Predicting fully-developed channel flow with zero-equation model

Md Mizanur Rahman ◽  
Khalid Hasan ◽  
Wenchang Liu ◽  
Xinming Li

A new zero-equation model (ZEM) is devised with an eddy-viscosity formulation using a stress length variable which the structural ensemble dynamics (SED) theory predicts. The ZEM is distinguished by obvious physical parameters, quantifying the underlying flow domain with a universal multi-layer structure. The SED theory is also utilized to formulate an anisotropic Bradshaw stress-intensity factor, parameterized with an eddy-to-laminar viscosity ratio. Bradshaw’s structure function is employed to evaluate the kinetic energy of turbulence k and turbulent dissipation rate epsilon  . The proposed ZEM is intrinsically plausible, having a dramatic impact on the prediction of wall-bounded turbulence. 

2019 ◽  
Vol 300 ◽  
pp. 11008
Carl H. Wolf ◽  
Andreas Burgold ◽  
Sebastian Henkel ◽  
Meinhard Kuna ◽  
Horst Biermann

The aim of this study is to propose a simplified calculation of the Mode I stress intensity factor K for the cruciform specimen design proposed by Brown and Miller. To calculate K, both cracks have to grow with a similar crack growth rate and the crack paths of the two single cracks with the length a should also be similar. The calculations are carried out on an aluminum specimen and a steel specimen. For all load cases and materials, the stresses resulting from the forces are first considered. It was found that the elastic constants E and ν have only a small influence of less than 3 %. In addition, the coupling between the forces of the load axes, which should be minimized by the slotted arms, is considered. Furthermore K-factors are calculated by FE for different crack lengths. These K-values together with the transmission factor allow to find a K-factor formula for cruciform specimens, which is based on the prescribed forces. Finally, the results of the FE calculation of the exact straight crack paths were compared to experimentally determined crack paths.

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