Advanced Combustion Engines

Christopher Goldenstein
December 9, 2011

Submitted as coursework for PH240, Stanford University, Fall 2011


In 2009, the United States' transportation sector consumed 13.3 million barrels of oil (558.6 million gallons) each day. This is equivalent to consuming nearly 1 million gallons of oil every 2.5 minutes and represents 70% of the total oil consumed by the US. [1] With national goals of reducing greenhouse gas emissions and dependence on foreign oil, it is obvious that improving the efficiency of combustion engines used in the transportation industry is a goal of utmost importance. This paper will focus on the fundamental problem restricting the efficiency of such engines and a discussion of the potential efficiency gains Homogenous Charge Compression Ignition (HCCI) engines and Pulsed Detonation Engines (PDEs) may bring to the transportation industry.

The Efficiency Problem

A point of criticism regarding combustion engines, is that they are inefficient. For example, advanced internal combustion engines found in modern automobiles have peak thermal efficiencies around 35-40% for gasoline and 40-45% for diesel. Massive marine diesel engines are capable of thermal efficiencies over 60%, however, these engines are exceptional in this regard. With this said, most people wonder why engineers cannot design much more efficient engines.

The problem at hand is that the 2nd law of thermodynamics limits the efficiency of all combustion engines. In 1824 Sadi Carnot showed that the most efficient cycle for a heat engine is one that does not generate entropy. The simplest and perhaps most confusing definition of entropy is that it is a metric for quantifying the chaos of a system, defined by Boltzmann's constant multiplied by the natural log of a system's multiplicity. For macroscopic systems, it is more appropriate to think of entropy as a thermodynamic quantity that describes the energy required to arrange an isolated, non-reacting system of particles into their equilibrium state. As a result, any process that generates entropy reduces the amount of energy that can be extracted from a system as useful work. Carnot showed that the maximum efficiency of such a heat engine is:

nth = 1 - TC/TH

where nth is the thermal efficiency, TC is the temperature of the cold reservoir and TH is the temperature of the hot reservoir. With typical combustion engines operating between 1750°K and 298°K, this equation states that the maximum efficiency for such an engine is 83%. Suddenly marine diesels with 60% efficiency look pretty good.

Carnot's efficiency limit represents the holy grail of engine design and it will never be reached in practice because all combustion engines generate entropy via friction, chemical mixing, heat transfer across finite temperature gradients, and the combustion process itself to name only a few mechanisms. With this said, the goal of every engine designer is to develop an engine that minimizes entropy generation.

Engines that Fight the 2nd Law

Many different engine cycles attempting to reduce entropy generation have been proposed, however, this paper focuses on two that have received recent attention in academia and industry: HCCI engines and PDEs.


HCCI engines are an attractive type of internal combustion engine that offer potential for improved efficiency and reduced emissions. In this device, fuel and air are mixed upon entering the cylinder and compressed until autoignition occurs. HCCI combustion occurs almost instantaneously as it is limited by chemical kinetics and not flame front propagation or fuel-air mixing as is the case in spark ignited (SI) and diesel engines respectively. As a result, HCCI engines are typically mechanically limited to very lean mixtures (low loads) to reduce the severity of the rapid and violent ignition event. [2]

Since the entire mixture ignites near simultaneously, HCCI engines are not limited by destructive engine knock and can therefore operate at diesel like compression ratios ( CR > 15 ). [2] This is a significant design improvement over conventional SI engines because engine efficiency increases as the compression ratio increases. For example, the thermal efficiency of an ideal Otto Cycle improves from 47% to 56% when the compression ratio is raised from 8 to 15. In addition, by operating lean, the working fluid in HCCI engines has a higher ratio of specific heats which also leads to larger thermal efficiency. Lastly, HCCI engines do not throttle the intake mixture and thus, do not pay a throttling work penalty.


PDEs offer potential as a more efficient propulsion engine for aircraft. PDEs usually consist of detonation tube acting as the combustor that is coupled to some type of work extraction device (e.g. a nozzle or turbine). A spark ignition system is used to initiate a flame which propagates down the tube until undergoing deflagration to detonation transition (DDT) at which point a supersonic detonation wave traverses the remainder of the tube, shock heating and compressing the remaining fuel-air mixture. As a result, the majority of the fuel is burned behind a detonation wave at an elevated ignition temperature and pressure. The high temperature and pressure combustion gases are then expanded to produce thrust.

From an ideal cycle analysis assuming calorically perfect ideal gases Roy et al. showed that an air-ethylene detonation cycle had a thermal efficiency of 45.2% compared to 43.5% and 31.5% for a Humphey and a Brayton cycle with the same compression ratio. [3] This analysis suggests that a PDE cycle has potential to be 43% more efficient than the Brayton cycle which is a simplified gas turbine cycle model. Critics of PDEs question whether or not the efficiency gains suggested by this elementary analysis are realizable, however, researchers continue to study these engines.


In short, significant emphasis has been placed on the development of combustion based engines with improved efficiency that consume conventional hydrocarbon based fuels. These engines attempt to minimize thermodynamically irreversible losses that have plagued combustion engines for decades. However, while these engines have potential for increased efficiency, they are extraordinarily complex. The analysis put forth here is grossly simplified and only useful for understanding the first principles involved. The nuances governing the ignition processes in both of these engines are not well understood and mastering the development of these engines will require advances in the current understanding of material science, turbulence, quantum chemistry, and optical diagnostics used to study these engines.

© 2011 Christopher Goldenstein. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] "Transportation Statistics Annual Report 2010," U.S. Department of Transportation, 2011.

[2] F. Zhao et al., eds., Homogenous Charge Compression Ignition (HCCI) Engines, (Soc. Automotive Engineers Inc., 2003).

[3] G. D. Roy et al., "Pulsed Detonation Propulsion: Challenges, Current Status, and Future Perspective," Prog. Energy Combustion Sci. 30, 545 (2004).