Scramjet engines promise to become a next-generation revolutionary technology for aerospace applications. Some of the significant challenges in rapid development of scramjets include complex flow physics; combustion; flow-combustion interactions; propulsion air-frame integration; coupled with difficulty in producing realistic experimental conditions. The role of Computational Fluid Dynamics (CFD), therefore, is crucial in design and development of the scramjet engines. The overall innovation includes development of a comprehensive Eulerian transported PDF methods framework coupled with an efficient RANS/LES flow solvers for simulating high-speed turbulent reacting flows and an innovative chemistry acceleration module achieving up to two orders of magnitude reduction in computing times for the Eulerian TPDF framework. In Phase I feasibility of the proposed Eulerian transported PDF approaches for accurately capturing turbulence-chemistry interactions will be demonstrated and analyzed. In Phase II, we will perform additional developments in the chemistry acceleration module and the Eulerian TPDF framework, such that a comprehensive, turbulent-combustion modeling framework, for low and high-Mach number reacting flows will be available at the end of Phase II.