On the buckling problem of a pressure vessel torispherical head due to internal pressure

The torispherical head of a circular cylindrical pressure vessel subjected to internal pressure can buckle if the head is very thin and the pressure is high enough. Previously, Aylward and Galletly analyzed this problem by the finite element method, considering the nonlinear prebuckling deformation. In this paper a numerical method is presented for buckling problems of the general axisymmetric shell, including consideration of its nonlinear behaviors in the prebuckling state. By using this method, the buckling problem of the torispherical head treated in Galletly's study is solved, and the results obtained by the present method are compared with Galletly's. It is found that the results coincide closely enough for practical purposes.     

Elastic buckling of,and first yielding in,thin torispherical shells subjected to internal pressure

With the aid of the non-linear shell buckling computer program BOSOR 4, the internal pressures at which elastic circumferential buckling (or wrinkling) take place in thin torispherical shells have been calculated. The maximum equivalent (or effective) stresses in the shells in the axisymmetric pre-buckled state were also obtained; from these, the pressures at which first yielding in the shells commences were determined for $\text{1 <}\text{σ}{}_{\mathrm{<mtext>yp</mtext>}}\text{E}\text{× 10}{}^3\text{< 4}$The calculations were performed for shells with $\text{diameter}\text{thickness}$ ratios of 500, 1000 and 2000; other geometric ratios, as detailed in the paper, were also varied. The computations were carried out for steel shells but the results have been presented in dimensionless form.Utilising the above results it is possible to determine whether a given torispherical end closure will buckle elastically or whether an elastic-plastic analysis of the shell is desirable. Factors which are conducive to elastic buckling are a high yield point, a low modulus of elasticity or a large value of the shell diameter-thickness ($\text{D}\text{t}$) ratio. For steel shells, elastic internal pressure buckling will occur (for some combinations of $\text{r}\text{D}$ and $\text{R}{}_{\mathrm{<mtext>S</mtext>}}\text{D}$) for $\text{D}\text{t}\text{= 2000}$ and $\text{σ}{}_{\mathrm{<mtext>yp</mtext>}}\text{E}\text{= 3 × 10}{}^{\mathrm{?3}}$. For $\text{D}\text{t}\text{= 1000}\text{and}\text{500}$, first yield always precedes elastic buckling for the parameters investigated. The failure mode for these cases is either elastic-plastic buckling or plastic collapse (an axisymmetric mode with large deformations).A comparison of the results of linear and non-linear elastic axisymmetric stress analyses of the shells shows that the linear theory sometimes underestimates the first yield pressure by considerable amounts. Limit pressures obtained from small-deflection shell theories can be too low in such cases.Also given in the paper are approximate simple expressions whereby the elastic internal buckling pressures of torispherical shells may be calculated. These expressions should be useful to designers.     

Flexibility factors for nozzles in the knuckle region of dished pressure vessel heads

Nozzles in the spherical part of pressure vessel heads may be designed according to BS5500 and/or with the solutions based on the work of Bijlaard. However, no solution has been available so far if the nozzle is in the knuckle region of the pressure vessel head. Furthermore the restraint forces and moments at the nozzles and thus the stresses due to them may be reduced if the flexibility of the support at the nozzle is taken into account in the calculation. This paper reports on the flexibilities and how they can be taken into account in the design.     

Stress concentration and flexibility factor of nozzles in ellipsoidal pressure vessel heads subject to external moment

Ellipsoidal heads are commonly used as end closures for cylindrical pressure vessels in chemical and process industries. In the design of nozzles in pressure vessels, stress and flexibility of the nozzle-vessel structure are important factors to be considered. In this paper, a parametric study of radial nozzles in ellipsoidal vessel heads, when the nozzles are subjected to overturning moments, is presented. The computer program KSHEL, which is based on elastic thin shell theory, was utilized. Stress concentration factors and flexibility factors were determined and are presented as graphs of dimensionless nozzle-vessel parameters.     

压力容器圆筒与凸形封头连接的边界效应分析及比较

本文阐述压力容器圆筒与半球形封头、椭圆封头连接时的边界效应及二者的比较,并用应力分析云图形象的说明了连接处的变形情况。     

Dynamics of plate heat exchangers subject to flow variations

A predictive model has been presented to suggest the transient response of plate heat exchangers, subjected to a step flow variation. The work also brings out the effect of the port to channel maldistribution on the performance of plate heat exchangers under the condition of flow variation. The results indicate that flow maldistribution affects the performance of the plate heat exchangers in the transient regime. A wide range of the parametric study has been presented which brings out the effects of NTU and heat capacity rate ratio on the response of the plate heat exchanger, subjected flow perturbation.To verify the presented theoretical model, appropriate experiments have been carried out. Experiments include the responses of the outlet temperatures subjected to inlet temperature transient in the circuit followed by a sudden change in flow rate in one of the fluids. Simulated performance has been compared to the performance measured in the experiments. Comparisons indicate that theoretical model developed for flow transient is capable of predicting the transient performance of the plate heat exchangers satisfactorily, under the given conditions of changed flow rates.     

Optimal synthesis of trigeneration systems subject to environmental constraints

Environmental information obtained through Life Cycle Analysis techniques has been incorporated into a Mixed Integer Linear Programming (MILP). The solution of the model provides the optimal configuration and operation of an energy supply system to be installed, minimizing the environmental burden associated with production of equipment and consumption of resources. Starting from a superstructure of cogeneration system with additional components highly interconnected, the energy supply system was optimized considering specific demands of a hospital located in Zaragoza, Spain. The objective functions took into account the kilograms of CO₂ released and Eco-indicator 99 Single Score. Also considered were price of energy resources, price and amortization possibilities of the equipment and options for selling surplus electricity to the electric grid. The effect of electricity generation conditions on the optimal configuration was examined by varying the source of electricity production in Spain and considering natural gas/electricity mixes from alternate countries. The ratio between local electricity emissions and natural gas emissions (α factor) was found to have the highest impact on the configuration of the system. Therefore the α factor could be considered the strongest influencing factor when deciding the optimal configuration of a system that minimizes environmental loads.     

利用微欧计检测机车电器系统

介绍如何使用微欧计对机车电器系统进行检测,并在检测过程中找出故障的具体部位.该检测方法的使用,直接显示了被测系统各部位的工作状态,对故障隐患作出及时、准确的预报,为检修工作人员对电器检修提供了依据,极大地提高了机车运用的可靠性.     

Thermal analysis of a metal foam subject to jet impingement

The present study conducted a thermal analysis on a FeCrAlY foam subjected to jet impingement cooling in a horizontal channel. The temperature distribution of the metal foam is captured with infrared thermography imaging camera for different jet velocities (219.5 ≤ Pe ≤ 548.9). Two dimensional numerical studies have been conducted to obtain the temperature contour of the metal foam and compared to the thermographic images. The thermographic images show inconsistencies in temperature variation across the metal foam due to the porosity within the metal foam. The temperature contours of the metal foam obtained numerically are found to be similar to the thermographic images. The top portion of the metal foam directly impinged by the jet of low velocities shows lowest temperature, but the heat near the heated surface is transferred majorly through conduction.     

Reliability estimation of pressurised pipelines subject to localised corrosion defects

This paper describes a probabilistic method for the assessment of the suitability of corroded pipelines under pressure loading. The method takes into account the uncertainties of the variables that influence suitability. The paper starts with a review of the various available techniques for the assessment of failure pressure of corroded pipelines and then develops a probabilistic limit state model from the available deterministic failure equations. The advanced first-order second moment method is then employed to estimate reliability. This approach is then applied to some typical examples. The results are presented in graphical form.     

Development of large-scale hydrogen liquefaction processes from 1898 to 2009

This paper presents a review of the development of large-scale hydrogen liquefaction processes throughout the world from 1898 to 2009. First, there is a concise literature review including numerous past, present, and future designs given such as the first hydrogen liquefaction device, long time ago simple theoretical processes, today's actual plants with efficiencies 20–30%, a list of the capacity and location of every hydrogen liquefaction plant in the world, and some modern more efficient proposed conceptual plants with efficiencies 40–50%. After that, further information about the development and improvement potential of future large-scale liquid hydrogen liquefaction plants is given. It is found that every current plant is based on the pre-cooled Claude system, which is still the same as was 50 years ago with little improvement. Methods to resolve the challenges of the future plants include proposing completely new configurations and efficient systems coupled with improved efficiencies of the main system components such as compressors, expanders, and heat exchangers. Finally, a summary and comparison of the process efficiencies are described, including a newly proposed Multi-component Refrigerant (MR) system being developed by NTNU and SINTEF Energy Research AS.     

The stability of crack growth in pipes subject to tensile loads

This paper presents a simple analysis for the stability of crack growth in 304 stainless steel pipes subject to tensile loads. The model of two identical part-through and part-circumference cracks, symmetrically situated with regard to the pipe cross-section, is examined for crack stability under displacement control tensile loading. Irrespective of the crack depth, the instability condition for a wide range of crack lengths, i.e. except for very short cracks and long cracks, is: $\text{2σ}{}_0\text{L}\text{πER}{}_{\mathrm{\chi }}\text{≡}\text{2L}\text{πR}\text{·}\text{1}\text{T}{}_{\mathrm{MAT}}\text{> 1}$ where σ₀ is the flow stress, E is Young's modulus, L is the pipe length, R is the pipe radius, χ is the crack tip opening angle, CTOA, associated with the crack growth and T_MAT is the material's tearing modulus. With a CTOA of 20° (i.e. T_MAT ～ 200), $\text{L}\text{R}$ must exceed 300 for instability. Since this number is far in excess of the $\text{L}\text{R}$ values for typical piping systems, the stability of cracks in pipes subject to tensile loads is essentially demonstrated.     

Tip‐vortex breakdown of wind turbines subject to shear

Sheared velocity profiles pervade all wind‐turbine applications, thus making it important to understand their effect on the wake. In this study, a single wind turbine is modeled using the actuator‐line method in the incompressible Navier–Stokes equations. The tip vortices are perturbed harmonically, and the growth rate of the response is evaluated under uniform inflow and a linear velocity profile. Whereas previous investigations of this kind were conducted in the rotating frame of reference, this study evaluates the excitation response in the fixed frame of reference, thus necessitating a frequency transformation. It is shown that increasing the shear decreases the spatial growth rate in the upper half of the wake while increasing it in the lower half. When scaled with the local tip vortex parameters, the growth rate along the entire azimuth collapses to a single value for the investigated wavenumbers. We conclude that even though the tip‐vortex breakdown is asymmetric in sheared flow, the scaled growth rates follow the behavior of axisymmetric helical vortices. An excitation amplitude reduction by an order of magnitude extends the linear growth region of the wake by one radius for uniform inflow. In the sheared setup, the linear growth region is extended further in the top half than in the bottom half because of the progressive distortion of the helical tip vortices. An existing model to determine the stable wake length was shown to be in close agreement with the observed numerical results when adjusted for shear.     

Fracture response of pipelines subject to large plastic deformation under bending

Demand for long-distance offshore pipelines is steadily increasing. High internal pressure combined with bending/tension, accompanied by large plastic strains, along with the potential flaws in girth welds make the structural integrity of pipelines a formidable challenge. The existing procedures for the fracture assessment of pipelines are based on simplified analytical methods, and these are derived for a load-based approach. Hence, application to surface cracked pipes under large deformation is doubtful. The aim of this paper is to understand and identify various parameters that influence the fracture response of cracks in pipelines under more realistic loading conditions. The evolution of CTOD of a pipeline segment with an external circumferential surface crack is investigated under pure bend loading as well as bending with internal pressure. Detailed 3D elastic–plastic finite element simulations are performed. The effects of crack depth, crack length, radius-to-thickness ratio and material hardening on fracture response are examined. The results show that at moderate levels of CTOD, the allowable moment capacity of the pipe decreases significantly with increase in internal pressure. Further, the variation of CTOD with strain can be well approximated by a simple linear relationship.     

Stability of free convection in a narrow porous layer subject to rotation

The stability and onset of convection in a narrow, fluid saturated porous layer subject to a centrifugal body force due to rotation is investigated analytically. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number. As a result, the corresponding eigenfunctions are evaluated at the convection threshold.     

Thermodynamic optimization alternatives: minimization of physical size subject to fixed power

This paper explores alternatives to the usual thermodynamic optimization formulation, where the thermodynamic performance of a system is improved subject to physical size constraints (e.g., entropy generation minimization). The alternative is to minimize the physical size subject to specified thermodynamic performance. It is shown that the alternate optimization leads to the same physical design—the same configuration—as the usual optimization. This is demonstrated by means of three examples: power plant model with two heat exchangers, power plant model driven by a hot stream of single‐phase fluid, and refrigerator model with irreversibility due to imperfect insulation. Copyright © 1999 John Wiley & Sons, Ltd.     

A new approach to ductile tearing assessment of pipelines under large-scale yielding

In this paper we focus on the issue of ductile tearing assessment for cases with global plasticity, relevant for example to strain-based design of pipelines. A proposal for a set of simplified strain-based driving force equations is used as a basis for calculation of ductile tearing. We compare the traditional approach using the tangency criterion to predict unstable tearing, with a new alternative approach for ductile tearing calculations. A criterion to determine the CTOD at maximum load carrying capacity in the crack ligament is proposed, and used as the failure criterion in the new approach. Compared to numerical reference simulations, the tangency criterion predicts conservative results with regard to the strain capacity. The new approach yields results in better agreement with the reference numerical simulations.     

A model of market power in electricity industries subject to peak load pricing

This paper studies the exercise of market power in price-regulated electricity industries under peak-load pricing and merit order dispatching, but where investment decisions are taken by independent generating companies. Within this context, we show that producers can exercise market power by under-investing in base-load capacity, compared to the welfare-maximizing configuration. We also show that when there is free entry with an exogenous fixed entry cost that is later sunk, more intense competition results in higher welfare but fewer firms.     

Heat transfer modelling of spherical particles subject to heating in a fluidized bed

This paper presents an analytical model for analyzing transient heat transfer between a brick particle and air flow during heating in a fluidized bed combustor. Both experimental and theoretical studies were carried out. The experimental investigation provided the temperature distributions at the centers of the spherical particles during heating. These data were presented in the dimensionless form and were compared with the results of the present analytical model. The theoretical investigation included two cases: e.g. Case 1 considered that the surface heat transfer coefficient is only the convection heat transfer coefficient; Case 2 also considered that the surface heat transfer coefficient is the sum of the convection and radiation heat transfer coefficients. Better agreement was found between the experimental data and the theoretical Case 2. The results of this study show that there is a dominant effect of the radiation heat transfer on the temperature distribution.     

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.