A study of the stability of horizontal cylindrical vessels filled with varying amounts of liquid— Part I: Experimental investigations

The instability behaviour of thin-walled horizontal cylindrical vessels supported by means of ring girders, or from rigid end plates, is examined experimentally during liquid filling. Selected results from a horizontal test on a large stainless steel horizontal storage vessel are presented to illustrate the way in which thin-walled vessels, of large radius/thickness ratios (300–650), behave during fill.Such results have provided the motivation for some 26 polyester film model cylinder tests. The models cover three different radius/thickness ratios (300, 400 and 500) and a range of length/radius ratios. They were supported at their ends and progressively filled with liquid. In each case the onset of instability was noted. In Part II¹ of this paper a theoretical approach is presented and compared with the experimental values in an effort to assess the validity of design methods currently in use.     

A Study of the Buckling Behaviour of Horizontal Saddle Supported Vessels

Previous experimental work, by one of the authors, examined the behaviour of end supported cylindrical vessels loaded centrally. It was found that the vessels failed by buckling when the radius to thickness ratio (R/t) was greater than 150. These results provided the motivation for examining the buckling behaviour of such vessels when they are supported, in a more conventional way, by using two saddles. In the cases examined it was noted that the stresses that cause buckling behaviour are the longitudinal and circumferential membrane stresses. These occur at four vessel locations, i.e. the zenith and nadir (top and bottom) of both the vessel mid-span and the saddle centre profiles. Known buckling formulae based on simple loading patterns, such as an axially loaded cylinder and a cylinder under pure bending, will be utilized in determining the allowable buckling stress. Present British Code rules and European recommendations will also be discussed. The allowable buckling load will be compared with theoretical stresses obtained from a small displacement linear elastic analysis, using a Fourier series method. From these results a design method will be presented.     

The derivation of the stresses in a pressurised pipe or cylindrical vessel with initial geometric imperfections

Several analytical methods are outlined to deal with the title problem when the vessel is free of external constraints. In essence these correspond to the Haigh equation, which provides a nonlinear relationship between the induced circumferential stress and the applied internal pressure. To make use of these analyses a survey of the cross sectional profile is required. The approach using an internal swinging arm has been found most useful. The extent to which an improved Haigh equation is valid is examined with reference to the pneumatic loading of a twin saddle supported horizontal vessel which contains imperfections and restraints at the supports.     

The thermal behaviour of thin cylindrical shells—I. Heat transfer and harmonic analysis

The combined heat transfer and thermal stress analysis of thin cylindrical shells is considered in this and a subsequent paper. This paper presents two typical heat transfer models and the harmonic analysis which is used to represent the temperature distributions as double Fourier coefficients. These models are (i) a circular hot spot caused by a postulated loss of part of the internal refractory lining in a high temperature cylindrical reactor vessel and (ii) a heated “band” caused by solar heating on a horizontal storage vessel. In the case of the hot spot the inside and outside surface temperature distributions vary independently in the axial and circumferential directions, with linear transition through the thickness. In the simpler case of solar heating, the through-thickness temperature gradient is negligible and the temperature only varies around the circumference. The use of the double Fourier coeficients to obtain the displacements and stresses is described in Part II     

Radial loading of a cylindrical vessel through a rectangular rigid attachment

This paper examines the behaviour of a cylindrical vessel which is radially loaded through a rigid attachment of rectangular plan form. The resulting radial and tangential interface forces between the vessel and the attachment are derived assuming that the attachment is fixed to the vessel at all points over the mating surface and subjected to a radial displacement. From these interfacial forces the stresses in an illustrative vessel are found to be some 37% higher than those which are obtained when a uniformly distributed radial interface pressure is assumed.     

The application of saturable turn-on snubbers to IGBT bridge-legcircuits

The turn-on loss of high-speed insulated gate bipolar transistors (IGBTs) accounts for a significant proportion of the total switching energy. In many applications, this loss is increased by the energy associated with diode reverse recovery of current. Such energy is absorbed by the IGBT switch at high voltage. Linear turn-on snubber inductors may be used to control the turn-on loss, diode reverse recovery, and electromagnetic compatibility (EMC). These snubbers have the disadvantage of involving substantial stored energy that must be reset, normally by dissipation. An alternative is to use a saturable turn-on snubber inductor, which stores substantially less energy than a linear inductor. In this paper, the suitability of saturable turn-on snubber inductors for use with IGBTs is investigated, and possible circuit topologies for single-ended and bridge-leg applications are proposed. Mathematical analysis, simulation, and practical results are presented for the saturable inductor turn-on snubber circuit topologies     

A study of the stability of horizontal cylindrical vessels filled with varying amounts of liquid—Part II: A theoretical approach and design considerations

A simplified theoretical approach to the problem of the stability of horizontal cylindrical vessels filled with liquid is proposed and is compared with the experimental results presented in Part I of this paper and with those of other investigators. In view of these comparisons certain design considerations are proposed for liquid storage vessels.     

A new soft-switching technique using a modified PWM schemerequiring no extra hardware

A new soft-switching PWM scheme for a three-phase, AC-DC, step-down unity power factor converter is described. The main advantage of the scheme is that it requires no additional hardware components to achieve a combination of zero current and voltage turn-off and zero and reduced voltage turn-on. The scheme relies on the repositioning of the PWM pulses within the carrier period to obtain natural commutation from one switching device to the next. The theoretical reduction in the total switching losses is mathematically shown to be 42% compared with the standard center-aligned PWM scheme used with the converter. A PSpice^TM simulation of the new scheme reveals soft-switching waveforms. Practical results are given to support the simulation results and heat-sink temperature rise results show a reduction in heat-sink temperature rise for the new scheme compared to the old     

A design philosophy for vertical storage vessels

A novel approach is examined for the storing of liquids in vertical vessels where optimum use is made of floor space and vessel plate material. This is accomplished by providing a series of curved vertical panels, or lobes, to form the vessel sides thereby achieving a membrane geometry in the circumferential plane.

The paper presents a simple design approach for these vessels based upon strain gauge data obtained during the hydraulic test of a 14 000 gal. vessel. The design philosophy used is applicable to other thin walled vessels, as for example those used in the storage of liquid gas under pressure and/or refrigeration.