Noncircular Cylinders Research Articles

Effect of strakes on the autorotational characteristics of noncircular cylinders

An experimental investigation is conducted to evaluate the effects of windward strakes on the autorotational characteristics of a typical noncircular cylinder. The results indicate that autorotational speeds are very sensitive to strake height and, more particularly, to their location. Reductions in autorotational speeds by as much as 75% were obtained for a strake height of h/b$ = 0.3 located at r/bQ = 0.2. Exploratory two-dimensional pressure measurements indicated that the strakes themselves develop significant, proor antiautorotational side forces depending on their location. A strip theory analysis showed that a reduction in ^c/ is mainly responsible for this phenomenon.

Maxwell’s equations for a transverse field

Hodge–deRham theory is applied to Maxwell’s equations for a transverse electromagnetic wave with a given wave-front surface S. It is shown that the E and B fields, considered as tangent fields to S, are harmonic in the sense of Hodge theory. If S is a spheroid it is known that the space of harmonic fields on S has dimension zero, and hence transverse fields with spheroidal wave fronts do not exist. The same result holds, but for a different reason, if S is a noncircular cylinder or a surface of revolution, and it is conjectured that smooth, singularity-free, transverse solutions to Maxwell’s equations exist only if S is a plane or a circular cylinder.

Coupling effects on torsional vibrations of prismatic bars

Due to the warping any torsional wave or disturbance in a noncircular cylinder is propagated with a higher velocity than that predicted by the elementary theory. This change of the wave velocity depending on wave length, i.e. the dispersion phenomenon, is accompanied by certain modifications of stresses and displacements. This paper presents a systematic investigation of these “coupling effects” within the framework of the linear theory of elasticity by means of the method of strained parameters and of the technique of Lindstedt-Poincare leading to exact solutions in the asymptotic sense. The dispersion is found to be related to the shearing stresses of higher order of magnitude and to the distortion of cross section which are consequences not only of the axial stresses and accelerations hut also of the plane stresses. The coupling between torsional and flexural vibrations which occur in the case of cross sections not having two axes of symmetry is also determined explicitly.

Scattering from finite bodies of translation: Plates, curved surfaces, and noncircular cylinders

Electromagnetic scattering from finite, conducting bodies of translation (BOT) is examined using a formulation based on the electric field integral equation (EFIE) and solved by the method of moments (MM). The present approach provides a systematic, unified treatment for a wide class of finite, thin scatterers at all angles of illumination and polarization. Both concave and convex surfaces are considered. An entire-domain Galerkin expansion along one dimension of the body and a piecewise continuous one along the other are used to represent the unknown current variations. The scattering cross sections, obtained with this formulation, are compared with published results using more specialized methods and further confirmed by experimental measurements.

Slender channel theory in flow between two cylinders

We consider high-Reynolds-number flow between a rotating inner circular cylinder and a fixed non-circular outer cylinder. The dimensionless gap width δ and the Reynolds number R are assumed to be related by Rδ=λ where λ is a constant. Then the governing equations (to first approximation) are shown to be the classical boundary-layer equations, but with unusual boundary conditions. Numerical solutions and analytic approximations are found in various cases.

Impulsively-Started Flow About Four Types of Bluff Body

Measurement of the forces acting on a circular cylinder and those on three other noncircular cylinders is reported. The results confirm and quantify the profound effects of the shedding of the first two or three vortices on all the characteristics of resistance and demonstrate that the evolution of the flow, and hence the forces, significantly depend on whether the separation points are fixed or mobile, or a combination thereof. The data are expected to form the basis of future numerical analysis based on refined discrete vortex models.

Stress and deformation analysis of an acoustical compliance tube for use in underwater sound projectors

To increase the compressibility of the oil chamber in large, oil-filled underwater transducers, small, sealed, gas-filled, hollow vessels have been used. For these vessels compressibility, coupled with strength, is needed. The stress and deformation problem of the noncircular cylinder under pressure loading is considered. Equations are developed for the volume change, the maximum stress, and the shape change. The equations are applied to a particular shape of flattened cylindrical tube, called the ’’dogbone’’ because of its cross-sectional outline. A specific practical case is worked out numerically for each of two different metals making up the tube.

Approximate Numerical Solutions for Two-Dimensional Potential Flow Problems

An approximate numerical method is proposed for solving two-dimensional potential flow problems. The method is included in the general class of “Method of Weighted Residuals.” Typical computed results are presented for the surface pressure distributions on an airfoil and single noncircular cylinders immersed in a uniform infinite stream.

A theory of turbulent flow round two-dimensional bluff bodies

By generalizing the theory of ‘rapid distortion’ of turbulence developed by Batchelor & Proudman (1954) it is shown in this paper that the turbulent velocity around a bluff body placed in a turbulent flow can be calculated outside and upstream of the regions of separated flow, if the incident turbulent flow satisfies the following conditions: (i) if a/Lx [Lt ] 1 or = O(1), Re−1$u^{\prime}_{\infty}/\overline{u}_{\infty} $ [Lt ] 1 [Lt ] Re½; (ii) if a/Lx [Gt ] 1, Re−1 [Lt ] $u^{\prime}_{\infty}$ [Lt ] 1/(a/Lx) and Re [Gt ] (a/Lx)2, where $Re = \overline{u}_{\infty} a/ν$, is the mean uniform incident velocity, $u^{\prime}_{\infty}$ is the r.m.s. velocity of the homogeneous incident turbulence, a is a transverse dimension of the body (the radius in the case of a circular cylinder), Lx is the integral scale of the incident turbulence and v is the kinematic viscosity.Detailed calculations are given for the flow around a circular cylinder with particular emphasis on the turbulence very close to the surface. (The results can be generalized to other cylindrical bodies.) Mean-square values and spectra of velocity have been found only in the limiting situations where the turbulence scale is very much larger or smaller than the size of the body, i.e. Lx [Gt ] a or Lx [Lt ] a. But, whatever the value of a/Lx, if the frequency is sufficiently large the results for spectra tend to those of the limiting situation where Lx [Lt ] a. The reason why the turbulence velocities have not been calculated for intermediate values of a/Lx is that closed-form solutions cannot be found and that the computing time then required is quite excessive. However, some computed results are used in the paper to suggest the qualitative behaviour of the turbulence when Lx is of order a. An important result of the theory is that it illuminates and distinguishes between the governing physical processes of distortion of the turbulence by the mean flow, the direct ‘blocking’ of the turbulence by the body, and concentration of vortex lines at the body's surface.The results of the theory have many applications, for example in calculating turbulent dispersion and fluctuating pressures on the body, as shown elsewhere by Hunt & Mulhearn (1973) and Hunt (1973).In conclusion the theoretical results are briefly compared with experimental measurements of turbulent flows round non-circular cylinders. A detailed comparison with measurements round circular cylinders will be published later by Petty (1974).

The vibrations of non-circular cylindrical shells with initial stresses

The differential equations which govern the vibrations with initial stresses of thin non-circular cylinders of arbitrary curvature are obtained by a variational approach. The initial stresses which are considered are stresses produced by axial loads, torsion, and normal pressure. The solution procedure is presented and numerical results are presented for the free vibrations of freely supported oval cylinders without initial stress. Frequency factors of oval cylinders are compared with those of circular cylinders as the length, thickness, and non-circularity are varied. The equivalence of the solutions for the free vibrations with and without initial axial stress is also established.

Singularities of the vacuum magnetic field around a noncircular plasma cylinder

A particular class of cylindrical plasma equilibria with noncircular cross-sections is examined.

The nonlinear membrane shell with application to noncircular cylinders

The nonlinear membrane problem is presented in terms of the curvatures and stresses (or strains) as field variables. As a part of the formulation, appropriate boundary conditions are studied.The significant features of the equations are discussed. Among the topics are included: dependence on initial shape, types of equations, ability to clarify anomalities of the linear membrane problem, stability and the membrane edge effect problem. A perturbation series scheme for the solution of the equations is also presented.The usefulness of the theory in solving practical problems is demonstrated by presenting a solution to the problem of the noncircular cylindrical membrane shell under lateral pressure.

Accuracy of Donnell's equations for noncircular cylinders

Accuracy of Donnell's equations for noncircular cylinders

Design program for short ring-reinforced oval cylinder

A computer program is presented which gives the displacements and the stress distribution in a hydrostatically loaded ring-reinforced noncircular cylinder. The solution on which the program is based is obtained by an asymptotic expansion procedure in which a typical bay of the stiffened cylinder is considered. The existence of two distinct characteristic lengths is used in the construction of two asymptotic series which, when combined, form the total solution. The solution to this problem was obtained by N.B. Nissel and W.P. Vatakos at the Polytechnic Institute of Brooklyn (see [1]). The computer program is written for a General Electric 605 Time Sharing Computer. A complete listing of the program including full documentation is presented. In addition, a typical computer run is included.

Asymptotic solution for pressurized noncircular cylinders with nonuniform rings

Abstract : An asymptotic expansion procedure is used to analyze hydrostatically loaded noncircular cylindrical shells. The asymptotic solution is combined with a solution for singly symmetric oval rings with variable cross-sectional properties to obtain the solution for pressurized noncircular cylinders with nonuniform rings. Numerical results are compared with existing solutions for doubly symmetric oval shells reinforced by uniform rings. The cross sections of these cylinders range from circular to ovals having a major-to-minor axis ratio of 1.3. Numerical results are also presented for oval cylinders reinforced by nonuniform oval rings. Cases of both singly and doubly symmetric rings are considered. (Author)

Sorption and desorption in non-circular cylinders

The sorption-desorption properties of cylinders with polygonal and rectangular cross-sections are examined. Emphasis is placed on the errors which might be incurred by the use of the commonly-adopted circular-cylinder assumption in the pore size distribution analysis of such materials.

Load-carrying capacity of stiffened non-circular cylinders in bending

Cylindrical shell beams of mono-symmetrical closed profile, stiffened by stringers and frames, are under consideration for a limit state of bending. Alternative systems of internal forces acting on the frame are determined for the cases: 1. (i) simultaneous deformations of the frame and the shell profile, provided that the sheet remains elastic, smooth and continuous with the frame, 2. (ii) when a second-order effect arises when a plastic hinge of the sheet is formed around the frame and the panel forces are no longer normal to the plane of the frame. Comments on the buckling of the frame and collapse of the cylinder are added.

Experiments on Rotating Flows between Noncircular Cylinders

Observations have been made on the onset of instability, and on the waveform both at onset and in the finite amplitude region for flows with closed nonrotationally symmetric streamlines. The effect of placing obstacles in the gap between concentric rotating circular cylinders is shown to depend primarily on the extent to which they modify the mean flow. The case of a square inner cylinder and circular outer cylinder is compared with the case of a circular inner cylinder and square outer cylinder. It is shown that the former arrangement, which is time-dependent, is much less stable than the latter. It is concluded that the shape of the boundaries in the Taylor double cylinder problem do not influence the stability markedly, other than by defining the clearance ratio, unless they make the problem time-dependent.

Asymptotic solution for short ring-reinforced oval cylinders.

Abstract : An asymptotic expansion procedure is applied to the analysis of a typical bay in a hydrostatically loaded, ring-reinforced, non-circular cylinder. The existence of two distinct characteristic lengths is used in the construction of two asymptotic series which, when combined, form the total solution. The procedure is similar to that proposed by E. Reissner for circular cylinders. The leading terms in the expansions for all stress resultants and deflections are obtained explicitly, and numerical results are compared to available theoretical and experimental data. (Author)

Deformation Equations for Non-Circular Cylinders

As far as is known, no explicit solution exists in the literature for the displacement equations in u, v and w, for a uniform cylinder of arbitrary cross section subjected to a lateral pressure loading. However, the advent of Ref. 1 now makes available an admirable treatise devoted entirely to the analysis of thin elastic shells. The equations developed in this reference apply only to linear problems, i.e. the displacements are assumed to be small in comparison with the thickness of the shell, but they are general enough to include all shells of arbitrary curvature. Unfortunately the generality of these equations inhibits their immediate use to cylindrical shell problems, and it is the purpose of this note to present the essential features of the theory for non-circular cylinders.