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正交非线性渗流定理
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Theorem of Orthogonal Non-Linear Flow in Porous Media By QI Chengwei ABSTRACT: Substituting the Orthogonal Power- Quotient Equation into the continuity equation of incompressible fluid steadily flowing in porous media, to achieve the governing equation of orthogonal non- linear flow in porous media at low velocities. This governing equation is a second order non-linear partial differential equation, thus except straight streamline fields, it’s extremely hard to be solved symbolically. Coordinating field theory with differential geometry, to qualitatively analyze geometric characteristics of the flow fields, and gain the‘theorem of orthogonal non-linear flow in porous media: Supposing that iso-intensity surfaces of pressure and streamlines of non- linear flow in porous media are orthogonal to each other, if the flow fields are curved streamline fields, then the streamlines of compressible or incompressible single- phase fluid non-linearly flowing in porous media and the streamlines of incompressible single-phase fluid linearly flowing in porous media are in different shapes under the same condition. Under the orthogonality hypothesis, the shapes of iso-intensity surfaces of pressure are also different.’Drawing an analogy with Stokes flow, to point out the possibility of non- orthogonality between iso- intensity surfaces of pressure and streamlines of the fluid non-linearly flowing in porous media. Key words: mechanics of fluids in porous media, geometric characteristics of flow fields, Orthogonal Power- Quotient Continuity Equation, curved streamline field, lemma, Streamline Curvature Vector Formula, Complex Curvature Formula, Shattering Fracturing |
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2017-03-28 23:25:05, 26.7 M
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