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This paper provides an analysis of high-pressure phenomena and its potential effects on the fundamental physics of fuel injection in Diesel engines. In particular, we focus on conditions when cylinder pressures exceed the thermodynamic critical pressure of the injected fuel and describe the major differences that occur in the jet dynamics compared to that described by classical spray theory. To facilitate the analysis, we present a detailed model framework based on the Large Eddy Simulation (LES) technique that is designed to account for key high-pressure phenomena. This framework is then used to perform a thermodynamic analysis of the flow. We focus on the experiments being conducted in the high-pressure combustion vessel at Sandia National Laboratories using n-heptane as a reference fuel. The calculations are performed by rigorously treating the experimental geometry and operating conditions, with detailed treatment of relevant thermophysical mixture properties.