The goal of this theoretical-experimental work is to model two-dimensional, unsteady (and steady) two phase flow combustion in internal combustion engines (and steady reactors) and to test and improve the model with parallel experimental programs. The purpose of this research is to make more detailed current understanding of this important family of combustion problems and to aid the development of cleaner and more efficient engines. In this paper, preliminary theoretical-experimental results of our efforts toward the stated goal are presented. The theoretical results are preliminary but prove the feasibility of detailed computations of combustion in internal combustion engines and show how informative such computations can be.In a section of this paper, preliminary results are reported of detailed computations of two-dimensional, unsteady sprays penetrating and vaporizing into an inert gas in a closed volume (without combustion). In a second section, preliminary results are given of detailed computations of an unsteady, two-dimensional fuel jet mixing and reacting with an oxidizer in the presence of an inert gas in a closed volume. In a third section, a closely controlled experimental program on a single cylinder reciprocating engine is described which is designed to yield detailed measurements of the calculated quantities.The above three topics are considered in the same paper for the following three reasons. All the theoretical results are intermediate steps toward the formulation and solution of a comprehensive model for two-phase, two-dimensional, unsteady, reactive turbulent flows. The experimental engine configurations have been purposely selected to match very closely those considered in the theoretical computations. These authors put great emphasis on the need and usefulness of matching detailed theoretical and experimental studies of this family of complex combustion problems.