Stream function of the two-dimensional flow problem, Robin potential, and the exterior Dirichlet problem

2004 ◽  
Vol 49 (2) ◽  
pp. 116-118
Author(s):  
V. G. Lezhnev
Keyword(s):  
Dirichlet Problem ◽  
Stream Function ◽  
Flow Problem ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow

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.

scholarly journals On the Exact Solutions of Couple Stress Fluids

2014 ◽  
Vol 1 ◽  
pp. 27-32 ◽  
Author(s):  
Waqar Khan ◽  
Faisal Yousafzai
Keyword(s):  
Exact Solutions ◽  
Stream Function ◽  
Couple Stress ◽  
Two Dimensional ◽  
Compatibility Equation ◽  
Flow Equations ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Stream Functions ◽  
Couple Stress Fluids

Exact solutions of the momentum equations of couple stress fluid are investigated. Making use of stream function, the two-dimensional flow equations are transformed into non-linear compatibility equation, and then it is linearized by vorticity function. Stream functions and velocity distributions are discussed for various flow situations.

Steady two-dimensional viscous flow in a jet

1972 ◽  
Vol 55 (1) ◽  
pp. 49-63 ◽  
Author(s):  
K. Capell
Keyword(s):  
Point Source ◽  
Viscous Flow ◽  
Closed Form ◽  
Stream Function ◽  
Asymptotic Expansions ◽  
Far Field ◽  
Two Dimensional ◽  
Complete Structure ◽  
Dimensional Flow ◽  
Two Dimensional Flow

An idealized two-dimensional flow due to a point source ofxmomentum is discussed. In the far field the flow is modelled by a jet region of large vorticity outside which the flow is potential. After use of the transformation\[ \zeta^3 = (\xi + i\eta)^3 = x + iy, \]the equations suggest naively obvious asymptotic expansions for the stream function in these two regions, namely\[ \sum_{n=0}^{\infty}\xi^{1-n}f_n(\eta)\quad {\rm and}\quad\sum_{n=0}^{\infty}\xi^{1-n}F_n(\eta/\xi) \]respectively. Consistency in matching these expansions is achieved by including logarithmic terms associated with the occurrence of eigensolutions.Fnis easy to find andJncan be found in closed form so the inner and outer eigensolutions may be fully determined along with the complete structure of the expansions.

scholarly journals The iterated equation of generalized axially symmetric potential theory. I. Particular solutions

1967 ◽  
Vol 7 (3) ◽  
pp. 263-276 ◽  
Author(s):  
J. C. Burns
Keyword(s):  
Potential Theory ◽  
Stream Function ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Symmetric Flow ◽  
Symmetric Potential ◽  
Dimensional Flow ◽  
Physical Problems ◽  
Two Dimensional Flow ◽  
Image Position

The iterated equation of generalized axially symmetric potential theory (GASPT) [1] is defined by the relations (1) where (2) and Particular cases of this equation occur in many physical problems. In classical hydrodynamics, for example, the case n = 1 appears in the study of the irrotational motion of an incompressible fluid where, in two-dimensional flow, both the velocity potential φ and the stream function Ψ satisfy Laplace's equation, L0(f) = 0; and, in axially symmetric flow, φ and satisfy the equations L1 (φ) = 0, L-1 (ψ) = 0. The case n = 2 occurs in the study of the Stokes flow of a viscous fluid where the stream function satisfies the equation L2k(ψ) = 0 with k = 0 in two-dimensional flow and k = −1 in axially symmetric flow.

Two-Dimensional Flow of Polymer Solutions Through Porous Media

1999 ◽  
Vol 2 (3) ◽  
pp. 251-262
Author(s):  
P. Gestoso ◽  
A. J. Muller ◽  
A. E. Saez
Keyword(s):  
Porous Media ◽  
Polymer Solutions ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow
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