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Experimental Validation of Exact Burst Pressure Solutions for Thick-Walled Cylindrical Pressure Vessels

Burst pressure is one of the critical strength parameters used in the design and operation of pressure vessels because it represents the maximum pressure that a vessel can withstand before failing. Historically, the Barlow formula was used as a design base for estimating burst pressure. However, it does not consider the plastic flow response for ductile steels and is applicable only to thin-walled cylinders (i.e., the diameter to thickness ratio D/t ≥ 20). A new multiaxial plastic yield theory was developed to consider the plastic flow response, and the associated theoretical (i.e., Zhu–Leis) solution of burst pressure was obtained and has gained extensive applications in the pipeline industry because it was validated by different full-scale burst test datasets for large-diameter, thin-walled pipelines in a variety of steel grades from Grade B to X120. The Zhu–Leis flow theory of plasticity was recently extended to thick-walled pressure vessels, and the associated exact flow solution of burst pressure was obtained and is applicable to both thin and thick-walled cylindrical shells. Many full-scale burst tests are available for thin-walled line pipes in the pipeline industry, but limited pressure burst tests exist for thick-walled vessels. To validate the newly developed exact solutions of burst pressure for thick-walled cylinders, this paper conducts a series of burst pressure tests on small-diameter, thick-walled pipes. In particular, six burst tests are carried out for three thick-walled pipes in Grade B carbon steel. These pipes have a nominal diameter of 2.375 inches (60.33 mm) and three nominal wall thicknesses of 0.154, 0.218, and 0.344 inches (3.91, 5.54, and 8.74 mm), leading to D/t = 15.4, 10.9, and 6.9, respectively. With the burst test data, comparisons show that the Zhu–Leis flow solution of burst pressure matches well the burst test data for thick-walled pipes. Thus, these burst tests validate the accuracy of the Zhu–Leis flow solution of burst pressure for thick-walled cylindrical vessels.

42 ENGINEERING

Evaluation of Maximum Allowable Working Pressure and Svensson Burst Pressure Recommended in API 579-1 2021 Edition

Abstract API 579-1/ASME FFS-1 2021 Edition provides the minimum wall thickness, the maximum allowable working pressure (MAWP), and the membrane stress equations for thin and thick-walled cylindrical shells subject to internal pressure in Section 2C.3.3.1 of Appendix 2C – Thickness, MAWP, and Stress Equations for an FFS Assessment. The minimum wall thickness and MAWP are determined using the hoop stress and the Tresca yield criterion. Section 2C.7 – Estimation of Burst Pressure newly added the Svensson method for calculating burst pressure of cylindrical shells under internal pressure, where the plastic yielding is characterized by the von Mises yield criterion. For thin-walled cylinders, the von Mises flow solution of burst pressure in Equation (2C.179) was recommended. For thick-walled cylinders, an implicit burst pressure solution in an integral equation (2C.176) was recommended. But this integral equation is inconvenient to use in practice. It is well known that the classic plasticity theory includes the Tresca and von Mises yield criteria, with the Tresca criterion predicting a lower bound solution and the von Mises criteria predicting an upper bound solution. In addition, the present author developed an average shear stress yield criterion that can determine more accurate limit and burst pressures for thin and thick-walled cylinders. This work uses these three yield criteria to evaluate the minimum required wall thickness, MAWP and Svensson burst pressure recommended in the API 579 code.

burst pressure

Evaluation of Maximum Allowable Working Pressure and Svensson Burst Pressure Recommended in API 579-1 2021 Edition

ABSTRACT API 579-1/ASME FFS-1 2021 Edition provides the minimum wall thickness, the maximum allowable working pressure (MAWP), and the membrane stress equations for thin and thick-walled cylindrical shells subject to internal pressure in Section 2C.3.3.1 of Appendix 2C – Thickness, MAWP, and Stress Equations for an FFS Assessment. The minimum wall thickness and MAWP are determined using the hoop stress and the Tresca yield criterion. Section 2C.7 – Estimation of Burst Pressure newly added the Svensson method for calculating burst pressure of cylindrical shells under internal pressure, where the plastic yielding is characterized by the von Mises yield criterion. For thin-walled cylinders, the von Mises flow solution of burst pressure in Equation (2C.179) was recommended. For thick-walled cylinders, an implicit burst pressure solution in an integral equation (2C.176) was recommended. But this integral equation is inconvenient to use in practice. It is well known that the classic plasticity theory includes the Tresca and von Mises yield criteria, with the Tresca criterion predicting a lower bound solution and the von Mises criteria predicting an upper bound solution. In addition, the present author developed an average shear stress yield criterion that can determine more accurate limit and burst pressures for thin and thick-walled cylinders. This work uses these three yield criteria to evaluate the minimum required wall thickness, MAWP and Svensson burst pressure recommended in the API 579 code.

burst pressure

Selective mass scaling for single-layer thick shell elements in DYNA3D

Hexahedral elements can be adapted to model thin and moderately thick structures by neglecting the coupling of through-thickness stress, resulting in a fully three-dimensional, but simplified, state of stress. These specialized elements, often referred to as “thick” or “solid” shells, are generally employed to model thin-walled structures using continuum mechanics-based material models. In explicit dynamics simulations, where computational speed is important, these elements are integrated with a single quadrature point and a set of anti-hourglassing (stabilizing) forces. Thick shells, by definition, have a thickness dimension smaller than their in-plane dimensions, and this small thickness often determines the stable time step size in simulations, despite the mechanics being approximated. To alleviate this limitation while retaining the relevant dynamics of thin-walled structures, selective mass scaling (SMS), or selective mass “augmentation,” has been proposed in the literature. In this technical report, we explore the application of SMS to single-layer thick shells in the simulation software DYNA3D.

42 ENGINEERING

An extended variational method for the resistive wall mode in toroidal plasma confinement devices

The external-kink stability of a toroidal plasma surrounded by a rigid resistive wall is investigated. The well-known analysis of Haney and Freidberg is rigorously extended to allow for a wall that is sufficiently thick that the thin-shell approximation does not necessarily hold. A generalized Haney–Freidberg formula for the growth-rate of the resistive wall mode is obtained. Thick-wall effects do not change the marginal stability point of the mode but introduce an interesting asymmetry between growing and decaying modes. Growing modes have growth-rates that exceed those predicted by the original Haney–Freidberg formula. On the other hand, decaying modes have decay-rates that are less than those predicted by the original formula. The well-known Hu–Betti formula for the rotational stabilization of the resistive wall mode is also generalized to take thick-wall effects into account. Increasing wall thickness facilitates the rotational stabilization of the mode, because it decreases the critical toroidal electromagnetic torque that the wall must exert on the plasma. On the other hand, the real frequency of the mode at the marginal stability point increases with increasing wall thickness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Microstructural evaluation of thin-wall sections of 316L stainless steel produced by laser powder-bed fusion processing

Laser powder bed fusion (LBPF) is a method of additive manufacturing (AM) that offers a means to fabricate complex components with features which rely upon the mechanical integrity of thin-wall (less than 0.4 mm thick) structures. The microstructure of a 316L AM thin wall is investigated as metallographically prepared from a cylindrical shell. Optimization is pursued through mechanical polishing and chemical etching to minimize the effects of surface roughness. Microanalysis measurements of the sectioned component reveal the sample has high microstructural fidelity, uniform composition and phase content across grain as well as powder layer boundaries within the thin wall. The results are attributed to a uniform thermal gradient at the part scale during rapid solidification.

36 MATERIALS SCIENCE

Multiphase Processing of the Water-Soluble and Insoluble Phases of Biomass Burning Organic Aerosol

Biomass burning is one of the most significant sources of organic aerosol in the atmosphere. Biomass burning organic aerosol (BBOA) has been observed to undergo liquid– liquid phase separation (LLPS) to give core–shell morphology with the hydrophobic phase encapsulating the hydrophilic phase, potentially impacting the evolution of light-absorbing components, i.e., brown carbon (BrC), through multiphase processes. Here, we demonstrate how multiphase processing differs between the watersoluble (i.e., hydrophilic) and insoluble (i.e., hydrophobic) phases of BBOA in terms of reactive uptake of ozone in a coated-wall flow tube. Effects of relative humidity (RH) and ultraviolet (UV) irradiation were investigated. Experimental timeseries were used to inform simulations using multilayer kinetic modeling. Among non-irradiated thin films, the uptake coefficient was greatest for the water-soluble phase at 75% RH (3 × 10 –5 , corresponding to a diffusion coefficient of BrC, D BrC , of 3 × 10 –9 cm 2 s –1 ) and least for the same phase at 0% RH (1 × 10 –5 , corresponding to D BrC of 1 × 10 –10 cm 2 s –1 ). The uptake coefficient for the water-insoluble phase fell between these two (about 1.5 × 10 –5 ), regardless of RH, and the corresponding D BrC increased only slightly (8 × 10 –10 cm 2 s –1 at 0% RH to 9 × 10 –10 cm 2 s –1 at 75% RH). The uptake coefficients of both phases at 0% RH decreased significantly after UV irradiation, consistent with a transition from viscous liquid to solid and supported by qualitative microscopy observations. Modeling multiphase ozone oxidation of primary BrC components in the atmosphere demonstrated, first, that LLPS may extend the lifetime of water-soluble BBOA encapsulated by water-insoluble species by a factor of 1.5 at moderate to high RH and, also, that UV irradiation may extend the lifetime of both phases by more than a factor of 2.5.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Conformable, Composite Tank for Liquid Hydrogen Storage in Heavy-duty Ground Transportation

Raytheon Technologies Research Center (RTRC), with its partners, Argonne National Labs and University of Dayton Research Institute proposed to design and manufacture a conformable composite tank prototype to store liquid Hydrogen (LH2) for heavy-duty truck applications. A dual-wall tank concept was proposed where an outer shell covers and protects an inner pressure vessel that stores liquid hydrogen. The inner pressure vessel is liner-less and designed with a conformable concept, derived from prior RTRC ARPA-E program where multiple vessels are coalesced into one, maximizing space utilization and reducing surface area for heat leak. The gap between the dual wall is evacuated of air pressure, and filled with multi-layer insulation to minimize radiative heat transfer. Fiber reinforced composites were proposed for light-weighting and conformable shape manufacture. To minimize LH2 leakage, carbon nanotubes-infused composites were proposed, in addition to use of thin plies. The project was divided into two 18-month budget periods (BP), BP1 and BP2, separated by a Go/No-Go gate review. The high-level goal for BP1 was to demonstrate the feasibility of the overall approach, the tank design, material selection, and manufacturing methodology, build and test a prototype tank; and the goal for BP2 was to design and manufacture a conformal tank per DOE requirements (minimum 20 kg of LH2) and perform a successful test of the tank. The program was terminated about two-thirds of the way through BP1. The outcome of this program would have permitted long-haul trucks and construction vehicles to use liquid Hydrogen, reducing the emission of green-house gases. This technology is applicable to other transportation sectors as well.

08 HYDROGEN

Axion interactions with domain and bubble walls

We show that interactions between axion-like particles (ALPs) and co-dimension one defects, such as phase-transition bubble walls and solitonic domain walls, can lead to important changes in the evolution of both walls and ALPs. The leading effect arises from the change in the ALP decay constant across the interface, which naturally follows from shift-symmetric interactions with the corresponding order parameter. Specifically, we show that for thin walls moving relativistically, an ALP background — such as e.g. axion dark matter — gives rise to a frictional force on the interface that is proportional to γ 2 , with γ the Lorentz factor of the wall, and that this effect is present in both the oscillating and frozen axion regimes. We explore the broader consequences of this effect for bubble and domain walls in the early universe, and show that this source of friction can be present even in the absent of a conventional medium such as radiation or matter. Possible implications include modifications to the dynamics of bubble and domain walls and their corresponding gravitational wave signatures, as well as the generation of a dark radiation component of ALPs in the form of ultra-relativistic ‘axion shells’ with Lorentz factor γ shell ≃ 2γ 2 ≫ 1 that may remain relativistic until the present day.

Axions and ALPs

Cathodic Protection Modeling for Hanford Underground Double-Shell Tank Farms

Hanford stores millions of gallons of radioactive and chemically hazardous waste from the production of weapon materials in tank farms consisting of underground carbon-steel storage tanks surrounded by reinforced concrete. Six of these Hanford tank farms use double-shell storage tanks (DSTs). The DST farms were constructed from 1968 to 1986 with a planned 40–50 year design life, so some are already operating beyond their initial life expectancy. Ultrasonic testing (UT) has indicated significant thinning on the bottom of the secondary (outer) liner of these tanks, believed to arise from groundwater intrusion driving concrete side corrosion. There is no direct access to the steel/concrete interface between the tank and the concrete pad, making it difficult to apply a chemical-based mitigation strategy or to conduct repairs, but cathodic protection (CP) is a possible method to inhibit further concrete-side corrosion. Hanford already uses CP to protect below grade steel piping within the tank farms and connected to the tanks, but this system was not designed to protect the tank bottoms. CP design must account for the structures surrounding the DSTs, including the steel reinforcing bars (rebar) within the concrete pad and vault, various process lines, and the existing CP system. In this study, finite element analysis (FEA) modeling was carried out to simulate CP protection of 1) a single tank and CP anode to develop options for modeling the rebar and to compare to a simpler circuit model and 2) the entire Hanford AN tank farm as a representative example consisting of seven tanks, associated piping, and both existing and new CP anodes. Both circuit and FEA models predict that significant protective current could be delivered to the bottoms of the tanks with the addition of tank-protection anodes below the depth of the tanks. Simulations with only the existing pipe-protection anodes active confirmed that only a very small current to the tank bottoms is predicted under present conditions. Multiple simplified representations of the dome and wall rebar were tested to reduce the computational complexity of the tank-farm simulations, resulting in modeling the rebar as edge elements with a prescribed effective circumference that matches the real rebar surface area. The geometry of the rebar is also simplified into horizontal hoops around the tank walls and radial rebar over the dome with increased effective circumference to retain the target surface area. This simplification was found to greatly reduce the complexity and solution time of the models without large changes in current distributions, especially to the tank bottom. A range of values were tested for model parameters such as soil and concrete resistivities and polarization resistance to investigate their impact on the current and electric potential distributions. Depending on the parameters used, FEA simulations predict some risk of overprotection, particularly on the piping system; since overprotection can also lead to surface damage associated with hydrogen gas generation at the interface (e.g. hydrogen embrittlement or damage to coatings), this needs to be considered when refining the design of the new CP system. Comparison between the FEA models and the circuit model representation demonstrated that the circuit model could not match the predicted FEA current distribution, even when using the exact same surface areas. This discrepancy appeared to be at least partly attributable to the impact of the relative positions of the tank components and anodes to each other and to the ground surface. The FEA model accounts for the relative positions since it solves the governing equations in three dimensions, but the circuit model cannot account for the positioning. In particular, the circuit model underpredicts the current to the tank bottom and overpredicts the current to the dome compared to FEA for the baseline geometry. The FEA models omitted the electrically isolated rebar in the bottom concrete slab. However, a circuit based stray current model estimated that only 2.1% of the total current through the slab would stray into the rebar, corresponding to ~0.21 A for a target current density of 2 mA/ft2 to the tank bottom. The estimated corrosion driven by this amount of stray current is predicted to yield a lifetime of >400 years for the minimum rebar diameter, assuming an acceptable cross-section area loss of 10%.

d'Entremont, Anna [Savannah River National Laborat