scholarly journals The Two-Phase Hell-Shaw Flow: Construction of an Exact Solution

2013 ◽  
Vol 18 (1) ◽  
pp. 249-257
Author(s):  
K.R. Malaikah
Keyword(s):  
Exact Solution ◽  
Velocity Potential ◽  
Time Dependent ◽  
Computational Domain ◽  
Phase Problem ◽  
Complex Velocity ◽  
Two Phase ◽  
Interface Evolution ◽  
Complex Velocity Potential ◽  
Branch Cuts

We consider a two-phase Hele-Shaw cell whether or not the gap thickness is time-dependent. We construct an exact solution in terms of the Schwarz function of the interface for the two-phase Hele-Shaw flow. The derivation is based upon the single-valued complex velocity potential instead of the multiple-valued complex potential. As a result, the construction is applicable to the case of the time-dependent gap. In addition, there is no need to introduce branch cuts in the computational domain. Furthermore, the interface evolution in a two-phase problem is closely linked to its counterpart in a one-phase problem

The almost-highest wave: a simple approximation

1979 ◽  
Vol 94 (2) ◽  
pp. 269-273 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Free Surface ◽  
Gravity Wave ◽  
Velocity Potential ◽  
Vertical Plane ◽  
Simple Approximation ◽  
Complex Velocity ◽  
Complex Velocity Potential

The crest of a steep, symmetric gravity wave is shown to be closely approximated by the expression \[ x+iy = \frac{\alpha +\gamma i\chi}{(\beta + i\chi)^{\frac{1}{3}}}, \] where x, y are co-ordinates in the vertical plane, χ is the complex velocity potential and α, β, γ are certain constants. This expression is asymptotically correct both for small and for large values of |χ|; and the free surface agrees with the exact profile calculated by Longuet-Higgins & Fox (1977) everywhere to within 1·5 per cent. The pressure at the surface is constant to within 5 per cent.

The solitary wave of maximum amplitude

1966 ◽  
Vol 26 (2) ◽  
pp. 309-320 ◽  
Author(s):  
Charles W. Lenau
Keyword(s):  
Power Series ◽  
Solitary Wave ◽  
Velocity Potential ◽  
Maximum Amplitude ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Complex Velocity ◽  
Constant Form ◽  
Complex Velocity Potential ◽  
Infinite Power

The maximum amplitude of the solitary wave of constant form is determined to be 0·83b, where b is the depth far from the crest. In the analysis it is assumed that the crest is pointed and the motion is two-dimensional and irrotational. The complex velocity potential is expressed in terms of known singularities and an infinite power series with unknown coefficients. Approximate solutions are obtained by truncating the power series after N terms, where N = 1, 3, 5, 7, and 9. The amplitude, a measure of the error, and several other pertinent quantities are computed for each value of N.

Random Forces Resulting From Internal Two-Phase Flow on Bends and Tees

2006 ◽  
Author(s):  
E. de Langre ◽  
J. L. Riverin ◽  
M. J. Pettigrew
Keyword(s):  
Two Phase Flow ◽  
Experimental Results ◽  
Time Dependent ◽  
Phase Flow ◽  
Water Mixture ◽  
Dimensionless Form ◽  
Two Phase ◽  
Practical Applications ◽  
Random Forces

The time dependent forces resulting from a two-phase air-water mixture flowing in an elbow and a tee are measured. Their magnitudes as well as their spectral contents are analyzed. Comparison is made with previous experimental results on similar systems. For practical applications a dimensionless form is proposed to relate the characteristics of these forces to the parameters defining the flow and the geometry of the piping.

Detonation-propelled shocks in tubular charges as a two-phase problem

2012 ◽  
Vol 340 (11-12) ◽  
pp. 900-909 ◽  
Author(s):  
Irina Brailovsky ◽  
Gregory Sivashinsky
Keyword(s):  
Phase Problem ◽  
Two Phase

A Developed Numerical Method for Turbulent Unsteady Fluid Flow in Two-Phase Systems with Moving Interface

2017 ◽  
Vol 14 (06) ◽  
pp. 1750063 ◽  
Author(s):  
A. M. Hegab ◽  
S. A. Gutub ◽  
A. Balabel
Keyword(s):  
Numerical Model ◽  
Gas Phase ◽  
Level Set ◽  
The Body ◽  
Phase System ◽  
Computational Domain ◽  
Two Phase ◽  
Moving Interface ◽  
Level Set Function ◽  
Gas System

This paper presents the development of an accurate and robust numerical modeling of instability of an interface separating two-phase system, such as liquid–gas and/or solid–gas systems. The instability of the interface can be refereed to the buoyancy and capillary effects in liquid–gas system. The governing unsteady Navier–Stokes along with the stress balance and kinematic conditions at the interface are solved separately in each fluid using the finite-volume approach for the liquid–gas system and the Hamilton–Jacobi equation for the solid–gas phase. The developed numerical model represents the surface and the body forces as boundary value conditions on the interface. The adapted approaches enable accurate modeling of fluid flows driven by either body or surface forces. The moving interface is tracked and captured using the level set function that initially defined for both fluids in the computational domain. To asses the developed numerical model and its versatility, a selection of different unsteady test cases including oscillation of a capillary wave, sloshing in a rectangular tank, the broken-dam problem involving different density fluids, simulation of air/water flow, and finally the moving interface between the solid and gas phases of solid rocket propellant combustion were examined. The latter case model allowed for the complete coupling between the gas-phase physics, the condensed-phase physics, and the unsteady nonuniform regression of either liquid or the propellant solid surfaces. The propagation of the unsteady nonplanar regression surface is described, using the Essentially-Non-Oscillatory (ENO) scheme with the aid of the level set strategy. The computational results demonstrate a remarkable capability of the developed numerical model to predict the dynamical characteristics of the liquid–gas and solid–gas flows, which is of great importance in many civilian and military industrial and engineering applications.

Sign in / Sign up

Export Citation Format

Share Document