ADMatInterfaceReactionZrCoHxPCT

Description

The composition of metal hydrides like zirconium-cobalt hydride (ZrCoHx) is described by pressure-composition-temperature (PCT) data. In TMAP8, the PCT curve can be imposed by an interface kernel that then dictates the material composition. Hence, the ADMatInterfaceReactionZrCoHxPCT interface kernel imposes the surface concentration of H in ZrCoHx based on the input pressure (Pa) and temperature (K). ADMatInterfaceReactionZrCoHxPCT is related to ADMatInterfaceReaction, but includes the ZrCoHx PCT curves. At the interface between a solid (main) and a gas (neighbor), it imposes: (1) where is the surface H concentration in mol/m, and are the backward and forward surface reaction rate in 1/s, respectively, is the composition in atomic fraction of H in ZrCoHx given a gas temperature and gas pressure , and is the zirconium-cobalt atomic density in mol/m.

Figure 1 shows the data used in this interface kernel. The experimental data was selected from several authors Jat et al. (2013) for (433.15 K) and (604.15 K) and Nagasaki et al. (1986) for (573.15 K) since a clean PCT curve is required for accurate modelling.

Figure 1: PCT data for ZrCoHx from Jat et al. (2013) and Nagasaki et al. (1986).

To include this PCT data in TMAP8 modelling capabilites the high and low pressure regions were extracted and regressed for the resulting equations.

The low pressure is captured as: (2)

The high pressure is captured as: (3)

Figure 2 shows the fitting and TMAP8 results used in this interface kernel.

Figure 2: PCT data for ZrCoHx from Jat et al. (2013) and Nagasaki et al. (1986) implemented in TMAP8, and test results.

The plateau representing phase transition is captured as: (4) with being the hydrogen partial pressure limit delineating the plateau in Pa and being the temperature in K. This fit is shown in Figure 3.

Figure 3: Fit phase transition region as pressure as a function of temperature.

The jump between the low low high pressure occurs if the atomic fraction is equal to 0.50, while from high to low pressure occurs if the atomic fraction is equal to 1.4. These end points follow the Eq. (2) and Eq. (3) maximum and minimum,respectively.

Test

(tmap8/test/tests/ZrCo_hydrogen_system/ZrCoHx_PCT.i) tests the implantation of the ZrCoHx PCT curves in TMAP8. The domain contains two blocks: gas (left) and ZrCoHx (right) with an interface between the two blocks. The diffusion is for this test case is given by (Yu et al., 2024) and the surface reaction rate is taken from (Jat et al., 2013) (). Note that the diffusion used is based on ZrH hydride since there is not diffusion value on ZrCo hydride. This should not affect the end results of the test case since simulation time goes until equlibrium is achieved. To model the interface, the input file employs the InterfaceDiffusion object to model the flux of hydrogen at the surface, and ADMatInterfaceReactionZrCoHxPCT to model the steady-state condition for the hydrogen concentration at the surface defined by: (5) where is the zirconium-cobalt atomic density.

The results of the high pressure test for (, ) = (433.15 K, Pa), (433.15 K, Pa), (573.15 K, Pa), and (604.15 K, Pa). The results of the low pressure test for (, ) = (433.15 K, Pa), (573.15 K, Pa), (604.15 K, Pa), and (604.15 K, Pa) are shown in Figure 2. Both show good agreement.

Example Input File Syntax

[InterfaceKernels<<<{"href": "../../syntax/InterfaceKernels/index.html"}>>>]
  [interface_reaction_ZrCoHx_PCT]
    type = ADMatInterfaceReactionZrCoHxPCT<<<{"description": "Implements a reaction to establish ReactionRate=k_f*u-k_b*v to compute the surface H concentration in ZrCoHx from the temperature and partial pressure based on the PCT curves with u the concentration in the solid and v (neighbor) the concentration in the gas in mol/m^3.", "href": "ADMatInterfaceReactionZrCoHxPCT.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = concentration_H_enclosure_2
    neighbor_var<<<{"description": "The variable on the other side of the interface."}>>> = concentration_H_enclosure_1
    neighbor_temperature<<<{"description": "The variable on the other side of the interface for temperature (K)."}>>> = temperature
    density<<<{"description": "Density of the solid in (mol/m^3)."}>>> = ${density_ZrCo}
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = interface_2
    forward_rate<<<{"description": "Forward reaction rate coefficient (1/s)."}>>> = 'reaction_rate_surface_ZrCoHx'
    backward_rate<<<{"description": "Backward reaction rate coefficient (1/s)."}>>> = 'reaction_rate_surface_ZrCoHx'
  []
[]

Input Parameters

References