The focus of this paper is on gaseous deflagration in piping systems and the corresponding implications on piping analysis and design. Unlike stable detonations that propagate at a constant speed and whose pressure-time histories can in some cases be predicted analytically, deflagration flame speeds and pressure-time histories are transient and depend on both the gas mixture and geometry of the pipe. This paper presents pressure and pipe strain data from gaseous deflagration experiments in long and short test apparatuses fabricated from either 2-inch or 4-inch diameter pipes. These data are used to demonstrate a spectrum of measured pressure-time histories and corresponding pipe response. It is concluded that deflagrations can be categorized as either “high” or “slow” speed with respect to pipe response. Slow deflagrations can be treated as quasi-static pressurizations, but high speed deflagrations can generate shock waves that dynamically excite the pipe. The existence of a transition from quasi-static to dynamic response has ramifications in regards to piping structural analysis and design, and a method for predicting the expected deflagration structural response using a semi-empirical flame acceleration model is proposed.

This paper proposes Piping Code rules to address the effects of hydrogen deflagrations inside piping. Previous work proposed a set of criteria for piping subject to detonation loading [PVP2012-78519, PVP2012-78525]. This paper provides criteria to evaluate the effect of deflagrations, which typically have a slower rise time and lower energy, inside the piping. These deflagration criteria, coupled with the previously cited detonation criteria, are being used at the Hanford Tank Waste Treatment and Immobilization Plant to evaluate piping systems subject to hydrogen accumulation. The previous papers did not investigate or propose criteria for deflagrations, as these were known to have lower pressures and slower pressure rise times, but are still of some significance for piping design. Recent work has shown that there exists a scenario in which the deflagration loading may be very significant: deflagrations in small gas pockets surrounded by large waste slugs. Depending on the assumptions used to develop the loading, the unbalanced forces on piping segments in a long piping system can become high during a deflagration event. Thus, for the set of criteria chosen for deflagration, the deflagration event may become the limiting event, especially if it is the more frequent event. The criteria proposed need to recognize this scenario and guide the user to possible solutions. This paper presents the original methodology for evaluating these “slug” events, briefly discusses the recent testing and theory being pursued to reduce the effect of the loading [PVP2015-45970, PVP2016-63260, PVP2016-63262], and then proposes criteria for evaluating deflagration induced stresses and loads.

The Hanford Tank Waste Treatment and Immobilization Plant (WTP) will process waste slurries that have the potential to generate flammable gases and will utilize a number of atmospheric vessels to store these slurries at various stages of the waste treatment process. Throughout the design process, provisions have been made to ensure that these flammable gasses are vented from these vessels and to eliminate potential sources of ignition. However, Bechtel National, Inc. (BNI) would like to be able to demonstrate that these vessels are capable of withstanding a limited number of unintended detonations. It is well known that pressure vessels may be designed for internal detonations. However, these loadings tend to cause very brief transients of high stress that can make traditional stress-based design rules to be difficult to meet. In the past decade, a number of strain-based design methodologies have become available, including ASME Boiler and Pressure Vessel Code (BPVC), Section VIII, Division 2, Part 5; ASME Section VIII, Division 3; ASME Section VIII, Division 3 Code Case 2564; and API 579-1 / ASME FFS-1. Each of these sets of rules permits some degree of plasticity in vessel design, but there are key differences in the specific provisions. In this paper, the use of these different sets of Code rules will be demonstrated in the context of the design of a WTP vessel for a single unintended detonation, and the advantages and disadvantages of these alternative design approaches will be discussed.

This paper introduces a simplified approach for analyzing local elastic hoop response of piping to reflected gaseous detonations and deflagration-to-detonation transitions (DDT). A consequence associated with gaseous explosions is the potential for DDT to occur near the end of a closed pipe or gas pocket. As an accelerating deflagration flame approaches a closed end, the unburned fuel ahead of the flame front is compressed to an elevated initial pressure. This process is often referred to as pressure piling or pre-compression, and the combination of detonation reflection with the elevated initial pressure, can produce extremely high peak pressures and large values of impulse. In this paper, the event where DDT occurs immediately ahead of the reflecting surface is referred to as a reflected-DDT (R-DDT). In addition to gas mixture and initial conditions, the peak pressure and shape of the pressure time-history associated with a reflected detonation or DDT is a function of the detonation propagation distance prior to reflection and the relative distance between the ignition location, the DDT location, and the reflecting surface. An empirical pressure time-history has been developed using pressure data from approximately 190 explosion tests using hydrogen and nitrous oxide mixtures in 2-inch and 4-inch pipe to describe events ranging from fully-developed reflected detonations to R-DDTs. The empirical model of the pressure time-history was validated by comparing measured elastic hoop strains to finite-element model predictions using the pressure time-history model. Part 2 of this paper compares the methodology to plastic response data.

This paper applies a simplified conservative approach for analyzing elastic-plastic response of piping due to reflected gaseous detonations and deflagration-to-detonation transitions (DDT). A consequence associated with gaseous explosions is the potential for DDT to occur near the end of a closed pipe or gas pocket. As an accelerating deflagration flame approaches a closed end, the unburned fuel ahead of the flame front is compressed to an elevated initial pressure. This process is often referred to as pressure piling or pre-compression, and the combination of detonation reflection with the elevated initial pressure can produce extremely high peak pressures and large values of impulse. In this paper, the event where DDT occurs immediately ahead of the reflecting surface is referred to as a reflected-DDT (R-DDT). Due to the extreme pressures that R-DDTs can achieve, the piping can frequently experience elastic-plastic deformation. In this second part, the pressure time-history modeling methodology developed for elastic response in part one is extended to elastic-plastic analysis. The inelastic response of the piping material is modeled using a lower-bound strain hardening curve at a single representative strain rate. The pressure model is compared to a published reflected detonation pressure model for the stoichiometric mixture of ethylene and oxygen, and finite-element analysis results using the simplified methodology are compared to two recent sets of published plastic deformation data from ethylene oxygen explosion tests in austenitic stainless steel tubing and piping.

This paper reports the results of experiments and finite element simulations on the structural response of piping systems to internal detonation loading. Specifically, the work described in this paper focuses on the forces that are produced at tee-junctions that lead to axial and bending structural responses of the piping system. Detonation experiments were conducted in a 2-in. (50 mm) diameter schedule 40 piping system that was fabricated using 304 stainless steel and welded to ASME B31.3 standards. The 4.1 m (162-in.) long piping system included one tee and was supported using custom brackets and cantilever beams fastened to steel plates that were bolted to the laboratory walls. Nearly-ideal detonations were used in a 30/70 H 2 -N 2 O mixture at 1 atm initial pressure and 300 K. Pressure and hoop, axial, and support strains were measured using a high-speed (1 MHz) digital data acquisition system and calibrated signal conditioners. It was concluded that detonations propagate through the run of a 90° tee with relatively little disturbance in either direction. The detonation load increases by approximately a factor of 2 when the detonation enters through the branch. The deflections of the cantilever beam supports and the hoop and axial pipe strains could be adequately predicted by finite element simulations. The support loads are adequately predicted as long as the supports are constrained to the piping. This paper shows that with relatively simple models, quantitative predictions of tee forces can be made for the purposes of design or safety analysis of piping systems subject to internal detonations.

This paper addresses the local effects of hydrogen detonations inside piping. It is the first in a two-part series of papers which assess the effects of detonations in piping systems relative to ASME Code allowables. The effects of internal detonations in piping systems are typically separated into two regimes: local effects and system effects. Local effects are often simplistically represented as pure hoop stresses resulting from the pressure acting radially on the inside circumference of the pipe. In reality, the interaction of the pipe wall and the propagating detonation wave is relatively complex, resulting in “waves” or “ripples” in the pipe wall. These areas of local, through-wall curvature lead to substantial axial stresses which may even exceed the hoop stresses. Furthermore, in the elastic regime, there is very little damping present in the pipe wall, leading to numerous stress cycles as the local bending waves move axially along the pipe wall. Fatigue effects of the combined hoop and axial cycling were evaluated using ASME Code Section VIII, Division 2 fatigue evaluation methodology. Analysis of strain gage data from a number of hydrogen detonation experiments in 2-inch and 4-inch Schedule 40 piping showed that the fatigue damage is generally driven by fewer than 10 large-magnitude fatigue cycles, which account for an average of 75% of the total fatigue damage. However, the results also demonstrate that for two detonation events with similar measured peak hoop or axial strain, the number of fatigue allowable events may vary dramatically depending on the shape of the strain response.

A Quantitative Risk Analysis (QRA) model has been developed to determine the frequency and severity (potential combustion loads) of postulated hydrogen event types in piping systems and proposed as a design-informing tool for the U.S. Department of Energy’s (DOE) Hanford Tank Waste Treatment and Immobilization Plant (WTP) at the Hanford Site near Richland, Washington. Specifically, the QRA provides a systematic, comprehensive methodology for assessing hydrogen events, including deflagrations, detonations, and deflagration-to-detonation transition (DDT) types in piping systems containing legacy nuclear waste streams being processed for vitrification. The events considered include normal operations as well as postulated upset conditions as a result of internal and external accidents. The QRA approach incorporates three sequential phases, including Operational Frequency Analysis (OFA), Gas Pocket Formation (GPF) and Event Progression Logic (EPL) models in the form of an integrated logic framework. The WTP piping design will be evaluated on a specific piping route basis using a probabilistic sampling approach, with the QRA providing the quantitative dynamic loads for evaluation according to the frequency and type of hydrogen event. The OFA is based on an industry standard fault tree computer model, CAFTA, and analyzes the frequency of combustible gas pocket formation in a piping system from three primary sources: (1) normal operations; (2) piping system-specific upset conditions affecting transfer operations; and (3) plant-wide initiating events such as fire and seismic accidents. A second output from the OFA is duration time for each event, quantifying the length of time that a gas pocket is likely to develop before the initiating event is terminated, with the information provided directly to QRA event tree models for assessing gas pocket growth. A team of safety, operations and engineering, developed the underlying logic of the fault tree model with the overall modeling approach following applicable nuclear/chemical industry guidance and standards for performing QRA applications. Primary inputs to the OFA module are initiating event, equipment reliability, and human/operator error data and their characteristic distributions, and are drawn from Hanford Site safety documentation, government and commercial sector sources, and related nuclear/chemical industry experience. This paper discusses the overall OFA module, its inputs, the outputs to the GPF and EPL modules, the relative importance of different initiating event conditions, key insights obtained to date, upcoming supporting uncertainty/sensitivity analyses, and summarizes technical peer review assessments.

Stresses in piping systems subject to hydrogen detonation loading are complex. There are high-frequency localized shell-type stresses, such as hoop membrane, longitudinal through-wall bending and hoop through-wall bending due to asymmetric modes. There are low-frequency gross beam-type stresses, similar to those from a waterhammer, as the unbalanced forces excite the beam bending and bar wave modes in the piping system. From a code compliance standpoint, all the stresses need to be considered and categorized in terms of the type of failure that they can cause. Part 1 developed a method to estimate the local shell stresses due to the detonation wave. This paper, Part 2, discusses an investigation into the global beam bending effects. It proposes a methodology for combining the beam and local shell effects, and evaluating the results in terms of complying with a typical piping code. The gross stresses due to the propagating detonation wave can be evaluated using beam-finite element models and time-history analysis, similar to analyses for waterhammer. As with waterhammer, these stresses are typically considered “occasional” loads. However, the beam stresses can coincide with very high hoop or radial shell stresses, due to the high peak pressures involved, so that the simple comparison of using longitudinal stresses may not be an adequate design check. This paper recommends a combination of shell-equivalent stresses and beam-stress intensities that result in a conservative comparison, when compared to a full time-history analysis, but one which is not overly conservative. With the exception of ASME Section III, Class 1, most U.S. piping codes do not provide rules for fatigue evaluation for loads other than displacement controlled loads. ASME B31.3 Appendix P provides guidance for pressure fluctuations, but the focus is primarily gross stress effects. The local effects from a detonation wave include both a “skin” stress effect on the inside surface and a through-wall bending effect due to the dynamic nature of the effects of the propagating wave. Both of these must be considered if the number of occurrences is significant. This paper proposes a method to consider these localized stresses that is patterned after the guidance in ASME Section III, NB-3600.

In late 2008, a Hydrogen in Piping and Ancillary Vessels (HPAV) Assessment Team was chartered by the U.S. Department of Energy’s (DOE) Office of River Protection (DOE-ORP) to investigate the extent of operational complexity in the Hanford Tank Waste Treatment and Immobilization Plant (WTP) due to conservatisms in hydrogen event analysis methodology and related design constraints. The HPAV Assessment Team recommended that a Quantitative Risk Analysis (QRA) be performed to analyze normal plant operating and upset conditions that can lead to accumulation of hydrogen in piping, and determine the frequency and severity of ensuing postulated hydrogen events such that WTP can make risk-informed decisions regarding hydrogen event mitigation strategies and improve operational flexibility. The QRA application is based on an in-depth review of hydrogen event-affected systems conducted by an interdisciplinary team of system engineers, process engineers, plant operations modelers, operators, and safety personnel to ensure facility ownership of the overall process. The QRA evaluates hydrogen event-affected systems for both normal system operations and possible upset conditions as a result of internal and external events (including human error). The Operational Frequency Analysis (OFA) and Event Progression Logic (EPL) analysis provide an integrated framework for the analysis of initiating events from which hydrogen accumulation can occur and the quantitative analysis of the physical progression of ensuing hydrogen ignition events. The purpose of this paper is to describe the QRA methodology, models, and testing used to quantify the system demand resulting from postulated hydrogen event types, frequencies, and severities, with emphasis on the latter stages of the QRA, overall execution and application.

This paper describes hydrogen and nitrous oxide detonation experiments that were performed using an approximately 200-ft long 2-inch schedule 40 piping system. The objective of these experiments was to develop an understanding of the loads and forces imposed by internal detonation on piping combinations representative of a typical industrial piping system. The apparatus contained numerous straight pipe lengths with 90° and 45° bends, 90° elbows, and a tee along with rigid foundation supports that were connected to the pipe using typical u-bolt fasteners. As a detonation wave propagates through a gas-filled piping system, the pipe begins to respond globally once a detonation encounters a change in flow direction, such as a bend, causing a pressure imbalance due to both the internal detonation pressure and change in momentum of the reaction products. The resultant force imparts both axial forces and moments on the pipe exciting both extensional and bending modes. The test data was used to validate two finite element (FE) models developed using the ANSYS finite-element program: a hybrid model that made use of both shell and beam elements, to determine the interaction between shell and beam modes, and an all beam element model. An additional beam element model was developed using the Bechtel National Inc. software ME101 that was also found to be in agreement with the measured and ANSYS calculated frequencies and support loads. In addition to the detonation testing, the finite-element models were validated against experimental modal analysis data of the piping system that identified the primary modal frequencies and vectors. These data were compared to the modes extracted from finite-element models of the piping system.

The use of a material in a design where failure carries environmental or health and safety risk requires computational design using a conservative strength model. The materials design engineer must determine and be able to justify a lower-bound stress-strain curve. This paper uses the AISI 304 / 304L system to demonstrate how such a model might be derived. It addresses the question of variability in materials properties. Also discussed is the contribution of strain-rate dependence that is relevant to applications involving impact or explosive loading conditions. Designers and those reviewing and approving designs are more comfortable with the use of temperature dependent than strain-rate dependent material properties. Ignoring strain-rate dependence can lead to overly conservative designs, even when the objective is a conservative design. The Mechanical Threshold Stress model is used to demonstrate, in the 304 / 304L system, a lower-bound temperature and strain-rate dependent constitutive model. This model implements a state-variable approach and easily accounts for temperature and strain-rate dependent material properties as well as strain hardening. A wealth of literature data is used to benchmark and validate the model. Comparison of model predictions with applicable ASME and ASTM code standards is described.

This paper reports the results of experiments, analytical models, and finite element simulations on the structural response of piping systems to internal detonation loading. Of particular interest are the interaction of detonations with 90° bends and the creation of forces that lead to axial and bending structural response of the piping system. The piping systems were fabricated using 304 stainless steel, 2-in. (50 mm) diameter schedule 40 commercial pipe with a nominal wall thickness of 0.154-in. (3.8 mm) and welded construction to ASME B31.3 standards. The piping was supported using custom brackets or cantilever beams fastened to steel plates that were bolted to the laboratory walls. Nearly-ideal detonations were used in a 30/70 H 2 -N 2 O mixture at 1 atm initial pressure and 300 K. The detonation speeds were close (within 1%) to the Chapman-Jouguet velocity and detonation cell sizes much smaller than the tube diameter. Pressure, displacement, acceleration and hoop, longitudinal, and support strains were measured using a high-speed (1 MHz) digital data acquisition system and calibrated signal conditioners. Detonation propagation through a bend generates a longitudinal stress wave in the piping that can be observed on the strain gauges and is predicted by both analytical models and finite element simulations. The peak magnitude of the bend force is approximately twice that due to the pressure alone since the peak momentum flux of the flow behind the detonation front is comparable to the pressure in the front. With relatively simple models, quantitative predictions of the bend forces can be made for the purposes of design or safety analysis of piping systems with internal detonations.