J. Fluid Mech. (2002), vol. 453, pp. 201–238. c  2002 Cambridge University Press DOI: 10.1017/S0022112001006887 Printed in the United Kingdom 201 Large-eddy simulation of the turbulent flow through a heated square duct By M. SALINAS V ´ AZQUEZ AND O. M ´ ETAIS LEGI-MOST, Institut National Polytechnique de Grenoble, BP 53X, 38041 Grenoble C´ edex 9, France (Received 7 February 2001 and in revised form 29 August 2001) Large-eddy simulations of a compressible turbulent square duct flow at low Mach number are described. First, we consider the isothermal case with all the walls at the same temperature: good agreement with previous incompressible DNS and LES results is obtained both for the statistical quantities and for the turbulent structures. A heated duct with a higher temperature prescribed at one wall is then considered and the intensity of the heating is varied widely. The increase of the viscosity with temperature in the vicinity of the heated wall turns out to play a major rˆ ole. We observe an amplification of the near-wall secondary flows, a decrease of the turbulent fluctuations in the near-wall region and, conversely, their enhancement in the outer wall region. The increase of the viscous thickness with heating implies a significant augmentation of the size of the characteristic flow structures such as the low- and high-speed streaks, the ejections and the quasi-longitudinal vorticity structures. For strong enough heating, the size limitation imposed by the lateral walls leads to a single low-speed streak located near the duct central plane surrounded by two high-speed streaks on both sides. Violent ejections of slow and hot fluid from the heated wall are observed, linked with the central low-speed streak. A selective statistical sampling of the most violent ejection events reveals that the entrainment of cold fluid, originated from the duct core, at the base of the ejection and its subsequent expansion amplifies the ejection intensity. 1. Introduction The turbulent flow inside a duct of square or rectangular cross-section is of con- siderable engineering interest. This flow is characterized by the existence of secondary flows (Prandtl’s flow of the second kind) which are driven by the turbulent motion. The secondary flow is a mean flow perpendicular to the main flow direction. It is relatively weak (1–3% of the mean streamwise velocity), but its effect on the transport of heat and momentum is quite significant. There is still much controversy about the relation between the secondary flow and the ejection mechanism from the wall. Many studies based upon the mean streamwise vorticity equation have shown that this secondary flow is generated by a balance between the secondary Reynolds stress gradients (Demuren & Rodi 1984; Brundet & Baines 1964; Gessner & Jones 1965; Gessner 1983). This generation has been investigated in detail by Huser & Biringen (1993) through a direct numerical simulation (DNS) of a square duct. They have found that the dominant turbulent mechanism is ejections from the wall. The frequency and intensity of these ejections vary significantly with the distance from the duct corner. Close to the corner, the