Scaling Guidelines for Converting Micro Turbines from Air to Supercritical CO2

Using a Radial Outflow Turbine versus a Radial Turbine

A radial outflow turbine can make the gas path geometry more workable for supercritical CO2 micro-turbines, but you pay for that with higher rotor stresses, more challenging aerodynamics, and usually a lower peak efficiency than the best axial or radial-inflow designs. It is a useful knob when your passages get tiny with sCO2, but it is not a free win.

Here is how to think about it.

Why sCO2 makes blades hard to size

At 300 C and high pressure, sCO2 density can be 100 to 200 kilograms per cubic meter or more. For a given mass flow, the required flow area equals mass flow divided by density times velocity. That makes inlet throats very small in micro hardware. In axial or radial-inflow stages you can run into unmanufacturable slots and excessive tip-clearance fractions.

What a radial outflow stage changes

Radial outflow moves the working fluid from small radius to large radius across the rotor. As the gas expands, its density drops and its volumetric flow rises. Outflow architecture naturally provides more annulus area because area scales with 2 pi times radius times blade height. Growing radius means you can grow area without making the blade height extreme. That directly helps with sCO2 where you need more area downstream.

Rule of thumb in text form:

Required flow area A equals 2 times pi times radius r times blade height b.

As r increases across the rotor, A can increase even if b is kept moderate.

That can keep minimum throats and tip gaps in a machinable range.

Specific pros for micro sCO2

1. Manufacturable passages

Outflow lets you start at a small radius where the dense sCO2 needs very little area and finish at a larger radius where the expanded flow needs more area. This reduces the need for ultra-tall blades or hairline throats.

2. Lower relative Mach at the inlet for a given speed

You can pick a modest inlet radius and shaft speed so that blade tip speed is reasonable where the speed of sound in sCO2 is lower than air.

3. Strong torque capability

Torque is roughly mass flow times change in angular momentum. Larger exit radius raises torque leverage, which is helpful at micro scale.

The trade-offs you must accept

1. Rotor stress rises fast

Centrifugal stress scales with radius squared times speed squared. Because the exit radius is larger, for the same rpm the rim stress at the outlet can be high. You will likely need to reduce rpm or thicken the rim and choose a stronger alloy.

2. Efficiency headroom

Best-in-class efficiencies are usually achieved by axial or radial-inflow layouts with good recuperation. Outflow rotors often suffer higher losses from turning and diffusion and can leave more swirl to clean up in the diffuser. Expect a few percentage points lower peak efficiency unless you invest heavily in optimization.

3. Bigger diameter hardware

The large discharge radius pushes up tip speed for a given rpm. If you limit rim stress by lowering rpm, your specific power may drop unless you add stages or increase temperature.

4. Diffuser and volute design becomes critical

You must recover kinetic energy at a large radius without separation. That adds length and some pressure-loss risk.

When radial outflow helps in practice

Very small machines where sCO2 makes axial or radial-inflow passages too tiny to manufacture or to seal reliably.

Moderate pressure ratios per stage, where the natural area growth of outflow can match the volumetric expansion without extreme blade heights.

Applications that value robustness and manufacturability over absolute peak cycle efficiency.

When to stay with axial or radial-inflow

If you can manufacture small passages and control tip clearances, axial or radial-inflow typically gives higher efficiency and lower rotor stress for the same rpm.

High pressure ratio or high temperature turbines aiming for maximum cycle efficiency generally favor axial or radial-inflow with strong recuperation.

Quick sizing guidance in text form

1. Pick your design point

Set inlet total pressure and temperature, outlet pressure, mass flow, and target shaft speed that respects rim stress at the largest radius.

2. Set inlet radius for a reasonable blade speed

Tip Mach equals blade speed divided by speed of sound. Keep tip Mach comfortably subsonic for a first pass.

3. Size inlet throat area

Area equals mass flow divided by density times axial velocity. With dense sCO2 the inlet area will be small; make sure minimum throat is manufacturable.

4. Grow radius to meet exit area

Target exit area equals inlet area multiplied by the volumetric expansion ratio. Use area equals 2 times pi times radius times blade height to pick an exit radius that avoids extreme blade height.

5. Check rotor stress

Rim stress scales with material density times radius squared times omega squared. If stress is high, reduce rpm, reduce exit radius, or thicken the rim.

6. Balance losses

Check relative Mach numbers and diffusion factors in stator and rotor passages. Keep solidity and stagger in ranges that limit separation. Plan a well-matched vaneless or vaned diffuser at the exit.

7. Iterate with tip clearance limits

Keep tip clearance divided by chord low. If it grows, increase chord rather than shrinking the throat to an unmachinable value.

Bottom line

A radial outflow turbine can be a practical way to make sCO2 micro-turbines manufacturable by letting the flow area grow with radius as the fluid expands. Expect easier sizing at the cost of higher rotor stress, larger diameter, and typically a modest efficiency penalty compared to axial or radial-inflow designs. If your main problem is tiny throats and sealing with dense sCO2, outflow is worth prototyping. If your main goal is maximum efficiency at a given temperature and pressure ratio, start with axial or radial-inflow and only pivot to outflow if manufacturing or clearance limits force the change.

Scaling Guidelines for Converting Micro Turbines from Air to Supercritical CO2

The use of supercritical CO2 (sCO2) as a working fluid in turbines is expanding rapidly due to its compact power density and efficiency potential. However, turbine stages originally designed for air cannot be directly used with CO2. The large difference in density and thermophysical properties requires careful re-scaling. Below is a guideline for adapting a micro turbine blade designed for air into one suitable for CO2 service.

Step 1. Establish the CO2 Design Point

Define the inlet total temperature, inlet total pressure, target pressure ratio, and desired mass flow. For CO2 at 300 degrees Celsius and 200 bar, the density is about 170 kilograms per cubic meter. By comparison, air at 300 degrees Celsius and 1 bar has a density of about 0.6 kilograms per cubic meter. This means CO2 is nearly 300 times denser than hot air.

Step 2. Preserve Similarity Parameters

To maintain aerodynamic similarity, you must hold the following non-dimensional values close to the air design:

Flow coefficient = axial velocity divided by blade speed

Stage loading = enthalpy drop per stage divided by blade speed squared

Relative exit Mach number = relative velocity at rotor exit divided by speed of sound

Solidity = blade chord divided by spacing

These parameters govern turning angles, losses, and efficiency.

Step 3. Flow Area and Speed Scaling

Mass flow equals density times area times axial velocity. For a given blade speed and flow coefficient, the required area scales inversely with density.

Example:

For air at 300 C, density = 0.6 kg per cubic meter. For CO2 at 200 bar, density = 170 kg per cubic meter.

If an air turbine needed an annulus area of 0.0011 square meters to pass 0.1 kg per second, then with CO2 at the same conditions, the area would be about 0.000004 square meters for the same mass flow. This is impractically small, so in practice you must reduce mass flow, reduce blade speed, or increase flow coefficient.

Step 4. Torque and Shaft Loading

Stage work equals stage loading multiplied by blade speed squared. Power equals mass flow times stage work. Torque equals power divided by rotational speed.

Because CO2 is so much denser, the same volumetric flow produces far more torque. Shafts, bearings, and gearboxes must be re-rated or the turbine speed must be reduced to keep torque manageable.

Step 5. Reynolds Number and Losses

Reynolds number equals density times velocity times characteristic length divided by viscosity. For CO2, density rises much more than viscosity, so Reynolds numbers are far higher than in air. This reduces profile losses but makes tip leakage and secondary flow losses dominant. Blades should be made thicker and with careful tip clearance design to avoid efficiency penalties.

Step 6. Tip Speed and Mach Numbers

The speed of sound in CO2 at 300 C is about 300 to 350 meters per second, compared to 500 to 600 meters per second in air. This means the same tip speed produces a higher Mach number in CO2. Designers must lower the rotational speed or increase throat areas to prevent choking and shock formation.

Step 7. Heat Transfer and Materials

Supercritical CO2 has higher thermal conductivity and specific heat than air. Blade and endwall surfaces will experience higher heat flux. Nickel-based alloys or stainless steels are recommended at turbine inlet temperatures above 500 C. Cooling designs may need resizing because CO2 alters coolant effectiveness.

Step 8. Seals and Bearings

High-pressure CO2 requires special seals and bearing designs. Elastomers must be resistant to rapid gas decompression, and PTFE or metallic seals are preferred. Dry gas seals and gas bearings are used in many sCO2 projects.

Example Mini Case

An air stage at 300 m per second blade speed with 0.5 flow coefficient and 1.0 stage loading passed 0.1 kg per second at 0.6 kg per cubic meter density. Required area was 0.0011 square meters.

At the same conditions, with CO2 at 170 kg per cubic meter, the required area would shrink to 0.000004 square meters for the same mass flow. This is not practical. Designers instead reduce blade speed, reduce mass flow, and increase passage size to ensure manufacturability.

Conclusion

Air turbine blades cannot simply be reused for supercritical CO2. Designers must account for far higher density, lower speed of sound, and increased torque. For low temperatures, condensing cycles with pumps (Rankine or ORC) are preferred, but for medium and high temperatures (above 300 C), sCO2 Brayton-type cycles with optimized blades are more efficient.

The transition requires redesign of blade passages, clearances, torque capacity, and materials. Proper scaling based on flow similarity, Mach limits, and manufacturable geometries ensures that the turbine will operate efficiently and safely with CO2 as the working fluid.

TEL: 1-608-238-6001 Email: greg@infinityturbine.com

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