Complex velocity potential for an ellipse and a circle in translation and rotation

1997 ◽  
Vol 2 (4) ◽  
pp. 252-257
Author(s):  
R. Sun ◽  
A.T. Chwang
Keyword(s):  
Velocity Potential ◽  
Complex Velocity ◽  
Complex Velocity Potential

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.

scholarly journals Asymmetric impact between liquid and solid wedges

2013 ◽  
Vol 469 (2150) ◽  
pp. 20120203 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Mapping Function ◽  
Solution Procedure ◽  
Contact Angles ◽  
The Body ◽  
Surface Shape ◽  
Parameter Plane ◽  
Complex Velocity Potential ◽  
The Impact

The hydrodynamic problem of impact between a solid wedge and a liquid wedge is analysed. The liquid is assumed to be ideal and incompressible; gravity and surface tension effects are ignored. The flow generated by the impact is assumed to be irrotational and therefore can be described by the velocity potential theory. The solution procedure is based on the analytical derivation of the complex-velocity potential in a parameter plane and the function mapping conformally the parameter plane onto the similarity plane. The mapping function is found as a combination of the derivatives of the complex potential in the similarity and parameter planes, through the integral equations for mixed and homogeneous boundary-value problems in terms of the velocity modulus and the velocity angle with the fluid boundary, together with the dynamic and kinematic boundary conditions. These equations are solved through a numerical method. The procedure is first verified through comparisons with some known results. Simulations are then made for a variety of cases, and detailed results are presented in terms of the free surface shape, streamlines, pressure distribution on the wetted solid surface, and contact angles between the free surface and the body surface.

scholarly journals Impact of liquids with different densities

2015 ◽  
Vol 766 ◽  
pp. 5-27 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu ◽  
A. A. Korobkin
Keyword(s):  
Velocity Potential ◽  
Normal Component ◽  
Mapping Function ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Complex Conjugate ◽  
Hodograph Method ◽  
Velocity Magnitude ◽  
Complex Velocity Potential ◽  
The Impact

AbstractThe collision of liquids of different densities is studied theoretically for the case of liquids having wedge-shaped configuration before the impact. Both liquids are assumed to be ideal and incompressible, and the velocity potential theory is used for the flow of each liquid. Surface tension and gravity effects are neglected. The problem is decomposed into two self-similar problems, one for each liquid. Across the interface between the liquids, continuity of the pressure and the normal component of the velocity is enforced through iteration. This determines the shape of the interface and other flow parameters. The integral hodograph method is employed to derive the solution consisting of analytical expressions for the complex-velocity potential, the complex-conjugate velocity, and the mapping function. They are all defined in the first quadrant of a parameter plane, in which the original boundary-value problem is reduced to a system of integro-differential equations in terms of the velocity magnitude and the velocity angle relative to the flow boundary. They are solved numerically using the method of successive approximations. The results are presented through streamlines, interface and free-surface shapes, the pressure and velocity distributions. Special attention is given to the structure of the splash jet rising as a result of the impact.

EXPERIMENTAL STUDY OF DRIFT OBJECTS USING SPATIOTEMPORAL DATA UNDER COMPLEX VELOCITY FIELD

2020 ◽  
Vol 76 (2) ◽  
pp. I_313-I_318
Author(s):  
Yu CHIDA ◽  
Nobuki FUKUI ◽  
Nobuhito MORI ◽  
Tomohiro YASUDA ◽  
Takashi YAMAMOTO
Keyword(s):  
Experimental Study ◽  
Velocity Field ◽  
Spatiotemporal Data ◽  
Complex Velocity

The Supersonic Flow Past a Slender Ducted Body of Revolution with an Annular Intake

1950 ◽  
Vol 1 (4) ◽  
pp. 305-318
Author(s):  
G. N. Ward
Keyword(s):  
Supersonic Flow ◽  
Velocity Potential ◽  
Operational Calculus ◽  
The Body ◽  
Body Of Revolution ◽  
Internal Flows ◽  
Flow Past ◽  
External Forces ◽  
Internal Pressures ◽  
Slender Body Of Revolution

SummaryThe approximate supersonic flow past a slender ducted body of revolution having an annular intake is determined by using the Heaviside operational calculus applied to the linearised equation for the velocity potential. It is assumed that the external and internal flows are independent. The pressures on the body are integrated to find the drag, lift and moment coefficients of the external forces. The lift and moment coefficients have the same values as for a slender body of revolution without an intake, but the formula for the drag has extra terms given in equations (32) and (56). Under extra assumptions, the lift force due to the internal pressures is estimated. The results are applicable to propulsive ducts working under the specified condition of no “ spill-over “ at the intake.

Sign in / Sign up

Export Citation Format

Share Document