DNS of heat transfer in transitional, accelerated boundary layer flow over a flat plate affected by free-stream fluctuations Jan G. Wissink a, * , Wolfgang Rodi b a School of Engineering and Design, Howell Building, Brunel University, Uxbridge UB8 3PH, UK b Institute for Hydromechanics, University of Karlsruhe, Kaiserstr. 12, D-76128 Karlsruhe, Germany article info Article history: Received 14 October 2008 Received in revised form 30 April 2009 Accepted 6 June 2009 Available online 2 July 2009 Keywords: Heat transfer Accelerating boundary layer Streaks abstract Direct numerical simulations (DNS) of flow over and heat transfer from a flat plate affected by free- stream fluctuations were performed. A contoured upper wall was employed to generate a favourable streamwise pressure gradient along a large portion of the flat plate. The free-stream fluctuations origi- nated from a separate LES of isotropic turbulence in a box. In the laminar portions of the accelerating boundary layer flow the formation of streaks was observed to induce an increase in heat transfer by the exchange of hot fluid near the surface of the plate and cold fluid from the free-stream. In the regions where the streamwise pressure gradient was only mildly favourable, intermittent turbulent spots were detected which relaminarised downstream as the streamwise pressure gradient became stronger. The relaminarisation of the turbulent spots was reflected by a slight decrease in the friction coefficient, which converged to its laminar value in the region where the streamwise pressure gradient was strongest. Ó 2009 Elsevier Inc. All rights reserved. 1. Introduction Free-stream turbulence in incoming flow can influence strongly heat transfer to turbine blades. The physical mechanisms involved are only just beginning to be understood (Mayle et al., 1998). Mainly two effects of free-stream turbulence impinging on the blade’s boundary layer can be distinguished: (1) Earlier transition on the suction side which leads to an increase in heat transfer due to turbulent motion of the boundary layer flow. (2) Increase in heat transfer in regions where the boundary layer remains laminar; here one can differentiate between:  Pretransitional/inactive regions of the suction side boundary layer.  The entire pressure side boundary layer. Free-stream turbulence can be either uniformly distributed or concentrated in wakes. To be able to predict the effects of free- stream turbulence impinging on a boundary layer one needs to know both the integral length-scale of this turbulence and its tur- bulence level. When free-stream turbulence is concentrated in wakes, also the frequency of these wakes should be taken into account. Several experiments have been performed to study the influ- ence of free-stream turbulence on ‘‘laminar” heat transfer – that is: the heat transfer in regions where the boundary layer is laminar – and on boundary layer transition. In their experimental studies of laminar heat transfer to a flat plate affected by free-stream fluctu- ations, Kestin et al. (1961) and Junkhan and Serovy (1967) discov- ered that in order for these fluctuations to be able to increase heat transfer, the affected laminar boundary layer flow needs to be accelerating. These findings were confirmed by the experiments of Schulz (1986), who measured heat-transfer distributions around a typical fore-loaded airfoil for several free-stream turbulence lev- els. Along the stagnation region at the leading edge, where the acceleration is very strong, the highest heat transfer was found. On the suction surface, where a laminar to turbulent transition oc- curs, the main effect was to cause an earlier onset of transition inducing a subsequent increase in heat transfer. Along the pressure side, where the highly accelerated boundary layer remains laminar, the main effect of the free-stream turbulence was to cause a large increase in laminar heat transfer. Liu and Rodi (1994a,b) performed heat-transfer measurements of flow in a model turbine cascade with incoming wakes. With increasing wake-frequency, the heat transfer along both the pressure side – with its strong acceleration – and the favourable pressure gradient portion of the suction side, was found to increase, see also Wissink and Rodi (2006). In the recent experiments of Choi et al. (2004), studying the effect of free-stream turbulence on turbine blade heat transfer, the grid-generated turbulence was shown to affect the heat transfer along both areas of the turbine blade with flow acceleration (i.e. the entire pressure side and approximately the upstream half of the suction side) and also along those areas which exhibit transi- tion to turbulence. Increasing the free-stream turbulence level 0142-727X/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.ijheatfluidflow.2009.06.003 * Corresponding author. Tel.: +44 1895 267371. E-mail address: jan.wissink@brunel.ac.uk (J.G. Wissink). International Journal of Heat and Fluid Flow 30 (2009) 930–938 Contents lists available at ScienceDirect International Journal of Heat and Fluid Flow journal homepage: www.elsevier.com/locate/ijhff