scholarly journals Diffraction of a plane wave by an almost circular cylinder

1961 ◽  
Vol 264 (1317) ◽  
pp. 246-268 ◽  
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Circular Cross Section ◽  
The Body ◽  
Maximum Deviation ◽  
Dimensional Problem ◽  
Plane Wave Incident ◽  
Method Of Solution ◽  
Watson Transformation ◽  
The Mean

The two-dimensional problem of an E-polarized plane wave incident on a perfectly conducting cylinder of almost circular cross-section is treated , the maximum deviation of the perimeter of the cross-section from a strict circle being regarded mathematically as an infinitesimal quantity whose second and higher powers are neglected. In the body of the paper the method of solution uses infinite Fourier transform techniques, but an analysis involving a Watson transformation, more traditional in this type of problem , is given in appendix A. Attention is for the most part directed to the case in which the mean radius of the cylinder is large compared to the wavelength, and the form of the solution then appropriate is examined in some detail. In particular, initial terms of asymptotic expansions in inverse powers of the mean radius to wavelength ratio are obtained for the ‘specular’ and for the ‘creeping’ contributions to the far field. It is shown that the former contributionis in agreement with that derived by the Luneberg—Kline method, and the latter with the prescription proposed by Keller. Various Bessel function results are required, some of which are derived in appendices.

Effects of Pin Shape and Array Orientation on Heat Transfer and Pressure Loss in Pin Fin Arrays

1984 ◽  
Vol 106 (1) ◽  
pp. 252-257 ◽  
Author(s):  
D. E. Metzger ◽  
C. S. Fan ◽  
S. W. Haley
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Pressure Loss ◽  
Flow Direction ◽  
Circular Cross Section ◽  
Cycle Performance ◽  
Mean Flow ◽  
Pin Fin ◽  
The Mean ◽  
Cooling Air

Modern high-performance gas turbine engines operate at high turbine inlet temperatures and require internal convection cooling of many of the components exposed to the hot gas flow. Cooling air is supplied from the engine compressor at a cost to cycle performance and a design goal is to provide necessary cooling with the minimum required cooling air flow. In conjunction with this objective, two families of pin fin array geometries which have potential for improving airfoil internal cooling performance were studied experimentally. One family utilizes pins of a circular cross section with various orientations of the array with respect to the mean flow direction. The second family utilizes pins with an oblong cross section with various pin orientations with respect to the mean flow direction. Both heat transfer and pressure loss characteristics are presented. The results indicate that the use of circular pins with array orientation between staggered and inline can in some cases increase heat transfer while decreasing pressure loss. The use of elongated pins increases heat transfer, but at a high cost of increased pressure loss. In conjunction with the present measurements, previously published results were reexamined in order to estimate the magnitude of heat transfer coefficients on the pin surfaces relative to those of the endwall surfaces. The estimate indicates that the pin surface coefficients are approximately double the endwall values.

An inverse scattering technique for electromagnetic bistatic scattering

1969 ◽  
Vol 47 (11) ◽  
pp. 1177-1184 ◽  
Author(s):  
V. H. Weston ◽  
W. M. Boerner
Keyword(s):  
Plane Wave ◽  
Scattered Field ◽  
Convex Surface ◽  
The Body ◽  
Total Field ◽  
Convex Shape ◽  
Plane Wave Incident ◽  
Smooth Body ◽  
Equivalent Sources ◽  
The Fourier Transform

It is shown that the total field produced by a plane wave incident upon a scattering body can be expressed at all points in space as the sum of the incident field and the Fourier transform of a quantity which is related to the scattering matrix. For points exterior to the minimum convex surface enclosing the body, the scattered field is reducible to a plane-wave representation which requires knowledge of the bistatic scattered field, for a fixed frequency and direction of incidence. It is shown that for certain cases, the resulting expression for the bistatic scattered field may be employed in interior portions of the minimum convex shape (including the body) in which case it represents the field arising from a set of equivalent sources. Alternative representations are also given. A technique is presented which yields the surface of a perfectly-conducting piecewise-smooth body from knowledge of the local total field. To achieve uniqueness, the technique must be applied for at least two different frequencies. Numerical results are presented which illustrate the technique.

The Structure and Function of the Basement Membrane Muscle System in Amphiporus lactifloreus (Nemertea)

1952 ◽  
Vol s3-93 (21) ◽  
pp. 1-15
Author(s):  
J. B. COWEY
Keyword(s):  
Basement Membrane ◽  
Cross Section ◽  
Circular Cross Section ◽  
The Body ◽  
Minimum Length ◽  
Muscle Fibres ◽  
Body Volume ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Sectional Shape

The body wall of A. lactifloreus has the following structure from the outside inwards. (i) A basement membrane of five to six layers immediately underlying the epithelium. Each layer consists of right-hand and left-hand geodesic fibres making a lattice, whose constituent parallelograms have a side length of from 5 to 6µ. The fibres are attached to one another where they cross; so there can be no slipping relative to one another. (ii) A layer of circular muscle-fibres running round the animal containing two systems of argyrophil fibres--one of fibres at intervals of 10µ. running parallel to the muscle-fibres and the other of fibres running radially through the layer from the basement membrane to the myoseptum. (iii) A myoseptum which is identical in structure with a single layer of the basement membrane (iv) A layer of longitudinal muscle, whose fibres are arranged in layers on each side of a series of longitudinal radial membranes. Membranes identical in structure with the basement membrane invest the nerve cords, the gut, the gonads, and the proboscis. The interrelations of argyrophil and muscle-fibres in the muscle layers is described and their functioning discussed. The system of inextensible geodesic fibres is analysed from a functional standpoint. The maximum volume enclosed by a cylindrical element (cross-section circular), of such a length that the geodesic makes one complete turn round it, varies with the value of the angle θ between the fibres and the longitudinal axis. When θ is 0° the volume is zero; it increases to a maximum when θ is 54° 44' and decreases again to zero when θ is 90°. The length of the element under these conditions varies from zero when θ is 90° to a maximum (the length of one turn of the geodesic) when θ is 0°. The body-volume of the worm is constant. Thus it has a maximum and minimum length when its cross-section is circular, and at any length between these values its cross-section becomes more or less elliptical. It is maximally elliptical when θ is 54° 44', i.e. when the volume the system could contain, at circular cross-section, is maximal. From measurements of the ratio of major to minor axes of this maximally elliptical cross-section, the maximum and minimum lengths of the worm relative to the relaxed length and values of θ at maximum and minimum length are calculated. The worm is actually unable to contract till its cross-section is circular; but measurements of its cross-sectional shape at the minimum length it can attain, permit calculation of the theoretical length and value of θ for this cross-sectional shape. Calculated values of length and the angle 6 agree well with the directly observed values.

The transmission of surface waves under surface obstacles

1961 ◽  
Vol 57 (3) ◽  
pp. 638-668 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Transmission Coefficient ◽  
Cross Section ◽  
Water Waves ◽  
Wave Train ◽  
Circular Cross Section ◽  
Great Distance ◽  
The Body ◽  
Radius Of Curvature

ABSTRACTA train of surface waves (water waves under gravity) is normally incident on a cylinder with horizontal generators fixed near the free surface, and is partially transmitted and partially reflected. At a great distance behind the cylinder the wave motion tends to a regular wave train travelling towards infinity; the ratio of its amplitude to the amplitude of the incident wave is the transmission coefficient . The transmission coefficient is studied when the wavelength is short compared to the dimensions of the body; physically (though not for engineering applications) this is the most interesting range of wavelengths, which corresponds to the range of shadow formation and ray propagation in optics and acoustics. The waves are then confined to a thin layer near the free surface, and the transmission under a partially immersed obstacle is then small. In the calculation the boundary condition at the free surface is linearized, viscosity is neglected, and the motion is assumed to be irrotational.At present the transmission coefficient is known only for a few configurations, all of them relating to infinitely thin plane barriers. A method is now given which is applicable to cylinders of finite cross-section and which is worked out in detail for a half-immersed cylinder of circular cross-section. The solution of the problem is made to depend on the solution of an integral equation which is solved by iteration. Only the first two terms can be obtained with any accuracy, and it appears at first that this is not sufficient to give the leading term in the transmission coefficient at short wavelengths; this difficulty is characteristic of transmission problems. By various mathematical devices which throw light on the mechanism of wave transmission, it is, nevertheless, found possible to prove that the transmission coefficient for waves of short wavelength λ and period 2π/ω incident on a half-immersed circular cylinder of radius a is asymptotically given bywhen N = 2πα/λ = ω2α/g is large. Earlier evidence had pointed towards an exponential law. It is suggested that transmission coefficients of order N−4 are typical for obstacles having vertical tangents and finite non-zero radius of curvature at the points where they meet the horizontal mean free surface. For obstacles having both front and rear face plane vertical to a depth a, is probably of order e−2N approximately; if only one of the two faces is plane vertical, is probably of order e−N approximately. Thus is seen to depend critically on the details of the cross-section.

The mechanisms of boring in Martesia striata Linné (Bivalvia: Pholadidae) and Xylophaga dorsalis Turton (Bivalvia: Xylophaginidae)

1969 ◽  
Vol 174 (1034) ◽  
pp. 123-133 ◽  
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Mantle Cavity ◽  
Body Fluids ◽  
The Body ◽  
Clockwise Rotation ◽  
Faecal Pellets ◽  
Adductor Muscles ◽  
Inhalant Siphon ◽  
Wood Boring

Penetration of timber by the wood-boring bivalves Martesia striata and Xylophaga dorsalis is effected by means of the cyclical repetition of a group of movements termed the boring cycle. In Martesia the boring cycle comprises first the retraction of the shell to the base of the burrow, followed by the abrasion of the wall of the burrow by movements of the shell caused by a single consecutive contraction of each of the adductor muscles. In Xylophaga similar movements are involved, but the boring cycle in this species has become elaborated by repetition of the contractions of the adductor muscles which may be repeated to give a series of up to 24 rocking movements of the shell about a dorso-ventral axis. In both species the boring cycle may be followed by movements involving anti-clockwise and clockwise rotation in the burrow, while simultaneously the siphons are partially withdrawn and re-extended; in both, longer term rotations in the burrow result in the production of a drop-shaped burrow of circular cross-section. In both species the material abraded from the base of the burrow is collected into the mantle cavity; in Martesia it is then ejected as pseudofaeces through the inhalant siphon at intervals during boring, while in Xylophaga a larger proportion passes into the gut and eventually collects in the form of faecal pellets to form a plug to the burrow. The pressures developed in the mantle cavity and haemocoele during boring are small compared to those in burrowing forms, but of the same order as those recorded from the related rock-boring pholad Zirphaea crispata , and it is concluded that the body fluids play a decreasing hydraulic role as specialization for boring increases.

Diffraction of an electromagnetic plane wave by a metallic sheet

1960 ◽  
Vol 257 (1290) ◽  
pp. 413-419 ◽  
Keyword(s):  
Plane Wave ◽  
Half Plane ◽  
Incident Wave ◽  
Oblique Angle ◽  
Conducting Material ◽  
Electromagnetic Plane Wave ◽  
Plane Wave Incident ◽  
Method Of Solution ◽  
Metallic Sheet ◽  
Electromagnetic Plane

A new generalized technique is developed for the solution of the problem of the diffraction of a plane-wave incident at an oblique angle on an imperfectly conducting half plane. It is shown that the solution may be deduced directly from the known scalar solutions for the half plane. The case when the incident wave is E-polarized is considered in detail. The method of solution is applicable to the case of an H-polarized wave and also to the case when the diffracting structure consists of a finite number of parallel sheets of conducting material. The solution for an arbitrary incident wave may be obtained by superposition of the plane wave solutions.

Natural Convection Heat Transfer From Long Horizontal Isothermal Cylinders

1994 ◽  
Vol 116 (1) ◽  
pp. 96-104 ◽  
Author(s):  
S. B. Clemes ◽  
K. G. T. Hollands ◽  
A. P. Brunger
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Cross Section ◽  
Body Height ◽  
Convection Heat Transfer ◽  
Circular Cross Section ◽  
Correlation Equation ◽  
The Body ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

A new set of measurements is reported on natural convection heat transfer in air from isothermal long horizontal cylinders of noncircular cross section at various orientations, covering the Rayleigh number (Ra) range from about 103 to about 109. The data are correlated reasonably well by a conduction layer model with a constant value (i.e., the same for all body shapes and orientations) of 5.42 for the Churchill-Usagi coefficient blending the laminar and turbulent asymptotes. The resulting correlation equation normally requires only the geometric specification of the body height and perimeter. This model is also tested against data in the literature on the subject problem, and found to be generally predictive, to within about ±10 percent. A new set of data covering the same Ra range is also reported for the circular cross-section case, i.e., the long horizontal isothermal circular cylinder. Comparison of this data with the several existing correlations for this well-known problems shows that the Kuehn and Goldstein equation predicts the data best, although the Raithby and Hollands equation also predicts the data very well, but only after a revision to the blending coefficient.

Finite amplitude effect on the stability of a jet of circular cross-section

1968 ◽  
Vol 34 (2) ◽  
pp. 299-313 ◽  
Author(s):  
D. P. Wang
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Direct Consequence ◽  
Finite Amplitude ◽  
Stable States ◽  
Characteristic Wavelength ◽  
Method Of Solution ◽  
Linearized Theory ◽  
The Stability ◽  
Unstable States

The effect of finite amplitude on the stable and unstable states of a column of an ideal fluid of circular cross-section under the action of surface tension is studied. The method of solution is a formal extension of the linearized theory; it consists of assuming that the exact solution may be expanded in a power series of a small parameter characterizing the amplitude. The calculation is carried out to the point where the first non-trivial term of the finite amplitude effect is obtained. For the stable states, the result shows that the characteristic wavelength of a disturbance which appears to be stationary with respect to an observer is decreased by the finite amplitude effect. For the unstable states, it reveals that the growth rate depends not only on the wavelength and the magnitude but also on the type of disturbance imposed initially. The last result is a direct consequence of the fact that two independent types of initial disturbance, the disturbance of the velocity field and the disturbance of the free surface, may be imposed simultaneously on the jet.

Analysis of Axially Loaded Annular Shells With Applications to Welded Bellows

1960 ◽  
Vol 82 (3) ◽  
pp. 741-753 ◽  
Author(s):  
M. Hetenyi ◽  
R. J. Timms
Keyword(s):  
Experimental Data ◽  
General Solution ◽  
Cross Section ◽  
Circular Cross Section ◽  
Radius Of Curvature ◽  
Approximate Design ◽  
Axial Forces ◽  
The Mean ◽  
Maximum Stresses ◽  
Toroidal Shells

A method is presented for the calculation of stresses and deflections in ring-shaped shells of circular cross section, subjected to axial forces. The solution is derived without the restriction imposed for toroidal shells by previous investigators, that the radius of curvature of the cross section is to be small in comparison with the mean radius of the torus. The range of applicability of the method is extended hereby to include the slightly arched convolutions used in the construction of welded bellows. By a rational reduction of the general solution approximate design formulas are obtained for the maximum stresses and deflections in bellows under axial forces and the calculated values are compared with experimental data.

scholarly journals The Sonic Resonance Method and the Impulse Excitation Technique: A Comparison Study

2021 ◽  
Vol 11 (22) ◽  
pp. 10802
Author(s):  
Tomáš Húlan ◽  
Filip Obert ◽  
Ján Ondruška ◽  
Igor Štubňa ◽  
Anton Trník
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Resonance Method ◽  
Resonant Frequencies ◽  
Mean Values ◽  
Impulse Excitation ◽  
The Mean ◽  
The Relationship ◽  
Resonant Method

In this study, resonant frequencies of flexurally vibrating samples were measured using the sonic resonant method (SRM) and the impulse excitation technique (IET) to assess the equivalency of these two methods. Samples were made from different materials and with two shapes (prism with rectangular cross-section and cylinder with circular cross-section). The mean values and standard deviations of the resonant frequencies were compared using the t-test and the F-test. The tests showed an equivalency of both methods in measuring resonant frequency. The differences between the values measured using SRM and IET were not significant. Graphically, the relationship between the resonant frequencies is a line with a slope of 0.9993 ≈ 1.

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