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 Three-Dimensional Inverse Method for Turbomachinery: Part I—Theory

1990 ◽  
Vol 112 (3) ◽  
pp. 346-354 ◽  
Author(s):  
J. E. Borges
Keyword(s):  
Velocity Field ◽  
Inverse Method ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Inverse Methods ◽  
Meridional Section ◽  
Low Speed ◽  
Present Procedure ◽  
Blade Row ◽  
The Mean

There are surprisingly few inverse methods described in the literature that are truly three dimensional. Here, one such method is presented. This technique uses as input a prescribed distribution of the mean swirl, i.e., radius times mean tangential velocity, given throughout the meridional section of the machine. In the present implementation the flow is considered inviscid and incompressible and is assumed irrotational at the inlet to the blade row. In order to evaluate the velocity field inside the turbomachine, the blades (supposed infinitely thin) are replaced by sheets of vorticity, whose strength is related to the specified mean swirl. Some advice on the choice of a suitable mean swirl distribution is given. In order to assess the usefulness of the present procedure, it was decided to apply it to the design of an impeller for a low-speed radial-inflow turbine. The results of the tests are described in the second part of this paper.

scholarly journals Re-examination of Large Scale Structure & Cosmic Flows

2014 ◽  
Vol 11 (S308) ◽  
pp. 310-317
Author(s):  
Marc Davis ◽  
Adi Nusser
Keyword(s):  
Perturbation Theory ◽  
Velocity Field ◽  
Gravity Field ◽  
Inverse Method ◽  
Large Scale ◽  
Linear Perturbation ◽  
Data Set ◽  
Galaxy Distribution ◽  
Standard Values ◽  
Linear Perturbation Theory

AbstractComparison of galaxy flows with those predicted from the local galaxy distribution ended as an active field after two analyses came to vastly different conclusions 25 years ago, but that was due to faulty data. All the old results are therefore suspect. With new data collected in the last several years, the problem deserves another look. The goal is to explain the 640 km/s dipole anisotropy of the CMBR. For this we analyze the gravity field inferred from the enormous data set derived from the 2MASS collection of galaxies (Huchra et al. 2005), and compare it to the velocity field derived from the well calibrated SFI++ Tully-Fisher catalog (Springob et al. 2007). Using the “Inverse Method” to minimize Malmquist biases, within 10,000 km/s the gravity field is seen to predict the velocity field (Davis et al. 2011) to remarkable consistency. This is a beautiful demonstration of linear perturbation theory and is fully consistent with standard values of the cosmological variables.

A Three Dimensional Inverse Method in Turbomachinery: Part I — Theory

1989 ◽  
Author(s):  
João Eduardo Borges
Keyword(s):  
Velocity Field ◽  
Inverse Method ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Inverse Methods ◽  
Meridional Section ◽  
Low Speed ◽  
Present Procedure ◽  
Blade Row ◽  
The Mean

There are surprisingly few inverse methods described in the literature that are truly three-dimensional. Here, one such method is presented. This technique uses as input a prescribed distribution of the mean swirl, i.e., radius times mean tangential velocity, given throughout the meridional section of the machine. In the present implementation the flow is considered inviscid and incompressible and is assumed irrotational at inlet to the blade row. In order to evaluate the velocity field inside the turbomachine, the blades (supposed infinitely thin) are replaced by sheets of vorticity whose strength is related to the specified mean swirl. Some advice on the choice of a suitable mean swirl distribution is given. In order to assess the usefulness of the present procedure, it was decided to apply it to the design of an impeller of a low-speed radial-inflow turbine. The results of the tests are described in the second part of this paper.

scholarly journals Series and integral representations of the Taylor coefficients of the Weierstrass sigma-function

2014 ◽  
Vol 34 (3) ◽  
pp. 429-442 ◽  
Author(s):  
Allal Ghanmi ◽  
Youssef Hantout ◽  
Ahmed Intissar
Keyword(s):  
Integral Representations ◽  
Taylor Coefficients ◽  
Sigma Function

Conformal mapping, Padé approximants, and an example of flow with a significant deformation of the free boundary

2014 ◽  
Vol 25 (6) ◽  
pp. 729-747 ◽  
Author(s):  
E. A. KARABUT ◽  
A. A. KUZHUGET
Keyword(s):  
Velocity Field ◽  
Free Boundary ◽  
Power Series ◽  
Conformal Mapping ◽  
Incompressible Fluid ◽  
Padé Approximants ◽  
Ideal Incompressible Fluid ◽  
Inertial Motion ◽  
Pade Approximants ◽  
Summation Of Series

A problem of plane inertial motion of an ideal incompressible fluid with a free boundary, which initially has a quadratic velocity field, is studied by semi-analytical methods. A conformal mapping of the domain occupied by the fluid onto a unit circle is sought in the form of a power series with respect to time. Summation of series is performed by using Padé approximants.

The oscillations of a viscous gravitating sphere

1969 ◽  
Vol 65 (1) ◽  
pp. 123-137
Author(s):  
D. P. McKenzie
Keyword(s):  
Velocity Field ◽  
General Solution ◽  
Laplace Transformation ◽  
Oscillating Solution ◽  
Asymptotic Solutions ◽  
Elastic Sphere ◽  
Remarkable Feature ◽  
Closed Loops ◽  
Asymptotic Expressions ◽  
Stream Lines

AbstractBy using a Laplace transformation, a general solution is obtained to the problem of the oscillations and velocity field of a viscous gravitating sphere. Lamb's oscillating solution and Darwin's exponentially decaying solution are derived as asymptotic expressions and their connexion demonstrated. Closed loops of stream lines are a remarkable feature of the flow, and the conditions for their existence are discussed. Asymptotic solutions are also obtained for the oscillations of a Maxwell sphere, and their relation to those of an elastic sphere investigated.

Generalised Hele-Shaw flow: A Schwarz function approach

2011 ◽  
Vol 22 (6) ◽  
pp. 517-532 ◽  
Author(s):  
N. R. McDONALD
Keyword(s):  
Free Boundary ◽  
Complex Potential ◽  
Singular Potential ◽  
Point Sources ◽  
Time Dependent ◽  
Potential Fields ◽  
Explicit Solutions ◽  
Centrifugal Forces ◽  
Schwarz Function ◽  
New Equation

An equation governing the evolution of a Hele-Shaw free boundary flow in the presence of an arbitrary external potential – generalised Hele-Shaw flow – is derived in terms of the Schwarz functiong(z,t) of the free boundary. This generalises the well-known equation ∂g/∂t= 2∂w/∂z, wherewis the complex potential, which has been successfully employed in constructing many exact solutions in the absence of external potentials. The new equation is used to re-derive some known explicit solutions for equilibrium and time-dependent free boundary flows in the presence of external potentials, including those with singular potential fields, uniform gravity and centrifugal forces. Some new solutions are also constructed that variously describe equilibrium flows with higher order hydrodynamic singularities in the presence of electric point sources and an unsteady solution describing bubbles under the combined influence of strain and centrifugal potential.

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