Computers and Fluids 194 (2019) 104314 Contents lists available at ScienceDirect Computers and Fluids journal homepage: www.elsevier.com/locate/compfuid Direct numerical simulation of incompressible turbulent boundary layers and planar jets at high Reynolds numbers initialized with implicit large eddy simulation Tomoaki Watanabe ∗ , Xinxian Zhang, Koji Nagata Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan a r t i c l e i n f o Article history: Received 22 June 2019 Revised 9 September 2019 Accepted 24 September 2019 Available online 25 September 2019 Keywords: Turbulent boundary layer Turbulent jet Direct numerical simulation Implicit large eddy simulation a b s t r a c t 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 de- velops 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 fluc- tuations, 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 apply- ing the ILES at the transitional flow region in the DNS of turbulent shear flows at high Reynolds numbers. © 2019 Elsevier Ltd. All rights reserved. 1. Introduction Turbulence is an important phenomenon in fluid dynamics, and it has been studied with theories, experiments, and numerical sim- ulations [1,2]. A direct numerical simulation (DNS) that numeri- cally solves Navier–Stokes equations without turbulence models is frequently used for studying turbulence. The DNS can provide reli- able three-dimensional flow data, which is difficult to obtain in ex- periments. The DNS needs to resolve all length scales in turbulent flows from the largest to the smallest. The characteristic length scale of the smallest scale of turbulent motions is the Kolmogorov length scale η, which decreases with Reynolds number. Therefore, the number of grid points used in the DNS, N, increases with the Reynolds number [2] as N ∼ Re 9/4 . The DNS of turbulence at high Reynolds number is of great interest in turbulence researches. As ∗ Corresponding author. E-mail address: watanabe.tomoaki@c.nagoya-u.jp (T. Watanabe). finer grid spacing is required at higher Reynolds number, the com- putational cost of DNS also increases with the Reynolds number. The DNS has been used to study transitional turbulent flows, such as mixing layers, boundary layers, and jets [3–5], where an initially laminar flow develops into turbulence. These simulations are often used to investigate a fully-developed turbulent region. For examples, statistics are often discussed in the self-similar re- gion of free shear flows based on the DNS [3,6]. However, an im- portant fraction of the computation time is spent for simulating the initial transitional region. For reducing the computational cost of DNS, some previous studies have combined a large eddy sim- ulation (LES) with the DNS. Because the LES does not have to re- solve small-scale motions, whose influences are modeled by sub- grid scale (SGS) models, larger grid spacing can be used in the LES compared with the DNS. Cifuentes et al. [7] conducted hy- brid LES/DNS of turbulent jet flame, where the LES was used in the regions close to the nozzle and the outflow boundary while a flow region of interests was simulated with the DNS. Hence, the LES was used to provide an inflow boundary condition of the https://doi.org/10.1016/j.compfluid.2019.104314 0045-7930/© 2019 Elsevier Ltd. All rights reserved.