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1.
Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock
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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.
本文通过对1980年以来长江上游10次洪涝过程的500hpa环流形势分析,并用车比雪夫多项式对500hpa高度场进行展开,研究了各类洪涝过程的中期演变特征,发现代表不同洪涝过程环流形势变化的不同的车氏系数值都有明显的特征变化,结合欧洲中心中期数值预告96小时500hpa高度场的车氏系数分析,可为洪涝暴雨的中期预报提供一种新的思路。 相似文献
3.
1 INTRODUCTIONThe South China Sea (SCS) is a semi-enclosedmarginal sea in western North Pacific Ocean withvery complex topography and is the important pas-sage connecting the Pacific and Indian Oceans. Ithas great impact to the global climate and a greatinterest of many oceanography researchers. Twodominant surface hydrographic and circulation fea-tures in the northern SCS are a strong fresh waterexpansion and a warm and high-salinity seawaterintrusion such as the SCS Diluted Water… 相似文献
4.
Kleomenis Tsiganis Harry Varvoglis Rudolf Dvorak 《Celestial Mechanics and Dynamical Astronomy》2005,92(1-3):71-87
It has recently been shown that Jupiter Trojans may exhibit chaotic behavior, a fact that has put in question their presumed long term stability. Previous numerical results suggest a slow dispersion of the Trojan swarms, but the extent of the ‘effective’ stability region in orbital elements space is still an open problem. In this paper, we tackle this problem by means of extensive numerical integrations. First, a set of 3,200 fictitious objects and 667 numbered Trojans is integrated for 4 Myrs and their Lyapunov time, TL, is estimated. The ones following chaotic orbits are then integrated for 1 Gyr, or until they escape from the Trojan region. The results of these experiments are presented in the form of maps of TLand the escape time, TE, in the space of proper elements. An effective stability region for 1 Gyr is defined on these maps, in which chaotic orbits also exist. The distribution of the numbered Trojans follows closely the TE=1 Gyr level curve, with 86% of the bodies lying inside and 14% outside the stability region. This result is confirmed by a 4.5 Gyr integration of the 246 chaotic numbered Trojans, which showed that 17% of the numbered Trojans are unstable over the age of the solar system. We show that the size distributions of the stable and unstable populations are nearly identical. Thus, the existence of unstable bodies should not be the result of a size-dependent transport mechanism but, rather, the result of chaotic diffusion. Finally, in the large chaotic region that surrounds the stability zone, a statistical correlation between TLandTE is found. 相似文献
5.
E. García L. De Haro C. O'Sullivan G. Cahill J. A. López Fernández F. Tercero B. Galocha J. L. Besada 《Experimental Astronomy》2003,15(3):173-193
A classical radioastronomy receiver is fed with a corrugated horn and an independent lens, both placed in a cryostat to lower
the noise temperature. The beam is focused and directed using a combination of elliptical and plane mirrors. This paper proposes
modifying the initial feeding system by placing the lens onto the horn aperture, thereby allowing a size reduction of the
horn and lens, and a simplification of their mechanical design. The profiled lens is shaped to correct the phase error on
the horn aperture. A quasi-optical model of the horn-plus-lens system has been developed using a Beam Mode Expansion (BME).
Results using both a hyperbolic-planar lens and a spherical-elliptical lens, as well as results obtained by using Geometrical
Optics (GO) with a Kirchoff–Huygens integration to get the far-field pattern, have been compared with measurements. As a direct
application, a full focusing system for the new 40-m radiotelescope at the “Centro Astronómico de Yebes” is presented for
the 22, 30 and 45 GHz bands. This paper has developed a QO model for a corrugated conical horn with a phase-correcting lens.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
7.
应用车贝雪夫多项式分析过渡季节(6—7月)澳大利亚冷高压与赤道辐合带的关系,得出了对赤道辐合带北移的主要形势以及过程演变特征,最后用合成方法得到它的演变概念模式,为赤道辐合带的北移影响西太平洋及南海地区提供了中期预报的依据。 相似文献
8.
Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem 总被引:3,自引:0,他引:3
A series of laboratory experiments was carried out to investigate the strong reflection of regular water waves over a train of submerged breakwaters. Rectangular and trapezoidal shapes of submerged breakwaters are employed and compared for reflecting capability of incident waves. Measured reflection coefficients of regular waves over impermeable submerged breakwaters are verified by comparing with those of the eigenfunction expansion method. A very good agreement is observed. Reflection coefficients of permeable submerged breakwaters are less than those of impermeable breakwaters. The trapezoidal shape is recommended for a submerged breakwater in terms of reflecting capability and practical application. 相似文献
9.
Tisseur(2000)研究了非齐次多项式特征值问题的条件数,所得结果的不足是对无穷特征值必须另外处理;Declieu和Tisseur(2003)运用微分几何方法研究了齐次多项式特征值问题的条件数,所得结果的不足之处是与系数矩阵的尺度化(scaling)有关。这两种条件数都有各自的应用范围。本文基于投影尺度引入齐次多项式特征值问题的条件数,其优点是与系数矩阵的尺度化无关,因而也许会有较广泛的应用。 相似文献
10.
Generally, the underwater flight vehicle (UFV) depth control system operates with the following problems: it is a multi-input multi-output (MIMO) system, it requires robustness, a continuous control input, and further, it has the speed dependency of controller parameters. To solve these problems, an expanded adaptive fuzzy sliding mode controller (EAFSMC), which is based on the decomposition method designed by using an expert knowledge and the decoupled sub-controllers and composition method designed by using the fuzzy basis function expansions (FBFEs), is proposed. To verify the performance of the EAFSMC, the depth control of UFV in various operating conditions is performed. Simulation results show that the EAFSMC solves all problems experienced in the UFV depth control system online. 相似文献