HydrogenEnergy

Hydrogen fuel cell

A PEM fuel cell from the electrochemistry up — the polarization curve and its three overpotentials, power and efficiency, an automotive stack, hydrogen consumption, thermal management, and dynamic load response.

DjiniousLabModelling & simulation

A PEM fuel-cell polarization curve — cell voltage falling with current density through the activation, ohmic and concentration loss regions

peak power density: 0.655 W/cm²peak power density
efficiency at rated: 43.9%efficiency at rated
200-cell stack @ 130 V: 22.6 kW200-cell stack @ 130 V
hydrogen consumption: 1.4 kg/hhydrogen consumption
steady operating temp: 82 °Csteady operating temp
design notebooks: 10design notebooks

Hydrogen in, electricity out — and where the volts go.

A fuel cell turns hydrogen and air straight into electricity, with water and heat as the only exhaust — no combustion, no Carnot ceiling. But the voltage you actually get is always less than the thermodynamics promises, and exactly how much less is the polarization curve. This program builds a PEM cell from its electrochemistry, traces that curve and the three losses that shape it, scales it into an automotive stack, and runs the fuel, thermal and dynamic behaviour a real system has to manage.

No flame, no Carnot limit.

Because a fuel cell converts chemical energy to electricity directly, it isn't bound by the Carnot efficiency of a heat engine. The reversible cell voltage is 1.23 V and the thermoneutral voltage — where all the reaction enthalpy would become electricity — is 1.48 V, giving a thermodynamic ceiling around 83%. The catch is that you only see that voltage at zero current; the moment you draw power, three overpotentials start eating into it, and the polarization curve is the map of that erosion.

A polarization curve of cell voltage versus current density with the activation, ohmic and concentration regions shaded — The polarization curve, the fuel cell's defining chart: voltage drops sharply at low current (activation — getting the reaction going), falls linearly through the middle (ohmic — membrane and contact resistance), and collapses near the limiting current (concentration — reactant starvation). The whole engineering of a cell is about flattening this curve.

A stacked breakdown of the open-circuit voltage partitioned into useful cell voltage and the activation, ohmic and concentration losses across current density — Where the volts go: the open-circuit voltage partitioned across current density into the useful cell voltage and the three losses. Activation dominates at low load, ohmic grows linearly, and concentration takes over at the high-current end — the budget a designer trades catalyst, membrane and flow-field against.

You can't have both at once.

Power density is voltage times current, so it climbs as you draw more current — until the falling voltage wins and it peaks, here at 0.655 W/cm². But efficiency is just the cell voltage divided by the thermoneutral voltage, so it falls the whole way. That tension sets the rated point: run near peak power and the cell is small but inefficient and hot; run at high voltage and it's efficient but large. The program picks the rated point at 0.65 V — 43.9% efficient — and sizes the stack from there.

Power density rising to a peak and efficiency falling monotonically, both against current density — The power-versus-efficiency tension on one chart: power density rises to a peak while efficiency falls monotonically. The rated operating point is a deliberate compromise on this curve — and it's where stack size, hydrogen cost and cooling load are all decided.

An automotive fuel-cell stack V-I and power curve — 200 cells in series delivering tens of kilowatts — From one cell to a stack: 200 cells in series over 300 cm² deliver 22.6 kW at 130 V — automotive scale. Series cells share the same current, so the weakest cell sets the limit; uniformity, not just average performance, is what a stack design has to guarantee.

An efficiency map over operating temperature and membrane resistance, brightest where both favour low loss — The operating envelope: efficiency over temperature and membrane resistance (which humidity controls). Warmer and wetter speeds the kinetics and lowers resistance, but too dry or too cold and performance falls off — the operating window a fuel-cell controller is built to hold.

Every spec is a number you can re-run.

The sign-off notebook re-derives each requirement from the same electrochemical model the program builds.

Result

Peak power density: 0.655 W/cm²
Efficiency at rated: 43.9%
Stack power: 22.6 kW @ 130 V
Hydrogen consumption: 60.9 g/kWh
Requirements verified: 6 / 6

Requirement

Peak power density: R-01
Efficiency at rated: R-02
Stack power: R-03
Hydrogen consumption: R-04
Requirements verified: PASS

0-D, design-grade electrochemistry.

The cell is a 0-D, semi-empirical model — Tafel activation, ohmic resistance and a concentration term — not a 1-D membrane-and-gas-diffusion-layer transport model; the thermal node is lumped and the stack is treated as uniform. That is exactly the fidelity fuel-cell sizing and system design need first: drawing the polarization curve, choosing the rated point, scaling the stack, budgeting hydrogen and cooling, and checking the dynamic response — on your own catalyst, membrane and operating numbers, before a detailed transport or CFD model.