A simplified bending analysis of imperfect spherical pressure vessels

An analytical solution is presented for spherical shells with imperfections in the geometry. The model is based on bending equations of the shell, and the imperfection is considered by an equivalent load approach. Particular expressions for cosine shape imperfections are developed, leading to explicit forms of the equations for displacements and stress resultants. Convergence studies for typical axisymmetric and local imperfections in thin spherical shells are presented, and the limitations of the solution regarding the amplitude of the imperfection are discussed.     

Axisymmetric versus non-axisymmetric flames in cylindrical tubes

The assumption of an axisymmetric flame shape is a typical compromise when the three-dimensional curved flame structure cannot be resolved because of numerical limitations. However, as demonstrated in the present paper, such an assumption is not realistic for the usual numerical configuration of a flame propagating in an “ideal” tube with no heat transfer to the walls. The stability of the axisymmetric flames (both convex and concave) is investigated with respect to non-axisymmetric perturbations. The eigenvalue stability problem is solved for different tube widths and thermal expansions of the burning matter. It is shown that the axisymmetric flames are unstable for any tube width in the case of realistically large thermal expansion. The obtained instability is stronger for concave than for convex flames. When thermal expansion is small, the axisymmetric flames are also found to be unstable for all tube radii of interest. This result agrees only in part with previous simulations of axisymmetric/non-axisymmetric flames in cylindrical tubes within the limit of ultimately small thermal expansion. Possible reasons for the disagreement are discussed. It is also demonstrated that thermal losses to the walls modify the flame shape. The critical level of the losses is obtained at which the axisymmetric flame shape is restored.     

Ram bending of a cylindrical pipe in the elastic range

The problem of ram bending of a straight cylindrical pipe is considered. Separate shell theory and finite element method (FEM) solutions are presented. The loading is idealized as a set of pads of uniform radial pressure, and results are given for the elastic range. Particular attention is paid to the FEM solution characteristics and the pipe springback behavior. The present study is a necessary preliminary step to the full elastic-plastic solution of the problem.     

Axisymmetric nonlinear rapid heating of FGM cylindrical shells

Large amplitude thermally induced vibrations of cylindrical shells made of a through-the-thickness functionally graded material (FGM) are investigated in the current research. All of the thermo-mechanical properties of the FGM shell are assumed to be functions of temperature and thickness coordinate. Shell is subjected to rapid surface heating on the ceramic-rich surface while the other surface of the shell is kept at reference temperature. One dimensional heat conduction equation is constructed and solved by means of a hybrid finite difference-Crank–Nicolson algorithm. The constructed heat conduction equation is nonlinear since the thermal conductivity is temperature dependent. With the aid of first-order shear deformation shell theory under the axisymmetric Donnell kinematic assumptions and von Kármán type of strain-displacement relations, the total energy of the shell is established. Implementing the conventional Ritz method, a set of nonlinear coupled algebraic equations are obtained which govern the dynamics of the shell under thermal shock. These equations are solved in time domain using the Newmark time marching scheme and the simple Picard successive method. Parametric studies are given to explore the dynamics of an FGM cylindrical shell under thermal shock.     

Optical transmittance measurements on a solar collector cover of cylindrical glass tubes

The transmittance of unpolarized light through a solar collector cover made of cylindrical glass tubes in a coplanar parallel close-packed array is dependent on the orientation of the cylindrical axes of the tubes in the plane of the cover. A maximum transmittance occurs when the axes are perpendicular to the plane of the angle of incidence, and a minimum transmittance occurs when the axes are parallel to the plane.At all orientations and at all angles of incidence the tubular cover has a markedly greater transmittance than does a cover formed from two parallel sheets of window glass.     

On the difference of fatigue strengths from rotating bending,four-point bending,and cantilever bending tests

Comparisons of piping fatigue data demonstrate that the fatigue strength from rotating bending tests is lower than that from cantilever and four-point bending tests, especially in the low-cycle fatigue life range. The lower strength from the rotating bending test is generally believed to result from the fact that in this test all the points on the piping surface are subjected to the maximum stress range. Consequently, the weakest point in the specimen always initiates and causes failure. On the contrary, in cantilever and four-point bending tests, the maximum stress range occurs only at the top and bottom extreme fibers, which may not contain the weakest point in the specimen. Hence, the pipes in rotating bending tests usually fail earlier in comparison with the other two tests. Finite element analyses for the three tests revealed another and more compelling reason for the lower fatigue strength from the rotating bending test. The results demonstrated that, for the same prescribed bending moment range, the inelastic strain range in rotating bending is higher than the ranges in four-point and cantilever bending tests. Experimental data also demonstrate a similar trend. The new observation suggests that fatigue data from these three tests should be analyzed or compared in terms of strain range, instead of nominal stress range.     

Plastic limit load of cylindrical shells with cutouts subject to pure bending moment

In this paper, the results of limit analyses of thin-walled cylindrical shells with a circular hole under the action of a pure bending moment are presented in dimensionless form for a wide range of geometric parameters. Analytical estimation of lower bound limit load is carried out using the feasible sequential quadratic programming (FSQP) technique. The finite element calculations of limit load consist of elastic–plastic and lower and upper bound predictions by elastic compensation methods. A testing device was made to perform experiments to obtain limit bending moment of cylinders with circular openings. The analytical and finite element calculations are compared with experimental results and their correlation is discussed. The finite element calculation results were found to be in good agreement with lower bound estimations by the nonlinear mathematical programming (FSQP) method and the formula proposed by Shu.     

Effects of radial thermal dispersion on fully-developed forced convection in cylindrical packed tubes

The fluid flow and heat transfer characteristics of a fully-developed forced convective flow in a cylindrical packed tube with symmetric heating are analyzed in this paper. The Darcy—Brinkman—Ergun model is used as the momentum equation, with the radial porosity variation of the packed column approximated by an exponential function. The method of matched asymptotic expansions is applied to construct a composite solution for the axial velocity profile of a hydrodynamically fully-developed flow. The interaction of inertial and wall channeling effects on the pressure drop and the axial velocity profile is illustrated. The effects of radial thermal dispersion and variable stagnant thermal conductivity are taken into consideration in the energy equation for a thermally fully-developed flow in the packed tube, which is heated circumferentially with constant heat flux or constant wall temperature. A wall function is used to model the wall effect on the transverse thermal dispersion process, and the predicted Nusselt numbers agree with existing experimental data. Numerical results of the corresponding heat transfer characteristics in the packed tubes, without introducing the wall function, are also presented for comparison.     

An investigation of the brazier effect of a cylindrical tube under pure elastic-plastic bending

The Brazier effect of originally straight cylindrical tubes under pure elastic-plastic bending is investigated by the deformation theory based on some deformation assumptions agreeing with numerous experiments. The expressions for bending moment and flattening ratio in terms of curvature are finally obtained.     

Constructal design of a PCM cylindrical heat sink with three-branched,two-stages dendritic tubes

Amputees who use prosthetic limbs suffer from the problem of high contact temperature between the socket of the prosthetic limb and the amputated part and lack of evaporation of sweat. These conditions lead to discomfort and failure to perform functions properly. In addition, these conditions help generate ulcers and accumulate harmful bacteria in this area. This paper presents a heatsink design to extract heat from the contact area. A cylindrical heat sink is designed for phase-changing materials with three branched tubes in two stages. The current heat sink is used to cool the contact area between the amputated part and the socket in the lower prostheses. Three distributions of pipe branches are proposed. The distribution and pipe lengths were obtained using a constructal design method. In the constructal design, the lengths of the branched tubes were the degrees of freedom, the objective function was the minimization of the inlet temperature to the heat sink, and the constraint was the volume of the cylindrical heat sink. The metabolic heat transfer during exercise was estimated and its value was used to calculate the size of the cylindrical heatsink and the selection of the phase change material by testing three of them: water, tridecane, and dodecane. It was found that water gives the highest latent heat of melting and the lowest volume in addition to its availability. On the other hand, two cooling fluids were tested: water and air. It was found that water as a cooling fluid gave the lowest flow and the largest heat capacity. Constructal theory was used to design a cylindrical heat sink using branched tubes for the coolant in two steps: the first with three branches, and the second with nine branches. The degree of freedom for constructal theory was the length of the branches through the choice of their end locations. It was found that the branches of the highest length led to a reduction in temperature from 40°C to 15.48°C compared with the single tube, which reduced the temperature to 23.87°C. All tests recorded a pressure drop within the acceptable range of 3.1–5.43 Pa for the branches examined. The research demonstrated that using constructal theory achieved the best thermal dissipation within a restricted volume.     

Use of the cylindrical instability stress for blunt metal loss defects in linepipe

Assessment of metal loss defects in gas pipelines can be analysed by a number of methods. In analyses with finite element methods a failure criterion is required. A material property is introduced, the cylindrical instability stress, which determines the plastic collapse of cylindrical pressure containing vessels. The use of this is extended to cover blunt metal loss defects. Some published finite element studies of defected vessels are re-analysed using this failure criterion.

The cylindrical instability stress is a more accurate failure criterion for plastic collapse in pipelines and pressure vessels than commonly used measures such as flow stress, Specified Minimum Yield Stress plus 10 ksi or multiplied by 1.1. It can be used in determining burst pressure of defected and un-defected pressure vessels and piping.     

On the concentrating capability of a circular cylindrical reflector

The concentration field of a circular cylindrical reflector is examined in accordance with the laws of geometric optics. The limits of the energy concentration zone that are defined by the envelopes of the reflected rays are shown. The parametric equations of the characteristic curve that coincides with the envelope are obtained. A technique for selecting the parameters of the circular cylindrical reflector based on the average magnitude of the energy concentration and the receiving strip width is presented. The location of the receiver in the reflector concentration field is justified.     

On the problem of thermal instability of explosive materials

The steady-state heat conduction equation obeyed by explosive materials is studied in order to be able to guarantee the existence of steady-state solutions when the boundary temperature is low enough, and to obtain some information about the onset of thermal instability. The calculated critical temperatures for a number of explosive materials are compared with those obtained experimentally.     

On the influence of temperature and viscosity fluctuations on interfacial instability

Recently, Pinarbasi and Liakopoulos [1] investigated the effect of variable viscosity on the interfacial stability of two-layer, plane, Poiseuille flow. Temperature and viscosity fluctuations were neglected based on the observation that their effect on the stability of single-layer, Poiseuille flow is very small [2,3]. It is shown in the present work that temperature and viscosity fluctuations, under some conditions, have a significant effect on the interfacial mode of instability, especially for large Prandtl numbers.     

Fouling thresholds in bare tubes and tubes fitted with inserts

Maya crude oil fouling reveals a straightforward dependency of initial fouling rate on surface temperature but a rather complex dependency on velocity in bare tubes, the initial fouling rate showing a maximum and then decreasing significantly towards zero as the velocity is increased. Surface shear stress clearly is an important parameter. CFD simulation of fluid flow in a tube fitted with a hiTRAN® insert reveals a complex distribution of surface shear stress. To compare the insert situation with the bare tube, an equivalent velocity concept is introduced on the basis that at a given average velocity the fluid flow results in the same average wall shear stress regardless of whether the tube is bare or is fitted with an insert. Using the equivalent velocity concept, the fouling data obtained using both a bare tube and a tube fitted with inserts can be correlated using a single model. Moreover, the fouling threshold conditions below which fouling is negligible, can be predicted for both situations.     

On the performance of cylindrical parabolic solar concentrators with flat absorbers

An integral relationship is developed for evaluating the intensity distribution on flat absorbers used with cylindrical parabolic solar concentrators. Calculations are presented for perfect cross-section concentrators using various models, rim angles, off-axis angles and defocusing amounts. Peak concentration ratios are shown to vary as the sine of the rim angle. Off-axis and defocused operations are shown to result in considerable reduced intensities. The effect of surface slope errors is also investigated. Normally distributed surface slop errors with a standard deviation of 0.25 degree are shown to reduce peak intensities by more than a factor of 3.