کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9476927 | 1323892 | 2005 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Exact solutions to radially symmetric two-phase flow for an arbitrary diffusivity
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
علوم زمین و سیارات
فرآیندهای سطح زمین
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Exact solutions to radially symmetric two-phase flow for an arbitrary diffusivity Exact solutions to radially symmetric two-phase flow for an arbitrary diffusivity](/preview/png/9476927.png)
چکیده انگلیسی
Over the past decade there have been a variety of exact solutions developed for one-dimensional two-phase flow, however when higher dimensions are considered there is a distinct scarcity of solutions. In this paper we consider the problem of radially symmetric two-phase flow, into an infinite medium of uniform initial saturation, subject to a constant flux V from a line source at the origin. We show that in the absence of gravity and when the two-phase diffusivity D is related to the fraction flow function f by βD = V df/dθ, where θ is the water content and β is a constant of proportionality, a new class of exact solutions can be found. In particular, when β = 2, we show that the solution is given by a simple quadrature for arbitrary D, and is fully integrable for specific functional forms of D. It has been shown by Weeks et al. [Weeks SW, Sander GC, Parlange J-Y. n-Dimensional first integral and similarity solutions for two-phase flow. ANZIAM J 2003;44:365-80] that when D obeys the above relation, a saturated zone does not grow around the line of injection, consequently we find for β = 1, the flow equation maps to one-dimensional single-phase flow under a saturated boundary condition. Consequently solutions developed for one-dimensional single-phase flow (exact or approximate) apply to radially symmetric two-phase flow. Solutions for β = 1 or 2 can be derived for either a wetting fluid displacing a non-wetting fluid, or a non-wetting fluid displacing a wetting fluid, however for arbitrary β numerical methods are required.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Water Resources - Volume 28, Issue 10, October 2005, Pages 1112-1121
Journal: Advances in Water Resources - Volume 28, Issue 10, October 2005, Pages 1112-1121
نویسندگان
G.C. Sander, J.-Y. Parlange, I.G. Lisle, S.W. Weeks,