The effects of capillarity on free-streamline separation

1975 ◽  
Vol 70 (2) ◽  
pp. 333-352 ◽  
Author(s):  
R. C. Ackerberg
Keyword(s):  
Surface Tension ◽  
Boundary Conditions ◽  
Pressure Gradient ◽  
Classical Solution ◽  
Capillary Wave ◽  
Small Region ◽  
Linear Boundary ◽  
Small Surface ◽  
First Approximation ◽  
Singular Behaviour

The effect of a small surface-tension coefficient on the classical theory of free-streamline separation from a sharp trailing edge is studied. The classical solution fails in a small region surrounding the edge, where it predicts singular behaviour, and an inner solution, satisfying linear boundary conditions, is required to obtain a uniformly valid first approximation. The solution valid near the edge removes the curvature and pressure-gradient singularities of the classical solution and predicts a standing capillary wave along the free streamline.

scholarly journals The viscosity of a fluid containing small drops of another fluid

1932 ◽  
Vol 138 (834) ◽  
pp. 41-48 ◽  
Keyword(s):  
Surface Tension ◽  
Boundary Conditions ◽  
Solid Particles ◽  
Complete Agreement ◽  
Small Surface ◽  
Liquid Drops ◽  
Viscous Forces ◽  
Fluid Drop ◽  
Combined Action ◽  
Experimental Researches

The viscosity of a fluid in which small solid spheres are suspended has been studied by Einstein as a problem in theoretical hydrodynamics. Einstein’s paper gave rise to many experimental researches on the viscosity of fluids containing solid particles, and it soon became clear that though complete agreement with the theory might be expected when the particles are true sphered, some modification is necessary when the particles are flattened or elongated. The theory of such systems was developed by G. B. Jeffery, who calculated the motion of ellipsoidal particles in a viscous fluid and their effect on the mean viscosity. Some of his conclusions have been verified by observation. So far no one seems to have extended Einstein’s work to liquids containing small drops of another liquid in suspension. The difficulties in the way of a complete theory when solid particles are replaced by fluid drops are almost insuperable, partly because the correct boundary conditions are not known, and partly because a fluid drop would deform under the combined action of viscous forces and surface tension. Even if the boundary conditions were known to be those commonly used in hydrodynamical theory, the calculation of the shape of the deformed drop would be exceedingly difficult. When the radius of the suspended drops or the velocity of distortion of the fluid are small, surface tension may be expected to keep them nearly spherical, and in that case Einstein’s analysis may be extended so as to include the case of liquid drops.

Numerical Analysis of the Primary Breakup Under High-Altitude Relight Conditions Applying the Embedded DNS Approach to a Generic Prefilming Airblast Atomizer

2013 ◽  
Author(s):  
Benjamin Sauer ◽  
Nikolaos Spyrou ◽  
Amsini Sadiki ◽  
Johannes Janicka
Keyword(s):  
Surface Tension ◽  
Boundary Conditions ◽  
High Altitude ◽  
Ambient Pressure ◽  
Planar Geometry ◽  
Slight Variation ◽  
Strong Impact ◽  
Wall Film ◽  
Primary Breakup ◽  
Liquid Wall

The primary breakup under high-altitude relight conditions is investigated in this study where ambient pressure is as low as 0.4 bar and air, fuel and engine parts are as cold as 265 K. The primary breakup is crucial for the fuel atomization. As of today, the phenomena dictating the primary breakup are not fully understood. Direct Numerical Simulations (DNS) of liquid breakup under realistic conditions and geometries are hardly possible. The embedded DNS (eDNS) approach represents a reliable numerical tool to fill this gap. The concept consists of three steps: a geometry simplification, the generation of realistic boundary conditions for the DNS and the DNS of the breakup region. The realistic annular airblast atomizer geometry is simplified to a Y-shaped channel representing a planar geometry. Inside this domain the eDNS is located. The eDNS domain requires the generation of boundary conditions. A Large Eddy Simulation (LES) of the entire Y-shaped channel and a Reynolds-Averaged Navier-Stokes Simulation (RANS) of the liquid wall film are performed prior to the DNS. All parameters are stored transiently on all virtual DNS planes. These variables are then mapped to the DNS. Thus, high-quality boundary conditions are generated. The Volume-of-Fluid (VOF) method is used to solve for the two-phase flow. The results provide a qualitative insight into the primary breakup under realistic high-altitude relight conditions. Instantaneous snapshots in time illustrate the behavior of the liquid wall film along the prefilmer lip and illustrate the breakup process. It is seen that a slight variation of the surface tension force has a strong impact on the appearance of the primary breakup. Case 1 with the surface tension corresponding to kerosene at 293 K indicates large flow structures that are separated from the liquid sheet. By lowering the surface tension related to kerosene at 363 K, the breakup is dominated by numerous small structures and droplets. This study proves the applicability of the eDNS concept for investigating breakup processes as the transient nature of the phase interface behavior can be captured. At this time, the authors only present a qualitative insight which can be explained by the lack of quantitative data. The approach offers the potential of simulating realistic annular highly-swirled airblast atomizer geometries under realistic conditions.

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

On the Existence and the Uniform Decay of a Hyperbolic Equation with Non-Linear Boundary Conditions

2000 ◽  
Vol 24 (2) ◽  
pp. 183-199 ◽  
Author(s):  
M. M. Cavalcanti ◽  
V. N. Domingos Cavalcanti ◽  
J. A. Soriano ◽  
L. A. Medeiros
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Linear Boundary ◽  
Uniform Decay ◽  
Non Linear
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