Alternative constitutive relation for momentum transport of extended Navier–Stokes equations

The classical Navier–Stokes equation(NSE)is the fundamental partial differential equation that describes the flow of fluids,but in certain cases,like high local density and temperature gradient,it is inconsistent with the experimental results.Some extended Navier–Stokes equations with diffusion terms taken into consideration have been proposed.However,a consensus conclusion on the specific expression of the additional diffusion term has not been reached in the academic circle.The models adopt the form of the generalized Newtonian constitutive relation by substituting the convection velocity with a new term,or by using some analogy.In this study,a new constitutive relation for momentum transport and a momentum balance equation are obtained based on the molecular kinetic theory.The new constitutive relation preserves the symmetry of the deviation stress,and the momentum balance equation satisfies Galilean invariance.The results show that for Poiseuille flow in a circular micro-tube,self-diffusion in micro-flow needs considering even if the local density gradient is very low.

Multiscale hierarchical analysis of rock mass and prediction of its mechanical and hydraulic properties

Engineering geological and hydro-geological characteristics of foundation rock and surrounding rock mass are the main factors that affect the stability of underground engineering. This paper presents the concept of multiscale hierarchical digital rock mass models to describe the rock mass, including its structures in different scales and corresponding scale dependence. Four scales including regional scale,engineering scale, laboratory scale and microscale are determined, and the corresponding scaledependent geological structures and their characterization methods are provided. Image analysis and processing method, geostatistics and Monte Carlo simulation technique are used to establish the multiscale hierarchical digital rock mass models, in which the main micro-and macro-structures of rock mass in different geological units and scales are reflected and connected. A computer code is developed for numerically analyzing the strength, fracture behavior and hydraulic conductivity of rock mass using the multiscale hierarchical digital models. Using the models and methods provided in this paper, the geological information of rock mass in different geological units and scales can be considered sufficiently,and the influence of downscale characteristics(such as meso-scale) on the upscale characteristics(such as engineering scale) can be calculated by considering the discrete geological structures in the downscale model as equivalent continuous media in the upscale model. Thus the mechanical and hydraulic properties of rock mass may be evaluated rationally and precisely. The multiscale hierarchical digital rock mass models and the corresponding methods proposed in this paper provide a unified and simple solution for determining the mechanical and hydraulic properties of rock mass in different scales.

深埋引水隧洞极硬岩TBM掘进及辅助破岩技术

秦岭深埋长距离引水隧洞极硬岩强度达到300 MPa以上,已成为制约隧洞掘进机(tunneling boring machine, TBM)高效施工的主要难题。针对秦岭引水隧洞极硬岩掘进施工问题,该文提出了基于TBM掘进隧洞的热能-机械耦合破岩方法,开展了有关微波、等离子体、火焰炬、水射流和钻孔劈裂的破岩试验以及数值计算和搭载设计,提出了5类辅助TBM破岩方法的适用性和搭载设计。研究结果表明:秦岭深埋引水隧洞岭南TBM掌子面岩体高含量石英吸收微波能力差、黑色极性矿物颗粒小,岩体微波劣化效应不显著,必须通过钻孔植入黑色极性矿物,增强岩体微波劣化效应;等离子体破岩方法采用超高电场密度能够产生显著的电力作用和热能破岩效果,可以将刀盘滚刀作为电极进行设计;火焰炬切割技术简单、易操作,但必须采取人工降温和热屏蔽措施;超高压水射流和钻孔超强劈裂破岩方法适用于掌子面岩体强度大于400 MPa, TBM掘进每日进尺小于1 m的工况。