor some of the names of the codes listed above to see if he wants me to go that track.

In the mean time, I am attempting to obtain a better representation of the heat transfer coefficient. My understanding is that this factor is dependent on the coolant flow conditions. It seems to me that I must make several assumptions (e.g. inlet/outlet temp., coolant flow velocity) to obtain this.

I am looking at a text by Todreas Nuclear Systems, Vol. I (here on p.426), and I am using the analogy that the temperature profile is analogous to an electrical circuit. That is, that the temp. drop (as seen in Todreas bottom of p. 426) can be represented by adding each respective region then multiplying by the linear power.

I think I am confused on how to get about assessing the heat transfer coefficient all together.

Fuel modeling/simulation codes have heat transfer correlations built in. If one is modeling a transient though, one will want a correlation developed for the particular transient conditions, e.g., low pressure and high or low flow.

PWR fuel rods usually use the Dittus-Boelter correlation, which is based on the Reynolds and Prandtl numbers. There are particular correlations for nucleate boiling, which can happen in high duty PWRs, and bulk boiling and more in BWRs. A transient could lead to dryout, where the local conditions exceed the critical heat flux.

Heat transfer coefficients depend on local heat flux, temperature, pressure, flow rate, quality, and phase change, surface roughness.

FRAPTRAN should be relatively easy to obtain from the NRC. Falcon source code is likely not available, although it's possible with restrictions from EPRI. BISON (INL) is available but not completely ready, and one's department may already have access. Transuranus is possibly available from ITU (Transuranium Institute, Karlsruhe). Femaxi (JAERI) may be difficult to acquire in time, if at all.

Besides the heat conductance from the cladding to the coolant, one would have to introduce a 'corrosion/oxidation' model to replace the Zr-alloy corrosion models in place.

 

[gmax137]

I think this talk about different computer codes is a waste of time unless and until you write out the problem you're trying to solve, and then try solving it yourself. After you do that, then you can look at someone else's work (ie, computer code) and see how their solution to the problem is different (better, worse) than yours.

There's more to this assignment than learning how to prepare input for a computer code (at least, I would hope that's the case).

Just my 2-cents

 

[FermiAged]

I would evaluate the fuel performance under 3 conditions:

1. Departure from nucleate boiling.

2. High linear power (from a rapid reactivity addition, for example).

3. Loss of coolant.

A ceramic coating would definitely decrease oxidation during a LOCA and thus reduce H2 production. On the other hand, I would expect the heat transfer coefficient to be reduced raising the fuel centerline temperature and stored energy. I also wonder if a rapid clad temperature rise would increase contact stress between the clad and the coating due to differential thermal expansion.