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《European Journal of Mechanics - B/Fluids》2007,26(2):271-283
This paper is a continuation of an earlier paper [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438] in which it is proposed that each Reynolds stress has its own velocity scale. Two of these, and , are directly related by definition to the r.m.s. of the wall-shear-stress fluctuations ( and ) in the streamwise and transverse directions. They are also velocity scales for the true dissipation of the turbulent kinetic energy and the Kolmogorov velocity and length scales at the surface. From asymptotic considerations it is shown that the other two scales are related to averages involving instantaneous gradients of wall-shear-stress fluctuations. The measurements, made using pulsed-wire anemometry into the viscous sublayer, show that and are also the velocity scales for the respective streamwise and transverse fourth-order velocity moments, together with the viscous velocity scale (). Normalised, the fourth-order moments show an inner-layer-like behaviour independent of both position and direction, like that seen in the second-order moments [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438]. However, not surprisingly, the third order moments exhibit an effect of mean shear, seen in the skewing of the probability distributions. Though not measured directly, the measurements imply the behaviour of the averaged products of fluctuations in wall-shear-stress and wall-pressure-gradient ( and ). Normalised, they also are independent of position and direction. Some of the results presented apply more generally to the near-wall region beneath turbulent flow. 相似文献
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Hot-wire velocity measurements are carried out in a turbulent boundary layer over a rough wall consisting of transverse circular rods, with a ratio of 8 between the spacing (w) of two consecutive rods and the rod height (k). The pressure distribution around the roughness element is used to accurately measure the mean friction velocity () and the error in the origin. It is found that remained practically constant in the streamwise direction suggesting that the boundary layer over this surface is evolving in a self-similar manner. This is further corroborated by the similarity observed at all scales of motion, in the region , as reflected in the constancy of Reynolds number () based on Taylor’s microscale and the collapse of Kolmogorov normalized velocity spectra at all wavenumbers.A scale-by-scale budget for the second-order structure function (, where u is the fluctuating streamwise velocity component and r is the longitudinal separation) is carried out to investigate the energy distribution amongst different scales in the boundary layer. It is found that while the small scales are controlled by the viscosity, intermediate scales over which the transfer of energy (or ) is important are affected by mechanisms induced by the large-scale inhomogeneities in the flow, such as production, advection and turbulent diffusion. For example, there are non-negligible contributions from the large-scale inhomogeneity to the budget at scales of the order of , the Taylor microscale, in the region of the boundary layer extending from to 0.6 ( is the boundary layer thickness). 相似文献
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Michele Serpilli 《Comptes Rendus Mecanique》2005,333(8):593-598
We consider an elastic beam formed by three layers, fixed at one end and loaded at the free end. We call adherents the upper and lower layers and and an adhesive layer . We denote by the thickness of each layer and we suppose that the stiffness of the adhesive layer is , with respect to that of the adherents. By an asymptotic analysis we obtain the zeroth order limit problem and the form of the second order displacements. To cite this article: M. Serpilli, C. R. Mecanique 333 (2005). 相似文献
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Houssem Badreddine Khemais Saanouni Carl Labergère Jean-Louis Duval 《Comptes Rendus Mecanique》2018,346(8):678-700
The initial plastic anisotropy parameters are conventionally determined from the Lankford strain ratios defined by (ψ being the direction of the loading path). They are usually considered as constant parameters that are determined at a given value of the plastic strain far from the early stage of the plastic flow (i.e. equivalent plastic strain of ) and typically at an equivalent plastic strain in between 20% and 50% of plastic strain failure (or material ductility). What prompts to question about the relevance of this determination, considering that this ratio does not remain constant, but changes with plastic strain. Accordingly, when the nonlinear evolution of the kinematic hardening is accounted for, the Lankford strain ratios are expected to evolve significantly during the plastic flow.In this work, a parametric study is performed to investigate the effect of the nonlinear kinematic hardening evolution of the Lankford strain ratios for different values of the kinematic hardening parameters. For the sake of clarity, this nonlinear kinematic hardening is formulated together with nonlinear isotropic hardening in the framework of anisotropic Hill-type (1948) yield criterion. Extension to other quadratic or non-quadratic yield criteria can be made without any difficulty. This parametric study is completed by studying the effect of these parameters on simulations of sheet metal forming by large plastic strains. 相似文献
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《International Journal of Solids and Structures》2007,44(18-19):6187-6200
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《International Journal of Solids and Structures》2006,43(3-4):459-474
The FEM is employed to study the effect of notch depth on a new strain-concentration factor (SNCF) for rectangular bars with a single-edge notch under pure bending. The new SNCF is defined under the triaxial stress state at the net section. The elastic SNCF increases as the net-to-gross thickness ratio h0/H0 increases and reaches a maximum at h0/H0 = 0.8. Beyond this value of h0/H0 it rapidly decreases to the unity with h0/H0. Three notch depths were selected to discuss the effect of notch depth on the elastic–plastic SNCF; they are the extremely deep notch (h0/H0 = 0.20), the deep notch (h0/H0 = 0.60) and the shallow notch (h0/H0 = 0.95). The new SNCF increases from its elastic value to the maximum as plastic deformation develops from the notch root. The maximum of the shallow notch is considerably greater than that of the deep notch. The elastic of the shallow notch is however less than that of the deep notch. Plastic deformation therefore has a strong effect on the increase in of the shallow notch. The variation in with M/MY, the ratio of bending moment to that at yielding at the notch root, is slightly dependent up to the maximum for the shallow notch. This dependence is remarkable beyond the maximum . On the other hand, the variation in with M/MY is independent of the stress–strain curve for the deep and extremely deep notches. 相似文献
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