Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part II: model validations

This is the second paper in a series of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. This paper (Part II—Model Validations) focuses on the evaluation of current analytical models, discussed in the first paper (Part I—Analytical Models) as well as finite element models for conducting crack-opening-area analyses of pipes with circumferential through-wall cracks. The evaluation was performed by direct comparisons of the predicted results with the test data from full-scale pipe fracture experiments. The results from 25 full-scale pipe fracture experiments, conducted in the Degraded Piping Program, the International Piping Integrity Research Group Program and the Short Cracks in Piping and Piping Welds Program, were used to verify the analytical models. The main objective was the evaluation of engineering analysis procedures (estimation methods) as well as the ability of the finite element method to predict crack-opening displacements and shapes in pipes with circumferential through-wall cracks. Statistics were developed to quantify the accuracy of the current predictive models. A wide variety of pipe fracture tests involving cracks in base metals, weld metals and bimetallic weld metals were analyzed. Pipes containing both simple through-wall cracks and complex cracks were evaluated.     

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part I: analytical models

Leak-before-break (LBB) analyses for circumferentially cracked pipes are currently being conducted in the nuclear industry to justify elimination of pipe whip restraints and jet impingement shields which are present because of the expected dynamic effects from pipe rupture. The application of the LBB methodology requires calculation of leak rates. The leak rates depend on the crack-opening area of the through-wall crack in the pipe. In addition to LBB analyses which assume a hypothetical flaw size, there is also interest in the integrity of actual leaking cracks corresponding to current leakage detection requirements in NRC Regulatory Guide 1.45, or for assessing temporary repair of Class 2 and 3 pipes that have leaks, as are being evaluated in ASME Section XI. The objectives of this study were to review, evaluate, and refine current predictive models for performing crack-opening-area analyses of circumferentially cracked pipes. A three-phase effort was undertaken to accomplish this goal. It is described here in a series of three papers generated from this study. In this first paper (Part I — Analytical models), a comprehensive review is performed to determine the current state-of-the-art in predicting crack-opening displacements for circumferentially cracked pipes under pure bending, pure tension, and combined bending and tension loads. Henceforth, new and improved analytical models and some preliminary results are presented for cases where current methods are inadequate or there are no available methods. Also, based on this review, a number of appropriate predictive models are identified for a systematic evaluation of their accuracy. The results of their evaluations will be presented and examined in the forthcoming companion papers (Part II — Model validations [1] and Part III — Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) [2].     

Modelling and measurement of residual stresses in autogenously welded stainless steel plates: Part 1 – fabrication and modelling

Fabrication details and finite element derived predictions of residual stress are presented for two types of 316 L stainless steel test specimens of simple geometry, both containing an autogenous (no filler material) weld bead. The specimens were conceived in order to validate analytical weld residual stress predictions, which are only available for components of simple geometry and which do not account for phase transformations. The numerical modelling presented was undertaken by four different participants as part of a small ‘round robin’. The simplicity of the specimens permitted conclusions to be drawn concerning the relative importance of various modelling parameters. It is demonstrated that the assumptions made regarding the material hardening behaviour have the most significant effect on the predicted residual stress fields. Maximum differences in residual stress magnitudes of approximately 250 MPa were seen, but in general the variations were around 100 MPa. This underlines the need for caution when considering numerical residual stress predictions and underlines the need to validate predictions with measurements.     

KI–T estimations for embedded flaws in pipes – Part I: Axially oriented cracks

This study reports a numerical investigation on the linear-elastic K_I and T-stress values over the front of elliptical cracks axially embedded in the wall of a pipe/cylindrical structure, under a uniform pressure applied on the inner surface of the pipe. The numerical procedure employs an interaction integral approach to compute the linear-elastic stress intensity factor (SIF) K_I and T-stress values from very detailed crack-front meshes. The verification study confirms the accuracy of the adopted numerical procedure in computing the K_I values based on existing results for external axial surface cracks in the wall of a cylindrical structure. The parametric investigation covers a wide range of geometric parameters including: the wall thickness to the inner radius ratio of the pipe (t/R_i), the crack depth over the wall thickness ratio (a/t), the crack aspect ratio (a/c) and the crack location measured by the ratio of the distance from the centerline of the crack to the outer surface of the pipe over the pipe wall thickness (e_M/t). Subsequent efforts develop, from a nonlinear curve-fitting procedure, a new set of equations to estimate the T-stress and K_I values at three critical front locations of the axial elliptical cracks: the crack-front point O nearest to the outer surface of the pipe, the crack-front point I nearest to the inner surface of the pipe and the crack-front point M on the centerline of the axial crack. These equations combine a second-order polynomial with a power-law expression to predict the pronounced variations in the T-stress and K_I values with respect to the geometric parameters. The coefficients of the new K_I and T-stress equations either take a constant value or incorporate the linear variation with respect to the pipe wall thickness over the inner radius ratio, t/R_i. The proposed equations demonstrate a close agreement with the finite element (FE) results, which indicate very strong dependence of the T-stress and K_I values at point O and point I on the corresponding ligament lengths, e_O and e_I.     

KI–T estimation for embedded flaws in pipes – Part II: Circumferentially oriented cracks

This paper, in parallel to the investigation on axially embedded cracks reported in the companion paper, presents a numerical study on the linear-elastic K_I and T-stress values over the front of elliptical cracks circumferentially embedded in the wall of a pipe/cylindrical structure, under a uniform pressure applied on the inner surface of the pipe. The numerical procedure employs the interaction-integral approach to compute the linear-elastic stress-intensity factor (SIF) K_I and T-stress values for embedded cracks with practical sizes at different locations in the wall of the pipe. The parametric study covers a wide range of geometric parameters for embedded cracks in the pipe, including: the wall thickness to the inner radius ratio (t/R_i), the crack depth over the wall thickness ratio (a/t), the crack aspect ratio (a/c) and the ratio of the distance from the centerline of the crack to the outer surface of the pipe over the pipe wall thickness (e_M/t). The parametric investigation identifies a significant effect of the remaining ligament length on both the T-stress and K_I values at the crack-front location (denoted by point O) nearest to the outer surface of the pipe and at the crack-front location (denoted by point I) nearest to the inner surface of the pipe. The numerical investigation establishes the database to derive approximate functions from a nonlinear curve-fitting procedure to predict the T-stress and K_I values at three critical front locations of the circumferentially embedded crack in a pipe: points O, I and M. The proposed T-stress and K_I functions utilize a combined second-order polynomial and a power-law expression, which presents a close agreement with the T-stress and K_I values computed from the very detailed finite element models. The comparison between the circumferentially embedded crack and the axially embedded crack indicates that both the T-stress and K_I values at crack-front points O and I in a circumferential crack equal approximately 50% the T-stress and K_I values at the corresponding front locations in an axial crack with the same crack depth ratio, the same crack aspect ratio and the same pipe wall thickness to the inner radius ratio.     

The instability of radial growth of a part-through and part-circumference circumferential crack in a stainless steel pipe subject to bending deformation. Part II—The effect of a superimposed axial compressive load

In the context of the integrity of nuclear reactor piping systems, this paper examines the effect of an axial compressive load, superimposed upon bending loads, on the unstable development of a part-through and part-circumference circumferential crack into a through-wall crack in a stainless steel pipe. Results are obtained for axial compressive stresses up to 20% of the material's yield stress, this being reckoned to be a reasonably large compressive stress level. The results show that if the bending deformation is load-controlled, the failure assessment should be based on the deformed pipe configuration, otherwise the failure predictions will be non-conservative. On the other hand, with displacement-controlled bending deformation an axial compressive stress does not have an adverse effect on crack stability.     

Numerical Method for Calculation of Complete Casting Processes—Part II: Validation and Application

In this article, the numerical method proposed in Part I is validated by applying it to relatively simple validation test cases with phase change as well as to real-life problems. First, the results of the 1-D calculations are compared with the analytical solutions for the Stefan problem with mushy zone. Then, the 2-D and 3-D calculations of the Bridgman crystal growth are compared with available experimental results. The ability to predict the residual stresses is demonstrated on an academic 2-D example. Finally, the results of calculation for two real-life industrial cases, injection casting and solidification of a multicomponent metal drill head, are presented and discussed.     

Availability,supply technology and costs of residual forest biomass for energy – A case study in northern China

In theory, China has vast potential forest resources for production of energy, but utilization on an industrial scale has been negligible. We assessed the practical possibilities and barriers for a forest energy business in a case study in northern China. The specific objectives of the study were 1) to assess the availability of forest biomass for energy production, 2) to determine feasible supply chains, and 3) to estimate the biomass fuel supply costs. Based on the case study results, the stand-level removals of the intended feedstock were low and the supply costs were relatively high. Suggestions for increasing the raw material basis, lowering the costs and further research and development were given. We conclude that although the case study area may not be promising from the feedstock point of view, the development could be started with small steps and proven technology. In order to avoid expensive mistakes further research for transfer of know-how and technology is needed.     

Is the H2 economy realizable in the foreseeable future? Part III: H2 usage technologies,applications, and challenges and opportunities

Energy enthusiasts in developed countries explore sustainable and efficient pathways for accomplishing zero carbon footprint through the H₂ economy. The major objective of the H₂ economy review series is to bring out the status, major issues, and opportunities associated with the key components such as H₂ production, storage, transportation, distribution, and applications in various energy sectors. Specifically, Part I discussed H₂ production methods including the futuristic ones such as photoelectrochemical for small, medium, and large-scale applications, while Part II dealt with the challenges and developments in H₂ storage, transportation, and distribution with national and international initiatives. Part III of the H₂ economy review discusses the developments and challenges in the areas of H₂ application in chemical/metallurgical industries, combustion, and fuel cells. Currently, the majority of H₂ is being utilized by a few chemical industries with >60% in the oil refineries sector, by producing grey H₂ by steam methane reforming on a large scale. In addition, the review also presents the challenges in various technologies for establishing greener and sustainable H₂ society.     

Lignites from the Plains region of Alberta,Canada—Part 1: Petrography and depositional environment

The petrography of two coal seams in Alberta was determined using reflected light microscopy. Random reflectance is 0.36%, indicating a lignite rank. Huminite is dominant over liptinite and inertinite. Maceral assemblage suggests a wet forest moor depositional paleoenvironment. The predominance of telohuminite and gelohuminite over detrohuminite and inertodetrinite reveals peat formation in a rather reducing environment and a rapid burial of the peat, which prevented any significant oxidation. A few intervals with high levels of oxyfusinite reveal periodic drops of the water table. Results coincide with the interpretation based on the Na/K ratio, which is used as an indicator of the rate of sedimentation.     

Optimization of Dimples in Microchannel Heat Sink with Impinging Jets——Part A: Mathematical Model and the Influence of Dimple Radius

With increasing heat fluxes caused by electronic components, dimples have attracted wide attention by researchers and have been applied to microchannel heat sink in modern advanced cooling technologies. In this work, the combination of dimples, impinging jets and microchannel heat sink was proposed to improve the heat transfer performance on a cooling surface with a constant heat flux 500 W/cm~2. A mathematical model was advanced for numerically analyzing the fluid flow and heat transfer characteristics of a microchannel heat sink with impinging jets and dimples(MHSIJD), and the velocity distribution, pressure drop, and thermal performance of MHSIJD were analyzed by varying the radii of dimples. The results showed that the combination of dimples and MHSIJ can achieve excellent heat transfer performance; for the MHSIJD model in this work, the maximum and average temperatures can be as low as 320 K and 305 K, respectively when mass flow rate is 30 g/s; when dimple radius is larger than 0.195 mm, both the heat transfer coefficient and the overall performance h/ΔP of MHSIJD are higher than those of MHSIJ.     

Properties of heavy section steel plates and forgings for nuclear vessels produced in Japan—Part 1. General properties

Commercial ferritic steels (ASTM A533B class 1 and A508 class 3) are the predominant materials used in nuclear pressure vessels. Strict requirements are imposed on such steels to provide adequate safety margins against the possibility of failure. This paper reports results from a cooperative programme organized by the Japan Welding Research Institute and involving 15 laboratories in which the properties of the steels were clarified. The data obtained showed the markedly superior properties of the steels now produced, when compared with the requirements and standards demanded for such steels.     

Statistical phonon transport model for multiscale simulation of thermal transport in silicon: Part II – Model verification and validation

In Part I, the statistical phonon transport (SPT) model for solving the phonon Boltzmann transport equation in a statistical framework was presented. In this part, verification and validation of the SPT model is performed. The three-phonon scattering model is evaluated by considering populations of phonons interacting within an enclosed volume of silicon. The capability of the SPT model to capture the unique aspects of phonon transport from the diffuse to the ballistic thermal transport regimes is verified. Steady-state and transient results are validated against analytical solutions, results from Monte Carlo models, and experimental data for homogeneous silicon.     

Analysis of chemical,electrochemical reactions and thermo-fluid flow in methane-feed internal reforming SOFCs: Part I – Modeling and effect of gas concentrations

Direct internal reforming solid oxide fuel cells (DIR SOFCs) have complicated distributions of temperature and species concentrations due to various chemical and electrochemical reactions. The details of these properties are studied by a 3-D numerical simulation in this work. The simulation modeling used governing equations (mass, momentum, energy and species balance equations) generally suitable to porous medium with porosity variable of zero (solid), 0.3 (porous medium) and 1.0 (fluid). Chemical kinetics equations for the internal reforming and shift reactions based on the Langmuir–Hinshelwood model were incorporated. Hydrogen and carbon monoxide oxidations were considered both participating in electrochemical reactions. The experimentally measured current density–potential curves were compared with the simulation data to validate the code, which revealed that the simulation model was able to predict the dilution effect of nitrogen and the mass transfer under high current densities. It is found that the temperature dramatically declined near the fuel inlet with strong endothermic reactions, but it increased along the fluid flow with electrochemically exothermic reactions. A low steam-to-carbon ratio (SCR) led to high steam reforming and water gas shift reaction rates, which generated a greater amount of hydrogen. Therefore, current density increased with low SCR. The average current density due to carbon monoxide electrochemical oxidation varies from 205.3 A/m² under an SCR of 2.0 to 47.6 A/m² under an SCR of 4.0. The average current density due to hydrogen electrochemical oxidation was 5535.4 A/m² under an SCR of 2.0, which was 27 times higher than that of carbon monoxide. The total current density ranged from 5740.8 A/m² under an SCR of 2.0 to 2268.9 A/m² under an SCR of 4.0.     

Final Shape of Precision Molded Optics: Part I—Computational Approach,Material Definitions and the Effect of Lens Shape

Coupled thermomechanical finite element models were developed in ABAQUS to simulate the precision glass lens molding process, including the stages of heating, soaking, pressing, cooling and release. The aim of the models was the prediction of the deviation of the final lens profile from that of the mold, which was accomplished to within one-half of a micron. The molding glass was modeled as viscoelastic in shear and volume using an n-term, prony series; temperature dependence of the material behavior was taken into account using the assumption of thermal rheological simplicity (TRS); structural relaxation as described by the Tool-Narayanaswamy-Moynihan (TNM)-model was used to account for temperature history dependent expansion and contraction, and the molds were modeled as elastic taking into account both mechanical and thermal strain. In Part I of this two-part series, the computational approach and material definitions are presented. Furthermore, in preparation for the sensitivity analysis presented in Part II, this study includes both a bi-convex lens and a steep meniscus lens, which reveals a fundamental difference in how the deviation evolves for these different lens geometries. This study, therefore, motivates the inclusion of both lens types in the validations and sensitivity analysis of Part II. It is shown that the deviation of the steep meniscus lens is more sensitive to the mechanical behavior of the glass, due to the strain response of the newly formed lens that occurs when the pressing force is removed.     

High heat flux flow boiling in silicon multi-microchannels – Part III: Saturated critical heat flux of R236fa and two-phase pressure drops

New experimental critical heat flux results for saturated boiling conditions have been obtained for R236fa flowing in a silicon multi-microchannel heat sink composed of 67 parallel channels, 223 μm wide, 680 μm high and with 80 μm thick fins separating the channels. The microchannel length was 20 mm. The footprint critical heat fluxes measured varied from 112 to 250 W/cm² and the wall critical heat fluxes from 21.9 to 52.2 W/cm² for mass velocities from 276 to 992 kg/m²s. When increasing the mass velocity, the wall critical heat flux was observed to increase. The inlet saturation temperatures (20.31 ? T_sat,in ? 34.27 °C) and the inlet subcoolings (0.4 ? Δ T_sub ? 15.3 K) were found to have a negligible influence on the saturated CHF. The best methods for predicting the data were those of Wojtan et al. [L. Wojtan, R. Revellin, J. R. Thome, Investigation of critical heat flux in single, uniformly heated microchannels, Exp. Therm. Fluid Sci. 30 (2006) 765–774] and Revellin and Thome [R. Revellin, J. R. Thome, A theoretical model for the prediction of the critical heat flux in heated microchannels, Int. J. Heat Mass Transfer 50 (in press)]. They both predict the experimental CHF results with a mean absolute error of around 9%. Using the critical vapour quality, an annular-to-dryout transition is also proposed as a limit in a diabatic microscale flow pattern map. Pressure drop measurements were measured and analysed, showing that the homogeneous model could correctly predict the observed trends.     

Users and disusers of box solar cookers in urban India—: Implications for solar cooking projects

The purpose of this study is to understand the reasons behind the continued use or disuse of solar cookers, and to outline the implications from the results of this study for future solar cooker projects. Twenty-eight families in three urban sites in Gujarat, India who have a solar cooker have been interviewed. Their experience with solar cookers and solar cooking is studied. Direct discussions with families who have practical experience with solar cooking, brings forth significant practical issues. The study shows that many disusers of solar cookers do not have a suitable place for their solar cookers. Other disusers could not adjust their daily routines with what solar cooking requires, and some disused their solar cookers because they were not interested in using them. Both objective factors and aspects of practical interest have been shown to be important issues for understanding the conditions of prospective users and the shaping of the projects and the relevant technologies. It is concluded that project developers should consider the potential users as an important partner in project development processes. For example project developers can by close dialogue with them, uncover and define practical parameters which have important bearing on higher usability of solar cookers.     

Sustainable gasification–biochar systems? A case-study of rice-husk gasification in Cambodia,Part I: Context,chemical properties,environmental and health and safety issues

Biochar is a carbon- and energy-rich porous material produced through slow pyrolysis of biomass, which has been proposed as a way of storing carbon in soils for the long-term (centurial to millennial timescales) but its production incurs an energy penalty. Gasification of rice husks at paddy mills combines the benefits of reasonably efficient delivery of energy with a reasonably high carbon char and ash mixture. The ca. 35% carbon content of the rice husk char is possibly a consequence of the protective shield of silica, preventing full exposure of the biomass to oxidation in the gasifier. In this paper we undertake an evaluation of the sustainability of this ‘gasification–biochar system’ (GBS) in Cambodia, where a rapid deployment of gasifiers is underway. In Part I, we describe the context and analyse (some of) the physical and chemical properties of the biochar. While there are some potential health, safety and environmental issues that require further analysis, they are problems that could be readily addressed in further research and appear to be resolvable. In Part II, we present results from field trials, summarise the data on the carbon abatement of the gasification–biochar system and present some preliminary economic data.     

D'Alembert's Solution in Thermoelasticity—Impact of a Rod Against a Heated Barrier: Part I. A Case of Uncoupled Strain and Temperature Fields

The problem of impact of a thermoelastic rod against a heated rigid barrier is considered, in so doing lateral surfaces and free end of the rod are heat insulated, while there is either free heat exchange between the rod and the rigid obstacle within contacting end or ideal thermal contact, as a particular case. The rod's thermoelastic behavior is described by the Green–Naghdi theory of thermoelasticity. D'Alembert's method, which is based on the analytical solution of equations of the hyperbolic type describing the dynamic behavior of the thermoelastic rod, is used as the method of solution. This solution involves four arbitrary functions which are determined from the initial and boundary conditions and are piecewise constant functions. The procedure developed enables one to analyze the influence of thermoelastic parameters on the values to be found, as well as to investigate numerically the longitudinal coordinate dependence of the desired functions at each fixed instant of the time beginning from the moment of the rod's collision with the barrier up to the moment of its rebound. The case of uncoupled stress and temperature fields is examined in the first part of the paper, while the case of coupling thermoelasticity is considered in detail in the companion paper. It has been shown that the possibility for generating the reflected thermal wave from the incident elastic wave at the free rod's end is unavailable in the case of the uncoupled strain and temperature fields, and that the rod's rebound may occur either at the moment of arrival at the contact place of the reflected elastic wave from the incident thermal wave or at the time when the reflected elastic wave from the incident elastic wave reaches the contact point.