scholarly journals Supercritical flow of an ideal fluid over a spillway

1977 ◽  
Vol 20 (2) ◽  
pp. 211-225
Author(s):  
I. L. Collings ◽  
R. Grimshaw
Keyword(s):  
Froude Number ◽  
Ideal Fluid ◽  
Asymptotic Expansions ◽  
Matched Asymptotic Expansions ◽  
Inviscid Fluid ◽  
Supercritical Flow ◽  
Irrotational Flow ◽  
Outer Expansion

AbstractThe irrotational flow of an incompressible, inviscid fluid over a spiliway is considered. The reciprocal ε of the Froude number is taken to be small and the method of matched asymptotic expansions is applied. The bed of the spillway is horizontal far upstream and makes an angle α with the horizontal far downstream. The inner expansion is valid upstream and over the spillway, but is invalid far downstream. The outer expansion which is valid downstream fails to satisfy the upstream conditions. Unknown constants in the outer expansion are determined by the matching and composite expansions obtained.

Nonlinearity of the three-dimensional flow past a flat blunt ship

1981 ◽  
Vol 108 ◽  
pp. 345-361 ◽  
Author(s):  
Gilles Fernandez
Keyword(s):  
Froude Number ◽  
Asymptotic Expansions ◽  
Three Dimensional ◽  
Matched Asymptotic Expansions ◽  
Three Dimensional Flow ◽  
Order Unity ◽  
Dimensional Flow ◽  
Flow Past

The nonlinearity of the gravity sea flow past a three-dimensional flat blunt ship with a length-based Froude number of order unity is studied using the method of matched asymptotic expansions. It is shown that the nonlinearity is important in an inner domain near the ship, whereas the flow in the rest of the fluid domain is the solution of a Neumann-Kelvin problem. Two possible inner solutions – a jet and a wave – are obtained and discussed.

The jet from a horizontal slot at large Froude number

1973 ◽  
Vol 73 (3) ◽  
pp. 515-529 ◽  
Author(s):  
G. Keady
Keyword(s):  
Asymptotic Expansion ◽  
Flow Field ◽  
Froude Number ◽  
Asymptotic Expansions ◽  
Complex Potential ◽  
Horizontal Plane ◽  
Two Dimensional ◽  
Outer Expansion ◽  
Two Dimensional Flow ◽  
Independent Variable

The two-dimensional flow in a jet, falling under gravity from a slot in a horizontal plane, is studied. The fluid is considered to be incompressible and inviscid; the flow is taken to be irrotational; and the reciprocal ε of the Froude number is considered to be small. By taking the complex potential as the independent variable we overcome the difficulty that the boundary geometry is not known in advance. The method of matched asymptotic expansions is applied. The first two terms of an inner asymptotic expansion and the first three of an outer one are found: the inner expansion is valid above and near the slot, but is inappropriate far downstream, while the outer expansion is valid far downstream, but fails to satisfy the conditions upstream. The two expansions are matched and ‘composite’ approximations, covering the whole flow field, are derived.

The Thin-Hydrofoil Thickness Problem Including Leading-Edge Corrections

1975 ◽  
Vol 19 (02) ◽  
pp. 122-129
Author(s):  
Allen Plotkin
Keyword(s):  
Froude Number ◽  
Asymptotic Expansions ◽  
Potential Flow ◽  
Leading Edge ◽  
Matched Asymptotic Expansions ◽  
Pitching Moment ◽  
Depth Ratio ◽  
Uniform Stream

The method of Keldysh and Lavrentiev is used to study the potential flow of a uniform stream past a submerged thin symmetric hydrofoil. An expression for the surface speed is obtained and the method of matched asymptotic expansions is used to develop corrections at the round leading edge. The pressure, lift, drag, and pitching moment are presented for the Joukowski hydrofoil with emphasis on the variation with thickness, Froude number, and chord-to-depth ratio.

On the use of the method of matched asymptotic expansions in propeller aerodynamics and acoustics

1992 ◽  
Vol 242 ◽  
pp. 117-143 ◽  
Author(s):  
H. H. Brouwer
Keyword(s):  
Asymptotic Expansions ◽  
Axial Flow ◽  
Matched Asymptotic Expansions ◽  
Analysis Method ◽  
Numerical Application ◽  
Outer Expansion ◽  
Line Equation ◽  
Practical Analysis ◽  
Lifting Line ◽  
Analytical Expressions

The applicability of the method of matched asymptotic expansions to both propeller aerodynamics and acoustics is investigated. The method is applied to a propeller with blades of high aspect ratio, in a uniform axial flow. The first two terms of the inner expansion and the first three terms of the outer expansion are considered. The matching yields an expression for the spanwise distribution of the downwash velocity. A numerical application shows that the first two terms of the inner solution do not yield an acceptable approximation for the downwash velocity. However, recasting the analytical expressions into an integral equation, similar to Prandtl's lifting line equation for wings, yields results for both aerodynamic and acoustic quantities, which agree well with experimental results. The method thus constitutes a practical analysis method for conventional propellers.

Asymptotic Methods for an Infinite Slider Bearing With a Discontinuity in Film Slope

1976 ◽  
Vol 98 (3) ◽  
pp. 446-452 ◽  
Author(s):  
J. A. Schmitt ◽  
R. C. DiPrima
Keyword(s):  
Boundary Layer ◽  
Film Thickness ◽  
Asymptotic Expansions ◽  
Asymptotic Expression ◽  
Asymptotic Methods ◽  
Matched Asymptotic Expansions ◽  
Slider Bearing ◽  
Trailing Edge ◽  
Slider Bearings ◽  
Special Cases

The method of matched asymptotic expansions is used to develop an asymptotic expression for the pressure for large bearing numbers for the case of an infinite slider bearing with a general film thickness that has a discontinuous slope at a point. It is shown that, in addition to the boundary layer of the pressure at the trailing edge, there is also a boundary layer in the derivative of the pressure at the point of discontinuity. The corresponding load formula is also derived. The special cases of the taper-flat and taper-taper slider bearings are discussed.

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