Thermodynamic Characterization Of Engine Exhaust Flows For Recovering Waste Exhaust Energy (Exergy)

The heavy-duty engine industry in the United States faces a difficult challenge in demonstrating engine technologies to achieve 55% brake thermal efficiency (BTE) for future heavy-duty diesel engines under the aegis of the US Department of Energy’s ongoing SuperTruck II program (US DOE, 2017).  BTE is a measure of the conversion of the fuel’s chemical energy to useful power at the engine shaft.  As part of the portfolio of strategies being considered to enable high BTE operation, various advanced low-temperature combustion strategies and waste energy recovery (WER) are significant.

As researchers work hard to squeeze every last percentage point of BTE of the internal combustion (IC) engine, it becomes increasingly important to either prevent or to recover the fuel’s chemical energy that is wasted.  Two major contributors to engine inefficiency include energy transferred in the form of heat transfer to the engine coolant and energy lost with hot exhaust gases that exit through the engine exhaust manifold.  Strictly speaking, it is not the energy that is important here, but the usable portion of the energy, technically called “exergy,” which is always defined with respect to an environment (known, somewhat dramatically, as the “dead state,” which by definition has zero exergy) (cf. Bejan, 2016).

“Global” exergy analyses of engine processes have been used previously to quantify the fractions of the fuel’s chemical exergy that are lost due to irreversible processes (most “real” energy conversion processes are “irreversible”).  Exergy destruction occurs in the combustion process and exergy is also lost with heat transfer to the coolant and with exhaust gas flows out of the engine.  Global exergy analyses provide percentage-wise distribution of exergy in various channels, thus identifying the sources of irreversibilities.  However, more detailed information is needed to reduce exergy destruction from these various sources.  For example, it is necessary to quantify time (or crank angle) -resolved exergy flows in engine exhaust to determine how to extract useful work but no previous study has examined this important aspect of exergy flows in exhaust gases.

Recently, Mahabadipour et al. (2018) performed the first characterization of crank angle-resolved exergy flows in the exhaust of a diesel engine from the perspective of exhaust WER.  In this work, the authors introduced a novel methodology that leveraged experimental high-speed exhaust pressure measurements with system-level engine simulations to calculate crank angle-resolved exhaust exergy.

They also presented the first results that quantify the thermal (i.e., due to temperature) and mechanical (due to pressure) components of exhaust exergy as well as the exergy apportionment between different temporal phases of the exhaust process such as the “blowdown” and the “displacement” phases.  Although these results were presented only for diesel combustion in a single-cylinder research engine, the technical approach introduced in this study is applicable for determining the types of exhaust WER devices that are most appropriate for different engine configurations and operating conditions.

Figure 1. Blowdown and displacement phasing at 1500 rpm, intake pressure of 1.2 bar [Mahabadipour et al., 2018]. (Republished with permission from Elsevier)

Figure 2. Crank angle-resolved total exergy rate (Ex) and its thermal (ExTH) & mechanical (ExME) portions at 1500 rpm and intake pressure of 2 bar [Mahabadipour et al., 2018]. (Republished with permission from Elsevier)
Various approaches have been considered for exhaust WER from IC engines.  For example, turbocharging, which recovers exhaust energy using a turbine to drive a compressor to compress fresh air to the engine intake, is a well-established exhaust WER strategy.  Turbocharging, which utilizes the thermal component of exhaust exergy, is ubiquitous in modern diesel engines and also becoming increasingly common in spark ignition engines.

Another exhaust WER strategy that recovers the thermal component of exhaust exergy utilizes an organic Rankine cycle (ORC)-based “bottoming cycle.”  In essence, ORC-based bottoming cycles are very similar to Rankine cycles utilized in thermal power plants except that ORC cycles employ organic working fluids (e.g., refrigerant mixtures) instead of steam.  In contrast to turbocharging and ORC cycles, other “direct” WER devices (e.g., positive displacement expanders) endeavor to directly utilize the mechanical component of the exhaust exergy.

In summary, Mahabadipour et al. provide a systematic approach, firmly rooted in fundamental thermodynamic principles, for engine designers to determine the best possible ways to recover exhaust exergy for a variety of engines and operating conditions to achieve potentially significant efficiency improvements.

These findings are described in the article entitled Crank angle-resolved exergy analysis of exhaust flows in a diesel engine from the perspective of exhaust waste energy recovery, recently published in the journal Applied Energy. This work was conducted by Hamidreza Mahabadipour, Kalyan Kumar Srinivasan, and Sundar Rajan Krishnan from the University of Alabama and Swaminathan Subramanian from Eaton Corporate Research and Technology.


  1. Bejan, A. (2016).  Advanced Engineering Thermodynamics, 4th Edition, Wiley, ISBN 978-1119052098
  2. Mahabadipour, H., Srinivasan, K.K., Krishnan, S.R., Subramanian, S. (2018).  Crank angle-resolved exergy analysis of exhaust flows in a diesel engine from the perspective of exhaust waste energy recovery.  Applied Energy, 216, 31-34, (
  3. US DOE (2017).  SupertTruck II, Vehicle Technologies Office Program Wide Selections to Accelerate the Development of Innovative Technologies; (accessed April 2, 2018)

About The Author

Sundar Krishnan

Sundar Rajan Krishnan is an associate professor at the University of Alabama in the Department of Mechanical Engineering. His research include: Internal Combustion Engines, Advanced Combustion Strategies, Alternative Fuels, Thermodynamic Simulations, and Waste Energy Recovery. He received his Ph.D. in mechanical engineering from the University of Alabama in 2005.

Speak Your Mind!


Gut Microbiota From Cradle To Grave: Does Age Or Lifestyle Matter More?

None of us need FaceApp to know the broad strokes of what will happen when we grow older: a few more wrinkles, a few more grey hairs, a little less muscle strength — accompanied, of course, by a lot more wisdom. A lesser-known change that occurs with age has to do with the gut microbiota […]

Algal Turf Scrubbing: Creating Helpful, Not Harmful, Algal “Blooms”

Thanks to the “green revolution,” food has never been cheaper or more abundant. Ironically, high-performance agriculture threatens our future ability to feed ourselves. Agriculture requires so much nitrogen and phosphorus fertilizer that it damages our soils, and the excess fertilizer pollutes local waters and the oceans, causing harmful algal blooms and extensive dead zones, threatening […]

Yellow Aesthetic: Why We’re Drawn To The Color Yellow

The yellow aesthetic is naturally appealing to people around the world. For whatever reason, humans can be drawn to specific colors such as red, blue, and even yellow, and the reason might be for the sheer reason that it elicits a specific emotion or mood. These colors grab your attention, they stand out among other […]

The Milky Way Galaxy’s Global Order And Mirror-Image Symmetry, Co-Rotation Radius, And The Local Incoming Mass

Can we “slice” a spiral arm into its components and order the slices? The Moon orbits around the Earth on a rough circle, the Earth orbits on a rough circle around the Sun, and the Sun orbits on a rough circle around the Center of our Galaxy known as the Milky Way. Gravitation is the […]

Heterogeneous Mixture Definition

While the term “heterogeneous mixture” sounds like it could be a complicated concept, in reality, it is actually quite simple. A mixture is made up of two or more substances, and in a heterogeneous mixture, those substances are not uniformly distributed, meaning that the substances that make up the mixture can be distinguished from one another […]

Machine-To-Machine Communication: Challenges And Future Opportunities

With the advent of machine-to-machine communication, the autonomous communication of smart devices will likely be a part of the human ecosystem/society in the coming years. Specifically, machines will interact to make a “smarter society,” where they can intelligently send messages for the actualization of various operations under our very eyes. This has interesting implications. Among others, doctors can get […]

Is NH3 Polar Or Nonpolar?

Ammonia, chemical formula NH3, is a colorless gas frequently used in the production of fertilizer, as a cleaning chemical, and in the creation of nitrogenous compounds. You might be wondering, is ammonia a polar molecule or nonpolar molecule? The answer is that ammonia is a polar molecule, with its polarity being influenced by its asymmetrical […]