Review of the development and applications of the Wiebe function: A tribute to the contribution of Ivan Wiebe to engine research

Abstract

Analytical functions approximating the burn rate in internal combustion engines are useful and cost-effective tools for engine cycle simulations. Most functions proposed to date are based on the law of normal distribution of a continuous random variable. The best known of these is the Wiebe function, which is used to predict the burn fraction and burn rate in internal combustion engines operating with different combustion systems and fuels. These include direct injection (DI) and indirect injection (IDI) diesel engines, classical spark ignition (SI) engines and gasoline direct injection (GDI) engines, engines with homogeneous charge compression ignition (HCCI) and premixed charge compression ignition (PCCI). This paper is a tribute to the lasting legacy of the Wiebe function and to the man behind it, Ivan Ivanovitch Wiebe. It includes a historical background to the development of the function in the mid 1950s in the Soviet Union, the controversy that surrounded its introduction, a description of the method used to arrive at the final formulation, and an overview of the many applications as prescriptive or predictive single-, double- and multi-function combustion models in engine research.

A review of free-piston linear engines

“…Those results are similar to those presented by Chiang et al [82]. Although many investigations have considered HCCI combustion in FPLEs, most of them used only simulations [22,24,[77][78][79][80][81][82]. To further understand HCCI combustion under real conditions, experimental studies need to be conducted.…”

“…To obtain successful HCCI combustion in an FPLE, a simplified model and cycle-tocycle coupling between piston motion and the combustion process need to be proposed. In control-oriented HCCI investigations, the single-Wiebe function can predict HCCI combustion [80][81][82]. One limitation of the single-Wiebe function is that it does not well predict combustion during the premix phase, as shown with a dieselfueled engine [80].…”

“…In control-oriented HCCI investigations, the single-Wiebe function can predict HCCI combustion [80][81][82]. One limitation of the single-Wiebe function is that it does not well predict combustion during the premix phase, as shown with a dieselfueled engine [80]. However, for gaseous engines (e.g., propanefueled engines), the single-Wiebe function seems to be the most useful option to fill the need in engine research for a simple combustion model with high computational efficiency.…”

Determination of Combustion Process Model Parameters in Diesel Engine with Variable Compression Ratio

“…In this paper is described the methodology of modelling combustion process, with purpose to see how the working regimes and (CR) value affect double Vibe function parameters [24]. If operation process of diesel engine with DI and premixed combustion is modeled, the use of double Vibe function is necessary [5].…”

An assessment of thermodynamic merits for current and potential future engine operating strategies

“…More accurate representation of the heat release rate can be achieved with techniques such as the Wiebe function, which requires the specification of shape parameters calculated by fitting experimental data, or in the case of diesel combustion requires the superposition of multiple Wiebe functions to accurately capture the shape. 32 Both these requirements remove the ability to make a priori predictions of thermal efficiency from a first-principles basis. As shown in Figure 10, the particulars of the shape of the heat release profile have relatively little impact on the overall efficiency prediction, provided that CA50 and CA25-75 are matched.…”