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 Approach to the Gust Problem for a Screw Propeller

1964 ◽  
Vol 8 (02) ◽  
pp. 29-53 ◽  
Author(s):  
J. Shioiri ◽  
S. Tsakonas
Keyword(s):  
Three Dimensional ◽  
Marine Propeller ◽  
Dimensional Approach ◽  
Nonstationary Flow ◽  
Surface Integral ◽  
Surface Approach ◽  
Surface Integral Equation ◽  
Screw Propeller ◽  
Blade Area ◽  
Unsteady Lift

The unsteady lifting-surface approach is utilized for the hull-induced gust problem in the marine propeller case and the corresponding surface integral equation is solved under the Weissinger approximation. The applicability of the Weissinger method to the nonstationary flow case is studied. The kernel function is evaluated after some mathematical simplification. From numerical calculations of unsteady lift due to the gust, which are restricted to a four-bladed propeller of sector form blade with different blade-area ratios and various pitch-diameter ratios, conclusions are drawn as to the dependence of unsteady lift on such important parameters as the blade-area and pitch-diameter ratios, and the nature of the three-dimensional effects in the unsteady gust problem is clarified.

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.

The Unsteady Loading on a Marine Propeller in a Nonuniform Flow

1964 ◽  
Vol 8 (05) ◽  
pp. 29-38
Author(s):  
Michael D. Greenberg
Keyword(s):  
Free Stream ◽  
Marine Propeller ◽  
Nonuniform Flow ◽  
Surface Integral ◽  
Practical Applications ◽  
Vortex Model ◽  
Surface Integral Equation ◽  
Lifting Surface ◽  
Finite Wing ◽  
Unsteady Loading

The lifting-surface integral equation governing the unsteady loading on a marine propeller in a nonuniform free stream is derived using a classical vortex model. The induced downwash is split into a part corresponding to a locally tangent flat finite wing and wake, plus parts corresponding to the effects of the "helicoidal deviation" from this, of the true blade and wake, and the interference from the other blades and their wakes. Strip-type approximations are tolerated on these terms while a lifting-surface formulation is retained for the dominant finite flat-wing portion. A simple numerical example is carried out and these effects are indeed found to be quite small; so small, in fact, that it may suffice to retain only the flat finite-wing terms in practical applications.

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.

Application of the Unsteady-Lifting-Surface Theory to the Study of Propeller-Rudder Interaction

1970 ◽  
Vol 14 (03) ◽  
pp. 181-194
Author(s):  
S. Tsakonas ◽  
W. R. Jacobs ◽  
M. R. Ali
Keyword(s):  
Numerical Procedure ◽  
Ideal Incompressible Fluid ◽  
Operator Technique ◽  
Surface Integral ◽  
New Approach ◽  
Surface Theory ◽  
Lifting Surface ◽  
Harmonic Components ◽  
Lifting Surfaces ◽  
Interaction Problem

The propeller-rudder interaction problem is studied by means of the unsteady-lifting- surface theory. Both surfaces of arbitrary geometry are immersed in a non-uniform flow- field (i.e., hull wake) of an ideal incompressible fluid. The boundary-value problem yields a pair of surface integral equations, the inversion of which is achieved by the so- called "generalized lift operator" technique, a new approach developed by the authors, in conjunction with the presently used "mode-collocation" method. The analysis demonstrates the mechanism of the interaction phenomenon by exhibiting the filtering effects of the propeller on the harmonic constituents of the wake which allow the rudder to be exposed only to the blade harmonic and multiples thereof. A numerical procedure adaptable to the CDC 6600 computer has been developed which furnishes information about (i) the steady and time-dependent pressure distribution on both lifting surfaces, and (ii) the resultant hydrodynamic forces and moments. A limited number of calculations exhibit the importance of some parameters such as axial clearance, number of blades, and harmonic components of the hull wake.

The Calculation of Marine Propellers Based on Lifting-Surface Theory

1961 ◽  
Vol 5 (03) ◽  
pp. 1-14
Author(s):  
Pao C. Pien
Keyword(s):  
High Speed ◽  
Design Method ◽  
Design Procedure ◽  
Rate Of Change ◽  
Numerical Work ◽  
Surface Theory ◽  
Marine Propellers ◽  
Propeller Design ◽  
Lifting Surface ◽  
Blade Area

Since the present theoretical propeller design method is based on the lifting-surface theory formulated by Ginzel and Ludwieg, an improvement to this lifting-surface theory is made first. Aside from the fact that the improved lifting-surface theory is more general with respect to blade outline and the loading distribution over the blade area, the most important improvement is in the method of obtaining the induced mean lines. In the new theory the induced mean line at any radius is derived from the down-wash distribution along the entire chord length rather than from the rate of change of the down wash at the middle chord as has been done by Ginzel and Ludwieg. The results obtained from the new method show that the induced mean line at any radius is not a function of the chordwise loading distribution at that radius alone but a function of the loading distribution over the entire blade area and the blade outline. Based on the improved theory a new theoretical propeller design method has been developed. The numerical work involved in this design method has been programmed into a high-speed computer for a special case of uniform chordwise loading distribution. Two design examples have been carried out in accordance with the new design procedure, one with skewed blade and the other with symmetrical blade. The experimental verification of the work presented here will be done in the near future.

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.

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.

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.

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