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

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.

1973 ◽  
Vol 17 (04) ◽  
pp. 196-207 ◽  
Author(s):  
S. Tsakonas ◽  
W. R. Jacobs ◽  
M. R. Ali

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.


1973 ◽  
Vol 17 (03) ◽  
pp. 129-139
Author(s):  
W. R. Jacobs ◽  
S. Tsakonas

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.


1987 ◽  
Vol 31 (03) ◽  
pp. 151-163
Author(s):  
J. Leclerc ◽  
P. Salaun

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.


Author(s):  
G. F. Homicz ◽  
J. A. Lordi

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.


1965 ◽  
Vol 9 (01) ◽  
pp. 1-12
Author(s):  
Tetsuo Nishiyama

Lifting-surface theory of a fully submerged hydrofoil advanced at constant forward speed under the fixed submersion depth is developed, and then the properties of the lift and resistance are discussed in detail in relation with the effect of the Froude number. The disturbing velocity potential is, first of all, derived from the linearized condition on the free water surface. Then, from the boundary condition over the lifting surface, constructed on the Küchemann's conception, a basic integral equation is obtained for the distribution of circulation over the span, from which the lift-curve slope and the sum of the induced and wave-making resistance can be computed readily. This integral equation is solved by DeYoung and Harper's method. Comparisons of theoretical lift and resistance with the experimental data by NASA confirm the appropriateness of the construction of the present theory; and also the effects of the Froude number on the characteristics is definitely clarified. Damping and Inertia Coefficients for a Rolling or Swaying Vertical Strip 1Discussion by W. R. Porter2IN Table 2, of this paper, the author presents values of the damping constant for a vertical strip in horizontal (sway) oscillation for tabular values of nondimensional frequency. In the Addendum, he relates that another table, Table 3, was independently checked and found to vary only by 1 in the fourth decimal place. An unwary person may assume the same to be probably true for Table 2; and, therefore, the misprinted value at frequency 2.000 is hereby reported. The interval in the table at this frequency is sufficiently large that the irregular value may be otherwise undetected. Table 2 Table 3 In addition to correcting the misprint, the table as calculated by the writer at the Computation Center, MIT, presents confirmation that the original Table 2, except at 2.000, varies at most by 1 in the fourth decimal place. This new table provides entry at more closely spaced and more conventional frequencies with digit zero in the third decimal place. The new table also presents the wave-height ratio for convenience. The relation between wave-height ratio and damping constant is mentioned in the Addendum to the paper. To complete the presentation, a graph is shown here for the wave-height ratio for the vertical strip and also for the circular cylinder in horizontal (sway) oscillation as calculated by the writer. Fig. 01Wave-height ratio as a function of nondimensional frequency for vertical strip and circular cylinder in horizontal (sway) oscillation


AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1788-1791
Author(s):  
Tetsuhiko Ueda

Author(s):  
Hidekazu Kodama ◽  
Masanobu Namba

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.


1964 ◽  
Vol 8 (05) ◽  
pp. 29-38
Author(s):  
Michael D. Greenberg

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.


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

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