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

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.