Proceedings in Applied Mathematics and Mechanics, 2 May 2008 A Complementary Numerical / Experimental Investigation on the Flow over Periodic Hills at 100 ≤ Re ≤ 10, 595 M. Breuer ∗1 , N. Peller 2 , Ch. Rapp 2 , and M. Manhart 2 1 Lehrstuhl f¨ ur Str¨ omungsmechanik, Universit¨ at Erlangen–N¨ urnberg, Cauerstr. 4, D–91058 Erlangen, Germany 2 Fachgebiet Hydromechanik, Technische Universit¨ at M¨ unchen, Arcisstr. 21, D–80290 M¨ unchen, Germany Copyright line will be provided by the publisher 1 Introduction and Objectives The paper presents a detailed analysis of the flow over smoothly contoured constrictions in a plane channel. This configuration represents a generic case of a flow separating from a curved surface with well-defined flow conditions which makes it espe- cially suited as benchmark case for computing separated flows. The setup follows the investigation of Fr¨ ohlich et al. [4] and complements it by numerical and experimental data over a wide range of Reynolds numbers. We present results predicted by direct numerical simulation (DNS) and highly resolved large–eddy simulation (LES) achieved by two completely independent codes. Furthermore, these numerical results are supported by experimental data from PIV measurements. The focus of this study is twofold. (i) Numerical and experimental data including mean velocity and Reynolds stresses are presented which can be referred to as reference data for this widely used standard test case. Physical peculiarities and new findings are described and confirmed independently by different codes and experimental data. (ii) Extending previous studies the flow is investigated in the range of 100 ≤ Re ≤ 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 turbulent flow stage are presented. For 700 ≤ Re ≤ 10, 595 turbulent statistics are analyzed in detail. Carefully undertaken DNS and LES predictions as well as cross-checking between different numerical and experimental results build the framework for physical investigations on the flow behavior. New interesting features of the flow were found. 2 Definition of the Flow Case and Experimental Setup The improvement of predictions for flow separation from curved surfaces and subsequent reattachment 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. [6] 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 dimensions of the domain are: L x =9.0 h, L y =3.036 h, and L z =4.5 h, where h denotes the hill height. The original Reynolds number was Re = 10, 595 where Re = U B h/ν is based on the hill height h, the bulk velocity U B taken at the crest of the first hill and the kinematic viscosity ν of the fluid. A water channel has been set up to investigate the flow experimentally. Water was chosen since it allows to determine the pressure distribution more accurately than in air. Furthermore, it guarantees a higher accuracy of the PIV measurements especially in instantaneous flows. The water was filtered, decalcified and chlorinated to avoid disturbances from lime stone and biofilm on the boundaries of the channel. A well pumps the water from a reservoir through a pipe with a diffuser into an intake reservoir that damps fluctuations. Several fixtures such as sieves, air intake filters and barriers abate the structures evolving from the entering jet. The rectangular channel which is 3.036 h high and 18 h wide is directly attached to the intake reservoir that is 18 h wide as well. The dimensions of the model relate to the hill height h that was chosen to be 50 mm. The wider extend in the spanwise direction in comparison to the computational domain was chosen to accomplish homogeneity in the center part of the channel [8]. The first part of the channel that is 10 h in length is followed by round flow straighteners that are approximately 0.44 h in diameter and 10 h long. A distance of 20 h lies between the flow straighteners and the foot of the first hill. In total ten hills were chosen to achieve periodicity in the streamwise direction [8], whereas the measurement section is between hill seven and eight. A rectangular section of 34 h lies between the foot of hill ten and the outlet reservoir. To check the periodicity in the streamwise direction 19 holes were drilled into the top cover of the channel. They are located one hill height off the center plane in order not to disturb the PIV measurements that were carried out in the center. For control of the homogeneity in the spanwise direction the pressure was recorded at 14 spanwise locations at hill eight. The velocity measurements were conducted with a 2D PIV system. A 190 mJ NdYAG laser emitting 532 nm pulses was used to generate a light sheet that was 0.7 mm wide. The images were recorded with a 4 MPx CCD camera and streamed ∗ Corresponding author: e-mail: mbreuer@lstm.uni-erlangen.de, Phone: +49 9131 852 9509, Fax: +49 9131 852 9503 Copyright line will be provided by the publisher