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Establishing the generality of three phenomena using a boundary layer with free-stream passing wakes. (English) Zbl 1221.76102
Summary: Direct numerical simulation was performed on an incompressible, smooth flat-plate boundary layer at unit molecular Prandtl number and constant surface temperature under free-stream periodically passing turbulent planar wakes over the momentum thickness Reynolds number range of \(80 \leqslant Re_{\theta } \leqslant 1850\). This inhomogeneous free-stream wake perturbation source with mean deficit differs markedly from the isotropic turbulent patch used in the previous studies of X. Wu and P. Moin [J. Fluid Mech. 630, 5–41 (2009; Zbl 1181.76084); “Transitional and turbulent boundary layer with heat transfer”, Phys. Fluids 22, No. 8, 8p. (2010), doi:10.1063/1.3475816]. Preponderance of hairpin vortices is observed in both the transitional and turbulent regions of the boundary layer. In particular, the internal structure of merged turbulent spots is a hairpin forest; the internal structure of infant turbulent spots is a hairpin packet. Although more chaotic in the turbulent region, numerous hairpin vortices are readily detected in both the near-wall and outer regions of the boundary layer up to \(Re_{\theta } = 1850\). This suggests that the hairpin vortices in the higher-Reynolds-number region are not simply the aged hairpin forests convected from the upstream transitional region. Temperature iso-surfaces in the companion thermal boundary layer are found to be a useful tracer in identifying boundary-layer hairpin vortex structures. Total shear stress overshoots wall shear stress in the transitional region and the excess relaxes gradually in the downstream turbulent region. This overshoot is shown to be associated with a localized streamwise acceleration of the streamwise velocity component. Breakdown of the wake-perturbed laminar boundary layer is closely related to the formation of hairpin packets out of quasi-streamwise vortices. Mean and second-order statistics are in good agreement with previous data on the standard turbulent boundary layer. Downstream of transition, normalized root-mean-square (r.m.s.) wall-shear-stress intensity shows almost no variation with \(Re_{\theta }\), whereas normalized r.m.s. wall-pressure intensity increases slightly. Taken together with the previous results of X. Wu and P. Moin [loc. cit.], the generality of the following three phenomena in quasi-standard boundary layers can be reasonably established, namely, preponderance of hairpin vortices in the transitional as well as in the turbulent regions up to \(Re_{\theta } = 1850\), transitional total shear stress overshoot, and a laminar-layer breakdown process closely tied to the formation of hairpin packets.

MSC:
76F40 Turbulent boundary layers
76D25 Wakes and jets
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