Some Problems of Boundary Conditions in the Cavitation

2002 ◽  
Author(s):  
Alexey G. Terentiev
Keyword(s):  
Surface Tension ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Gravity Field ◽  
Constant Pressure ◽  
Calculated Data ◽  
Cavitating Flow ◽  
Capillary Surface ◽  
Flow Problems ◽  
Cavity Boundary

Most of cavitation problems are considered by standard conditions i.e. Neumann’s condition on the boundary, constant pressure on the cavity boundary and undisturbed flow in infinty. In this paper cavitating flow problems are considered by following conditions: a) evaporation from free boundary into the cavity, b) capillary surface tension on the boundary of the cavity, c) simulated gravity field in a flow, d) compressibility of the fluid. All these problems have been investigated analytically and obtained a number of calculated data.

scholarly journals A Special Class of Univalent Functions in Hele-Shaw Flow Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Paula Curt ◽  
Denisa Fericean
Keyword(s):  
Surface Tension ◽  
Free Boundary ◽  
Viscous Fluid ◽  
Time Evolution ◽  
Special Class ◽  
Geometric Property ◽  
Univalent Functions ◽  
Property A ◽  
Flow Problems ◽  
Planar Flows

We study the time evolution of the free boundary of a viscous fluid for planar flows in Hele-Shaw cells under injection. Applying methods from the theory of univalent functions, we prove the invariance in time ofΦ-likeness property (a geometric property which includes starlikeness and spiral-likeness) for two basic cases: the inner problem and the outer problem. We study both zero and nonzero surface tension models. Certain particular cases are also presented.

Boundary conditions for gas flow problems from anisotropic scattering kernels

2015 ◽  
Vol 56 (10) ◽  
pp. 103101 ◽  
Author(s):  
Quy-Dong To ◽  
Van-Huyen Vu ◽  
Guy Lauriat ◽  
Céline Léonard
Keyword(s):  
Boundary Conditions ◽  
Gas Flow ◽  
Anisotropic Scattering ◽  
Flow Problems

scholarly journals Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 461
Author(s):  
Kenta Oishi ◽  
Yoshihiro Shibata
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Transmission Conditions ◽  
Well Posedness ◽  
Anisotropic Space ◽  
Free Boundary Conditions ◽  
Incompressible Magnetohydrodynamics

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On the free surface, free boundary conditions for MHD flow and transmission conditions for electromagnetic fields are imposed. We proved the local well-posedness in the general setting of domains from a mathematical point of view. The solutions are obtained in an anisotropic space Hp1((0,T),Hq1)∩Lp((0,T),Hq3) for the velocity field and in an anisotropic space Hp1((0,T),Lq)∩Lp((0,T),Hq2) for the magnetic fields with 2<p<∞, N<q<∞ and 2/p+N/q<1. To prove our main result, we used the Lp-Lq maximal regularity theorem for the Stokes equations with free boundary conditions and for the magnetic field equations with transmission conditions, which have been obtained by Frolova and the second author.

scholarly journals Identification of Corrosion on a Hollow Tube Using Vibration

2014 ◽  
Vol 564 ◽  
pp. 176-181
Author(s):  
S.T. Cheng ◽  
Nawal Aswan Abdul Jalil ◽  
Zamir A. Zulkefli
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Impact Loading ◽  
Structural Damage ◽  
Natural Frequencies ◽  
Localized Corrosion ◽  
Free Boundary Conditions ◽  
The Impact ◽  
Impact Vibration

Vibration based technique have so far been focused on the identification of structural damage. However, not many studies have been conducted on the corrosion identification on pipes. The objective of this paper is to identify corrosion on pipes from vibration measurements. A hollow pipe, 500 mm in length with 63.5 mm in diameter was subjected to impact loading using an impact hammer to identify the natural frequency of the tube in two conditions i) without any corrosion and ii) with an induced localized 40 mm by 40 mm corrosion at the middle of the pipe. The shift of natural frequencies of the structures under free boundary conditions was examined for each node of excitation. The results showed that there is a shift in natural frequency of the pipe, between 3 and 4 Hz near to the corrosion area. It can suggested that that the impact vibration is capable of identifying of localized corrosion on a hollow tube.

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