In the unresolved 0D modeling approach, the following transport equation for electric field potential is solved:

(18–25)

The electric field and the electrochemistry interact solely at the electrolyte interface. Ansys Fluent treats the electrolyte interface as an impermeable wall. The potential field must have a “jump" condition applied to the two sides of this wall to account for the effect of the electrochemistry. To closely couple the electrochemical behavior to the potential field calculation, all the electrochemical effects (the voltage jump due to Nernst, the voltage reduction due to activation, and the Ohmic losses due to the resistivity of the electrolyte) must be included in the jump condition. The jump condition is linearized for the voltage reduction due to activation. This interface condition relates the potential on the anode side and the cathode side of the electrolyte and has the following form:

(18–26)

where and are the activation overpotential of the anode and the cathode, respectively, is the open circuit potential, and is the ohmic overpotential of the electrolyte and catalyst layers calculated by:

(18–27)

where , , and are the thicknesses of the membrane zone, anode catalyst layer, and cathode catalyst layer, respectively; and , , and are the electrical conductivities of the membrane zone, anode catalyst layer, and cathode catalyst layer, respectively.

To estimate the activation overpotential of the anode and cathode ( and ), the Butler-Volmer equations are used:

(18–28)

(18–29)

where

subscripts and denote the anode and cathode zones, respectively

, denote the local species concentration and the reference value for the local species concentration, respectively (kmol/m3)

= specific active surface area (1/m)

= reference exchange current density per active surface area (A/m2)

= concentration dependence

and = anode and cathode transfer coefficients of the anode electrode, respectively (dimensionless)

and = anode and cathode transfer coefficients of the cathode electrode, respectively (dimensionless)

= surface overpotential

= Faraday constant (9.65x107 C/kmol)

= the universal gas constant

= temperature

After solving the potential equation, the current density generated at the electrolyte interface can be obtained. Based on the current density, the volumetric source and sink terms for each species and energy equations in the adjacent computational cells can be calculated.

The volumetric source terms (kg/m³-s) for liquid water, hydrogen, and oxygen due to electrochemistry reactions are calculated at the adjacent cells of the interface. The source terms due to electrochemistry reactions are shown in Table 18.3: Source Terms for Species and Liquid Water due to Electrochemistry Reactions in the Unresolved 0D Approach:

In the above table, , , and are the molecular mass of water, oxygen, and hydrogen, respectively, is the current density at the electrolyte interface, is the area of the electrolyte interface, and is volume of the adjacent computational cell.

The heat source due to electrochemistry reactions in the adjacent computational cells is calculated as:

(18–30)

where is temperature, is the number of electrons involved in the electrochemistry reactions, and and are the entropy changes in Equation 20–13 and Equation 20–14, respectively.