An “Exact” Linear Lifting-Surface Theory for a Marine Propeller in a Nonuniform Flow Field

1973 ◽  
Vol 17 (04) ◽  
pp. 196-207 ◽  
Author(s):  
S. Tsakonas ◽  
W. R. Jacobs ◽  
M. R. Ali
Keyword(s):  
Considerable Increase ◽  
Present Model ◽  
Numerical Procedure ◽  
Computer Time ◽  
Nonuniform Flow ◽  
Blade Loading ◽  
Surface Theory ◽  
Marine Propellers ◽  
Lifting Surface ◽  
The Mathematical Model

The mathematical model used in previous Davidson Laboratory adaptations of linearized unsteady lifting surface theory to marine propellers has been revised by removing the so-called "staircase" approximation of the blade wake and replacing it by an "exact" helicoidal blade wake. A new numerical procedure and program based on the present model have been developed to evaluate the steady and unsteady blade loading distributions, which are used to determine the bearing forces and moments. Systematic calculations of these forces and moments for a series of propellers show better agreement on the whole with experimental measurements than did the earlier calculations for the same series. In addition, the chordwise loading distributions are much smoother than obtained previously. However, the quantitative improvement must be weighed against the considerable increase in computer time over the old method.

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.

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.

Unsteady Lifting-Surface Theory for Ship Screws: Derivation and Numerical Treatment of Integral Equation

1975 ◽  
Vol 19 (04) ◽  
pp. 243-253
Author(s):  
W. van Gent
Keyword(s):  
Integral Equation ◽  
Early Stage ◽  
Nonuniform Flow ◽  
Linear Combinations ◽  
Surface Theory ◽  
Lifting Surface ◽  
Analytical Integration ◽  
Method Of Solution ◽  
The Mathematical Model ◽  
Steady Load

In an early stage of studies concerned with lifting-surface theory for ship screws, the Netherlands Ship Model Basin initiated the development of a numerical solution of the mathematical model. To achieve this, a rigorous method was followed consisting of separation of regular and singular parts of the kernel of the integral equation, preparation of numerical procedures for integration of the regular parts, and analytical integration of the singular parts. The general solution includes the steady load due to blade geometry in uniform flow, the unsteady load in nonuniform flow, and the unsteady load due to propeller vibrations. The pressure distribution in the chordwise direction is represented by a series of linear combinations of Chebyshev polynomials. In this paper an account is given of this method of solution.

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.

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.

Propeller Loading Distributions

1969 ◽  
Vol 13 (04) ◽  
pp. 237-257
Author(s):  
S. Tsakonas
Keyword(s):  
Numerical Procedure ◽  
New Approach ◽  
Surface Theory ◽  
Linearly Independent ◽  
Lifting Surface ◽  
Numerical Program ◽  
Theoretical Results ◽  
Made In

The present study reports the improvements made in the numerical procedure for evaluating propeller loading distributions which had been developed at Davidson Laboratory by adaptation of the unsteady-lifting-surface theory. A new approach, based on the fact that the assumed Birnbaum chordwise modes are not linearly independent, has achieved stability for the chordwise distribution, which had otherwise shown no sign of convergence with increasing number of modes. Other refinements of the numerical program, including provision for arbitrary blade camber variation and overlapping of blade wakes, have improved the accuracy of both chordwise and spanwise loading distributions and brought the theoretical results closer to experiment.

Unsteady Lifting Surface Theory for a Rotating Cascade of Swept Blades

1990 ◽  
Vol 112 (3) ◽  
pp. 411-417 ◽  
Author(s):  
H. Kodama ◽  
M. 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.

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