Flow over periodic hills – Numerical and experimental study in a wide range of Reynolds numbers M. Breuer a, * , N. Peller b , Ch. Rapp b , M. Manhart b a Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany b Fachgebiet Hydromechanik, Technische Universität München, D-80290 München, Germany article info Article history: Received 4 February 2008 Received in revised form 16 May 2008 Accepted 19 May 2008 Available online 28 May 2008 abstract The paper presents a detailed analysis of the flow over smoothly contoured constrictions in a plane chan- nel. This configuration represents a generic case of a flow separating from a curved surface with well- defined flow conditions which makes it especially suited as benchmark case for computing separated flows. The hills constrict the channel by about one third of its height and are spaced at a distance of 9 hill heights. This setup follows the investigation of Fröhlich et al. [Fröhlich J, Mellen CP, Rodi W, Temm- erman L, Leschziner MA. Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J Fluid Mech 2005;526:19–66] and complements it by numerical and experimental data over a wide range of Reynolds numbers. We present results predicted by direct numerical simulations (DNS) and highly resolved large-eddy simulations (LES) achieved by two com- pletely independent codes. Furthermore, these numerical results are supported by new experimental data from PIV measurements. The configuration in the numerical study uses periodic boundary condi- tions in streamwise and spanwise direction. In the experimental setup periodicity is achieved by an array of 10 hills in streamwise direction and a large spanwise extent of the channel. The assumption of peri- odicity in the experiment is checked by the pressure drop between consecutive hill tops and PIV mea- surements. The focus of this study is twofold: (i) Numerical and experimental data are presented which can be referred to as reference data for this widely used standard test case. Physical peculiarities and new findings of the case under consideration are described and confirmed independently by different codes and experimental data. Mean velocity and pressure distributions, Reynolds stresses, anisotropy- invariant maps, and instantaneous quantities are shown. (ii) Extending previous studies the flow over periodic hills is investigated in the wide range of Reynolds numbers covering 100 6 Re 6 10; 595. Starting at very low Re the evolution and existence of physical phenomena such as a tiny recirculation region at the hill crest are documented. The limit to steady laminar flow as well as the transition to a fully turbu- lent flow stage are presented. For 700 6 Re 6 10; 595 turbulent statistics are analyzed in detail. Carefully, undertaken DNS and LES predictions as well as cross-checking between different numerical and experi- mental results build the framework for physical investigations on the flow behavior. New interesting fea- tures of the flow were found. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction 1.1. Case definition The prediction of flow separation from curved surfaces and sub- sequent reattachment is complicated by several phenomena including irregular movement of the separation and reattachment lines in space and time, strong interactions with the outer flow, transition from a boundary layer type of flow to a separated shear layer with failure of the law-of-the wall and standard model assumptions for either attached flows or free shear layers. The improvement of flow prediction by Reynolds-averaged Navier– Stokes (RANS) simulation or large-eddy simulation (LES) in such flows is dependent on reliable data of generic test cases including the main features of the respective flow phenomena. The flow over periodically arranged hills in a channel as proposed by Mellen et al. [33] has been used as benchmark test case since it represents well- defined boundary conditions, can be computed at affordable costs and nevertheless inherits all the features of a flow separating from a curved surface and reattaching on a flat plate. The geometry of the test case is shown in Fig. 1. The dimensions of the domain are L x ¼ 9:0h, L y ¼ 3:036h, and L z ¼ 4:5h, where h denotes the hill height. In order to motivate why this case is especially useful for basic investigations of the performance of turbulence models – not only subgrid-scale (SGS) models but also statistical models in the RANS 0045-7930/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compfluid.2008.05.002 * Corresponding author. Fax: +49 9131 852 9579. E-mail addresses: mbreuer@lstm.uni-erlangen.de (M. Breuer), n.peller@bv. tum.de (N. Peller). Computers & Fluids 38 (2009) 433–457 Contents lists available at ScienceDirect Computers & Fluids journal homepage: www.elsevier.com/locate/compfluid