Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
Currently Skimming:
A Three-Dimensional Theory for the Design Problem of Propeller Ducts in a Shear Flow
A Three-Dimensional Theory for the Design Problem of Propeller Ducts in a Shear Flow
Pages 645-666
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 645... ...
,U U U~,U2,U3,U4 u (u,v,w) Modified Bessel functions of order m And, index of radial node i1,i2,ip,kp _ Functions of shear param eters for propeller loading index of radial node Parameter in x-wise Fourier transform Function in downwash calcu lation Downwash kernel function Pressure, respectively its x-wise Fourier transform Strength of pressure dipole, respectively its x-wise Fourier transform Legendre function of second kind and half order Strength of source distribu tion Radius, distance between two joints Transformed radius Right-hand side of type equation Function of source distribu tion Duct thickness Undisturbed axial velocity, respectively its modulus Reference velocity Parameters in analytical defined wake Disturbance velocity Axial, radial and circumfer ential components of distur bance velocity Fluid velocity V(O)
|
From page 646... ...
Following the developments in the numerical methods for the calculation of potential flow on lifting bodies, methods for the hydrodynamic analysis of ducted propellers evolved to a greater degree of sophistication. More accurate panel representations of the duct geometry have been employed for axisymmetric flow [11]
|
From page 647... ...
Section 3 deals with the numerical procedures employed so far to solve the integral equation and compute the velocity field. In section 4 the results of sample calculations illustrating the effects of shear in the velocity field due to a non-symmetric duct in a wake field are presented and discussed.
|
From page 648... ...
(9) for the external force fields F representing the duct and propeller loadings and for the rate of expansion field ~ representing the duct thickness in the linearized theory.
|
From page 649... ...
(17) can be reduced by the use of Fourier transforms to a system of coupled one-dimensional integral equations for the pressure disturbance harmonics.
|
From page 650... ...
Evaluating the derivatives of the terms involving the Bessel functions we finally obtain ~ (a at + a at)
|
From page 651... ...
da (46) n=-0 0 The function ~ takes different forms for the effects of dumct loading, thickness and propeller loading.
|
From page 652... ...
This fact has major consequences for the computation of the velocity field because, as shown in the next section, differentiation of the pressure in the radial direction is required to derive the radial velocity component from the radial momentum equation. In the pursuit of an accurate numerical solution of the integral equation (45)
|
From page 653... ...
2.5. Velocity Field In accordance with the decomposition of the pressure field into its potential and interaction parts, we write for the disturbance velocity ~ -(0)
|
From page 654... ...
2.6. Duct Boundary Conditions We describe the duct surface by specifying the deviations of the outer and inner surfaces from the reference cylinder due to the conical angle, camber and thickness distributions of the duct sections, Fig.
|
From page 655... ...
Here we will only discuss the results concerning the effects of duct loading on the velocity field. The wake field chosen is a sinusoidal perturbation superposed to the axisymmetric wake field used by Lee in ref.
|
From page 656... ...
Since the theory is linear, the disturbance pressure and velocities are proportional to the loading coefficient CL, and the results hold for an arbitrary loading. The results are presented for a considerably high duct loading and a strongly sheared inflow which may be considered as representatives of a typical ducted propeller application.
|
From page 657... ...
Nevertheless, for this strongly sheared inflow and, in contrast with the uniform flow case, the present method predicts in shear flow an increase to the axis of the disturbance velocity due to the duct. Again near the axis the interaction velocity and thus, the disturbance velocity due to the duct is influenced by the local error in the pressure distribution.
|
From page 658... ...
(63) is the second term which couples the negative radial velocities with a large positive value of the shear parameter a (note that for this wake field this parameter is larger than on the base axisymmetric wake)
|
From page 659... ...
By separating the potential pressure from the interaction pressure, the integral equation governing the interaction part may be in principle solved with great accuracy using suitable numerical procedures. The solution of the potential part and, more specifically, the computation of the corresponding induced velocity field can be obtained from the results of duct lifting surface theory.
|
From page 660... ...
REFERENCES 1. Oosterveld, M.W.C., "Wake Adapted Ducted Propellers," Doctor's Thesis, Netherlands Ship Model Basin Publ.
|
From page 661... ...
and Coney, W.B., "A Systematic Method for the Design of Ducted Propellers " Fourth International Symposium on Prac tical Design of Ships and Mobile Units, 1989, Varna, Bulgaria.
|
From page 662... ...
36. Baker, C.T.H., The Numerical Treatment of Integral Equations, Clarendon Press, Oxford, 1977, pp.
|
From page 663... ...
(98) Propeller Loading (O)
|
From page 664... ...
Using the results for the Fourier transforms of the modified Bessel functions [37] it may be shown that P (ink)
|
From page 665... ...
Although the interaction with shear covers only a particular aspect of the propulsor-hull interaction, the question may be addressed without considering in detail the shear producing mechanism which is the presence of the ship's hull with its boundary layer and wake. From an untheoretical point of view, it would be interesting to know for a given sheared inflow velocity field what are the load distributions on the duct reference cylinder and on the propeller disk which minimize the kinetic energy of the fluid left far behind the ducted propeller system and which satisfy a given thrust constrains".
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.