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.

Application of Lifting-Surface Theory to the Prediction of Hydroelastic Response of Hydrofoil Boats

1968 ◽  
Vol 12 (04) ◽  
pp. 286-301
Author(s):  
C. J. Henry
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Mode Shapes ◽  
Operator Technique ◽  
Elastic Mode ◽  
Surface Theory ◽  
Lifting Surface ◽  
Modes Of Vibration ◽  
Elastic Modes

In this report a theoretical procedure is developed for the prediction of the dynamic response elastic or rigid body, of a hydrofoil-supported vehicle in the flying condition— to any prescribed transient or periodic disturbance. The procedure also yields the stability indices of the response, so that dynamic instabilities such as flutter can also be predicted. The unsteady hydrodynamic forces are introduced in the equations of motion for the elastic vehicle in terms of the indicia I pressure-response functions, which are de rived herein from lifting-surface theory. Thus, the predicted vehicle-response includes the effects of three-dimensional unsteady flow conditions at specified forward speed. The natural frequencies and elastic modes of vibration of the vehicle and foil system in the absence of hydrodynamic effects are presumed known. A numerical procedure is presented for the solution of the downwash integral equations relating the unknown indicial pressure distributions to the specified elastic-mode shapes. The procedure is based on use of the generalized-lift-operator technique together with the collocation method.

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.

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.

The three-dimensional interaction of a streamwise vortex with a large-chord lifting surface: theory and experiment

1996 ◽  
Vol 322 ◽  
pp. 51-79 ◽  
Author(s):  
Gustavo C. R. Bodstein ◽  
Albert R. George ◽  
C.-Y. Hui
Keyword(s):  
Boundary Layer ◽  
Pressure Distribution ◽  
Potential Flow ◽  
Velocity Potential ◽  
Lateral Displacement ◽  
Three Dimensional ◽  
Leading Edge ◽  
Vortex Filament ◽  
Soap Bubble ◽  
Lifting Surface

The three-dimensional vortex flow that develops around a close-coupled canard-wing configuration is characterized by a strong interaction between the vortex generated at the canard and the aircraft wing. In this paper, a theoretical potential flow model is devised to uncover the basic structure of the pressure and velocity distributions on the wing surface. The wing is modelled as a semi-infinite lifting-surface set at zero angle of attack. It is assumed that the vortex is a straight vortex filament, with constant strength, and lying in the freestream direction. The vortex filament is considered to be orthogonal to the leading-edge, passing a certain height over the surface. An incompressible and steady potential flow formulation is created based on the three-dimensional Laplace's equation for the velocity potential. The boundary-value problem is solved analytically using Fourier transforms and the Wiener-Hopf technique. A closed-form solution for the velocity potential is determined, from which the velocity and pressure distributions on the surface and a vortex path correction are obtained. The model predicts an anti-symmetric pressure distribution along the span in region near the leading-edge, and a symmetric pressure distribution downstream from it. The theory also predicts no vertical displacement of the vortex, but a significant lateral displacement. A set of experiments is carried out to study the main features of the flow and to test the theoretical model above. The experimental results include helium-soap bubble and oil-surface flow pattern visualization, as well as pressure measurements. The comparison shows good agreement only for a weak interaction case, whereas for the case where the interaction is strong, secondary boundary-layer separation and vortex breakdown are observed to occur, mainly owing to the strong vortex-boundary layer interaction. In such a case the model does not agree well with the experiments.

Unsteady Linearized Lifting-Surface Theory in the Presence of a Free Surface

1987 ◽  
Vol 31 (03) ◽  
pp. 151-163
Author(s):  
J. Leclerc ◽  
P. Salaun
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Unknown Function ◽  
Pressure Difference ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Thin Structures ◽  
Surface Theory ◽  
Lifting Surface ◽  
The Right

A new lifting-surface theory is developed for the computation of three-dimensional hydrodynamic pressures on thin structures in the presence of a free surface. Two interesting cases are treated: the steady case and the supercritical unsteady case. The theory is linearized and the problem is reduced to the solution of an integral equation where the unknown function is the pressure difference between the elements of the structure and the right-hand side the angle of attack. Forces and moments are presented in both the steady and unsteady cases. This theory allows the analysis of flutter and the study of steady drag and of the turn of ships.

Unsteady Lifting Surface Theory for a Marine Propeller of Low Pitch Angle With Chordwise Loading Distribution

1965 ◽  
Vol 9 (03) ◽  
pp. 79-101 ◽  
Author(s):  
S. Tsakonas ◽  
W. R. Jacobs
Keyword(s):  
Incidence Angle ◽  
Three Dimensional ◽  
Weighted Average ◽  
Marine Propeller ◽  
Surface Integral ◽  
Dimensional Solution ◽  
Surface Theory ◽  
Lifting Surface ◽  
Blade Area ◽  
Thrust And Torque

This study is third in a series of investigations applying the unsteady lifting-surface theory to the marine propeller case. In the present investigation, the surface integral equation is solved for a mathematical model where the chordwise loading is taken as the first term of Birnbaum's lift distribution (flat-plate chordwise distribution), in conjunction with Glauert's lift operator, which, in essence, satisfies the chordwise boundary conditions by a weighted average. It is shown that this model is an improvement over the modified Weissinger model used previously in this series, because it contains as a nucleus the exact two-dimensional solution, and thus it provides a sounder basis for determining the three-dimensional effects. The blade-loading is determined for a propeller operating in flow disturbances induced by the presence of a hull and by the blade-camber and incidence-angle effects. The stationary loading obtained by the present model is less than that obtained by the modified Weissinger model, whereas the nonstationary loading is slightly larger. The results of numerical calculations are applied to the problem of propeller vibratory thrust and torque, and comparison is made with previous theoretical and experimental values. Conclusions of the earlier studies as to the dependence of loading on the important parameters—blade-area ratio, aspect ratio and pitch—are confirmed by the present results.

Three-Dimensional Lifting-Surface Theory for an Annular Blade Row

1979 ◽  
Author(s):  
G. F. Homicz ◽  
J. A. Lordi
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Computer Time ◽  
Two Dimensional ◽  
Blade Loading ◽  
Surface Theory ◽  
Lifting Surface ◽  
Strip Theory ◽  
Blade Row ◽  
Flow Through

A lifting-surface analysis is presented for the steady, three-dimensional, compressible flow through an annular blade row. A kernel-function procedure is used to solve the linearized integral equation which relates the unknown blade loading to a specified camber line. The unknown loading is expanded in a finite series of prescribed loading functions which allows the required integrations to be performed analytically, leading to a great savings in computer time. Numerical results are reported for a range of solidities and hub-to-tip ratios; comparisons are made with both two-dimensional strip theory and other three-dimensional results.

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