Second-law analyses applied to internal combustion engines operation

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Abstract

This paper surveys the publications available in the literature concerning the application of the second-law of thermodynamics to internal combustion engines. The availability (exergy) balance equations of the engine cylinder and subsystems are reviewed in detail providing also relations concerning the definition of state properties, chemical availability, flow and fuel availability, and dead state. Special attention is given to identification and quantification of second-law efficiencies and the irreversibilities of various processes and subsystems. The latter being particularly important since they are not identified in traditional first-law analysis. In identifying these processes and subsystems, the main differences between second- and first-law analyses are also highlighted. A detailed reference is made to the findings of various researchers in the field over the last 40 years concerning all types of internal combustion engines, i.e. spark ignition, compression ignition (direct or indirect injection), turbocharged or naturally aspirated, during steady-state and transient operation. All of the subsystems (compressor, aftercooler, inlet manifold, cylinder, exhaust manifold, turbine), are also covered. Explicit comparative diagrams, as well as tabulation of typical energy and exergy balances, are presented. The survey extends to the various parametric studies conducted, including among other aspects the very interesting cases of low heat rejection engines, the use of alternative fuels and transient operation. Thus, the main differences between the results of second- and first-law analyses are highlighted and discussed.

Introduction

Internal combustion engine simulation modeling has long been established as an effective tool for studying engine performance and contributing to evaluation and new developments. Thermodynamic models of the real engine cycle have served as effective tools for complete analysis of engine performance and sensitivity to various operating parameters [1], [2], [3], [4], [5], [6].

On the other hand, it has long been understood that traditional first-law analysis, which is needed for modeling the engine processes, often fails to give the engineer the best insight into the engine's operation. In order to analyze engine performance—that is, evaluate the inefficiencies associated with the various processes—second-law analysis must be applied [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. For second-law analysis, the key concept is ‘availability’ (or exergy1). The availability content of a material represents its potential to do useful work. Unlike energy, availability can be destroyed which is a result of such phenomena as combustion, friction, mixing and throttling. The relationships needed to evaluate availability content, the transports of availability and availability destruction can be found in Refs. [7], [8], [9], [10], [11], [12], [13], [14].

The destruction of availability—often termed irreversibility—is the source for the defective exploitation of fuel into useful mechanical work in a compression or spark ignition engine. The reduction of irreversibilities can lead to better engine performance through a more efficient exploitation of fuel. To reduce the irreversibilities, we need to quantify them. That is we need to evaluate the availability destructions-we need the second-law analysis [12], [17], [18].

Objectives of second-law application to internal combustion engines are:

  • To weigh the various processes and devices, calculating the ability of each one of these to produce work.

  • To identify those processes in which destruction or loss of availability occurs and to detect the sources for these destructions.

  • To quantify the various losses and destructions.

  • To analyze the effect of various design and thermodynamic parameters on the exergy destruction and losses.

  • To propose measures/techniques for the minimization of destruction and losses, to increase overall efficiency.

  • To propose methods for exploitation of losses—most notably exhaust gas to ambient and heat transfer to cylinder walls—now lost or ignored.

  • To define efficiencies so that different applications can be studied and compared, and possible improvements measured.

Many studies have been published in the past few decades (the majority during the last 20 years), concerning second-law application to internal combustion engines—one such review paper is written by Caton [19]. The present work expands considerably upon that paper, with a different philosophy and perspective, providing details about equations used for second-law application to internal combustion engines operation, i.e. state properties, basic first-law equations, fuel chemical availability, availability equations for the engine cylinder and each engine's subsystem, entropy balance equations, second-law efficiency and basic relations for the application of the second-law analysis during transient operation. It also covers all recent publications in light of new developments such as alternative fuels and transient operation. Details about the main data, i.e. engine characteristics, modeling assumptions, etc. and—in particular—the findings of each previous study are given in this paper. Tabulation of energy and availability balances is given for many types of engines, accompanied by figures showing the effect of the most important parameters on the second-law performance of internal combustion engines.

Section snippets

Availability of a system

The availability of a system in a given state can be defined as the maximum useful work that can be produced through interaction of the system with its surroundings, as it reaches thermal, mechanical and chemical equilibrium. Usually, the terms associated with thermomechanical and chemical equilibration are differentiated and calculated separately.

For a closed system experiencing heat and work interactions with the environment, the following equation holds, for the thermomechanical availability

First-law arguments used in tandem with second-law analyses of internal combustion engines2

The majority of studies concerning second-law application to internal combustion engines are based on a preceding first-law mathematical modeling of the various processes inside the cylinder and its subsystems. These will be discussed briefly as they constitute the basis for the second-law analysis.

State properties

For the evaluation of specific internal energy of species i, the following relation can be applied according to JANAF Table thermodynamic data [1], [5], [46], [47]:ui(T)=Rsi[(n=15ainnTn)+ai6T]where constants ain for the above polynomial relation can be found, for example, in Refs. [1], [5]. Two sets of data are available for constants ain, one for temperatures up to 1000 K and another for temperatures from 1000 to 5000 K. The reference temperature is 298 K. Also,hi(T)=ui(T)+RsiTThe rate of

Engine analysis: application of exergy balance to internal combustion engines

In the following subsections, the equations will be given that deal with the exergy balance applied to the engine cylinder and its subsystems in order to evaluate the various processes irreversibilities. However, the fuel chemical availability must first be defined.

Second-law or exergy or exergetic efficiencies

An efficiency is defined in order to be able to compare different engine size applications or evaluate various improvements effects, either from the first- or the second-law perspective. The second-law (or exergy or availability) efficiency also found in the literature as effectiveness or exergetic efficiency, measures how effectively the input (fuel) is converted into product, and is usually of the form [7], [8], [9], [10], [11], [12], [13], [14], [23]:ε=AvailabilityoutinproductAvailabilityin=1

Review of various parameters effect on the second-law balance of fundamental modes of steady-state, in-cylinder operation

To the best of the authors' knowledge, the first studies of internal combustion engines operation that included exergy balance in the calculations were, around 1960, the works of Traupel [62], and Patterson and Van Wylen [63]. Most of the studies, however, were published from the second half of the 80s onwards, as will be discussed in the following Subsections. The most important findings of each research group will be presented and analyzed in the following sections. By so doing, we will be

Low heat rejection engines

During the last two decades there has been an increasing interest in the low heat rejection (or sometimes loosely termed ‘adiabatic’) engine. The objective of a low heat rejection cylinder is to minimize heat loss to the walls, eliminating the need for a coolant system. This is achieved through the increased level of temperatures inside the cylinder resulting from the insulation applied to the cylinder walls [1], [2], [3], [4], [5], [33], [88], [89], [90], [91]. By so doing, a reduction can be

Review of second-law balances applied to transient operation

The transient response of naturally aspirated and turbocharged (compression ignition) engines forms a significant part of their operation and is of critical importance, due to the often non-optimum performance involved. For the diesel engines used for industrial applications, such as generators, rapid loading is required together with zero (final) speed droop for the base units, as well as rapid start-up for the stand-by ones. For other less critical (in terms of speed change) applications,

Overall-comparative results

Data and results from the analyses discussed in 7 Review of various parameters effect on the second-law balance of fundamental modes of steady-state, in-cylinder operation, 8 Review of second-law balance of other engine configurations, 9 Review of second-law balances applied to transient operation are summarized below. Table 6 summarizes the basic data of the previous research works in the field of second-law application to internal combustion engines. It includes, among other things,

Summary and conclusions

A detailed survey was presented concerning the works committed so far to the application of the second-law of thermodynamics in internal combustion engines. Detailed equations were given for the evaluation of state properties, the first-law of thermodynamics, fuel chemical availability, the second-law of thermodynamics applied to all engine subsystems and the definition of second-law efficiencies together with explicit examples.

The research in the field of the second-law application to internal

Acknowledgements

The authors would like to thank Assistant Prof D.C. Kyritsis with University of Illinois at Urbana-Champaign for his kind assistance with literature gathering, and Dr E.G. Pariotis for his valuable consultation in preparing the figures.

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