Direct numerical simulation of incompressible turbulent boundary layers and planar jets at high Reynolds numbers initialized with implicit large eddy simulation

Abstract

A direct numerical simulation (DNS) initialized with an implicit large eddy simulation (ILES) is performed for temporally evolving planar jets and turbulent boundary layers. In the ILES, an initial laminar flow develops into a fully developed state of the planar jet or the boundary layer. Subsequently, the DNS is started from the flow field obtained by the ILES. This hybrid ILES/DNS methodology is tested for the planar jet and boundary layer by comparing the results with full DNS started from the initial laminar flow. The ILES results used as the initial conditions of the DNS do not possess small-scale fluctuations. However, the small-scale fluctuations in the DNS grow with time and develop well within an interval of the integral time scale, where the influences of initial conditions taken from the ILES disappear for an energy spectrum of velocity fluctuations. The DNS initialized with the ILES well reproduces small-scale characteristics of turbulence, such as Reynolds number dependence of skewness and flatness of velocity derivative and energy spectrum of velocity fluctuations in the inertial subrange and viscous range. The DNS initialized with the ILES predicts well statistics dominated by large scales, such as 1st- and 2nd-order statistics and longitudinal auto-correlation function, in agreement with previous experimental and numerical studies. Reynolds number dependence of the mean velocity, root-mean-squared velocity fluctuations, Reynolds stress, shape factor, and skin friction in the turbulent boundary layers in the present DNS are consistent with previous experimental studies. These investigations confirm advantages of applying the ILES at the transitional flow region in the DNS of turbulent shear flows at high Reynolds numbers.