Dynamic subdivided relative humidity model of a polymer electrolyte membrane fuel cell
The development of a control-oriented dynamic relative humidity model for a polymer electrolyte membrane (PEM) fuel cell stack is presented. This model is integrated with a first law based thermal model, which tracks energy flow within four defined control volumes in the fuel cell; the cathode channel, anode channel, coolant channel, and fuel cell stack body. Energy and mass conservation equations are developed for each control volume.
On top of mass conservation, electro-drag and osmosis models were also implemented within the model to account for the major modes of vapor transfer through the membrane between the anode and cathode. Requisite alterations to the thermal model as well as mass flow rate calculations are also discussed.
Initially, the model utilized a single lumped control volume for the calculation of all values each channel (anode and cathode). This lumped value method is computationally inexpensive, and makes the model optimal for control design. However, investigation of the mass-based Biot number showed the need for greater granularity along the length of the channels to properly capture the relative humidity dynamics. In order to improve the resolution of the model, while still minimizing the computation expense, the model was subdivided into a series of lumped value models. The cathode channel was the point of focus as it is the major concern from a controls perspective. This method captures the proper trends found in far more complex CFD models, while still maintaining a quick calculation time. Different levels are subdivision (3 and 6 submodels) are investigated, and the differences discussed. Particularly, temperature range, relative humidity range, the effect on the modeled voltage, and calculation time are compared.
This control-oriented model is low order and based on lumped parameters, which makes the computational expense low. Formulation of this model enables the development of control algorithms to achieve optimal thermal and water management.