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Interplay of surface geometry and vorticity dynamics in incompressible flows on curved surfaces

Applied Mathematics and Mechanics(English Edition) 2017年第9期38卷 1191-1212页

作者： Qian SHI Yu CHEN Xilin XIE Department of Aeronautics and Astronautics Fudan UniversityShanghai 200433China

Incompressible viscous flows on curved surfaces are considered with respect to the interplay of surface geometry, curvature, and vorticity dynamics. Free flows and cylindrical wakes over a Gaussian bump are numerically solved using a surface vorticity- stream function formulation. Numerical simulations show that the Gaussian curvature can generate vorticity, and non-uniformity of the Gaussian curvature is the main cause. In the cylindrical wake, the bump dominated by the positive Gaussian curvature can significantly affect the vortex street by forming velocity depression and changing vorticity transport. The results may provide possibilities for manipulating surface flows through local change in the surface geometry.

关键词： two-dimensional flow vorticity dynamics incompressible viscous curvature

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Rheological Analysis of CNT Suspended Nanofluid with Variable Viscosity: Numerical Solution

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Communications in Theoretical Physics 2017年第6期67卷 681-687页

作者： Noreen Sher Akbar Zafar Hayat Khan DBS&H CEME National University of Sciences and Technology Department of Mathematics University of Malakand Dir (lower) Khyber Pakhtunkhwa

In this article, we discuss the two-dimensional stagnation-point flow of carbon nanotubes towards a stretching sheet with water as the base fluid under the influence temperature dependent viscosity. Similarity transformations are used to simplify the governing boundary layer equations for nanofluid. This is the first article on the stagnation point flow of CNTs over a stretching sheet with variable viscosity. A well known Reynold's model of viscosity is used. Single wall CNTs are used with water as a base fluid. The resulting nonlinear coupled equations with the relevant boundary conditions are solved numerically using shooting method. The influence of the flow parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are explored and presented in forms of graphs and interpreted physically.

关键词： two-dimensional flow variable nanofluid viscosity stagnation-point flow stretching sheet carbon nanotubes numerical solution

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Analytical model of 2D leakoff in waterflood-induced fractures

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Journal of Rock Mechanics and Geotechnical Engineering 2023年第7期15卷 1713-1733页

作者： Igor Reznikov Dimitry Chuprakov Ilmir Bekerov Schlumberger Moscow Research MoscowRussia

Waterflood-induced fractures,also known as self-induced fractures,spontaneously form at injection wells during *** fractures propagate long distances through rock,allowing injected fluids to travel far away from a well,both within and outside the flooding ***,the me-chanics of waterflood-induced fracture propagation is similar to that of hydraulic fractures,which are intentionally created for reservoir *** models developed for hydraulic fractures can also be applied to waterflood-induced ***,waterflood-induced fractures are typically pumped with much larger volumes of water or brine and grow much longer in *** a result,fluid leakoff from waterflood fractures into the formation is more extensive and two-dimensional(2D),a characteristic that is often ignored in a majority of modern fracturing simulators,making their appli-cation to waterflood fractures *** this work,we revisit the problem of leakoff for long-growing waterflood-induced fractures and develop a new analytical model for fluid leakoff that provides improved predictions of fracture geometry and can be easily implemented in fracturing *** incorporate the developed solution into the classical Perkins-Kern-Nordgren(PKN)model of fracture growth,which shows that the choice of the Carter or a 2D leakoff model greatly impacts fracture ge-ometry at large *** conducted parametric study shows while a toughness-dominated regime af-fects fracture evolution,most of fracture lifetime occurs in a viscosity-and-leakoff-dominated *** also develop an asymptotic solution for a leakoff profile in the limiting case of 2D leakoff domination(~~M and~~K).Finally,we study 3D fracture growth and out-of-zone injection with three layers and a complex structure of *** study shows that ignoring the 2D leakoff during simulation results in a significant overestimation of fracture geometry *** present work,thus,plays an impor

关键词： Waterflooding Leakoff Analytical model Hydraulic fracturing two-dimensional flow

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A MODIFIED SIMPLE ALGORITHM FOR 2-D flow IN OPEN CHANNEL

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Journal of Hydrodynamics 2000年第3期12卷 68-74页

作者： Han Long-xi, Jin Zhong-qing College of Water Resources and Environment, Hohai Universit y, Nanjing 210024, P.R.China Hehai Univ Nanjing China

For two-dimensional wa ter flow in open channel, by discritizing hydrodynamic differential equation of conservative form, the corresponding algebraic equations were derived which invo lve the relationship between velocity and depth. Based on the relationship, this paper deduced a modified formula of velocity correction for SIMPLE algorithm. A s a test case, the flow in a prismatic channel with two different slopes was com puted and a good result was obtained.

关键词： two-dimensional flow conservative form SIMPLE algorithm velocity correction

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Shear-Induced Structure Change and flow-Instability of CTAB-NaSal Aqueous Solution in the flow between Parallel Plates

Shear-Induced Structure Change and Flow-Instability of CTAB-...

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The 4th Pacific Rim Conference on Rheology

作者： Mayumi Ouchi Tsutomu Takahashi Masataka Shirakashi Department of Mechanical Engineering Nagaoka University of Technology Graduate School 1603-1 KamitomiokaNagaokaNIIGATA940-2188Japan Department of Mechanical Engineering Nagaoka University of Technology 1603-1 KamitomiokaNagaokaNIIGATA940-2188Japan Department of Mechanical Engineering Nagaoka University of Technology 1603-1 KamitomiokaNagaokaNIIGATA940-2188Japan

＜正＞ CTAB/NaSal aqueous solution forms worm-like micelles at a certain concentration. This system causes the shear-induced structure change, SIS, when both shear rate and strain exceed a certain critical value. In this state, the solution becomes opaque. In this study, the flow behavior of this surfactant solution in the parallel plates flow cell with abruptly contraction entry was observed. The three-dimensional structure of SIS region and occurrence of the flow-instability on the start-up flow were examined by visualizing the flow in both the x-z and x-y planes. The sample became opaque in the whole area between the parallel plates immediately after the flow started. After a while, the two thin opaque layers were formed near the upper and lower glass plates in x-y plane. At a next stage, a whiter band area occurred at the entry region. The flow field was kept two-dimensionality but it lost uniformity on the flow direction that is the x-direction. In the next stage, a horseshoe shape unstable area was generated and the flow field in the whole area became the three-dimensional unstable state. Finally, in the range of flow rate of this study, the flow field returned to stable state after occurrence of the flow-instability.

关键词： shear-induced structure flow-instability two-dimensional flow aqueous surfactant solution.

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