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.

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.

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-Induced Velocity Field Due to Thickness and Loading Effects

1975 ◽  
Vol 19 (01) ◽  
pp. 44-56
Author(s):  
W. R. Jacobs ◽  
S. Tsakonas
Keyword(s):  
Velocity Field ◽  
High Speed ◽  
Thickness Distribution ◽  
Numerical Procedure ◽  
Thickness Effect ◽  
Thin Body ◽  
Flow Disturbance ◽  
Blade Thickness ◽  
Resultant Velocity ◽  
Induced Velocity

Blade thickness plays a dual role, contributing to the lifting characteristics of the blade because of its nonplanar form as well as to its nonlifting characteristics due to the generation of a symmetrical flow disturbance. However, since the so-called "nonplanar thickness" has been shown to have little effect on the blade pressure distribution and thus presumably to have a negligible effect on the velocity and pressure fields around an operating propeller, the present investigation is limited to the so-called "symmetrical flow disturbance thickness." The effect of this thickness on the oscillatory velocity field around the propeller is studied by means of the "thin body" approach, where the blade section is represented by a source-sink distribution of strength proportional to the slope of the blade thickness distribution. A numerical procedure is devised and adapted to the CDC-6600 high-speed digital computer for the evaluation of the thickness effect on the velocity field. The total propeller-induced velocity field is then obtained by adding the computed velocity components due to thickness, with proper phase, to the results due to propeller loading calculated by means of the lifting-surface theory. Sets of calculations performed for a 3-blade propeller operating in a 3-cycle screen-generated wake and for a 5-blade propeller operating in a realistic hull wake reveal that the effect of thickness in forming the components of the resultant velocity varies from moderate to large, depending on the magnitude of the thickness distribution, on the location of the field point, and on the intensity of the nonuniformity of the inflow field.

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.

Theory and Measurements of the Propeller-Induced Vibratory Pressure Field

1972 ◽  
Vol 16 (02) ◽  
pp. 124-139
Author(s):  
W. R. Jacobs ◽  
J. Mercier ◽  
S. Tsakonas
Keyword(s):  
High Speed ◽  
Pressure Field ◽  
Processing Technique ◽  
Experimental Program ◽  
Signal Processing Technique ◽  
Experimental Procedure ◽  
Surface Theory ◽  
Blade Frequency ◽  
Development Center ◽  
Theoretical Results

A theory has been developed, based on lifting surface theory, for evaluation of the pressure field generated by an operating propeller in a nonuniform inflow field. In addition, an experimental procedure and a signal processing technique for measuring small pressure levels accurately have been established and utilized in an extensive experimental program. Theoretical results obtained by means of a computer program developed for the CDC 6600 high-speed digital computer agree well with those of experiments conducted at Davidson Laboratory and at the Naval Ship Research and Development Center. The difficulty of accurately establishing by measurements the decay of small pressures at points farther than one radius from the propeller precludes the possibility of determining the blade-frequency force exerted on a flat boundary by integrating the measured signatures. In contrast, integration of double the theoretical free-space pressure over the flat boundary appears to be a feasible and meaningful approach.

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 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.

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