Resonance Integral Calculation on pincell example

User Support
1

Hi everyone,

I am stuck on how to calculate the resonance integral of selected nuclides and compare with Chart of Nuclides values.

I took a look into Bryan Herman 4-factor formula approach . And then I was thinking of tallying the absorption rate \langle \Sigma_a \Phi \rangleover the volume (V) with the nuclide of interest at resonance energies (incoming neutrons @ 1eV to 20keV), yielding:

RI = \frac {\langle \Sigma_a \Phi \rangle}{N \cdot V}

as I assume the output absorption rate in OpenMC is

\langle \Sigma_a \Phi \rangle = \int_{\Delta E} \int_V \Sigma_a \Phi dE dV = N \cdot V \int_{\Delta_E} \sigma_a \Phi de = N \cdot V \cdot RI
\langle \Sigma_a \Phi \rangle = \int_{\Delta E} \int_V \Sigma_a \Phi dE dV = N \cdot V \int_{\Delta_E} \sigma_a \Phi de = N \cdot V \cdot RI1274×120

in unit of [absorptions / second]

where: N is the nuclide number density.

Bryan already told me to tally the response function MT-102, using
102 , so eq. above turns into:

\langle \Sigma_{\gamma} \Phi \rangle = \int_{\Delta E} \int_V \Sigma_{\gamma} \Phi dE dV = N \cdot V \int_{\Delta_E} \sigma_{\gamma} \Phi de = N \cdot V \cdot RI
\langle \Sigma_{\gamma} \Phi \rangle = \int_{\Delta E} \int_V \Sigma_{\gamma} \Phi dE dV = N \cdot V \int_{\Delta_E} \sigma_{\gamma} \Phi de = N \cdot V \cdot RI1278×120

I did it on the pincell example, adding this lines to tallies.xml:



U-238
102

The results was:

2

Hi Matheus,

The Resonance Integral is defined as reaction rate / cm^3 which your equation correctly reflects. But the reference value you are reporting is in terms of barns so it has been normalized by the flux. Since the resonance integral reference you are using probably assumed a 1/E flux-weighting, that means they had divided by log(Ehigh/Elow). I did that real quick and it still didn’t bring the answer to 277 barns. Did you try perhaps a similar calculation in a problem with only U-238 in an infinite homogeneous media? Comparing the result obtained from that model with the chart reference would be more apples-to-apples and help you rule out other physics.

By the way, I am a developer on OMC as well as a student as UM; if you have any questions that you don’t think need this message board feel free to drop me an e-mail. I’m also on the 4th floor of ERB but may not be in frequently before this project is due (I’m assuming this is related to 561?).

Hope this helps,
Adam Nelson

3

HI all,

the approach resulted correct, but to assure the “1/E”, a high dilution \delta = {N_M \over N_A}must be obtained. But by lowering the absorber density (N_A) as much as OpenMC stills runs (too low, it crashes, “ERROR: No fission sites banked on processor 0”). The opposite way (increasing H_2O) did not resulted in satisfactory results.

For U-238, δ = 3.6 × 10³, the tallied result was \langle \Sigma_{\gamma} \Phi \rangle = 1.82 \times 10^{-3}, yielding RI = 275.61 b (Chart of Nuclide 277 b)

The only modification for the pincell (MIT BEAVRS) example was the Boron removal, besides N changing.

To calculate for non-fissionable nuclides, a two box (Moderator and Absorber) with 1 cm² and a 1 MeV neutron source was employed.

Results are below.

Thanks Adam and Herman for the tips

Matheus