Evaluating a Tesla Disc Micro Turbine for Supercritical CO2

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Tesla Disc Turbine vs Conventional Bladed Stages

Here is a practical, engineering-focused take on whether a stacked-disc Tesla design helps compared with conventional bladed stages.

TLDR

A Tesla disc turbine can be made to run on sCO2, but the fluid’s low viscosity means you must use very small inter-disc gaps and high rim speeds to get useful shear traction.

That drives tough manufacturing tolerances, high windage losses, and significant disk stress at micro scale.

For clean, single-phase sCO2, a small bladed radial-inflow or axial stage will usually be more efficient and smaller.

A Tesla stack can make sense if you need extreme foul-tolerance, two-phase acceptance, or you want a very simple rotor with no thin blades.

How a Tesla turbine produces torque

A Tesla rotor transfers momentum through boundary-layer shear instead of pressure forces on blades. Useful traction scales with dynamic viscosity times shear area times velocity gradient across the gap.

Very simple scaling:

Shear stress tau is roughly mu times dv/dy.

For a gap g and a disk surface speed U, the average shear scales like mu times U divided by g.

Torque per disk scales like shear stress times wetted area times radius.

Implication: to get high torque with a low-viscosity working fluid like sCO2 you must make g very small and U large, or stack many discs to increase wetted area.

What sCO2 properties mean for a Tesla rotor

Density: high, typically 80 to 250 kg per cubic meter for 300 C and 100 to 300 bar.

Viscosity: relatively low, often of order 0.05 to 0.08 mPa s near 300 C.

Speed of sound: lower than air at the same temperature, roughly 300 to 350 m per second.

Result: low viscosity hurts boundary layer traction; high density increases windage loss and aerodynamic drag if clearances are generous.

Design response:

Inter-disc gaps often must be in the 0.05 to 0.3 mm range for micro hardware.

Rim speeds must be high while staying subsonic versus local speed of sound and within disk stress limits.

Pros of a Tesla disc stack for sCO2

1. Manufacturing robustness

No thin airfoils, tolerant of small erosive particles or droplets. If your loop has occasional two-phase slugs, a Tesla rotor tolerates them far better than fine blading.

2. Simple, compact rotor

A flat pack of discs is easy to assemble and balance. For very small machines, that simplicity is attractive.

3. Broad off-design tolerance

Shear-based torque falls off smoothly with flow; you often avoid sharp stall or choke.

Cons and practical hurdles

1. Efficiency headroom

For clean, single-phase working fluids, small Tesla turbines typically run well below the isentropic efficiencies of good bladed stages. Expect maybe 30 to 60 percent for careful small designs versus 70 to 85 percent for well designed micro bladed stages.

2. Tiny gaps and tight tolerances

To get traction with low viscosity sCO2 you need sub-millimeter gaps with tight parallelism. That raises cost and risks rotor rub with thermal growth.

3. Windage and case heating

High density sCO2 means large windage losses in the shroud and cavity. You often need careful shrouding, minimum leakage paths, and possibly case cooling.

4. Disk stress and speed limits

Achieving high rim speed with multiple thin discs pushes hoop stress. You will likely need high strength alloys and conservative safety factors.

5. Recuperation and cycle matching

sCO2 cycles live or die on good recuperation. A Tesla turbine causes higher pressure drops for a given power, which can hurt cycle efficiency if you are not careful with nozzle and volute design.

First-cut sizing heuristics

Use these to sanity-check a concept before detailed CFD or rig work.

1. Choose your design point

Set turbine inlet total temperature, inlet total pressure, outlet pressure, and target mass flow. Pull real-gas properties at those states.

2. Pick a target rim speed and radius

Keep tip Mach comfortably subsonic. A common first pass is U equals 0.5 to 0.7 times speed of sound at the rotor inlet state. Check disk hoop stress for your chosen alloy and thickness.

3. Gap selection

Start with g around 0.1 to 0.2 mm for micro scale. If viscosity is 0.06 mPa s and U is 150 m per second, the average shear stress order of magnitude is tau about mu times U divided by g which is 0.00006 times 150 divided by 0.0002 which is about 45 pascals. That is small per square meter; you need lots of area and many discs.

4. Disc count and diameter

Total shear area equals number of discs times two faces per disc times disc area in the active radius band. Increase disc count until the product of shear stress and area at your radius band delivers the target torque, then check pressure drop and leakage.

5. Flow path and nozzles

Most power comes from accelerating the flow in inlet nozzles then letting it spiral through the disc pack. Keep nozzle Mach number below 1 unless you intend choked operation. Avoid large secondary cavities that add windage.

6. Leakage and shrouds

Use very small tip and side gaps to limit bypass. Consider labyrinth features or close clearance rings. Every extra millimeter of leakage annulus will cost a chunk of power because sCO2 is dense.

7. Thermal and rotordynamics

Model thermal growth to keep gaps open but small at temperature. Check critical speeds with closely spaced thin discs; add spacers and stiff hubs as needed.

Back-of-envelope comparison at micro scale

Assume a few kilowatts class machine at 300 C and 150 bar inlet, expanding to 100 bar.

Bladed radial-inflow micro stage

Expect isentropic efficiency perhaps 70 percent with good manufacturing and a decent volute and diffuser. Very small throats but good cycle efficiency.

Tesla disc stack of similar diameter

Expect isentropic efficiency perhaps 40 to 55 percent if gaps are 0.1 to 0.2 mm and rim speed is high. You may recover some manufacturability and robustness, but you give up cycle efficiency.

If your primary pain with the bladed option is unmanufacturably tiny throats or debris tolerance, a Tesla stack can be the pragmatic choice. If your focus is best efficiency per kilogram or per liter, a bladed stage wins.

When a Tesla sCO2 micro turbine is worth prototyping

You expect occasional two-phase operation or fouling and want a rotor that survives.

You cannot machine or hold blade passages that a bladed micro stage requires.

You value simplicity and quick iteration more than peak efficiency.

You can accept wider power turndown at the cost of lower top efficiency.

When to stick with bladed stages

You have clean, single-phase sCO2 and can machine small passages.

You need the best cycle efficiency and smallest heat-rejection hardware.

You want lower disk stress at a given power.

Practical build notes

Disc material: high strength stainless or nickel alloys; consider shot peening.

Spacers: precision ground rings or dimples to set uniform gaps; plan for thermal expansion.

Bearings and seals: gas bearings or magnetic bearings preferred; dry gas seals; CO2-compatible elastomers rated for rapid gas decompression.

Test path: start with cold nitrogen or air to shake down rotordynamics and leakage, then move to CO2 with careful instrumentation of pressure, temperature, and vibration.

Bottom line

A Tesla disc turbine can run on supercritical CO2 and can solve specific manufacturability and robustness problems at the micro scale. The price is lower peak efficiency, tighter tolerances, and higher sensitivity to windage and stress. If your program’s constraints are dominated by tiny bladed throats and sealing, a Tesla stack is worth a prototype. If you are chasing maximum cycle efficiency and compact recuperators, a conventional bladed radial-inflow or axial stage remains the better first choice.

Evaluating a Tesla Disc Micro Turbine for Supercritical CO2

Overview

Designing micro turbines for supercritical CO2 creates unique sizing challenges. The fluid is dense and has relatively low viscosity, which can force very small flow passages in bladed stages. A Tesla disc turbine, which transfers momentum by boundary layer shear between closely spaced rotating discs, offers a simple rotor with no thin blades and good foul tolerance. This article explains when a Tesla disc stack helps, the tradeoffs you must accept, and how to size a first prototype.

How a Tesla Disc Turbine Works

A Tesla turbine uses boundary layer drag rather than pressure forces on airfoils. Flow is injected tangentially at the disc periphery through nozzles, spirals inward between discs, and exits near the hub. Torque comes from shear traction on the disc faces. With supercritical CO2, you get:

High density, which boosts available power for a given volumetric flow

Low viscosity, which reduces shear traction unless the disc gaps are very small and rim speed is high

Where a Tesla Stack Can Help

1. Manufacturability

Micro bladed turbines can demand hairline throats and tight tip clearances. A disc stack replaces airfoils with flat discs and narrow gaps, which some teams find easier to build and iterate.

2. Debris and two phase tolerance

A disc stack is generally more tolerant of droplets, fine solids, or momentary wet operation than very fine blading.

3. Smooth off design behavior

Torque tends to roll off smoothly with flow changes, avoiding abrupt stall or choke typical of some bladed cascades.

Key Tradeoffs

1. Efficiency headroom

Small Tesla turbines typically achieve lower isentropic efficiency than good bladed micro stages. As a planning band, expect about 30 to 60 percent for careful disc designs, versus about 70 to 85 percent for well executed bladed stages at similar conditions.

2. Gap and tolerance demands

To regain shear with low viscosity CO2, inter disc gaps often need to be about 0.05 to 0.3 millimeter. Holding uniform gaps across a hot rotor is nontrivial.

3. Windage and case heating

Dense CO2 increases windage losses in shrouds and cavities. The housing and seals must minimize parasitic drag.

4. Disk stress and speed limits

High rim speed is attractive for shear traction but raises hoop stress. You will need high strength alloys and conservative safety factors.

5. Pressure drop and recuperation

Tesla stages can drive higher pressure drop for a given power. Supercritical CO2 cycles depend on strong recuperation; extra drop can reduce overall cycle efficiency.

First Pass Sizing Heuristics

Use these steps to get a credible starting point before detailed CFD and rig testing. Keep all calculations in plain text so you can copy them into notes.

1. Fix the design point

Set inlet total temperature, inlet total pressure, outlet pressure, and target mass flow. Example: 300 degrees C, 150 bar to 100 bar, mass flow for desired power.

2. Choose rim speed and diameter

Keep tip Mach comfortably subsonic for CO2. A practical starting range is rim speed equal to 0.5 to 0.7 times the local speed of sound. Check hoop stress for the chosen disc thickness and alloy.

3. Select inter disc gap

Start with gap g between 0.1 and 0.2 millimeter for micro scale. Smaller gaps raise shear but increase risk of contact during thermal growth.

4. Estimate shear traction

Average shear stress approximation in plain text: shear equals viscosity times surface speed divided by gap.

Example with CO2 viscosity 0.06 milli Pascal second, surface speed 150 meters per second, gap 0.0002 meter.

Compute: 0.00006 Pascal second times 150 divided by 0.0002 equals about 45 Pascal.

Conclusion: traction per square meter is modest, so you need many discs and adequate radius to build torque.

5. Set disc count and active radius band

Total shear area equals number of discs times two faces per disc times the annular area between inlet and outlet radii. Increase disc count until shear area times average shear stress provides the target torque at your design speed.

6. Nozzle and volute

Accelerate flow in multiple small nozzles feeding the disc periphery. Keep nozzle Mach comfortably below 1 unless you intend choked operation. Balance total nozzle area with your mass flow and available pressure ratio.

7. Leakage control

Minimize bypass with close shrouds and short leakage paths. Even a small bypass annulus can waste significant power because CO2 is dense.

8. Thermal and rotordynamics

Model thermal growth so gaps remain positive at temperature. Check critical speeds for a multi disc rotor and add spacers or stiffer hubs if needed.

Materials, Seals, and Bearings

Discs and hubs: high strength stainless or nickel alloys, consider shot peening for fatigue life

Spacers: precision ground rings or tabs to set uniform gaps, account for thermal expansion

Seals: dry gas seals or PTFE and metallic combinations rated for rapid gas decompression with CO2

Bearings: gas or magnetic bearings avoid oil ingestion, otherwise isolate oil with proven CO2 compatible seals

Back of Envelope Comparison

Assume a few kilowatts class micro unit at 300 degrees C with inlet pressure around 150 bar and outlet around 100 bar.

Bladed radial inflow turbine

Isentropic efficiency around 70 percent is a reasonable target with good manufacturing, a well designed volute, and diffuser.

Tesla disc stack of similar outer diameter

Isentropic efficiency around 40 to 55 percent is a pragmatic target if gaps are 0.1 to 0.2 millimeter and rim speed is high but subsonic. Expect better manufacturability and robustness, but lower cycle efficiency.

When to Choose a Tesla Stack

Your main blocker is manufacturability or sealing of tiny bladed throats

You expect occasional two phase operation or fouling

You prioritize simplicity and fast prototyping over peak efficiency

When to Prefer Bladed Stages

You can machine and hold small passages and clearances

You need the best possible cycle efficiency and smallest heat rejection system

You want lower windage and lower rotor stresses at a given power

Practical Test Path

1. Commission with nitrogen or air at reduced pressure to verify rotordynamics and leakage

2. Move to CO2 stepwise in pressure and temperature while monitoring vibration, case temperature, and pressure drop

3. Map efficiency versus mass flow and rim speed, then iterate disc gaps and nozzle area accordingly

Conclusion

A stacked disc Tesla turbine can make a supercritical CO2 micro turbine more buildable and more tolerant of off design and debris, but it usually gives up efficiency compared to a well designed bladed stage. For programs dominated by manufacturability limits and ruggedness requirements, a Tesla stack is worth prototyping. For programs chasing maximum thermal efficiency and compact heat exchangers, a bladed radial inflow or axial stage remains the better starting point.