Direct numerical simulation of a turbulent boundary layer up to Re h = 2500 Jae Hwa Lee, Hyung Jin Sung ⇑ Department of Mechanical Engineering, KAIST, 335 Gwahangno, Yuseong-Gu, 305-701, Republic of Korea article info Article history: Received 30 June 2010 Received in revised form 6 October 2010 Accepted 1 November 2010 Available online 24 November 2010 Keywords: Turbulent boundary layer Direct numerical simulation abstract Direct numerical simulations (DNSs) of a turbulent boundary layer (TBL) with Re h = 570–2560 were performed to investigate the spatial development of its turbulence characteristics. The inflow simulation was conducted in the range Re h = 570–1600 by using Lund’s method. To resolve the numerical periodicity induced by the recycling method, we adopted a sufficiently long streamwise domain of x/h in,i = 1000 (=125d 0,i ), where h in,i is the inlet momentum thickness and d 0,i is the inlet boundary layer thickness in the inflow simulation. Furthermore, the main simulation with a length greater than 50d 0 was carried out independently by using the inflow data, where d 0 is the inlet boundary layer thickness of the main simulation. The integral quantities and the first-, second- and higher-order turbulence statistics were compared with those of previous data, and good agreement was found. The present study provides a use- ful database for the turbulence statistics of TBLs. In addition, instantaneous field and two-point correla- tion of the streamwise velocity fluctuations displayed the existence of the very large-scale motions (VLSMs) with the characteristic widths of 0.1–0.2d and that the flow structure for a length of approxi- mately 6d fully occupies the streamwise domain statistically. Ó 2010 Elsevier Inc. All rights reserved. 1. Introduction The spatial characteristic of TBLs is an important issue in many fluid dynamics engineering applications and many challenges re- main in theory, scaling, physical understanding, experimental techniques, and numerical simulations (Marusic et al., 2010a). Although the characteristics of TBLs have been the subject of numerous experimental and numerical studies, significant discrep- ancies remain in the profiles of all mean and fluctuating turbulence components even at very similar Reynolds numbers due to varia- tions in the experimental set-up and the numerical schemes as well as in the prescription of the inflow boundary conditions. Honkan and Andreopouloos (1997) compared the turbulence sta- tistics of TBLs obtained in several numerical and experimental studies and found that no consistent trend in the Reynolds stress components in the near-wall regions of TBLs. Very recently, Schlat- ter and Örlü (2010b) assessed the direct numerical simulation (DNS) datasets for spatially developing turbulent boundary layers through the analysis of both basic integral quantities and mean and fluctuation profiles. They found that the numerical simulation of TBLs is very sensitive to, e.g. proper inflow condition, sufficient settling length and appropriate box dimensions, and hence a DNS has to be considered as a numerical experiment governed by the chosen simulation set-up (Kasagi and Shikazono, 1995). For further progress in the investigation of these characteristics of TBLs, it is required the availability of accurate and reliable high-resolution DNS data for spatially developing TBLs with various numerical set-up such as inflow boundary condition, box dimensions and others. To date, DNSs of TBLs have provided complete time-dependent and spatial information for the study of the mechanisms of wall turbulence, albeit at relatively low Reynolds numbers. Wu and Moin (2009) simulated a nominally-zero-pressure-gradient boundary layer over a smooth flat plate developing from transition to turbulent flow in the range 80 6 Re h 6 940. They showed that a preponderance of hairpin-shaped coherent structures is observed in both the latter parts of the transition process and in the fully tur- bulent state. This simulation is valuable in that the flow evolves from a laminar Blasius boundary layer, undergoes a bypass transi- tion, and reaches a fully turbulent state. However, these numerical results obtained from DNSs of TBLs are confined to Reynolds numbers that are low relative to those of turbulent channel flows (Hoyas and Jimenez, 2006). The main reason for this restriction is that the characteristics along the streamwise direction of spatially developing TBLs prohibit the usage of periodic boundary condi- tions downstream. In a turbulent channel flow, the flow does not evolve spatially and therefore, spectral algorithms can be applied in the streamwise and spanwise directions, which enable highly efficient computation. The methods of Wu and Moin (2009) and others describe the boundary conditions at the inlet and the outlet in a TBL by using laminar boundary layer profiles and convective boundary conditions, and then the laminar boundary layer rapidly becomes a turbulent flow with a sufficiently strong finite 0142-727X/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.ijheatfluidflow.2010.11.001 ⇑ Corresponding author. Tel.: +82 42 350 3027; fax: +82 42 350 5027. E-mail address: hjsung@kaist.ac.kr (H.J. Sung). International Journal of Heat and Fluid Flow 32 (2011) 1–10 Contents lists available at ScienceDirect International Journal of Heat and Fluid Flow journal homepage: www.elsevier.com/locate/ijhff