Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock          下载免费PDF全文

N. Zolfaghari  E. Dontsov  A. P. Bunger 《国际地质力学数值与分析法杂志》2018,42(4):587-617

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   

Constraints on a planetary origin for the gap in the protoplanetary disc of GM Aurigae   总被引：1，自引：0，他引：1  

W. K. M. Rice  Kenneth Wood  P. J. Armitage  B. A. Whitney  J. E. Bjorkman 《Monthly notices of the Royal Astronomical Society》2003,342(1):79-85

  相似文献   

Atmospheric radiative transfer simulation for atmospheric correction of remote sensing data     

Yunfei Bao Shengbo Chen 《东北亚地学研究》2006,9(1):100-108

IntroductionThe radiance leaving the earth-atmosphere sys-tem which can be sensed by a satellite borne ra-diometer is the sum of radiation emission fromtheearth surface and each atmospheric level that aretransmittedtothe top of the atmosphere.The radia-tion emissionfromthe earthsurface andthe radianceof each atmospheric level can be separated fromtheradiance at the top the atmospheric level a satellitemeasured.Thus,the earth surface parameters willbe retrieved from the surface radiance after a…  相似文献   

Non-Sobolev modelling of radiation-pressure-driven flows in active galactic nuclei     

Doron Chelouche  Hagai Netzer 《Monthly notices of the Royal Astronomical Society》2003,344(1):223-232

We present a new general scheme for calculating the structure and dynamics of radiation-pressure-driven photoionized flows. The new method goes one step beyond the Sobolev approximation. It involves a numerical solution of the radiative transfer in absorption lines, including the effects of differential expansion and line interactions such as line locking and blanketing. We also present a new scheme for calculating the radiation pressure due to trapped line photons in finite, differentially expanding flows. We compare our results for the radiation pressure force with those obtained using the Sobolev approximation and show the limitations of the latter. In particular, we demonstrate that the Sobolev method gives a poor approximation near discontinuity surfaces and its neglect of line blanketing can lead to erroneous results in high-velocity flows. We combine the newly calculated radiation pressure force with self-consistent photoionization and thermal calculations to study the dynamics and spectral features of broad absorption-line flows and highly ionized gas flows in active galactic nuclei (AGN). A comparison with Sobolev-type calculations shows that the latter overestimates the terminal velocity of the flow and, conversely, underestimates its opacity. We also show that line locking on broad emission lines can have a significant effect on the dynamics and spectral features of AGN flows.  相似文献   

Statistical description of the radiation field in a homogeneous medium of finite optical thickness     

A. G. Nikoghossian 《Astrophysics》2006,49(2):228-239

The problem of finding statistical averages which characterize the radiation field in a semi-infinite atmosphere has been discussed by the author in a series of papers. In this paper some of the results obtained there are generalized to media of finite optical thickness. The average number of scattering events undergone by a photon during its random walk in an atmosphere and the average time required for this are determined. Three different types of averages are considered, depending on the photon characteristics over which the averages are taken. Special attention is devoted to the asymptotic behavior of these quantities for media with large optical depths taking the influence of continuum absorption into account. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 263–275 (May 2006).  相似文献   

The efifect of wave breaking on surface wave imaging by Synthetic Aperture Radar     

孙建  管长龙  史剑 《中国海洋湖沼学报》2006,(1)

The effect of ocean wave breaking as a non-Bragg mechanism on backscattering cross-section and modulation transfer functions (MTF) of radar was investigated based on Bragg resonance theory and parametric method. The result showed that the additional effect of wave breaking on backscattering cross-section is not more than 20% except for the small incident angle of VV polarized electromagnetic (e.m.) wave but is significant for HH polarized e.m. wave. Breaking waves lead to increase in the modulus of tilt modulation MTF and the larger the wind speed, the faster the increase. For large incident angle, the modulus of tilt modulation MTF with wave breaking decreases quickly with incident angle for HH polarization and approach to that without wave breaking for VV polarization. The hydrodynamic MTF increases 30%-60% when considering wave breaking and the increase is larger for HH polarization than for VV polarization.  相似文献   

Radiative Transfer in Inhomogeneous Atmospheres. III     

A. G. Nikoghossian 《Astrophysics》2004,47(3):412-421

The approach proposed in the previous parts of this series of papers is used to solve the radiative transfer problem in scattering and absorbing multicomponent atmospheres. Linear recurrence relations are obtained for both the reflectance and transmittance of these kinds of atmospheres, as well as for the emerging intensities when the atmosphere contains energy sources. Spectral line formation in a one-dimensional inhomogeneous atmosphere is examined as an illustration of the possibility of generalizing our approach to the matrix case. It is shown that, in this case as well, the question reduces to solving an initial value problem for linear differential equations. Some numerical calculations are presented.  相似文献   

A multi‐level parallelized substructuring‐frontal solution for coupled thermo/hydro/mechanical problems in unsaturated soil     

H.R. Thomas  H.T. Yang  Y. He  P.J. Cleall 《国际地质力学数值与分析法杂志》2003,27(11):951-965

This paper proposes a multi‐level parallelized substructuring–frontal combined algorithm for the analysis of the problem of thermo/hydraulic/mechanical behaviour of unsaturated soil. Temperature, displacement, pore water pressure and pore air pressure are treated as the primary variables in a non‐linear analysis. Details are given firstly of the substructuring–frontal combined approach. The incorporation of the algorithm in a multi‐level parallel strategy is then discussed. The parallel processing can thus be carried out at different substructural levels. The method thus developed impacts, in a positive way, on both computer storage requirement and execution time. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

Impact of the seasonal variations of composition on the temperature field of Titan’s stratosphere     

Sébastien Lebonnois  Frédéric Hourdin  David Luz 《Icarus》2003,163(1):164-174

We investigate the role of seasonal variations of Titan’s stratospheric composition on the temperature. We use a general circulation model coupled with idealized chemical tracers that reproduce variations of ethane (C₂H₆), acetylene (C₂H₂), and hydrogen cyanide (HCN). Enhancement of the mole fractions of these compounds, at high latitudes in the winter hemisphere relative to their equatorial values, induces a relative decrease in temperature above approximately 0.2 mbar, with a peak amplitude around −20 K, and a relative increase in temperature below, around 1 mbar, with a peak amplitude around +7 K. These thermal effects are mainly due to the variations of the cooling to space induced by the varying distributions. The ethane, acetylene, and hydrogen cyanide variations affect the cooling rates in a similar way, with the dominant effect being due to ethane, though its latitudinal variations are small.  相似文献   

2D/3D Dust Continuum Radiative Transfer Codes to Analyze and Predict VLTI Observations     

I. Pascucci  Th. Henning  J. Steinacker  S. Wolf 《Astrophysics and Space Science》2003,286(1-2):113-118

Radiative Transfer (RT) codes with image capability are a fundamental tool for preparing interferometric observations and for interpreting visibility data. In view of the upcoming VLTI facilities, we present the first comparison of images/visibilities coming from two 3D codes that use completely different techniques to solve the problem of self-consistent continuum RT. In addition, we focus on the astrophysical case of a disk distorted by tidal interaction with by-passing stars or internal planets and investigate for which parameters the distortion can be best detected in the mid-infrared using the mid-infrared interferometric device MIDI. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献