If I need a very small heat engine, should I consider external combustion?

Question

In internal combustion heat engines, there is no heat transfer through walls required between the source of heat and the expanding medium. With an external combustion system, we heat the expanding medium by transferring heat through the walls of some type of enclosure such as a boiler or cylinder. The boundary layer of a gas doesn't transfer heat very fast. But for the external combustion case, consider what happens if we build larger or smaller versions of the same engine design.

Assume a scale factor $\alpha$ times each length dimension. It would appear that the ratio of surface area divided by enclosed volume varies by $\frac{1}{\alpha}$. Then the time required to heat a given volume of expanding medium is changed by a factor alpha. Take $\alpha = 0.1$, then you have ten times the area heating a volume of medium.

I can picture an empty saucepan on a hot stove. Dump in a quart of water. After awhile it will heat up. Compare to the case of dropping a single drop of water which sizzles into steam.

Now, bear with me a moment while I picture the time required to heat the gases in an IC engine at time of combustion as being fast, something like the width dimension divided by the speed of sound in the compressed gas. If I take alpha as smaller and smaller, the external combustion case (boiler) gets faster and faster. How small do we have to get before we are heating our volume of gas through the wall at speeds comparable to the IC case? Yes, I know about choking in compressible fluid flow, but small pipes may not be needed in our external engine design.

Question #1: If I need a very small engine, should I consider external combustion? Let's say I'm willing to trade some power to mass ratio to get quiet operation.

Question #2: Should I consider ganging multiple scaled-down external combustion engines to get the advantages like quiet operation, self-starting, etc. to get any required power?

As a background comment, note the following regarding IC engine size scales:

In their book "On Size and Life", 1983, Scientific American Books, Inc., pp. 60-65, Thomas A. McMahon and John Tyler Bonner compare commercial IC engines from the smallest to the largest. They note that larger power users such as planes and ships use multiple cylinders per engine and multiple engines per vehicle, partly because "the requirements of cooling apparatus are relatively more expensive, both in subtracted power and added mass, the larger the engine becomes". I believe this is because of the difficulty of cooling the cylinders having smaller and smaller surface area available per unit volume as size increases. They note that 757,778 Webra Speedys have the same mass as one huge marine engine, yet would have about 12 times the power if you could somehow link them together. It's 3.33 hp/kg for the model airplane engine, 0.27 hp/kg for the giant diesel.

Answer 1

I have done a lot of work with small sterling heat engines. While decreasing the size generally does have a favorable effect on your heat transfer, your energy density doesn't increase substantially over the feasible range. Other issues come into play, like being able to fabricate an engine that small while keeping internal friction low. Also your cylinder head area to cylinder ring circumference ratio decreases; yielding a lower efficiency cylinder.

For increasing sterling engine power density, I usually added fins to the inside and outside of the heat transfer wall to increase the surface area without shrinking the parts to impractical sizes.

A heat engine is not going to match the power density of an internal combustion engine (unless you switch to exotic materials and run very high temperatures perhaps). And it is certainly not the match the power density of an electric motor. A Stirling engine's niche is low-maintenance waste-heat to electrical conversion.

For portable power tools, electric is the way to go. Energy density of lithium ion is quite high, and battery technology increases every day. Electric motors have highly controllable speeds and torques, especially with brushless dc motors (variable frequency). Electric systems are also much much lower maintenance.

Answer 2

Most small external combustion engines have abysmal efficiency compared to internal combustion ones - simply, most of heat is vented without ever getting transferred to the working gas/liquid. They are so inferior, you'll be considerably better off with an electric engine instead.

You only use a tiny combustion engine if you really need considerable torque and excellent mass efficiency - and even that to a degree; model airplane engines are about as small as you can reasonably get (and they are awfully loud), and slowly losing to electric anyway. Anything smaller will lose to electric due to overhead of structural/mechanics/friction.