How Much Power Could a One Inch Dyson Style Impeller Produce as a Supercritical CO2 Micro Turbine

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How Much Power Could a One Inch Dyson Style Impeller Produce as a Supercritical CO2 Micro Turbine

Summary

Using a tiny centrifugal impeller of about 1 inch diameter as a turbine with supercritical CO2 is feasible in principle, but the extractable power is modest and strongly dependent on speed, pressure ratio, passage dimensions, and efficiency. With aggressive but defensible assumptions, the realistic output is on the order of about 1 to 3 kilowatts. Pushing far beyond this risks choking the passages, excessive stresses, or large efficiency losses.

Key assumptions for a first pass estimate

1. Rotor geometry

Diameter about 1.0 inch which is 25.4 millimeters, tip radius about 12.7 millimeters. Effective rim passage height between 0.5 and 1.0 millimeter after allowing for blade thickness and shrouds.

2. Operating point for the working fluid

Supercritical CO2 near 300 C and 150 bar at turbine inlet, expanding to about 115 bar. This is a pressure ratio of about 1.3. CO2 density at these conditions is roughly 150 to 170 kilograms per cubic meter. Speed of sound is roughly 300 to 350 meters per second.

3. Rotational speed

100,000 revolutions per minute typical of small high speed blowers. This gives a tip speed around 133 meters per second using tip speed equals pi times diameter times rpm divided by 60.

4. Turbine performance

Small improvised micro hardware tends to low to mid efficiencies. Use a stage isentropic efficiency in the 0.5 to 0.6 band for a first pass.

Temperature and enthalpy drop estimate in text format

Use a simple gas relation to estimate the isentropic temperature drop for an expansion from pressure ratio 1.3 at 300 C. Treat gamma approximately equal to 1.3 and heat capacity cp approximately equal to 0.9 kilojoules per kilogram kelvin for an order of magnitude check.

1. Compute the isentropic temperature ratio using T2 over T1 equals pressure ratio to the power of (gamma minus 1) over gamma.

With pressure ratio 1.3 expansion, use p2 over p1 equals 1 divided by 1.3 which is about 0.769.

Exponent equals 0.3 divided by 1.3 which is about 0.231.

Temperature ratio is 0.769 raised to 0.231 which is about 0.94.

Temperature drop is about 6 percent of inlet absolute temperature.

With T1 about 573 kelvin, delta T is about 34 kelvin.

2. Isentropic enthalpy drop equals cp times delta T which is about 0.9 times 34 equals about 30 kilojoules per kilogram.

3. Real enthalpy drop equals isentropic efficiency times isentropic drop.

With 0.6 efficiency, delta h is about 0.6 times 30 equals about 18 kilojoules per kilogram.

This sets the available work per unit mass if losses are reasonable.

Mass flow and power estimate using simple area velocity logic

Define an effective rim flow area A as circumference times effective passage height.

Area A equals 2 times pi times radius times passage height.

Example A with 0.5 millimeter rim height

Radius r equals 0.0127 meters.

Height b equals 0.0005 meters.

Area equals 2 times pi times 0.0127 times 0.0005 which is about 4.0 times 10 to the minus 5 square meters.

Pick a representative throughflow velocity at the rim. Use axial or radial component on the order of 20 to 50 meters per second to keep relative Mach numbers modest. Use 26 meters per second for a conservative case and 50 meters per second for an optimistic case.

Compute mass flow m dot equals density times area times velocity.

Conservative case

Density 150 kg per m3, area 4.0e minus 5 m2, velocity 26 m per s.

m dot equals 150 times 4.0e minus 5 times 26 which is about 0.15 kg per s.

Optimistic case

Use velocity 50 m per s.

m dot equals 150 times 4.0e minus 5 times 50 which is about 0.30 kg per s.

Compute power P equals m dot times delta h.

Conservative power

0.15 kg per s times 18 kJ per kg equals about 2.7 kW.

Optimistic power

0.30 kg per s times 18 kJ per kg equals about 5.4 kW.

These values are upper bound style because they do not subtract leakage, incidence losses, diffuser losses, and any mismatch from using an air impeller as a turbine. A factor of about one half is reasonable for improvised use, which yields roughly 1 to 3 kW.

Cross check using torque and shaft speed

At 100,000 rpm the angular speed is about 10,472 radians per second.

If the stage loading parameter is around one, the torque tau can be approximated by tau equals mass flow times stage loading times blade speed times radius.

With mass flow 0.10 kg per s, stage loading about one, blade speed 133 m per s, and radius 0.0127 m, torque is about 0.17 newton meter.

Power equals torque times angular speed which is 0.17 times 10,472 equals about 1.8 kW.

This cross check supports the 1 to 3 kW range.

Practical constraints and cautions

1. Material and stress

Consumer blower impellers are often plastic or thin aluminum. They are not rated for supercritical CO2 temperatures and pressures or for expanding flow in reverse. Hoop stress margins at 100,000 rpm must be checked for the chosen alloy and thickness.

2. Seals and containment

A supercritical CO2 loop at over 100 bar requires gas seals, back to back dry gas seals or similar, and a pressure rated casing. A consumer vacuum housing is not appropriate.

3. Aerodynamic mismatch

A Dyson impeller is designed as a compressor for air with specific incidence and diffusion design. Running it as a turbine with supercritical CO2 means the blade metal angles, passages, and leakage paths are not optimized. Expect lower efficiency and narrow stable range.

4. Thermal and rotordynamics

CO2 density is high, which increases windage and cross coupled forces. Bearings and rotor dynamics must be sized for the dense gas.

Bottom line

A one inch Dyson style impeller repurposed as a supercritical CO2 turbine could, on paper, deliver on the order of 1 to 3 kilowatts at around 100,000 rpm if fed with a modest pressure ratio near 1.3 and with careful sealing and housing. Much higher quoted powers from simple area times velocity math are unlikely to be realized once you include real leakage and mismatched aerodynamics. For serious development, a purpose designed radial inflow or small axial stage for supercritical CO2 will deliver higher efficiency and better mechanical margins while staying in a similar power class.