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   

A MESO-β SCALE SIMULATION OF THE EFFECTS OF BOREAL FOREST ECOSYSTEM ON THE LOWER ATMOSPHERE     

王汉杰  Yi-FanLI  AloysiusK.LO 《Acta Meteorologica Sinica》2001,(1)

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   

Studying Hydrodynamic Instability Using Shock-Tube Experiments     

O. Sadot  K. Levy  A. Yosef-Hai  D. Cartoon  Y. Elbaz  Y. Srebro  G. Ben-Dor  D. Shvarts 《Astrophysics and Space Science》2005,298(1-2):305-312

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   

Three-dimensional Layer-integrated Modelling of Estuarine Flows with Flooding and Drying   总被引：1，自引：0，他引：1  

B. Lin  R.A. Falconer 《Estuarine, Coastal and Shelf Science》1997,44(6):737-751

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   

天然感潮河道水流紊动特性分析   总被引：5，自引：0，他引：5  

卢金友徐海涛  姚仕明 《海洋工程》2005,23(3):70-77

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   

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  

蔡树群  王文质 《海洋工程》2001,19(1):84-87

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   

一个湍能封闭模型对风暴潮海底底应力的应用研究     

魏更生  汪景庸 《中国海洋大学学报(自然科学版)》1994,(2)

将一个三维湍能封闭模型应用于开阔海区的风暴潮，通过数值计算探讨了Ｔａｙｌｏｒ底摩擦二次率的拖曳系数随空间的分布及拖曳系数与水深、海底粗糙度、风向和风速等因素的关系。本文对底摩擦二次率的可靠性做了评价。  相似文献   

Eddy Diffusion Coefficients of Suspended Particulate Matter: Effects of Wind Energy Transfer and Stratification     

Lars Chresten Lund-Hansen  Morten Pejrup  Jens Valeur  Anders Jensen 《Estuarine, Coastal and Shelf Science》1994,38(6)

Gross sedimentation rates (GSR) have been measured using sediment traps placed at nine different levels above the bed (0·3, 0·5, 0·8, 1·0, 2·0, 4·0, 6·0, 8·0 and 10·0 m). The sediment traps were deployed for 1·25 years and recovered 28 times during the study period. Low average GSR values of 5·5 g m^-2 day^-1 were obtained at 10·0 m, and high average GSR values of 114·8 g m^-2 day^-1 were obtained at 0·3 m. An expression for the eddy diffusion coefficient of suspended particulate matter (K_s), based on the measured GSR is given. The expression has been used for modelling of K_s at the different trap levels above the bed. High values (≈42 cm² s^-1) of K_s were obtained at the upper traps, whereas low values (≈2 cm² s^-1) were obtained near the bed. Comparison between level of turbulent energy in terms of shear stress at the boundaries of the water column, i.e. from the wind and the bed flow, showed that wind energy exceeded that of the bed flow by a factor 16. At 5·0 m K_s was positively correlated (r=0·66) to the eddy diffusion coefficient of momentum (K_m) derived from the wind energy transfer to the water, giving an average β of 0·5 for K_s =βK_m. The density difference between surface and bottom waters has been designated a parameter of stratification, and is discussed in relation to variations of K_s and K_m .  相似文献   

Study on the characteristics of the marine boundary layer in the Equatorial Pacific     

Zhang Ziyu  Zhou Mingyu 《海洋学报(英文版)》1994,13(2):225-236

ＳｔｕｄｙｏｎｔｈｅｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｔｈｅｍａｒｉｎｅｂｏｕｎｄａｒｙｌａｙｅｒｉｎｔｈｅＥｑｕａｔｏｒｉａｌＰａｃｉｆｉｃ￥ＺｈａｎｇＺｉｙｕａｎｄＺｈｏｕＭｉｎｇｙｕ（ＲｅｃｅｉｖｅｄＡｕｇｕｓｔ２１，１９９３；ａｃｃｅｐｔｅｄ...  相似文献   

The Structure of A Turbulent Jet in A Crossflow-Effect of Jet-Crossflow Velocity     

李行伟  匡翠萍  陈国谦 《中国海洋工程》2002,(1)

A comprehensive numerical study on the three-dimensional structure of a turbulent jet in crossflow is performed. The jet-to-crossflow velocity ratio (R) varies in the range of 2 - 16; both vertical jets and inclined jets without excess streamwise momentum are considered. The numerical results of the Standard two-equation k-ε model show that the turbulent structure can be broadly categorised according to the jet-to-crossflow velocity ratio. For strong to moderate jet discharges, i.e. R> 4, the jet is characterized by a longitudinal transition through a bent-over phase during which the jet becomes almost parallel with the main freestream, to a sectional vortex-pair flow with double concentration maxima; the computed flow details and scalar mixing characteristics can be described by self-similar relations beyond a dimensionless distance of around 20-60. The similarity coefficients are only weakly dependent on R. The cross-section scalar field is kidney-shaped and bifurcated, vvith distinct double concentr  相似文献