Zeleznik Frank J., McBride Bonnie J. Modeling the Internal Combustion Engine

NASA Reference Publication 1094. — Cleveland, Ohio: Lewis Research Center, 1985. — 309 p.A mathematical model of the internal combustion engine has been constructed and implemented as a computer program suitable for use on large digital computer systems. The model strikes a balance between three competing factors: (1) the desire for physical realism, (2) the extent of experimental information on the physical processes occurring in the engine, and (3) the capabilities of today's generation of computers. The result is a flexible and computationally economical model based on a system of ordinary differential equations for cylinder-averaged properties. The computer program is capable of multicycle calculations, with some parameters varying from cycle to cycle, and has restart capabilities that permit continuation of a sequence of cycle calculations or the recalculation of earlier cycles with altered assumptions. It can accommodate a broad spectrum of reactants, permits changes in physical properties, and offers a wide selection of alternative modeling functions without any reprogramming. It readily adapts to the amount of in-formation available in a particular case because the model is actually a hierarchy of five models of differing complexity. The models range from a simple model requiring only thermodynamic properties to a very complex one demanding full combustion kinetics, transport properties, and poppet valve flow characteristics. These five models can be defined precisely only by the governing equations. However, they can still be classified approximately according to their treatment of several important features of the internal combustion engine. This classification is shown in the accompanying table, where level 1 represents the simplest model and level 5 the most complex. The calculations are based on the premise that heat transfer is expressible in terms of a heat transfer coefficient and that the cylinder average of kinetic plus potential energies remains constant. Furthermore, during combustion the pressures of the burned and unburned gases are assumed to be equal and their heat transfer areas are assumed to be proportional to their respective mass fractions. Although the model cannot resolve spatial gradients, it does not assume spatial uniformity.
The mathematical model, the numerical techniques, and the associated computer program are all discussed in the four chapters of this report. Chapter I, "Construction of Mathematical Models of the Internal Combustion Engine," briefly summarizes the history of experimental and modeling studies of the internal combustion engine and derives the mathematical model. Chapter II, "Numerical Integration of Ordinary Differential Equations," analyzes the integration techniques used to implement the model. Chapter III, "Numerical Details and Definitions of Cycle Performance Parameters," gives the precise forms of all equations used in the computer program and defines the calculated parameters that are used as measures of cycle performance. It also defines the fresh charge to the engine and gives the representation used for the thermodynamic and transport properties. Chapter IV, "The Organization and Use of Computer Program ZMOTTO," describes program capabilities and input requirements. It presents the results of six sample calculations and briefly describes each computer program routine.