多孔介质中卡森流体的分形分析

研究了非牛顿流体中的卡森流体在多孔介质中的流动特性.基于服从分形分布的弯曲毛细管束模型,运用分形几何理论推导出了该流体在多孔介质中流动的流量、流速、启动压力梯度和有效渗透率的分形解析解.模型中的每一个参数都有明确的物理意义,它将卡森流体在多孔介质中的流动特性与多孔介质的微结构参数有机联系起来.文中给出了卡森流体的流速、启动压力梯度和有效渗透率随着各影响因素的变化趋势,并进行了讨论.所得分形模型可以更深刻地理解卡森流体在多孔介质中流动的内在物理机理. 关键词： 多孔介质 卡森流体 分形     

Physical analysis on improving the recovery accuracy of the Earth’s gravity field by a combination of satellite observations in along-track and cross-track directions

The physical investigations on the accuracy improvement to the measurement of the Earth＇s gravity field recovery are carried out based on the next-generation Pendulum-A/B out-of-plane twin-satellite formation in this paper. Firstly, the Earth＇s gravity field complete up to degree and order 100 is, respectively, recovered by the collinear and pendulum satellite formations using the orbital parameters of the satellite and the matching accuracies of key payloads from the twin GRACE satellites. The research results show that the accuracy of the Earth＇s gravity field model from the Pendulum-A/B satellite formation is about two times higher than from the collinear satellite formation, and the further improvement of the determination accuracy of the Earth＇s gravity field model is feasible by the next-generation Pendulum-A/B out-of-plane twin-satellite formation. Secondly, the Earth＇s gravity field from Pendulum-A/B complete up to degree and order 100 is accurately recovered based on the orbital parameters of the satellite （e.g., an orbital altitude of 400 km, an intersatellite range of 100 km, an orbital inclination of 89° and an orbital eccentricity of 0.001）, the matching accuracies of space- borne instruments （e.g. 10-6 m in the intersatellite range, 10-3 m in the orbital position, 10-6 m/s in orbital velocity, and 10-11 m/s2 in non-conservative force）, an observation time of 30 days and a sampling interval of 10 s. The measurement accuracy of the Earth＇s gravity field from the next-generation Pendulum-A/B out-of-plane twin-satellite formation is full of promise for being improved by about l0 times compared with that from the current GRACE satellite formation. Finally, the physical requirements for the next-generation Pendulum-A/B out-of-plane twin-satellite formation are analyzed, and it is proposed that the satellite orbital altitude be preferably designed to be close to 400±50 km and the matching precision of key sensors from the Pendulum-A/B mission be about one order of magnitude higher tha     

Efficient and rapid accuracy estimation of the Earth’s gravitational field from next-generation GOCE Follow-On by the analytical method

Firstly, a new analytical error model of the cumulative geoid height using the three-dimensional diagonal tensors of satellite gravity gradiometry (SGG) is introduced based on the variance-covariance matrix principle. Secondly, a study for the requirements demonstration on the next-generation GOCE Follow-On satellite gravity gradiometry system is developed using different satellite orbital altitudes and measurement accuracies of satellite gravity gradiometer by the new analytical error model of SGG. The research results show that it is preferable to design satellite orbital altitudes of 300 km-400km and choose the measurement accuracies of 10-13/s2 -10-15/s2 from satellite gravity gradiometer. Finally, the complementarity of the four-stage satellite gravity missions, including past CHAMP, current GRACE, and GOCE, and next-generation GOCE Follow-On, is contrastively demonstrated for precisely recovering the Earth’s full-frequency gravitational field with high spatial resolution.     

A Geometrical Model for Tortuosity of Tortuous Streamlines in Porous Media with Cylindrical Particles

We present a three-dimensional geometry model for tortuosity of streamlines in porous media with randomly placed cylindrical particles. The proposed model is expressed as functions of porosity and geometrical parameters with no empirical constant. This might be helpful for understanding the physical mechanism for tortuosity of streamlines in three-dimensional porous media. The model predictions are found to be in good agreement with the experimental data available.     

A contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

The accuracy of the Earth’s gravitational field measured from the gravity field and steady-state ocean circulation explorer(GOCE),up to 250 degrees,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij from the satellite gravity gradiometry(SGG) are contrastively demonstrated based on the analytical error model and numerical simulation,respectively.Firstly,the new analytical error model of the cumulative geoid height,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij are established,respectively.In 250 degrees,the GOCE cumulative geoid height error measured by the radial gravity gradient V zz is about 2 1/2 times higher than that measured by the three-dimensional gravity gradient V ij.Secondly,the Earth’s gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient V zz and three-dimensional gravity gradient V ij by numerical simulation,respectively.The study results show that when the measurement error of the gravity gradient is 3×10 12 /s 2,the cumulative geoid height errors using the radial gravity gradient V zz and three-dimensional gravity gradient V ij are 12.319 cm and 9.295 cm at 250 degrees,respectively.The accuracy of the cumulative geoid height using the three-dimensional gravity gradient V ij is improved by 30%-40% on average compared with that using the radial gravity gradient V zz in 250 degrees.Finally,by mutual verification of the analytical error model and numerical simulation,the orders of magnitude from the accuracies of the Earth’s gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients,respectively.Therefore,it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10 13 /s 2-10 15 /s 2 for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.     

Fractal Analysis of Power-Law Fluid in a Single Capillary

The fractai expressions for flow rate and hydraulic conductivity for power-law fluids in a single capillary are derived based on the fractai nature of tortuous capillaries. Every parameter in the proposed expressions has clear physical meaning. The flow rate and hydraulic conductivity for power-law fluids are found to be related to the tortuosity fractal dimension and the power-law index. The flow rate for power-law fluids increases with the increasing power-law index but decreases with the increasing tortuosity fractal dimension. Good agreement between the model predictions for flow in a fractai capillary and in a converging-diverging duct is obtained. The results suggest that the fractal capillary model can be used to model the power-law fluids with different rheologicai properties.     

单毛细管中赫切尔-巴尔克莱流体的分形分析

运用分形理论给出了非牛顿流体中的赫切尔-巴尔克莱流体在单毛细管中的渗流分形模型. 此模型将赫切尔-巴尔克莱流体的流量、流速、启动压力梯度和有效渗 透率与流体的流变特性、毛细管的结构参数联系起来, 并且不含经验常数, 每个参数都具有明确的物理意义, 所得分形模型更能体现出赫切尔-巴尔克莱流体流动的内在物理机理.     

Accurate and rapid error estimation on global gravitational field from current GRACE and future GRACE Follow-On missions

Firstly, the new combined error model of cumulative geoid height influenced by four error sources, including the inter-satellite range-rate of an interferometric laser (K-band) ranging system, the orbital position and velocity of a global positioning system (GPS) receiver and non-conservative force of an accelerometer, is established from the perspectives of the power spectrum principle in physics using the semi-analytical approach. Secondly, the accuracy of the global gravitational field is accurately and rapidly estimated based on the combined error model; the cumulative geoid height error is 1.985× 10^-1~m at degree 120 based on GRACE Level 1B measured observation errors of the year 2007 published by the US Jet Propulsion Laboratory (JPL), and the cumulative geoid height error is 5.825× 10^ - 2~m at degree 360 using GRACE Follow-On orbital altitude 250~km and inter-satellite range 50 km. The matching relationship of accuracy indexes from GRACE Follow-On key payloads is brought forward, and the dependability of the combined error model is validated. Finally, the feasibility of high-accuracy and high-resolution global gravitational field estimation from GRACE Follow-On is demonstrated based on different satellite orbital altitudes.     

Effect of Clusters on Thermal Conductivity in Nanofluids

We propose a new model for the effective thermal conductivities of nanottuids, which is derived from the fact that nanoparticles and clusters coexist in the fluids. The effects of the compactness and the perfectness of the contact between nanoparticles in clusters on the effective thermal conductivity of nanofluids are analysed. The proposed model indicates that the effective thermal conductivity of nanofluids decreases with the increasing concentration of clusters. The model predictions are compared with and are in good agreement with the available experimental data.     

Physical Explanation of Influence of Twin and Three Satellite Formation Mode on the Accuracy of Earth's Gravitational Field

The simulated results of the influence of twin and three satellite formation mode on the accuracy of GRACE Earth＇s gravitational field are interpreted from the viewpoint of physics. Because the effective satellite observation information of Earth＇s gravitational field recovery from three-satellite formation mode is only one time more than that of twin satellites, the improvement of the accuracy of Earth＇s gravitational field is far lower than one order of magnitude based on the simple two-times differences between three satellites. Three efficient ways of improving largely the accuracy of measurement of the Earth＇s gravitational field in the future international satellite gravity measurement programme, including proper decrease of satellite orbital altitude, the increase of accuracy from key payloads and an innovation of satellite observation mode are proposed.