Direct numerical simulation (DNS) is used to study the effects of mean lateral divergence and convergence on wall-bounded turbulence, by applying uniform irrotational temporal deformations to a plane-channel domain. This extends a series of studies of similar deformations. Fast and slow straining fields are considered, leading to a matrix of four cases, all corresponding to zero-pressure-gradient (ZPG) flows along the centreplane in ducts with constant rectangular cross-sectional area but varying aspect ratio. The results are used to address basic physical and modelling questions, and create a database that allows detailed yet straightforward testing of turbulence models. Initial tests of three representative one-point models reveal meaningful differences. The extra-strain effects introduced by the matrix of fast and slow divergence and convergence are documented, separating the direct effects of the strain from the indirect ones that alter the shear rate and change the distance from the wall. Some findings are predictable, and none contradict experimental findings. Others require more thought, notably an asymmetry between the effect of convergence and divergence on the peak turbulence kinetic energy.

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A mathematical model has been introduced for determining the most advantageous conditions for parts formation when end milling operations. This model consists of a linear objective function and linear inequality constraints and takes into account the kinetics of thermal processes in the cutting zone. The equation determines the processing time was used as the objective function and constraint inequalities are related with the functional parameters and the parameters of the milling process and determines the quality of the machining.

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