An Approximate Solution for Incompressible Flow About an Ellipsoid Near a Plane Wall

1950 ◽  
Vol 17 (2) ◽  
pp. 154-158
Author(s):  
Phillip Eisenberg
Keyword(s):  
Approximate Solution ◽  
Velocity Distribution ◽  
Closed Form ◽  
Incompressible Flow ◽  
Velocity Potential ◽  
Plane Wall ◽  
Wall Effect ◽  
Pressure Distributions

Abstract Using the method of successive images, an approximate solution for the velocity potential is obtained in closed form for incompressible flow about an ovary ellipsoid near a plane wall. The velocity distribution is computed from this solution in two ways. The first computation properly predicts differences in velocities on opposite half-meridians of the ellipsoid. A second method results in a symmetric velocity distribution but is useful for rapid estimates of the average wall effect. Pressure distributions calculated by this theory are compared with values measured on 4:1 and 6:1 ellipsoid models.

Gust Loading on a Thin Aerofoil

1971 ◽  
Vol 22 (3) ◽  
pp. 301-310 ◽  
Author(s):  
B. D. Mugridge
Keyword(s):  
Approximate Solution ◽  
Closed Form ◽  
Incompressible Flow ◽  
Velocity Component ◽  
Closed Form Expression ◽  
Sound Power ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Form Expression ◽  
Final Expression

SummaryA closed-form expression is derived which gives an approximate solution to the lift generated on a two-dimensional thin aerofoil in incompressible flow with a normal velocity component of the form exp [i(ωt–xx+yy)]. The inaccuracy of the solution when compared with other published work is compensated by the simplicity of the final expression, particularly if the result is required for the calculation of the sound power radiated by an aerofoil in a turbulent flow.

A closed-form formulation of HRBF-based surface reconstruction by approximate solution

2016 ◽  
Vol 78 ◽  
pp. 147-157 ◽  
Author(s):  
Shengjun Liu ◽  
Charlie C.L. Wang ◽  
Guido Brunnett ◽  
Jun Wang
Keyword(s):  
Approximate Solution ◽  
Closed Form ◽  
Surface Reconstruction

Approximate Analysis of Penetration of a Cylindrical Roller Into a Thin Elastic Coating

1990 ◽  
Vol 112 (3) ◽  
pp. 460-468 ◽  
Author(s):  
Tsung-Ju Gwo ◽  
Thomas J. Lardner
Keyword(s):  
Approximate Solution ◽  
Closed Form ◽  
Approximate Analytical Solution ◽  
Experimental Studies ◽  
Preliminary Design ◽  
Two Dimensional ◽  
Rigid Substrate ◽  
Closed Form Solutions ◽  
Finite Element Calculations ◽  
Cylindrical Roller

An approximate analytical solution to the problem of two-dimensional indentation of a frictionless cylinder into a thin elastic coating bonded to a rigid substrate has been obtained using the approach introduced by Matthewson for axisymmetric indentation. We show by comparing the results of the approximate solution to the exact solutions and to finite element calculations that the approximate solution is accurate for a/h> 2. The advantage of this approach is that the results are expressed in closed form and the accuracy of the approximate solution improves with increasing values of a/h. For a/h>2, for a given load, the theory overestimates the value of a/h compared to the exact solution by less than 10 percent. In many experimental studies and in preliminary design, it is convenient to have closed-form solutions exhibiting the dependence of the parameters.

A Theoretical Investigation of the Jet-Flap Compressor Cascade in Incompressible Flow

1972 ◽  
Vol 94 (4) ◽  
pp. 249-260
Author(s):  
U. Stark
Keyword(s):  
Incompressible Flow ◽  
Time Pressure ◽  
Inviscid Flow ◽  
Compressor Cascade ◽  
Pressure Distributions ◽  
Simplifying Assumptions ◽  
Stagger Angle ◽  
First Time ◽  
Theoretical Results ◽  
Insight Into

The use of jet flaps gives a new possibility of achieving high turning cascades. In this paper a new theory for unstaggered cascades with jet flaps, developed under simplifying assumptions, is described. With the help of this theory, besides turning angles and lift coefficients, for the first time pressure distributions on, and jet slope distributions behind, the blades were calculated. The effect of stagger angle on the turning angles and lift coefficients is determined with the help of the Schlichting method, using the concept of the equivalent flat plate cascade. Sample calculations illustrate the theory and, at the same time, give an insight into the behavior of cascades with jet flaps in inviscid flow. Results of previously published experiments on cascades with jet flaps, where they fulfill the conditions of the theory, are compared with the theoretical results and demonstrate satisfactory agreement.

Further Developments in the Aerodynamic Analysis of Unsteady Supersonic Cascades—Part 1: The Unsteady Pressure Field

1977 ◽  
Vol 99 (4) ◽  
pp. 509-516 ◽  
Author(s):  
J. M. Verdon
Keyword(s):  
Velocity Potential ◽  
Pressure Field ◽  
Supersonic Stream ◽  
Axial Velocity Component ◽  
Unsteady Pressure ◽  
Pressure Distributions ◽  
Successive Solution ◽  
Construction Procedure ◽  
Present Procedure ◽  
Dependent Variables

This paper presents, in two parts, a theoretical investigation of the aerodynamic response produced by an oscillating cascade placed in a supersonic stream with subsonic axial velocity component. Predictions are based on the successive solution of two linear boundary value problems which treat the velocity potential and the pressure, respectively, as basic dependent variables. A solution for the potential has been reported earlier and is used here to provide upper surface blade pressure distributions. This information serves as a boundary condition for the second problem. The solution for the unsteady pressure field, described in Part 1, is obtained by a construction procedure which parallels that used earlier to determine the potential. With the present procedure, blade pressure difference distributions and aerodynamic coefficients are accurately and efficiently determined for both subresonant and superresonant blade motions. Supersonic resonance phenomena and selected numerical results are discussed in Part 2 of the paper.

A Method for Inverse Aerofoil and Cascade Design by Surface Vorticity

1982 ◽  
Author(s):  
R. I. Lewis
Keyword(s):  
Velocity Distribution ◽  
Incompressible Flow ◽  
Design Tool ◽  
The Body ◽  
Surface Velocity ◽  
Classical Solutions ◽  
Analysis Tool ◽  
Attached Flow ◽  
Turbomachine Blade

Surface vorticity theory, normally considered as an analysis tool, has been modified to operate as a design tool whereby the shapes of components may be found to produce a prescribed surface velocity in incompressible flow. The basis of the method is presented and checked against classical solutions for cylindrical and diamond shaped struts with fully attached flow. A procedure for turbomachine blade or aerofoil design is outlined and illustrated with back checks via Martensen’s method. The method allows specification of velocity distribution on either or both surfaces of the body. If only one surface of an aerofoil or blade is prescribed, the user is allowed to specify profile thickness also.

On the Approximate Solution of Viscous-Flow Problems

1963 ◽  
Vol 30 (2) ◽  
pp. 263-268 ◽  
Author(s):  
J. A. Schetz
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Viscous Flow ◽  
Closed Form ◽  
New Method ◽  
Two Dimensional ◽  
General Technique ◽  
Closed Form Solutions ◽  
Flow Problems

The need for a general technique for the approximate solution of viscous-flow problems is discussed. Existing methods are considered and a new method is presented which results in simple closed-form solutions. The accuracy of the method is demonstrated by comparisons with the results of known exact solutions, and finally the general technique is employed to determine a new solution for the fully expanded two-dimensional laminar nozzle problem.

Some physical interpretations of potentials representing supersonic motion of compressible fluids

1949 ◽  
Vol 45 (2) ◽  
pp. 246-250
Author(s):  
R. K. Tempest
Keyword(s):  
Incompressible Flow ◽  
Velocity Potential ◽  
Compressible Fluids ◽  
Polar Coordinates ◽  
Supersonic Speed ◽  
Small Perturbations ◽  
Stream Flows ◽  
Cylindrical Polar Coordinates ◽  
Image Position ◽  
Supersonic Motion

1. Compressible and incompressible flow. Small perturbations in an otherwise uniform stream of compressible fluid moving at supersonic speed are described by the approximate linearized equation for the velocity potential. When the stream flows in the z-direction, the equation assumes the formwhere M is the Mach number of the flow and α2 is positive. In cylindrical polar coordinates (r, z), the equation may be written aswhich is Laplace's equation in coordinates (iαr, z). We may therefore relate potentials of incompressible flow which are solutions of (1·2) to potentials of compressible flow which are solutions of (1·1).

The Virtual Mass of a Sphere Moving Toward a Plane Wall

1977 ◽  
Vol 44 (1) ◽  
pp. 166-167 ◽  
Author(s):  
D. J. Jeffrey ◽  
H.-S. Chen
Keyword(s):  
Closed Form ◽  
Potential Flow ◽  
Plane Wall ◽  
Virtual Mass ◽  
Flow Past ◽  
Flow Past A Sphere

The axisymmetric potential flow past a sphere almost touching a plane wall is solved in closed form and the solution used to show that the Virtual mass of the sphere is finite This result clears up a difficulty uncovered in calculations by Small and Weihs.

Sign in / Sign up

Export Citation Format

Share Document