Comments on Jacobs and Tsakonas: “Propeller Loading-Induced Velocity Field by Means of Unsteady Lifting Surface Theory”

1982 ◽  
Vol 26 (04) ◽  
pp. 266-268
Author(s):  
Theodore R. Goodman
Keyword(s):  
Velocity Field ◽  
Velocity Potential ◽  
Fourier Component ◽  
Surface Theory ◽  
Lifting Surface ◽  
Induced Velocity ◽  
Total Velocity

In the cited paper (2) a formula is given for the lth Fourier component of the velocity potential of an N-bladed propeller [equations (9) and (10) of the paper], (2). The total velocity potential is then, of course, given by the sum of all the components.

Propeller Loading-Induced Velocity Field by Means of Unsteady Lifting Surface Theory

1973 ◽  
Vol 17 (03) ◽  
pp. 129-139
Author(s):  
W. R. Jacobs ◽  
S. Tsakonas
Keyword(s):  
Velocity Field ◽  
High Speed ◽  
Pressure Field ◽  
Numerical Procedure ◽  
Nonuniform Flow ◽  
Surface Theory ◽  
Loading Function ◽  
Lifting Surface ◽  
Space Function ◽  
Induced Velocity

An analysis based on the lifting surface theory has been developed for evaluation of the vibratory velocity field induced by the loading of an operating propeller in both uniform and nonuniform inflow fields. The analysis demonstrates that in the case of nonuniform flow the velocity at any field point is made up of a large number of combinations of the frequency constituents of the loading function with those of the space function (propagation or influence function). A numerical procedure has been developed adaptable to a high-speed digital computer (CDC 6600), and the existing program, which evaluates the steady and unsteady propeller loadings, the resulting hydrodynamic forces and moments, and the pressure field, has been extended to include evaluation of the velocity field as well. This program should thus become a highly versatile and useful tool for the ship researcher or designer.

scholarly journals An Unsteady Lifting Surface Theory for Ducted Fan Blades

1991 ◽  
Author(s):  
Ray M. Chi
Keyword(s):  
Velocity Potential ◽  
Three Dimensional ◽  
Surface Theory ◽  
Unsteady Pressure ◽  
Aerodynamic Pressure ◽  
Unsteady Aerodynamic ◽  
Ducted Fan ◽  
Pressure Distributions ◽  
Lifting Surface ◽  
Perturbation Velocity

A frequency domain lifting surface theory is developed to predict the unsteady aerodynamic pressure loads on oscillating blades of a ducted subsonic fan. The steady baseline flow as observed in the rotating frame of reference is the helical flow dictated by the forward flight speed and the rotational speed of the fan. The unsteady perturbation flow, which is assumed to be potential, is determined by solving an integral equation that relates the unknown jump in perturbation velocity potential across the lifting surface to the upwash velocity distribution prescribed by the vibratory motion of the blade. Examples of unsteady pressure distributions are given to illustrate the differences between the three dimensional lifting surface analysis and the classical two dimensional strip analysis. The effects of blade axial bending, bowing (i.e., circumferential bending) and sweeping on the unsteady pressure load are also discussed.

An Unsteady Lifting Surface Theory for Ducted Fan Blades

1993 ◽  
Vol 115 (1) ◽  
pp. 175-188 ◽  
Author(s):  
R. M. Chi
Keyword(s):  
Velocity Potential ◽  
Three Dimensional ◽  
Surface Theory ◽  
Unsteady Pressure ◽  
Aerodynamic Pressure ◽  
Unsteady Aerodynamic ◽  
Ducted Fan ◽  
Pressure Distributions ◽  
Lifting Surface ◽  
Perturbation Velocity

A frequency domain lifting surface theory is developed to predict the unsteady aerodynamic pressure loads on oscillating blades of a ducted subsonic fan. The steady baseline flow as observed in the rotating frame of reference is the helical flow dictated by the forward flight speed and the rotational speed of the fan. The unsteady perturbation flow, which is assumed to be potential, is determined by solving an integral equation that relates the unknown jump in perturbation velocity potential across the lifting surface to the upwash velocity distribution prescribed by the vibratory motion of the blade. Examples of unsteady pressure distributions are given to illustrate the differences between the three-dimensional lifting surface analysis and the classical two-dimensional strip analysis. The effects of blade axial bending, bowing (i.e., circumferential bending), and sweeping on the unsteady pressure load are also discussed.

Unsteady Lifting Surface Theory for a Rotating Cascade of Swept Blades

1989 ◽  
Author(s):  
Hidekazu Kodama ◽  
Masanobu Namba
Keyword(s):  
Three Dimensional ◽  
Acoustic Power ◽  
Aerodynamic Characteristics ◽  
Blade Loading ◽  
Surface Theory ◽  
Numerical Examples ◽  
Lifting Surface ◽  
Blade Flutter ◽  
Annular Cascade ◽  
Remarkable Reduction

A lifting surface theory is developed to predict the unsteady three-dimensional aerodynamic characteristics for a rotating subsonic annular cascade of swept blades. A discrete element method is used to solve the integral equation for the unsteady blade loading. Numerical examples are presented to demonstrate effects of the sweep on the blade flutter and on the acoustic field generated by interaction of rotating blades with a convected sinusoidal gust. It is found that increasing the sweep results in decrease of the aerodynamic work on vibrating blades and also remarkable reduction of the modal acoustic power of lower radial orders for both forward and backward sweeps.

Lifting-Surface Theory for an Oscillating T-Tail

AIAA Journal ◽  
1974 ◽  
Vol 12 (1) ◽  
pp. 28-37 ◽  
Author(s):  
KOJI ISOGAI
Keyword(s):  
Surface Theory ◽  
Lifting Surface

Derivation by a Transform Method of Integral Equations of Unsteady Lifting Surface Theory in Subsonic and Supersonic Flow

1979 ◽  
Vol 30 (4) ◽  
pp. 529-543
Author(s):  
Shigenori Ando ◽  
Akio Ichikawa
Keyword(s):  
Fourier Transforms ◽  
Integral Transforms ◽  
Physical Models ◽  
Streamwise Direction ◽  
Fourier Inversion ◽  
Transform Method ◽  
Inviscid Flows ◽  
Surface Theory ◽  
Method Of Integral Equations ◽  
Lifting Surface

SummaryApplications of “integral transforms of in-plane coordinate variables” in order to formulate unsteady planar lifting surface theories are demonstrated for both sub- and supersonic inviscid flows. It is concise and pithy. Fourier transforms are exclusively used, except for only Laplace transform in the supersonic streamwise direction. It is found that the streamwise Fourier inversion in the subsonic case requires some caution. Concepts based on the theory of distributions seem to be essential, in order to solve the convergence difficulties of integrals. Apart from this caution, the method of integral transforms of in-plane coordinate variables makes it be pure-mathematical to formulate the lifting surface problems, and makes aerodynamicist’s experiences and physical models such as vortices or doublets be useless.

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