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.

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 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.

scholarly journals Some accurate solutions of the lifting surface integral equation

1993 ◽  
Vol 35 (2) ◽  
pp. 127-144 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Integral Equation ◽  
Aspect Ratio ◽  
Surface Integral ◽  
Surface Integral Equation ◽  
Lifting Surface ◽  
Line Theory ◽  
Limiting Behaviour ◽  
Ratio Limit ◽  
Wing Tips

AbstractThis note describes a simple numerical method for solution of the lifting surface integral equation of aerodynamics, and provides benchmark computations of up to 7 figure accuracy for flat rectangular wings of arbitrary aspect ratio. The nature of the large aspect ratio limit is also investigated numerically and asymptotically. This enables determination of the limiting behaviour near the wing tips, which is compared to the predictions of lifting line theory. Generalisations to non-rectangular wings are discussed.

scholarly journals Accuracy of surface integral equation matrix elements in plasmonic calculations

2015 ◽  
Vol 32 (3) ◽  
pp. 485 ◽  
Author(s):  
T. V. Raziman ◽  
W. R. C. Somerville ◽  
O. J. F. Martin ◽  
E. C. Le Ru
Keyword(s):  
Integral Equation ◽  
Matrix Elements ◽  
Surface Integral ◽  
Surface Integral Equation
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