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Adaptive finite difference methods for liquid membranes
Author(s) -
Ramos J. I.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620340309
Subject(s) - froude number , mechanics , radius , mathematics , mathematical analysis , membrane , rate of convergence , amplitude , ordinary differential equation , differential equation , physics , control theory (sociology) , geometry , chemistry , optics , flow (mathematics) , channel (broadcasting) , biochemistry , computer security , control (management) , management , computer science , electrical engineering , economics , engineering
A domain‐adaptive technique and an iterative, block bidiagonal method are used to analyse the unsteady dynamics of annular liquid membranes subject to fluctuations in the mass injected into the volume enclosed by the membranes. The domain‐adaptive technique maps the unknown, time‐dependent, curvilinear geometry of the liquid membrane into a unit interval. The condition that the membrane's radius is zero at the convergence point is used to determine the convergence length, which is governed by an ordinary differential equation. This equation is solved iteratively together with those which govern the fluid dynamics equations. A block bidiagonal technique is used to determine the mass per unit length, radius, and axial and radial velocity components of the membrane. It is shown that the pressure of the gases enclosed by the liquid membrane responds instantaneously to changes in and exhibits the same periodic behaviour as the mass injection rate. The convergence length takes a delay time to respond to the mass injection rate fluctuations. The magnitude of this delay time increases as the Froude and Weber numbers and the nozzle exit angle are increased. The amplitude of the oscillations of both the convergence length and the pressure coefficient increases as the pressure difference across the membrane and the amplitude of the mass injection rate fluctuations are increased.