Presets
Playback
Apparatus
Model checks
The science
What is modelled
The collector is a large glazed roof over the ground; the air under it warms and flows inward. The warm air in the tall stack is lighter than the outside air, so the pressure difference at the base drives a flow. A turbine takes a share of that pressure and the rest drives the air through the stack.
Equations
- Collector heat balance
m cp ΔT = A (τα G − U ΔT / 2). - Buoyancy pressure
ΔP = ρ g H ΔT / T0. - Stack flow
(1 − x) ΔP = (1 + K) ρ v² / 2,m = ρ As v. - Electric power
P = ηt x ΔP As v.
Checks run in the page
- Bisection solution against a separate fixed-point iteration.
- Energy balance of the collector.
- Optimum turbine share 2/3 at fixed temperature rise.
- Order-of-magnitude comparison with a 50 kW prototype.
Honest simplifications
Constant absorptance and loss coefficient, no ground heat storage, no wind, no day cycle and a lumped friction coefficient. Results indicate trends, not a plant design.
What to try
- Press Short stack and see how strongly the chimney height matters.
- Move the turbine share and compare the coupled curve with the dashed 2/3 optimum.
- Press Cloudy morning: output drops far faster than the sunlight.