timeDependentAxialProfile

Description

The timeDependentAxialProfile class in OFFBEAT allows you to set a time dependent average fast flux.

It is also possible to apply a an axial profile to the fast flux. Note that even if the fast flux is constant over time, the axial profile might change over time, depending on the profile type chosen by the user.

The fast fluence will evolve in time according to the local value of the fast flux.

Formulation

The final local fast flux value is derived as a combination of rod-average fast flux and axial profile, as follows:

\[ \begin{aligned} fastFlux(t, z) = \phi(t) \cdot g(z,t) \end{aligned} \]

where:

• \(z\) is the relative axial position (0...1)
• \(t\) is the current time
• \(g(z,t)\) is the axial profile
• \(\phi\) is the rod-average fast flux in n/cm2/s.

The axial profile is expected to be normalized to 1.

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Options

The timeDependentAxialProfile fast flux model requires the user to specify a few additional parameters in the fastFluxOptions sub-dictionary located within the solverDict.

Parameters in fastFluxOptions:

timePoints	A list of time values at which the \(\phi\) is provided. The time unit depend on the userTime selected by the user (seconds by default).
fastFlux	A list of \(\phi\) values in \(n/cm^2/s\), one value per time-point.
timeInterpolationMethod	Select the time interpolation method for time steps that fall in between the time points indicated in the timePoints list.
materials	A list of material (or cellZones names) where the fast flux source model applies.
axialProfile	A sub-dictionary that specifies the type of axial profile.

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Usage

Here is a code snippet of the solverDict to be used for the case of a fast flux that ramps from 0 to 1e13 n/cm2/s in 1hr time, remains constant for a year, and then ramps down to 0 in 1 hr. This particular example considers flat (i.e. uniform) axial profile.

fastFlux timeDependentAxialProfile;

fastFluxOptions
{
    //           t0  1hr    1yr       1yr+1hr
    timePoints  ( 0   3600   31536000  31539600);
    fastFlux    ( 0   1e13   1e13      0       );

    timeInterpolationMethod linear; //step;

    materials ( fuel cladding);

    axialProfile
    {
        type flat;
    }
}

For a time-dependent axial profile, one can modify the axialProfile sub- dictionary selecting the timeDependentTabulated. Other options might be available (see axialProfile class):

fastFluxOptions
{
    // .. The rest of the dictionary may remain unchanged

    axialProfile
    {
        // Example: time dependent axial radial profile.
        type            timeDependentTabulated;

        // List of time points for axial profile
        timePoints      ( 0 3600 31539600 );

        // List of axial locations for axial profile
        axialLocations  ( 0.0 0.5 1.0 );

        // 2D table for axial profile (z is x axis; time is y axis)
        // The user provides a 2D table (z-vs-time) of normalized fast flux
        // values (normalized to the average).
        // Other options might be available (see axialProfile class).
        data
        (
            ( 1.0 1.0 1.0 )
            ( 0.5 1.0 1.5 )
            ( 0.8 1.1 1.0 )
        );

        // Select the axial interpolation method
        axialInterpolationMethod    linear;

        // Select the time interpolation method for time steps that fall in between
        // the time points indicated in the timePoints list above
        timeInterpolationMethod     linear;
    }

}

As the time point or data lists might be quite long for a realistic history, making the solver dictionary less readable, the user can create separate files and include them in the fastFluxOptions dictionary using the #include command. In the example below the files are stored in the folder constant/lists. E.g.:

fastFluxOptions
{
    timePoints  #include "$FOAM_CASE/constant/lists/timePoints";
    fastFlux    #include "$FOAM_CASE/constant/lists/avgPower";
    timeInterpolationMethod linear;

    ...
}