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.

Analytical Solutions for Laminar Fully-Developed Flow in Microchannels With Non-Circular Cross-Section

2009 ◽  
Author(s):  
A. Tamayol ◽  
M. Bahrami
Keyword(s):  
Experimental Data ◽  
Pressure Drop ◽  
General Solution ◽  
Cross Section ◽  
Cross Sections ◽  
Analytical Solutions ◽  
Circular Cross Section ◽  
Fully Developed Flow ◽  
Wide Range ◽  
Simply Connected

Analytical solutions are presented for laminar fully-developed flow in micro/minichannels of hyperelliptical and regular polygonal cross-sections. The considered geometries cover a wide range of common simply connected shapes including circle, ellipse, rectangle, rhomboid, star-shape, equilateral triangle, square, pentagon, and hexagon. Therefore, the present approach can be considered as a general solution. Predicted results for the velocity distribution and pressure drop are successfully compared with existing analytical solutions and experimental data collected from various sources for a variety of geometries, including: polygonal, rectangular, circular, elliptical, and rhombic cross-sections.

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.

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.

Unsteady viscous flow in a curved pipe

1971 ◽  
Vol 45 (1) ◽  
pp. 13-31 ◽  
Author(s):  
W. H. Lyne
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Kinematic Viscosity ◽  
Asymptotic Theory ◽  
Circular Cross Section ◽  
Radius Of Curvature ◽  
Curved Pipe ◽  
Unsteady Viscous Flow

The flow in a pipe of circular cross-section which is coiled in a circle is studied, the pressure gradient along the pipe varying sinusoidally in time with frequency ω. The radius of the pipeais assumed small in relation to the radius of curvature of its axisR. Of special interest is the secondary flow generated by centrifugal effects in the plane of the cross-section of the pipe, and an asymptotic theory is developed for small values of the parameter β = (2ν/ωa2)½, where ν is the kinematic viscosity of the fluid. The secondary flow is found to be governed by a Reynolds number$R_s = \overline{W}^2a/R \omega\nu$, where$\overline{W}$is a typical velocity along the axis of the pipe, and asymptotic theories are developed for both small and large values of this parameter. For sufficiently small values of β it is found that the secondary flow in the interior of the pipe is in the opposite sense to that predicted for a steady pressure gradient, and this is verified qualitatively by an experiment described at the end of the paper.

scholarly journals Magnetic Moment Distribution in Ferromagnetic Co?Mn Alloys

1993 ◽  
Vol 46 (5) ◽  
pp. 667 ◽  
Author(s):  
TJ Hicks ◽  
AR Wildes
Keyword(s):  
Experimental Data ◽  
Cross Section ◽  
Composition Range ◽  
Critical Concentration ◽  
Cross Section Data ◽  
Section Data ◽  
Environment Model ◽  
Moment Distribution ◽  
The Mean ◽  
The Moment

Using the magnetic environment model, the moment distributions for ferromagnetic COl_xMnx alloys in the composition range (0 < x < 0�25) were calculated from the mean saturating moments of the alloys. The calculation also gives the mean moment of each species as a function of concentration. The predictions correspond extremely well with the existing experimental data. In particular, the increase in the correlation length close to the ferromagnetic critical concentration is clear in the cross section data and model.

Pulsating flow in a curved tube

1973 ◽  
Vol 59 (4) ◽  
pp. 693-705 ◽  
Author(s):  
R. G. Zalosh ◽  
W. G. Nelson
Keyword(s):  
Flow Field ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Circular Cross Section ◽  
Analytic Solutions ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Tube Cross Section ◽  
Curved Tube

An analysis is presented of laminar fully developed flow in a curved tube of circular cross-section under the influence of a pressure gradient oscillating sinusoidally in time. The governing equations are linearized by an expansion valid for small values of the parameter (a/R) [Ka/ων]2, where a is the radius of the tube cross-section, R is the radius of curvature, ν is the kinematic viscosity of the fluid and K and ω are the amplitude and frequency, respectively, of the pressure gradient. A solution involving numerical evaluation of finite Hankel transforms is obtained for arbitrary values of the parameter α = a(ω/ν)½. In addition, closed-form analytic solutions are derived for both small and large values of α. The secondary flow is found to consist of a steady component and a component oscillatory at a frequency 2ω, while the axial velocity perturbation oscillates at ω and 3ω. The small-α flow field is similar to the low Dean number steady flow configuration, whereas the large-α flow field is altered and includes secondary flow directed towards the centre of curvature.

scholarly journals Accounting for the Scale Factor in Determining the Compressed Concrete Strength of Concrete-Filled Steel Tube Elements

2019 ◽  
Vol 278 ◽  
pp. 03003
Author(s):  
Elvira P. Chernyshova ◽  
Vladislav E. Chernyshov
Keyword(s):  
Experimental Data ◽  
Axial Compression ◽  
Cross Section ◽  
Concrete Strength ◽  
Circular Cross Section ◽  
Steel Tube ◽  
Scale Factor ◽  
Concrete Filled Steel Tube ◽  
New Formula

The published experimental data on the influence of the concrete samples dimensions on their strength under axial compression had been analyzed in the article. The mechanism of this influence is revealed from the positions of strength statistical theories. The known dependences are given and a new formula is proposed for taking into account the scale factor in determining the strength of compressed concrete. An algorithm for calculating the strength of centrally compressed concrete-filled steel tube elements (CFSTE) with a circular cross-section taking into account the scale factor is shown.

Axial Loading of Bonded Rubber Blocks

2002 ◽  
Vol 69 (6) ◽  
pp. 836-843 ◽  
Author(s):  
J. M. Horton ◽  
G. E. Tupholme ◽  
M. J. C. Gover
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Closed Form ◽  
Cross Section ◽  
Shape Factor ◽  
Circular Cross Section ◽  
Axial Loading ◽  
Theory Of Elasticity ◽  
Governing Equations ◽  
Lateral Profile

Axially loaded rubber blocks of long, thin rectangular and circular cross section whose ends are bonded to rigid plates are studied. Closed-form expressions, which satisfy exactly the governing equations and conditions based upon the classical theory of elasticity, are derived for the total axial deflection and stress distribution using a superposition approach. The corresponding relations are presented for readily calculating the apparent Young’s modulus, Ea, the modified modulus, Ea′, and the deformed lateral profiles of the blocks. From these, improved approximate elementary expressions for evaluating Ea and Ea′ are deduced. These estimates, and the precisely found values, agree for large values of the shape factor, S, with those previously suggested, but also fit the experimental data more closely for small values of S. Confirmation is provided that the assumption of a parabolic lateral profile is invalid for small values of S.

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