# Hydrogen Pickup

Hydrogen flux BC that simply multiplies the time derivative of the oxide thickness by a pickup factor to get flux. Units are for H concentration in wt.ppm.

## Description

The HydrogenPickup BC is used to model the flux of hydrogen into the clad that is caused by oxide growth. The flux is approximated as a constant fraction of the hydrogen liberated by oxide growth at the interface between the coolant water and the clad.

note:BC Requires Coupling to Oxide Thickness Variable

This BC must be coupled to a variable that gives the thickness of the oxide over time, such as with the OxideAux kernel. For this to work properly, OxideAux must be set to execute on linear; it will not work if the OxideAux is set to execute only at the end of the time steps.

The waterside corrosion reaction of the zirconium alloy cladding generates hydrogen at the water-oxide interface: (1) Some of the hydrogen migrates through the oxide layer and dissolves in the cladding, where it is slightly soluble. The fraction of the hydrogen produced by the corrosion reaction that ends up in the cladding is termed the hydrogen pickup fraction. Although the mechanism for hydrogen migration through the oxide layer is a topic of active research, the pickup fraction has been well characterized for various zirconium alloys. For example, Couet et al. (2014) found the instantaneous hydrogen pickup fraction to be a strong function of alloying elements and to be a complex function of the exposure time.

In Bison, the user specifies a fixed instantaneous hydrogen pickup fraction, so that the average total concentration of hydrogen (including dissolved hydrogen and hydrogen as ZrH) in the cladding is roughly proportional to the thickness of the oxide layer (Courty et al., 2014): (2) where is the hydrogen pickup fraction (-), is the Pilling-Bedworth ratio for ZrO and is equal to 1.56 (-), is the oxide thickness (m), is the initial thickness of the cladding (m), is the molecular weight of hydrogen (g/mol), and is the molecular weight of zirconium (g/mol).

The hydrogen pickup model in Bison can be coupled to any of the oxide growth models described in the Cladding and Corrosion Page.

## Example Input Syntax


[./hydrogen_pickup]
type = HydrogenPickup
variable = hydrogen_in_solution_ppm
boundary = left
oxide_thickness = oxide_thickness
pickup_fraction = 0.15
[../]
(test/tests/hydride/hydride_rim/hydride_rim.i)

## Input Parameters

• variableThe name of the variable that this boundary condition applies to

C++ Type:NonlinearVariableName

Description:The name of the variable that this boundary condition applies to

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

• oxide_thicknessCoupled oxide thickness

C++ Type:std::vector

Description:Coupled oxide thickness

### Required Parameters

• fuel_pin_geometryName of the UserObject that reads the pin geometry from the mesh.

C++ Type:UserObjectName

Description:Name of the UserObject that reads the pin geometry from the mesh.

Default:0.00066

C++ Type:double

• pickup_fraction0.15Fraction of hydrogen created by oxidation that is absorbed into the cladding.

Default:0.15

C++ Type:double

Description:Fraction of hydrogen created by oxidation that is absorbed into the cladding.

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• save_inThe name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

C++ Type:std::vector

Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Default:False

C++ Type:bool

Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

• diag_save_inThe name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

C++ Type:std::vector

Description:The name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

• vector_tagsnontimeThe tag for the vectors this Kernel should fill

Default:nontime

C++ Type:MultiMooseEnum

Description:The tag for the vectors this Kernel should fill

• extra_vector_tagsThe extra tags for the vectors this Kernel should fill

C++ Type:std::vector

Description:The extra tags for the vectors this Kernel should fill

• matrix_tagssystemThe tag for the matrices this Kernel should fill

Default:system

C++ Type:MultiMooseEnum

Description:The tag for the matrices this Kernel should fill

• extra_matrix_tagsThe extra tags for the matrices this Kernel should fill

C++ Type:std::vector

Description:The extra tags for the matrices this Kernel should fill

## References

1. Adrien Couet, Arthur T. Motta, and Robert J. Comstock. Hydrogen pickup measurements in zirconium alloys: relation to oxidation kinetics. Journal of Nuclear Materials, 451(1 - 3):1 – 13, 2014. URL: http://www.sciencedirect.com/science/article/pii/S0022311514001081, doi:http://dx.doi.org/10.1016/j.jnucmat.2014.03.001.[BibTeX]
2. Olivier Courty, Arthur T. Motta, and Jason D. Hales. Modeling and simulation of hydrogen behavior in Zircaloy-4 fuel cladding. Journal of Nuclear Materials, 452:311â€“320, 2014. URL: http://dx.doi.org/10.1016/j.jnucmat.2014.05.013, doi:10.1016/j.jnucmat.2014.05.013.[BibTeX]