A geometry model for tortuosity of flow path in porous media

A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity and there is no empirical constant in this model. The model predictions are compared with those from available correlations obtained numerically and experimentally, both of which are in agreement with each other. The present model can also give the tortuosity with a good approximation near the percolation threshold. The validity of the present tortuosity model is thus verified.

Fractal geometry model for effective thermal conductivity of three-phase porous media

An approximate model, a fractal geometry model, for the effective thermal conductivity of three-phase/unsaturated porous media is proposed based on the thermal-electrical analogy technique and on statistical self-similarity of porous media. The proposed thermal conductivity model is expressed as a function of porosity (related to stage n of Sierpinski carpet), ratio of areas, ratio of component thermal conductivities, and saturation. The recursive algorithm for the thermal conductivity by the proposed model is presented and found to be quite simple. The model predictions are compared with the existing measurements. Good agreement is found between the present model predictions and the existing experimental data. This verifies the validity of the proposed model. (C) 2004 American Institute of Physics.

Character of simplified Navier-Stokes (SNS) equations near separation point for two-dimensional laminar flow over a flat plate

It is proved that the simplified Navier-Stokes (SNS) equations presented by Gao Zhi[1], Davis and Golowachof-Kuzbmin-Popof (GKP)[3] are respectively regular and singular near a separation point for a two-dimensional laminar flow over a flat plate. The order of the algebraic singularity of Davis and GKP equation[2,3] near the separation point is indicated. A comparison among the classical boundary layer (CBL) equations, Davis and GKP equations, Gao Zhi equations and the complete Navier-Stokes (NS) equations near the separation point is given.

Orientation preference and fractal character of short fatigue cracks in a weld metal

Short fatigue crack behaviour in a weld metal has been further investigated. The Schmid factor and the fractal dimension of short cracks on iso-stress specimens subjected to reversed bending have been determined and then applied to account for the distribution and orientation characteristics of short fatigue cracks. The result indicates that the orientation preference of short cracks is attributed to the large values of Schmid factor at relevant grains. The Schmid factors of most slip systems, which produced short cracks, are less than or equal to 0.4. Crack length measurements reveal that short crack path, compared to that of long crack, possesses a more stable and relatively larger value of fractal dimension. This is regarded as one of the typical features of short cracks.