Approximate Numerical Solutions for Two-Dimensional Potential Flow Problems

1978 ◽  
Vol 100 (1) ◽  
pp. 122-124 ◽  
Author(s):  
A. Kieda ◽  
H. Yano
Keyword(s):  
Numerical Method ◽  
Surface Pressure ◽  
Potential Flow ◽  
General Class ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Weighted Residuals ◽  
Flow Problems ◽  
Pressure Distributions ◽  
Method Of Weighted Residuals

An approximate numerical method is proposed for solving two-dimensional potential flow problems. The method is included in the general class of “Method of Weighted Residuals.” Typical computed results are presented for the surface pressure distributions on an airfoil and single noncircular cylinders immersed in a uniform infinite stream.

On the Application of a Linearized Unsteady Potential-Flow Analysis to Fan-Tip Cascades

1986 ◽  
Vol 108 (1) ◽  
pp. 59-67
Author(s):  
W. J. Usab ◽  
J. M. Verdon
Keyword(s):  
Potential Flow ◽  
Vibrational Frequency ◽  
Numerical Solutions ◽  
Flow Analysis ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Good Qualitative Agreement ◽  
Blade Loading ◽  
Unsteady Aerodynamic ◽  
Flow Phenomena

A linearized potential flow analysis, which accounts for the effects of nonuniform steady flow phenomena on the unsteady response to prescribed blade motions, has been applied to five two-dimensional cascade configurations. These include a flat-plate cascade and three cascades which are representative of the tip sections of current fan designs. Here the blades are closely spaced, highly staggered, and operate at low mean incidence. The fifth configuration is a NASA Lewis cascade of symmetric biconvex airfoils for which experimental measurements are available. Numerical solutions are presented that clearly illustrate the effects and importance of blade geometry and mean blade loading on the linearized unsteady response at high subsonic inlet Mach number and high blade-vibrational frequency. In addition, a good qualitative agreement is shown between the analytical predictions and experimental measurements for the cascade of symmetric biconvex airfoils. Finally, recommendations on the research needed to extend the range of application of linearized unsteady aerodynamic analyses are provided.

Numerical Solutions of Nonsteady Two-Dimensional Transonic Flows

1979 ◽  
Vol 101 (3) ◽  
pp. 341-347 ◽  
Author(s):  
M. Couston ◽  
J. J. Angelini
Keyword(s):  
Numerical Solutions ◽  
Low Frequency ◽  
Two Dimensional ◽  
Lattice Method ◽  
Alternating Direction Implicit ◽  
Flow Problems ◽  
Present Procedure ◽  
Alternating Direction ◽  
Trailing Edge Flaps ◽  
Doublet Lattice Method

An alternating-direction implicit algorithm is applied to solve an improved formulation of the low-frequency, small-disturbance, two-dimensional potential equation. Linear solutions are presented for oscillating trailing edge flaps, plunging and pitching flat-plate airfoils, and compared with results obtained by a doublet-lattice-method. Nonlinear calculations for both steady and unsteady flow problems are then compared with results obtained by using the complete Euler equations. The present procedure allows one to solve complex aerodynamic problems, including flows with shock waves.

A rapidly convergent procedure for solving the equations of subsonic potential flow. I. Numerical solutions

1960 ◽  
Vol 255 (1280) ◽  
pp. 101-113 ◽  
Keyword(s):  
Potential Flow ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Local Density ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Approximation Solution ◽  
Flow Equations ◽  
Bernoulli’S Equation ◽  
First Approximation

The subsonic potential flow equations for a perfect gas are transformed by means of dependent variables s = ( ρ / ρ 0 ) n q/ a 0 and σ = 1/2 In ( ρ 0 / ρ ), where q is the local velocity, ρ and a the local density and speed of sound, and the suffix 0 indicates stagnation conditions, n is a parameter which is to be chosen to optimize the approximations. Bernoulli’s equation then becomes a relation between s 2 and σ which is independent of initial conditions. A family of first-approximation solutions in terms of the incompressible solution is obtained on linearizing. It is shown that for two-dimensional flow, the choice n = 0∙5 gives results as accurate as those obtained with the Karman—Tsien solution. The exact equations are then transformed into the plane of the incompressible velocity potential and stream function and the first-approximation results substituted in the non ­linear terms. The resulting second-approximation equations can then be solved by a relaxation method and the error in this approximation estimated by carrying out the third-approximation solution. Results are given for a circular cylinder at a free-stream Mach number, M ∞ = 0∙4, and a sphere at M ∞ = 0∙5. The error in the velocity distribution is shown to be less than ±1 % in the two-dimensional case. A rough and ready compressibility rule is formulated for axisymmetric bodies, dependent on their thickness ratios.

Flows of thin streams with free boundaries

1973 ◽  
Vol 59 (3) ◽  
pp. 417-432 ◽  
Author(s):  
Joseph B. Keller ◽  
James Geer
Keyword(s):  
Channel Flow ◽  
Potential Flow ◽  
Slenderness Ratio ◽  
Asymptotic Series ◽  
Two Dimensional ◽  
Free Boundaries ◽  
Complex Flow ◽  
Flow Problems ◽  
Different Types ◽  
Wall Flow

A method is developed for determining any thin steady two-dimensional potential flow with free and/or rigid boundaries in the presence of gravity. The flow is divided into a number of parts and in each part the flow and its free boundaries are represented as asymptotic series in powers of the slenderness ratio of the stream. There are three basic flows, having two, one and no free boundaries and called jet flow, wall flow and channel flow, respectively. First the three expansions for these flows are found, extending results of Keller & Weitz (1952). They are called outer expansions to distinguish them from the inner expansions which apply near the ends of the stream or at the junction of two different types of flow. The inner and outer expansions must be matched at a junction to find how the emerging flow is related to the entering flow. This process can be continued to build up any complex flow involving thin streams. The method is illustrated in the case of a wall flow that leaves the wall to become a jet, which includes the case of a waterfall treated by Clarke (1965) in a similar way. In part 2 (to be published) other inner expansions are found and matched to outer expansions, providing the ingredients for the construction of the solutions of many flow problems.

scholarly journals Numerical Solution for the 2D Linear Fredholm Functional Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Neda Khaksari ◽  
Mahmoud Paripour ◽  
Nasrin Karamikabir
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Unknown Function ◽  
Numerical Solutions ◽  
Functional Integral ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Linear Integral ◽  
Linear Integral Equations

In this work, a numerical method is applied for obtaining numerical solutions of Fredholm two-dimensional functional linear integral equations based on the radial basis function (RBF). To find the approximate solutions of these types of equations, first, we approximate the unknown function as a finite series in terms of basic functions. Then, by using the proposed method, we give a formula for determining the unknown function. Using this formula, we obtain a numerical method for solving Fredholm two-dimensional functional linear integral equations. Using the proposed method, we get a system of linear algebraic equations which are solved by an iteration method. In the end, the accuracy and applicability of the proposed method are shown through some numerical applications.

Explicit Approximations for Calculating Potential Flow About a Body

1983 ◽  
Vol 27 (01) ◽  
pp. 1-12
Author(s):  
F. Noblesse ◽  
G. Triantafyllou
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Wave Resistance ◽  
Two Dimensional ◽  
Regular Waves ◽  
Practical Applications ◽  
Flow Problems ◽  
Unbounded Fluid

Several explicit approximations for calculating nonlifting potential flow about a body in an unbounded fluid are studied. These approximations are shown to be exact in the particular cases of flows due to translations of ellipsoids, and they are compared with the exact potential for two-dimensional flows about ogives in translatory motions. Two approximations, given by formulas (31) and (32) in the conclusion, appear to be of particular interest for practical applications, and they can be extended to free-surface flow problems, for example, ship wave resistance, and radiation and diffraction of regular waves by a body.

Sign in / Sign up

Export Citation Format

Share Document