Optimal design of a Type 3 hydrogen vessel: Part I—Analytic modelling of the cylindrical section

The present paper aims to study the cylindrical section of a Type 3 high-pressure hydrogen storage vessel, combining an aluminium liner which prevents gas diffusion and an overwrapped composite devoted to reinforce the structure. Today, this technique is widely used but still requires consistent time investments whenever a competitive solution, involving to definitely increase weight efficiency, is needed. The laminate composite is assumed to be an elasto-damage material whereas the liner behaves as an elasto-plastic material. Based on the classical laminate theory and on Hill's criterion to take into account the anisotropic plastic flow of the liner, the model provides an exact solution for stresses and strains on the cylindrical section of the vessel under thermomechanical static loading. Part I focuses on the theoretical background. The effect of the stacking sequence on the gap occurrence, on the residual stress magnitude and on the structure stiffness may then be investigated. This will be done and be compared with results of experiments which are carried out on prototypes in the second part of this paper before an optimization is performed.     

Fatigue life evaluation of high pressure hydrogen storage vessel

By combining the micromechanics and continuum damage mechanics, a theoretical model is proposed to perform the fatigue evaluation of high pressure hydrogen storage vessel under cyclic internal pressure, which concentrates on the fatigue properties of the aluminum liner. Results show that the fatigue lifetime of vessel relates to the finite element mesh size, crack density and ratio in an element, cyclic loading amplitude and stress status at the liner. Effects of the mesh size and crack density on the fatigue lifetime of vessel are discussed. In addition, numerical results are also compared with those by experiments.     

Fatigue life prediction and verification of high-pressure hydrogen storage vessel

A fatigue life prediction method is developed for the high-pressure hydrogen storage vessel based on theoretical research and experimental verification. Firstly, the finite element model of vessel was built considering wound angle of head, thickness and number of the composite layer, then simulation was performed. The optimum range of autofrettage pressure was obtained by FEA with consideration of the DOT-CFFC and CGH2R standards. The influence of autofrettage pressure, metal liner thickness, and fiber thickness on vessel fatigue life was discussed under internal pressure cyclic load. Finally, the experimental verification was carried out. It was found that fatigue failure first occurred in middle cylinder. The experiment results agree well with theory analysis. Their average error is 6.33%.     

Analysis of multi-layered thick-walled filament-wound hydrogen storage vessels

In this paper a three-dimensional elasticity analysis on multi-layered thick-walled filament-wound hydrogen storage vessels is outlined. An exact solution to stresses of the metal liner and each anisotropic layer is presented, based on Lekhnitskii's theory and the generalized plane strain assumption. The governing equation for determining the radial displacement of the hydrogen vessel is derived and the stresses in the cylindrical coordinates are then obtained. The matrix equation that determines the integration coefficients of the governing equation is formulated by considering the boundary and interface conditions. The normal and in-plane shear stresses and the twisting rate of the vessel are calculated for various thicknesses of the aluminum liner; the results are then compared to those presented by Xia et al. It is shown that the addition of the liner significantly reduces the stress magnitude of the hydrogen vessel; this stress magnitude decreases as the liner thickness increases. The results also revealed that the twisting effect is reduced by increasing the liner thickness. The ratio of hoop-to-axial stress is no longer a constant through the vessel wall and varies within the wall thickness. In addition, various combinations of anisotropic composites and isotropic liner materials are here examined to pinpoint preferable material combinations that lead to a lower equivalent stress level of the liner and higher strength reserve of the composite laminate.     

圆形断面隧洞衬砌内力分布的解析计算模型

隧洞衬砌的内力计算有不同方法,重点讨论了软基土中圆形隧洞衬砌内力的计算方法。根据均质圆形隧洞围岩压力对称周期性变化以及衬砌结构微元体轴向力和弯矩的静力平衡方程,分析得到了衬砌内力的解析表达式。并将解析分析结果与实测结果进行了对比分析。     

Concentration of plastic strains in steel liners due to concrete cracks in the containment wall

A substantial part of nuclear containments in US and Europe are designed with an outer bearing concrete structure and an inner sealing consisting of a tight-welded steel liner. The liner constitutes the ultimate leak-barrier, which prevents leakage at high internal pressure loads. The purpose of this paper is to show which influence a through-wall concrete crack may have on the strain level in the liner. A non-linear bar model is used to evaluate the liner behavior. It is shown that the effect from friction between the concrete and liner could be significant and cause high concentration of plastic strain. The influence of friction on the liner is verified by an experimental program presented in this paper. One of the conclusions is that concentrations of strain due to friction increase with decreasing liner thickness. This is important to consider when results from scale tests are interpreted. Scale models, which have thinner liners, could get significantly higher liner strain than the actual full-scale containment.     

The behaviour of ferritic weldments in thick section pipe at elevated temperature

A major collaborative research programme is being carried out within the CEGB to examine the correlation between data, produced from a range of test methods, which are currently used in the design of welded steam pipes. In the part of the programme reported here, the elastic and creep deformation occurring in low alloy ferritic steel pipe-to-pipe weldments has been studied in pressure vessel experiments conducted at 565°C and 455 bar internal steam pressure. The welds were made in parent pipe using mild steel and low alloy 1CrMo, 2CrMo and weld metals. All the weldments were post-weld heat treated for 3 h at 700°C prior to testing. In addition, the weldments, represented as parent material, heat affected zone and weld metal, have been analysed to determine stresses and strains using a finite element three-material model.The main features of the macro- and micro-structures of the four weldments are briefly described. Results are then presented for the elastic and creep deformations observed in both the hoop and axial directions in the weldments. The experimental creep strain data are then used as a basis for calculating the stationary state stresses present on the surface of the weldments. The surface stationary state stress distribution and corresponding steady state strain rates, determined using the finite element model, are then presented.The pressure vessel experimental results and the data from the finite element analysis are discussed in terms of the hoop and axial deformation in the weldments. An assessment is then made of the correlation between the results from the experimental and analytical approaches. Finally, the practical implications of the present results are considered with respect to the design of operating plant.     

Methodology to improve the lifetime of type III HP tank with a steel liner

The present paper aims at studying a high-pressure hydrogen storage vessel, combining a steel liner and a wrapped composite reinforcement. Nowadays, this means of storage is notably used in transport. However, limits appear insofar as fatigue problem happens when the operating pressure is 700 bar. This matter has to be solved. This study tries to arrange a method to build a 700 bar vessel which could resist to cyclic pressure loading, and particularly focuses on the behaviour of the liner which seems to be the critical element to control. In addition, as a large part of this gaseous storage is bound to be on board, the composite optimization and thus weight optimization is considered.     

Limit and burst pressures for a cylindrical shell intersection with intermediate diameter ratio

This paper provides results of inelastic stress analysis for a vessel–nozzle intersection with intermediate diameter ratio (d/D=0.526) under increasing internal pressure loading from experimental and non-linear finite element methods. The determination of the limit load due to internal pressure is performed by an experimental study for comparison with finite element analysis. The spread of plastic area for the analytical model vessel is provided. Also a burst test of the model vessel is carried out to provide some data to justify the existing design method and the basis for developing an advanced design guideline for shell intersections under internal pressure loading.     

Optimization of type III pressure vessels using genetic algorithm and simulated annealing

The present work proposes two methodologies for the optimization of a Type III pressure vessel: genetic algorithms and simulated annealing. The vessel is considered to have a capacity of 10 L, a working pressure of 70 MPa and a safety factor of 2.35. An objective function is proposed based on design variables (composite thicknesses) and two penalty factors that evaluate the performance of the liner and the composite material. Numerical analysis shows that the proposed methodologies produce more efficient designs, reducing weight between 5.7% and 7.1% vs. previously published results.     

Fracture behaviour of large scale pressure vessels in the hydrotest

Within the Nordic Countries a four-year research programme in the area of elastic-plastic fracture mechanics was initiated in 1985. This programme aims to assess the leak-before-break (LBB) criteria for pressure vessels and piping. The main experimental effort of the programme is to rupture large size pressure vessels, one having dimensions resembling those of a nuclear reactor pressure vessel, under internal pressure. Artificial flaws were made on the inner wall of the vessels. The dimensions of the flaws were defined by calculations so that the LBB condition was just anticipated during the test. For the time being two tests have been performed. The first test with a large pressure vessel was pressurized by water at 60°C, which was the lowest acceptable temperature for the hydrotest. In this paper experimental details including flaw preparation, instrumentation and material characterization are described. The fracture behaviour as well as experimental results of the tests are reported and compared to the analytical solutions of the analyses.     

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.     

Experimental Investigation of the Defrosting Process on Domestic Refrigerator Finned Tube Evaporators

Frost formation is an important problem for household refrigerator and air conditioning equipment manufacturers. When frost accumulates on the evaporator surface, it acts as a thermal insulator and reduces heat flow. Therefore, frost negatively affects evaporator performance. The purpose of this study is to decrease energy consumption and increase the efficiency of the defrosting process. In the first part of the experiment, frost formation on a no-frost refrigerator evaporator at real operating conditions was investigated. The ambient temperature was maintained at a constant 23°C. It was observed that when the evaporation temperature reaches –35°C, the frost formation on the evaporator exhibits a rather dense structure that is unlike the needle-type structure observed at higher temperatures. In the second part of the experiment, the defrosting process was observed with an endoscopic camera, and the initial melting points were investigated. The experiment revealed that although the heater density is higher on the lower rows, the frost on the higher rows of the evaporator melts faster. On the theoretical side, we prepared an analytical model that calculates the melting time of the frost on the fin. The experimental and theoretical results are within 5%.     

Heat Transfer Studies of a Heat Pipe

The present investigation reports a theoretical and experimental study of a wire screen heat pipe, the evaporator section of which is subjected to forced convective heating and the condenser section to natural convective cooling in air. The theoretical study deals with the development of an analytical model based on thermal resistance network approach. The model computes thermal resistances at the external surface of the evaporator and condenser as well as inside the heat pipe. A test rig has been developed to evaluate the thermal performance of the heat pipe. The effects of operating parameters (i.e., tilt angle of the heat pipe and heating fluid inlet temperature at the evaporator) have been experimentally studied. Experimental results have been used to compare the analytical model. The heat transfer coefficients predicted by the model at the external surface of the evaporator and condenser are reasonably in agreement with experimental results.     

活塞动力学仿真及在拉缸分析中的应用

针对某型发动机开发实验过程中出现的拉缸现象,建立活塞一连杆组动力学模型,并进行数值仿真分析。通过一个工作循环的模拟,获得了活塞与缸套之间的接触应力及间隙、活塞在缸套中的瞬时运动特性,并与实验结果对比,找出拉缸产生的原因,为优化活塞外轮廓形线提供了理论依据。     

Study of the steady and transient temperature field and heat flow in the combustion chamber components of a medium speed diesel engine using finite element analyses

The present work describes the development of a model for the calculation of the temperature field and heat flow in the combustion chamber components of internal combustion piston engines, which occur both under steady and transient engine operating conditions. Two and three-dimensional finite-element analyses were implemented for the representation of the complex geometry metal components (piston, liner and cylinder head). The model is applied for the piston and liner of a medium speed diesel engine, for which relevant experimental data exist in the literature. Special care is given for accurately specifying the thermal boundary conditions (temperatures and heat transfer coefficients). Gas side boundary conditions are calculated using a thermodynamic cycle simulation code, including spatial variation of the gas side heat transfer coefficient. Coolant sides (water on the external liner surface and oil on the piston undercrown surface) boundary conditions are calculated using correlations pertaining to real engine conditions. Also an effort is made to model the piston-ring belt-liner complex thermal paths using equivalent thermal circuits. A satisfactory degree of agreement is found between theoretical predictions and experimental measurements, revealing that the finite-element methods presented are successful in formulating this kind of problem, giving accurate results with reasonable computational cost. The utilization of the model reveals very clearly the essential role of engine operating transients (sudden changes in speed and/or load) in the generation of sharp temperature excursions in the metal components until a new steady state is reached. The phenomenon should be taken into account for correct engine design and safe operation (i.e. the avoidance of high local stresses).     

Modeling the effects of loading scenario and thermal expansion coefficient on potential failure of cryo-compressed hydrogen vessels

A multiscale thermomechanical model for a simplified Type-3 cryogenic, compressed-hydrogen (H₂) storage vessel is described in this paper. The model accounts for the temperature-dependent elastic-plastic behavior of the vessel's carbon/epoxy composite overwrap and aluminum alloy liner. The homogenized thermo-elastic-plastic behavior for the individual laminae of the vessel layup is obtained using an incremental Eshelby-Mori-Tanaka approach associated with a micromechanical failure criterion to predict laminar failure while a standard elastic-plastic constitutive model is used to describe the behavior of the typical aluminum alloy assumed for the liner. The vessel's response to external loadings is modeled using a finite element method. Four loading scenarios, representing four thermomechanical cycles applied to the vessel, are analyzed to evaluate constituent and laminar stresses as well as the associated failure criterion during the cycle according to these scenarios. The model can provide helpful guidance to mitigate thermal stresses by selecting a suitable loading scenario, optimizing the layup, and tailoring the thermomechanical properties of the resin matrix.     

On the application of probabilistic fracture mechanics to the reliability and inspection of pressure vessels

A probabilistic fracture mechanics model was developed to analyse the failure probability of a typical high power density reactor pressure vessel. The major causes for the nuclear reactor pressure vessel failure include fatigue, corrosion fatigue and brittle failure. All these causes are greatly affected by the stress loading conditions, material properties (aged by neutron damage), and defects embedded in the structure. Both an analytical first-order second-moment approximation and a hybrid methodology were employed in this study. In addition to the static scatter of the pre-existing cracks and material properties, a random walk model based on the operating history was introduced to represent the random occurrence of the abnormal transient stresses. The failure mode is defined as the brittle failure caused by a critical crack, meaning the stress intensity factor around a critical crack exceeding the fracture toughness of the pressure vessel material. Through a sample study on a typical high power density nuclear power plant, it was found that the vessel failure probability is about 4 × 10⁻⁴ at the 40th year of operation and the failure rate is in the order of 5 × 10⁻⁶ per vessel per year, which had reasonable agreement with the value of 10⁻⁴−10⁻⁶ as reported based on real-world statistics. In addition to the failure probability caused by fatigue crack growth, the reliability of a Low Temperature Overpressure incident was also evaluated.     

Evaluation of effective material properties of spiral wound gasket through homogenization

In this paper, a homogenization methodology is proposed to determine the material properties of spiral wound gaskets (SWGs) using finite element analysis through representative volume elements (RVE) of the gaskets. The constituents of this RVE are described by elasto-plastic material properties. The RVE are subjected to six load cases and the volume averaged responses are analyzed simultaneously to predict the anisotropic properties. The mechanical behaviour is simplified to an orthotropic material model with Hill’s plasticity model and the properties are verified with micro-mechanical simulation and experimental results available in the literature. Reasonable agreement is obtained between the results. Formulae for elastic properties are also derived by a simplified analytical method based on lamination theory and compared with those obtained from homogenization.     

An analytical model to predict the thermal performance of a novel parallel flow packed bed solar air heater

A design of a parallel flow solar air heater with packed material in its upper channel and capable of providing a higher heat flux compared to the conventional non-porous bed double flow systems is presented. An analytical model describing the various temperatures and heat transfer characteristics of such a parallel flow packed bed solar air heater (PFPBSAH) has been developed and employed to study the effects of the mass flow rate and varying porosities of the packed material on its thermal performance. The model employs an iterative solution procedure to solve the governing energy balance equations describing the complex heat and mass exchanges involved. To validate the proposed analytical model, comparisons between theoretical and experimental results showed that good agreement is achieved with reasonable accuracy. Also, PFPBSAH is found to perform more efficiently than the conventional non-porous double flow solar air heaters with 10–20% increase in its thermal efficiency. Furthermore, the effect of the fraction of mass flow rate in the upper or lower flow channel of PFPBSAH device on its performance, has also investigated theoretically. The fraction of the mass flow rate in the respective channels of the PFPBSAH is shown to be dominant parameter in determining the effective thermal efficiency of the heater.