Previous efforts aimed at increasing the efficiencies of systems where a piston engine serves as a primary work producer have led to interest in operating direct-injection, compression-ignition (DI/CI) engines at overall stoichiometric or fuel-rich equivalence ratios. In order to extend the current understanding of DI/CI combustion to applications in this regime, a phenomenological model is proposed. The model builds on previous conceptual and phenomenological models that describe steady, reacting free jets and applies the underlying concepts to a spatially confined, transient system. The model is assessed in its ability to describe and interpret experimental data through comparisons to experimental data collected in this regime, with a particular focus on its ability to address the observed trends in exhaust gas species concentrations. Through this comparison to experimental data, potential insights provided by the model are discussed.