Asymmetric two-dimensional jet efflux from a channel

1977 ◽  
Vol 80 (1) ◽  
pp. 1-15
Author(s):  
C. Samuel Martin
Keyword(s):  
Experimental Data ◽  
Analytical Approach ◽  
Two Dimensional ◽  
Asymmetric Case ◽  
Hodograph Plane ◽  
Single Jet ◽  
Von Mises ◽  
Two Jets ◽  
Direct Use ◽  
Special Case

Irrotational flow of two-dimensional jets from a channel is treated without direct use of a logarithmic hodograph plane. An analytical approach is introduced for solving the general problem of two jets issuing from a channel with three end plates. Numerical values of the contraction coefficient and the angle of jet deflexion are obtained for the special case where the two jets are located symmetrically and all the end plates are in line. Limiting cases of the resulting single-jet problem are the symmetric and asymmetric configurations solved by von Mises. Results for the asymmetric case improve upon the theoretical values reported by von Mises, and compare favourably with existing experimental data.

Modelling of Moisture Movement in Wood during Outdoor Storage

2001 ◽  
Vol 6 (2) ◽  
pp. 3-14 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
I. Juodeikienė ◽  
A. Kajalavičius
Keyword(s):  
Experimental Data ◽  
Finite Difference ◽  
Climatic Conditions ◽  
Two Dimensional ◽  
Moisture Movement ◽  
Finite Difference Technique ◽  
Long Term Storage ◽  
Space Formulation ◽  
Term Storage

A model of moisture movement in wood is presented in this paper in a two-dimensional-in-space formulation. The finite-difference technique has been used in order to obtain the solution of the problem. The model was applied to predict the moisture content in sawn boards from pine during long term storage under outdoor climatic conditions. The satisfactory agreement between the numerical solution and experimental data was obtained.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

scholarly journals Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2152
Author(s):  
Gonzalo García-Alén ◽  
Olalla García-Fonte ◽  
Luis Cea ◽  
Luís Pena ◽  
Jerónimo Puertas
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Experimental Dataset ◽  
River Hydraulics ◽  
Shallow Water Models ◽  
Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

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.

MASS FUNCTION OF HALOS: A NEW ANALYTICAL APPROACH

2004 ◽  
Vol 13 (07) ◽  
pp. 1345-1349 ◽  
Author(s):  
JOSÉ A. S. LIMA ◽  
LUCIO MARASSI
Keyword(s):  
Power Law ◽  
Free Parameter ◽  
Analytical Approach ◽  
Mass Function ◽  
New Method ◽  
Power Law Distribution ◽  
The Press ◽  
The Universe ◽  
Special Case

A generalization of the Press–Schechter (PS) formalism yielding the mass function of bound structures in the Universe is given. The extended formula is based on a power law distribution which encompasses the Gaussian PS formula as a special case. The new method keeps the original analytical simplicity of the PS approach and also solves naturally its main difficult (the missing factor 2) for a given value of the free parameter.

scholarly journals A Mathematical Method for Determining the Parameters of Functional Dependencies Using Multiscale Probability Distribution Functions

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1085
Author(s):  
Ilya E. Tarasov
Keyword(s):  
Experimental Data ◽  
Probability Distribution ◽  
Integrated Circuits ◽  
Distribution Functions ◽  
Independent Parameter ◽  
Functional Dependencies ◽  
Computing Device ◽  
System On A Chip ◽  
Error Probability Distribution ◽  
Special Case

This article discusses the application of the method of approximation of experimental data by functional dependencies, which uses a probabilistic assessment of the deviation of the assumed dependence from experimental data. The application of this method involves the introduction of an independent parameter “scale of the error probability distribution function” and allows one to synthesize the deviation functions, forming spaces with a nonlinear metric, based on the existing assumptions about the sources of errors and noise. The existing method of regression analysis can be obtained from the considered method as a special case. The article examines examples of analysis of experimental data and shows the high resistance of the method to the appearance of single outliers in the sample under study. Since the introduction of an independent parameter increases the number of computations, for the practical application of the method in measuring and information systems, the architecture of a specialized computing device of the “system on a chip” class and practical approaches to its implementation based on programmable logic integrated circuits are considered.

scholarly journals On the Bean critical-state model in superconductivity

1996 ◽  
Vol 7 (3) ◽  
pp. 237-247 ◽  
Author(s):  
L. Prigozhin
Keyword(s):  
Variational Inequalities ◽  
Critical State ◽  
Existence And Uniqueness ◽  
Critical State Model ◽  
Type Ii ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Uniqueness Of The Solution ◽  
Type Ii Superconductivity ◽  
Special Case

We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.

Effects of Curvature on Laminar Boundary Layers in Sink-Type Flows

1969 ◽  
Vol 91 (3) ◽  
pp. 353-358 ◽  
Author(s):  
W. A. Gustafson ◽  
I. Pelech
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Momentum Equation ◽  
Similarity Solutions ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Thickness Increase ◽  
Laminar Boundary Layers ◽  
Converging Channel ◽  
Special Case

The two-dimensional, incompressible laminar boundary layer on a strongly curved wall in a converging channel is investigated for the special case of potential velocity inversely proportional to the distance along the wall. Similarity solutions of the momentum equation are obtained by two different methods and the differences between the methods are discussed. The numerical results show that displacement and momentum thickness increase linearly with curvature while skin friction decreases linearly.

Site-bond percolation in two-dimensional kagome lattices: Analytical approach and numerical simulations

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
M. I. González-Flores ◽  
A. A. Torres ◽  
W. Lebrecht ◽  
A. J. Ramirez-Pastor
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Bond Percolation ◽  
Two Dimensional
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