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A one-dimensional, non-equilibrium, compressible law of the wall model is proposed to increase the accuracy of heat transfer predictions from computational fluid dynamics (CFD) simulations of internal combustion engine flows on engineering grids. Our 1D model solves the transient turbulent Navier-Stokes equations for mass, momentum, energy and turbulence under the thin-layer assumption, using a finite-difference spatial scheme and a high-order implicit time integration method. A new algebraic eddy-viscosity closure, derived from the Han-Reitz equilibrium law of the wall, with enhanced Prandtl number sensitivity and compressibility effects, was developed for optimal performance. Several eddy viscosity sub-models were tested for turbulence closure, including the two-equation k-epsilon and k-omega, which gave insufficient performance.

Diesel piston bowl geometry can affect turbulent mixing and therefore it impacts heat-release rates, thermal efficiency, and soot emissions. The focus of this work is on the effects of bowl geometry and injection timing on turbulent flow structure. This computational study compares engine behavior with two pistons representing competing approaches to combustion chamber design: a conventional, re-entrant piston bowl and a stepped-lip piston bowl. Three-dimensional computational fluid dynamics (CFD) simulations are performed for a part-load, conventional diesel combustion operating point with a pilot-main injection strategy under non-combusting conditions. Two injection timings are simulated based on experimental findings: an injection timing for which the stepped-lip piston enables significant efficiency and emissions benefits, and an injection timing with diminished benefits compared to the conventional, re-entrant piston.