Stagnation-point flow under free-stream turbulence

Abstract

In this paper, the effects of free-stream turbulence on stagnation-point flow and heat transfer are investigated through large eddy simulation (LES) of homogeneous isotropic turbulence impinging upon an isothermal elliptical leading edge. Turbulent mean flow and Reynolds stress profiles along the stagnation streamline, where the mean flow is strain dominant, and at different downstream locations, where the mean flow gradually becomes shear-dominated, are used to characterize evolution of the free-stream turbulence. The Reynolds stress budgets are also obtained, and the turbulence anisotropy is analysed through the balance between the mean flow strain and the velocity pressure gradient correlation. In the presence of free-stream turbulence, intense quasi-streamwise vortices develop near the leading edge with a typical diameter of the order of the local boundary-layer thickness. These strong vortices cause the thermal fluxes to peak at a location much closer to the wall than that of the Reynolds stresses, resulting a greater sensitivity to free-stream turbulence for the heat transfer than the momentum transfer. The heat transfer enhancement obtained by the present LES agrees quantitatively with available experimental measurements. The present LES results are also used to examine the eddy viscosity and pressure-strain correlations in Reynolds stress turbulence models.

Direct numerical simulation of heat transfer from the stagnation region of a heated cylinder affected by an impinging wake

“…These structureswhich were found earlier in the numerical simulations of Xiong & Lele (2007) and have already been derived from the theories of Hunt (1973) and Xiong & Lele (2004) were observed to be formed when the vortical structures of the incoming wake were stretched by the strongly accelerating, almost wall-parallel flow in the stagnation region of the cylinder. As a result of this stretching, the vortical structures became long and thin, and their axes tended to align with the direction of flow around the cylinder except at the stagnation line.…”

“…Additionally, in figure 22(b) the circumferential vortical structures near the cylinder have been made visible using the λ 2 -criterion. As predicted by Hunt (1973) and Xiong & Lele (2007), near the cylinder the accelerating flow is observed to severely stretch the vortical structures of the wake into thin, elongated tubes that are aligned with the direction of flow and completely wrap around the stagnation region of the cylinder (see figure 22b). The spatial distribution of these vortex tubes corresponds to the disturbance pattern that is found on the cylinder's boundary layer, as illustrated in figure 22(a).…”

“…In a later DNS of the accelerating flow over and laminar heat transfer from a flat plate under the influence of grid turbulence in the free stream, observed the same mechanism responsible for causing an increase in heat transfer. An LES study of stagnation-point flow and heat transfer under free-stream turbulence was performed by Xiong & Lele (2007). Also in this case, intense quasi-streamwise vortices were observed to develop owing to the strong vortex stretching near the leading edge, and these were found to be the direct cause of the heat transfer enhancement predicted.…”

Linear global instability of non-orthogonal incompressible swept attachment-line boundary layer flow

“…Receptivity has been addressed by Floryan & Dallmann (1990), who studied the effect of wavy-surface roughness on linear amplification of modal perturbations satisfying the GH Ansatz in incompressible flow and found that this type of roughness generates streamwise vorticity. Xiong & Lele (2007), building upon and extending the vorticity amplification theory of Sutera (1965), addressed the effect of length scales of free-stream turbulence on the distortion and linear amplification of unsteady disturbances inside the swept Hiemenz boundary layer, and arrived at a parameter relating the free-stream and the inherent boundary-layer scales as being the determining parameter to describe this phenomenon. Collis & Lele (1999) also investigated surface roughness, but concentrated on its effect in a region of a parabolic cylinder body where stationary cross-flow vortices are generated and showed that curvature and non-parallel effects were the major counteracting competitive mechanisms in order to predict the initial amplitude of the stationary cross-flow vortices.…”

“…A compressible non-orthogonal stagnation-line flow model valid at small Mach numbers has been first presented by . More realistic models of boundary-layer flow in the vicinity of swept leading edges have been studied by Lin & Malik (1997), who introduced curvature effects in the incompressible orthogonal swept attachment-line boundary layer, while compressible laminar steady states pertinent to orthogonal stagnation flows have been obtained by direct numerical simulation (DNS) in the neighbourhood of swept cylinders of circular (Collis & Lele 1999), elliptic (Xiong & Lele 2007) and parabolic (Mack, Schmid & Sesterhenn 2008) cross-sections.…”