I-5 Complex Potential, Velocity Potential and Joukowski Transformation

2009 ◽  
pp. 151-180
Keyword(s):  
Complex Potential ◽  
Velocity Potential ◽  
Potential Velocity

A note on Stokes's stream function for motion with a spherical boundary

1953 ◽  
Vol 49 (1) ◽  
pp. 169-174 ◽  
Author(s):  
S. F. J. Butler
Keyword(s):  
Circular Cylinder ◽  
Stream Function ◽  
Complex Potential ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Irrotational Flow ◽  
Circle Theorem ◽  
Spherical Boundary

The circle theorem of Milne-Thomson(1) connecting the complex potential in a two-dimensional irrotational flow about a circular cylinder with that of the flow when the cylinder is absent has a three-dimensional counterpart in the result due to Weiss (3) for the perturbed velocity potential in an unlimited irrotational flow when the rigid spherical boundary r = a is inserted.

scholarly journals Airplane Vortices Evolution Near Ground

2021 ◽  
Vol 11 (1) ◽  
pp. 457
Author(s):  
Josep M. Duró ◽  
Josep M. Bergadà
Keyword(s):  
Complex Potential ◽  
Velocity Potential ◽  
Minimum Time ◽  
Atmospheric Conditions ◽  
Potential Equation ◽  
Vortical Structures ◽  
Pressure Fields ◽  
Flow Circulation ◽  
Time Required ◽  
Over Time

Airport traffic around the world has sharply increased over the years; as a result, airports need to be enlarged and the landing or taking off times between two consecutive airplanes must be reduced. To precisely determine the minimum time required between two consecutive airplanes, it is essential to understand the main physical characteristics of the vortices generated under airplanes’ wings and their evolution under different atmospheric conditions. In the present paper, such information is obtained through the complex potential equation of a vortex together with the potential Bernoulli equation. The process starts with the characteristic complex potential equation, which is simplified to find the velocity potential function. Then, the temporal movement of the vortices’ central core, the velocity and pressure fields around the vortical structures and the effect of the crosswind on the vortices’ displacement, velocity and pressure fields are obtained. The paper shows how optimizing the process of measuring and calculating the vortices’ behavior could save a certain amount of time between airplanes, therefore increasing airport throughput. This paper introduces a potential flow method, which is coupled with the temporal variation of the flow circulation, to predict the vortices’ behavior and movement over time. The inclusion of circulation decay over time is employed to simulate the viscosity effect over the vortical structures. The in-house code generates results in less than one minute and needs to be seen as a tool to determine, for each airport and crosswind condition, the minimum time needed between two consecutive airplanes.

scholarly journals Free-Boundary Seepage from Asymmetric Soil Channels

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Adrian Carabineanu
Keyword(s):  
Velocity Field ◽  
Free Boundary ◽  
Complex Potential ◽  
Inverse Method ◽  
Integral Representations ◽  
Taylor Coefficients ◽  
Seepage Loss ◽  
Stream Lines ◽  
Potential Velocity

We present an inverse method for the study of the seepage from soil channels without lining. We give integral representations of the complex potential, velocity field, stream lines, free phreatic lines, and contour of the channel by means of Levi-Civitá's functionω. For different values of the Taylor coefficients ofω, we calculate numerically the contour of the channel, the phreatic lines, the seepage loss, the velocity field, the stream lines, and the equipotential lines. Examples are given for various symmetric or asymmetric channels, with smooth contours or with angular points.

A New Approach to the Theory of Thin, Slightly Cambered Profiles

1957 ◽  
Vol 24 (2) ◽  
pp. 177-182
Author(s):  
F. S. Weinig
Keyword(s):  
Complex Variable ◽  
Complex Potential ◽  
Imaginary Axis ◽  
Velocity Potential ◽  
Order Approximation ◽  
New Approach ◽  
The Real ◽  
First Order ◽  
First Order Approximation ◽  
Derivatives Of

Abstract If real and imaginary parts of a function of a complex variable are interpreted as velocity potential and stream function, then real and imaginary parts of the kth derivatives are the (k–1) st derivatives of the velocity components in the direction of the real and negative imaginary axis. For slightly cambered profiles that deviate little from the real axis and have the shape of a polynomial of nth order, the imaginary part of the nth derivative of the complex potential is constant in first-order approximation. It is easy to establish such functions of the complex variable in the case of single as well as cascade profiles. Integration then yields the intended results. While there is no continuing need for such a method for single profiles, it is needed for cascades of profiles.

Multipole expansions in the theory of surface waves

1953 ◽  
Vol 49 (4) ◽  
pp. 707-716 ◽  
Author(s):  
R. C. Thorne
Keyword(s):  
Circular Cylinder ◽  
Surface Waves ◽  
Complex Potential ◽  
Velocity Potential ◽  
The Body ◽  
Two Dimensional ◽  
Exact Form ◽  
Dimensional Problem ◽  
Different Types ◽  
Multipole Expansions

Problems dealing with the generation of surface waves in water involve the consideration of singularities of different types in the liquid. In the case when bodies are present in the liquid, waves may be either generated by the movement of the body, or reflected from the body. The two cases are essentially equivalent, and the resulting motion can be described by a series of singularities placed within the body. The boundary conditions on the surface of the body give equations from which the exact form of the potential can be obtained. Ursell (10) has solved in this manner the problem, earlier discussed by Dean(1), of the generation of surface waves by a submerged circular cylinder. In this two-dimensional problem he used a series of complex potential functions arising from multipoles at the centre of the cylinder, but the velocity potential of the motion could have been described, without the introduction of the stream function, in terms of the velocity potentials of the multipoles.

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.

scholarly journals Local Dynamic Path Planning for an Ambulance Based on Driving Risk and Attraction Field

2021 ◽  
Vol 13 (6) ◽  
pp. 3194
Author(s):  
Fang Zong ◽  
Meng Zeng ◽  
Yang Cao ◽  
Yixuan Liu
Keyword(s):  
Path Planning ◽  
Potential Field ◽  
Velocity Potential ◽  
Attractive Potential ◽  
Local Dynamic ◽  
Repulsive Potential ◽  
Ambulance Personnel ◽  
Lane Changing ◽  
Dynamic Path Planning ◽  
Dynamic Path

Path planning is one of the most important aspects for ambulance driving. A local dynamic path planning method based on the potential field theory is presented in this paper. The potential field model includes two components—repulsive potential and attractive potential. Repulsive potential includes road potential, lane potential and obstacle potential. Considering the driving distinction between an ambulance and a regular vehicle, especially in congested traffic, an adaptive potential function for a lane line is constructed in association with traffic conditions. The attractive potential is constructed with target potential, lane-velocity potential and tailgating potential. The design of lane-velocity potential is to characterize the influence of velocity on other lanes so as to prevent unnecessary lane-changing behavior for the sake of time-efficiency. The results obtained from simulation demonstrate that the proposed method yields a good performance for ambulance driving in an urban area, which can provide support for designing an ambulance support system for the ambulance personnel and dispatcher.

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

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