Asymptotic Expansions for Two Dimensional Symmetrical Laminar Wakes

2002 ◽  
Vol 82 (4) ◽  
pp. 219 ◽  
Author(s):  
M. Belan ◽  
D. Tordella
Keyword(s):  
Asymptotic Expansions ◽  
Two Dimensional ◽  
Laminar Wakes

scholarly journals Two-dimensional resonators with small openings

1982 ◽  
Vol 24 (1) ◽  
pp. 2-27 ◽  
Author(s):  
G. R. Bigg ◽  
E. O. Tuck
Keyword(s):  
Natural Frequency ◽  
Asymptotic Expansions ◽  
Velocity Potential ◽  
Low Frequency ◽  
Matched Asymptotic Expansions ◽  
Two Dimensional ◽  
Acoustic Response ◽  
Closed Cavity ◽  
Small Opening

AbstractThe acoustic response of a two-dimensional nearly-closed cavity to an excitation through a small opening is examined, using the method of matched asymptotic expansions. The Helmholtz mode of vibration is discussed using a low-frequency expansion of the velocity potential in the cavity interior. The variation in frequency and magnitude of the resonator response is explored, both for the Helmholtz and the natural-frequency modes.

The Interaction of Thermal Radiation in Optically Thick Boundary Layers

1967 ◽  
Vol 89 (4) ◽  
pp. 309-312 ◽  
Author(s):  
J. L. Novotny ◽  
Kwang-Tzu Yang
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Boundary Layers ◽  
Optical Thickness ◽  
Asymptotic Expansions ◽  
Energy Equation ◽  
Two Dimensional ◽  
Small Temperature ◽  
Dimensional Boundary

An analysis is presented to examine the role of the Rosseland or optically thick approximation in convection-radiation interaction situations. The analysis is formulated for the flow of a gray gas in a laminar two-dimensional boundary layer under the restriction of small temperature differences within the flow field. The boundary-layer energy equation is treated using the method of matched asymptotic expansions based on a parameter which characterizes the optical thickness of the gas. Two illustrative examples of the resulting equations are presented.

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.

Triple-deck solutions for supersonic flows past flared cylinders

1987 ◽  
Vol 179 ◽  
pp. 469-487 ◽  
Author(s):  
Ph. Gittler ◽  
A. Kluwick
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Asymptotic Expansions ◽  
Numerical Solutions ◽  
Reynolds Numbers ◽  
Hysteresis Phenomenon ◽  
Two Dimensional ◽  
Planar Flow ◽  
Laminar Boundary Layers ◽  
External Flows

Using the method of matched asymptotic expansions, the interaction between axisymmetric laminar boundary layers and supersonic external flows is investigated in the limit of large Reynolds numbers. Numerical solutions to the interaction equations are presented for flare angles α that are moderately large. If α > 0 the boundary layer separates upstream of the corner and the formation of a plateau structure similar to the two-dimensional case is observed. In contrast to the case of planar flow, however, separation can occur also if α < 0, owing to the axisymmetric effect of overexpansion and recompression. The separation point then is located downstream of the corner and, most remarkable, a hysteresis phenomenon is observed.

Transonic flow around the leading edge of a thin airfoil with a parabolic nose

1993 ◽  
Vol 248 ◽  
pp. 1-26 ◽  
Author(s):  
Z. Rusak
Keyword(s):  
Pressure Distribution ◽  
Stagnation Point ◽  
Asymptotic Expansions ◽  
Potential Flow ◽  
Angle Of Attack ◽  
Leading Edge ◽  
Two Dimensional ◽  
Small Disturbance ◽  
Outer Expansion ◽  
Inner Region

Transonic potential flow around the leading edge of a thin two-dimensional general airfoil with a parabolic nose is analysed. Asymptotic expansions of the velocity potential function are constructed at a fixed transonic similarity parameter (K) in terms of the thickness ratio of the airfoil in an outer region around the airfoil and in an inner region near the nose. These expansions are matched asymptotically. The outer expansion consists of the transonic small-disturbance theory and it second-order problem, where the leading-edge singularity appears. The inner expansion accounts for the flow around the nose, where a stagnation point exists. Analytical expressions are given for the first terms of the inner and outer asymptotic expansions. A boundary value problem is formulated in the inner region for the solution of a uniform sonic flow about an infinite two-dimensional parabola at zero angle of attack, with a symmetric far-field approximation, and with no circulation around it. The numerical solution of the flow in the inner region results in the symmetric pressure distribution on the parabolic nose. Using the outer small-disturbance solution and the nose solution a uniformly valid pressure distribution on the entire airfoil surface can be derived. In the leading terms, the flow around the nose is symmetric and the stagnation point is located at the leading edge for every transonic Mach number of the oncoming flow and shape and small angle of attack of the airfoil. The pressure distribution on the upper and lower surfaces of the airfoil is symmetric near the edge point, and asymmetric deviations increase and become significant only when the distance from the leading edge of the airfoil increases beyond the inner region. Good agreement is found in the leading-edge region between the present solution and numerical solutions of the full potential-flow equations and the Euler equations.

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