Theoretical limits of scaling-down internal combustion engines

Small-scale energy conversion devices are being developed for a variety of applications; these include propulsion units for micro aerial vehicles (MAV). The high specific energy of hydrocarbon and hydrogen fuels, as compared to other energy storing means, like batteries, elastic elements, flywheels and pneumatics, appears to be an important advantage, and favors the ICE as a candidate. In addition, the specific power (power per mass of unit) of the ICE seems to be much higher than that of other candidates. However, micro ICE engines are not simply smaller versions of full-size engines. Physical processes such as combustion and gas exchange, are performed in regimes different from those that occur in full-size engines. Consequently, engine design principles are different at a fundamental level and have to be re-considered before they are applied to micro-engines. When a spark-ignition (SI) cycle is considered, part of the energy that is released during combustion is used to heat up the mixture in the quenching volume, and therefore the flame-zone temperature is lower and in some cases can theoretically fall below the self-sustained combustion temperature. Flame quenching thus seems to limit the minimum dimensions of a SI engine. This limit becomes irrelevant when a homogeneous-charge compression-ignition (HCCI) cycle is considered. In this case friction losses and charge leakage through the cylinder-piston gap become dominant, constrain the engine size and impose minimum engine speed limits. In the present work a phenomenological model has been developed to consider the relevant processes inside the cylinder of a homogeneous-charge compression-ignition (HCCI) engine. An approximated analytical solution is proposed to yield the lower possible limits of scaling-down HCCI cycle engines. We present a simple algebraic equation that shows the inter-relationships between the pertinent parameters and constitutes the lower possible miniaturization limits of IC engines.