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1.
The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.  相似文献   
2.
空间数据仓库的认知过程   总被引:3,自引:3,他引:0  
从理论上探讨了空间数据仓库的认知过程.主要是十一个层次的世界模型通过十个算子转换的过程,对十一个层次世界及十个算子概念进行了较详细地讨论,并用代数系统对其进行了定义。  相似文献   
3.
Based on the Intensive Field Campaign(IFC-1)data of Boreal Ecosystem-Atmosphere Study(BOREAS).a three-dimensional meso-β scale model is used to simulate the effect of boreal forests onthe lower atmosphere.A fine horizontal resolution of 2 km×2 km is used in order to distinguish thevegetative heterogeneity in the boreal region.A total of 20×25 grid points cover the entire sub-modeling area in BOREAS' South Study Area(SSA).The ecosystem types and their coverage ineach grid square are extracted from the North American Land Cover Characteristics Data Base(NALCCD)generated by the U.S.Geographical Survey(USGS)and the University of Nebraska-Lincoln(UNL).The topography of the study area is taken from the Digital Elevation Map(DEM)of USGS.The model outputs include the components of the energy balance budget within the canopyand at the ground.the turbulence parameters in the atmospheric boundary layer and the wind.temperature and humidity profiles extending up to a height of 1500 m.In addition to the fine timeand spatial step,the unique feature of the present model is the incorporation of both dynamic andbiological effects of the Boreal forest into the model parameterization scheme.The model resultscompare favorably with BOREAS' IFC-1 data in 1994 when the forest was in the luxuriant growingperiod.  相似文献   
4.
The hydrodynamic instability, which develops on the contact surface between two fluids, has great importance in astrophysical phenomena such as the inhomogeneous density distribution following a supernova event. In this event acceleration waves pass across a material interface and initiate and enhance unstable conditions in which small perturbations grow dramatically. In the present study, an experimental technique aimed at investigating the above-mentioned hydrodynamic instability is presented. The experimental investigation is based on a shock-tube apparatus by which a shock wave is generated and initiates the instability that develops on the contact surface between two gases. The flexibility of the system enables one to vary the initial shape of the contact surface, the shock-wave Mach number, and the density ratio across the contact surface. Three selected sets of shock-tube experiments are presented in order to demonstrate the system capabilities: (1) large-initial amplitudes with low-Mach-number incident shock waves; (2) small-initial amplitudes with moderate-Mach-number incident shock waves; and (3) shock bubble interaction. In the large-amplitude experiments a reduction of the initial velocity with respect to the linear growth prediction was measured. The results were compared to those predicted by a vorticity-deposition model and to previous experiments with moderate- and high-Mach number incident shock waves that were conducted by others. In this case, a reduction of the initial velocity was noted. However, at late times the growth rate had a 1/t behavior as in the small-amplitude low-Mach number case. In the small-amplitude moderate-Mach number shock experiments a reduction from the impulsive theory was noted at the late stages. The passage of a shock wave through a spherical bubble results in the formation of a vortex ring. Simple dimensional analysis shows that the circulation depends linearly on the speed of sound of the surrounding material and on the initial bubble radius.  相似文献   
5.
Details are given of the refinement and application of a thee-dimensional (3-D) layer-integrated numerical model of tidal circulation, with the aim of simulating severe tidal conditions for practical engineering applications. The mode splitting strategy has been used in the model. A set of depth-integrated 2-D equations are first solved to give the pressure gradient, and the layer-integrated 3-D equations are then solved to obtain the vertical distributions of the flow velocities. Attention has been given to maintaining consistency of the physical quantities derived from the 2-D and 3-D equations. A TWO=layer mixing length turbulence model for the vertical shear stress distribution has been included in the model. Emphasis has been focused on applying the model to a real estuary, which is geometrically complicated and has large tidal ranges giving rise to extensive flooding and drying. The model has been applied to three examples, including: wind-driven flow in a rectangular lake, tidal circulation in a model rectangular harbour, and tidal circulation in a large estuary. Favourable results have been obtained for both the simple and complex flow beds.  相似文献   
6.
天然感潮河道水流紊动特性分析   总被引:5,自引:0,他引:5  
采用多谱勒三相流速仪,在长江口徐六泾水文观测断面分别进行了涨潮、落潮时中泓与近岸垂线的流速观测,根据这些观测资料,对天然感潮河段潮流紊动的周期、频率、概率密度函数等进行了定量的数学描述,并对时均流速、紊动强度、雷诺应力等沿垂线分布进行了分析计算。  相似文献   
7.
将模糊化(拓扑)导算子进行了公理化,并且给出了若干模糊化(拓扑)导算子的刻画;同时建立了模糊化(拓扑)导算子和模糊化(拓扑)闭包算子之间的关系。  相似文献   
8.
提出了混合型单调算子对的概念,并给出了其不动点的存在唯一性;研究了它在微分方程组的具体应用.  相似文献   
9.
亚像素定位的关键问题研究   总被引:1,自引:0,他引:1  
分析了控制点标志的选择与设计,采用了图像处理、Hough变换、角点与直线高精度定位算子等方法,实现了中南大学近景摄影测量二维控制场1 350个人工标志点的自动识别和亚像素定位,仿真图检测平均精度达到±0.05像素。  相似文献   
10.
湍流数值模拟中封闭模式应用的局限性   总被引:1,自引:0,他引:1  
通过对琼州海峡的潮流场特征进行数值模拟,指出了选择不同的特征混合长度表达式对数值模拟结果的影响,表明了基于特征混合长度理论的流封闭模式在近海湍流数值模拟中应用的局限性。  相似文献   
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