Fuel Cell Simulation
Theory: oxygen and water change along the channel
Overview
If a polarization curve describes cell performance, why solve the channels too?
A polarization curve averages the whole cell, but conditions vary inside. Air enters at the channel inlet; as it travels, oxygen is consumed and thins while product water accumulates. Near the outlet there is less oxygen, electrode reactions slow and current falls. Near the inlet, dry air pulls water from the membrane and resistance rises. More air raises outlet oxygen but dries the membrane further and costs more compressor power. How much air to supply (stoichiometry) is a balance of these, and channel simulation is how it is studied.
Oxygen and water balance
λ is stoichiometry and 3.76 the nitrogen-to-oxygen ratio of air. Each mole of oxygen consumed produces 2 mol of water. Inlet air is dry and all water is vapour. The 300 cm² cell runs at 1.0 A/cm² (300 A, 0.635 V, 190.5 W).
Outlet voltage penalty and compressor power
b is the Tafel slope (0.0304 V); 80 °C, 150 kPa absolute; saturation vapour pressure 47.4 kPa at 80 °C. The compressor raises 101.3 to 150 kPa at 0.7 efficiency, 50.8 kJ/kg specific work.
Bacon's five kilowatts
Among the pioneers who scaled fuel cells to practical size was Britain's Bacon, who spent years refining high-pressure alkaline fuel cells and demonstrated a 5 kW unit in 1959. His design was taken up in the United States and led to spacecraft power systems. Scaling from small laboratory cells to practical units raised the problem of distributing gas and water across the whole cell — the same challenge facing channel design today.
Worked examples
Example 1: stoichiometry and outlet conditions (300 cm², 1.0 A/cm²)
| Stoichiometry | Outlet O₂ (dry basis) | Outlet RH | Outlet voltage penalty | Air flow | Compressor power |
|---|---|---|---|---|---|
| 1.2 | 4.2% | 94% | 0.061 V | 0.13 g/s | 6.5 W (3.4%) |
| 1.5 | 8.1% | 78% | 0.036 V | 0.16 g/s | 8.2 W (4.3%) |
| 2.0 | 11.7% | 60% | 0.022 V | 0.21 g/s | 10.9 W (5.7%) |
| 3.0 | 15.1% | 41% | 0.013 V | 0.32 g/s | 16.3 W (8.6%) |
Compressor share is relative to the 190.5 W cell output. The outlet voltage penalty reflects thinner outlet oxygen versus 21% at the inlet.
At stoichiometry 1.2 the outlet humidity is 94%. If the membrane doesn't dry, isn't that good?
Too humid is dangerous too. The 94% assumes vapour only and is an average; channel walls and diffusion layers are cooler, so water condenses into liquid there. Liquid water blocking fine pores of the diffusion layer and channels stops oxygen reaching the catalyst, and current near the outlet collapses (flooding). At stoichiometry 1.2 outlet oxygen is only 4.2% and the outlet penalty a large 0.061 V; flooding starves oxygen further and can disturb local potential and damage catalyst. At stoichiometry 3 the membrane dries, resistance rises and compressor power is heavy. Around 2 is common because it lies between the two failure modes. Real designs combine inlet humidification, channel geometry and coolant temperature distribution, tuning them with channel simulation so humidity and current inside the cell are as uniform as possible.
Modelling workflow
- Express the polarization curve as a function of oxygen concentration and membrane water content.
- Discretise channels inlet to outlet and solve oxygen, water and temperature balances.
- Compute local current from local oxygen and membrane state.
- Include condensed water and its effect on oxygen transport.
- Vary stoichiometry, humidification and cooling to maximise net power after auxiliaries.
“A stack whose voltage wandered at low load”
In one fuel cell stack, some cell voltages wandered only at low load. Channel simulation showed that at low load air flow was small and slow, failing to push condensed water out, so water accumulated and intermittently blocked channels. Switching to control that keeps stoichiometry higher at low load with a minimum flow eliminated the wandering.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Inlet oxygen everywhere | Outlet loss missed | Solve along channel |
| All water as vapour | Flooding missed | Include condensation |
| Ignoring auxiliaries | Stoichiometry set too high | Compare net output |
| Constant membrane resistance | Drying effect missed | Function of water content |
| Rated load only | Low-load flooding missed | Across load range |
I'd like to learn related topics.
Related pages include fuel cell modelling (polarization curve), water electrolysis, electrolysis simulation, battery degradation and supercapacitor modelling.