Abstract

Light emissions during chemical reactions provide insights into various scenarios to better understand explosions and water hammers. For example, hydrogen burning and explosions emit blue light, organic carbon combustion and explosions emit combinations of blue and yellow light, water phase changes emit infrared and less visible white light, and white light explosions ignite when multiple chemical reactions are involved. Since experimental tests to observe infrared light during water hammers have not yet been performed, test data from water boiling tests and volcanoes are compared to larger water hammer and steam explosion incidents. Considering these facts and examining a series of photos and videos from the literature and Internet, determinations are proven with respect to water hammers, steam explosions, Piper Alpha water hammer explosions, and chemical explosions. Such evidence proves that steam explosions are important for water hammer accidents, but chemical explosions explain other explosions that have long been considered to be steam explosions. These other explosions include nuclear power plant explosions, hydro-volcanic explosions, and hydrogen explosions, where some of these explosions are, in fact, related to water hammers. This article is primarily a photographic essay to explain the differences between different types of explosions and water hammers, although combustion and explosion principles are expanded and explained to support this essay.

Introduction

Each chemical reaction and phase change in a chemical or combustion process emits photons of light, and each chemical reaction or phase change has characteristic wavelengths or colors, when photons are emitted during electron level changes within atomic orbitals [1]. During combustion, light emissions are further complicated by numerous chemical reactions. For example, hydrogen combustion in air comprises 23 different chemical reactions, and the single carbon molecule of methane comprises 325 distinct chemical reactions in air [2]. Even so, hydrogen and oxygen ultimately burn to form water, and methane in air ultimately burns to form water and carbon dioxide. More complex carbon molecules can induce thousands of chemical reactions. Through observations, the primary goal of this essay is to relate light emissions to different explosion processes to describe and explain nuclear power plant and the Piper Alpha oil rig (oil platform) explosions in terms of other explosions.

Definitions

To relate emissions to explosions, some terms need definition.

  • A deflagration is a fire that travels at a velocity much lower than the speed of sound. Flame speeds for hydrocarbons are on the order of 0.45 m/s, and flame speeds for hydrogen are on the order of 1.7 m/s.

  • An explosion is a sudden release of energy.

  • A detonation is a sudden release of energy with an associated detonation wave, which travels at a supersonic velocity—5 to 10 times the speed of sound for the gas of concern. Also note that hydrogen explosion conditions are 18.56 times the initial pressure and 12.47 times the initial temperature [2].

  • Water hammers cause shock waves in liquid-filled pipes, where these pressure waves travel in an enclosing pipe at velocities below the unconfined velocity, or speed, of sound for the liquid.

  • Steam explosions result from the rapid expansion of water into water vapor.

  • Thermolytic explosions result from thermolysis that breaks water into hydrogen and oxygen at high temperatures, which can then explode.

  • Chemical explosions result from chemical reactions, where heat may be required to initiate explosions.

  • Autoignition occurs when a substance is heated to a temperature and pressure that cause that substance to ignite and explode, where compression can autoignite flammable gases.

  • Deflagration to detonation transition occurs when a fire transitions into an explosion, where the detonation depends on geometry and flammable gas concentrations. For example, a run-up length in terms of meters is commonly required for a detonation to occur in a pipe, where a spark source ignites a flame that explodes at a small distance from the spark. Transition does not occur for lengths less than five pipe diameters.

  • Phreatic explosions, or hydro-volcanic explosions, occur when molten lava suddenly enters water to initiate explosions.

  • Explosion limits describe the minimum and maximum oxygen concentrations required to ignite an explosion. Too much or too little oxygen will prevent an explosion, where explosion limits vary with respect to the temperatures and pressures of the gases, and on the geomety of the system.

  • Vapor collapse water hammers occur when vapor spaces form in piping, and the vapor spaces then suddenly collapse to initiate pressures, which can be in excess of 7 MPa (∼1000 psi).

  • Radiolysis is the process of breaking water down into hydrogen and oxygen by radiation.

A Discussion of Light Emissions During Fires and Explosions

By using these terms and referencing a series of videos and photographs, a coherent discussion of light emission and explosions is possible. The conclusions presented here may differ from the opinions of the experimenters who performed referenced tests, where the intent here is to build on the excellent experimental work of others. This discussion will start with deflagrations, transition into explosions, and then end with discussions of water hammers, steam explosions, hydro-volcanic explosions, and the Piper Alpha oil rig explosions. Ordinarily these diverse topics might seem unrelated, but light emissions couple these topics to establish new findings with respect to explosions. Even so, some research has already been completed to relate light emissions to explosions [3].

A foundation of deflagrations (fire combustion waves) and detonations (explosive shock waves) backgrounds further discussions, where different explosion types are considered with respect to light emissions.

Deflagrations

Combustion processes of hydrogen and carbon compounds are central to this research, where methane burns blue, organic carbon compounds burn yellow as soot burns, and hydrogen burns as a faint blue color.

When methane fuel burns efficiently, the flame is blue like in your home (Fig. 1) [4]. However, when methane combustion is inefficient, soot forms, and this soot burns as a yellow color within the flame (Fig. 2).1

When carbon compounds burn inefficiently, the flame is typically yellow, where the soot in the flame reignites to emit that yellow light. An example of soot ignition is shown for the condition of flashover, where soot near a ceiling reignites to cause extremely dangerous fire conditions (Fig. 3).2 Flashovers have resulted in fatal night club fires and occur in many other fires.

Hydrogen burns as a blue color (Fig. 4) [5]. Note that water formation accounts for blue colors for hydrogen and lean methane, where polar water molecules emit blue light on formation and both hydrogen and oxygen do not emit light. Quantum mechanics describes light emissions as electrons change from one atomic orbital to another for different chemicals.

Detonations in Air

Detonations further complicate the combustion process of explosive solids and explosive gases as shown in Fig. 5.3 Note that the shock wave from the solid explosive, or point charge, travels much faster than combustion products. Essentially, there is a high-pressure shock wave followed by high temperatures, which are in turn followed by combustion products. The high temperatures and pressures behind the advancing shock wave distort light waves to permit viewing of the shock. When an explosion occurs in air, the velocity slows down since the shock wave expands spherically. That is, for a point charge, solid explosive, the shock wave travels in air where no further combustion occurs at the shock wave. During nuclear explosions, a distinct heat wave follows the shock wave at a later moment.

Detonations in Piping

In piping, combustion continues at the shock wave if the pipe is full of flammable gas in the absence of liquid in the piping.

Piping Hydrogen Explosion Tests.

To clarify these statements, test data are presented for 2-in. Schedule 40 piping, where 4 in. Schedule 40 piping tests were performed as well [6]. Hydrogen and oxygen inside the piping were ignited by a spark source. Then, high-frequency pressure measurements described pressures inside the piping at various locations along the piping, which are shown in Fig. 6. A detonation wave travels inside the pipe—along the bore of the pipe—at a supersonic velocity, Fig. 6 shows the movement of such a wave along the pipe lengths for the tests.

Note that the shock wave travels at a supersonic velocity, and the internal piping pressures decrease to residual pressures in the wake of the shock. In this figure, all of the pressures are under 5 MPa, where the pressures are re-zeroed in the figure at 5 MPa, 10 MPa, 15 MPa, etc. The test section of the pipe is also shown in Fig. 6, where pressure transducers were located from one end of the pipe to the other, and the maximum pressure is negligibly affected as the shock wave travels along the length of the pipe from a spark source.

Hydrogen and Organic Explosion Experiment.

A hydrogen explosion test was performed, where hydrogen was contained in the pipe with a polyethylene cover.4 Figure 7 shows the explosions, where the white hydrogen exploded first, and then the polyethylene exploded in a yellow flash at the periphery of the hydrogen combustion products.

Deflagration to Detonation

Deflagration to detonation transition is even more complicated than point charge explosions. An experimental deflagration to detonation transition process is shown for a porous explosive in a polycarbonate tube (Fig. 8) [7].5 Note that the deflagration moves at a near constant velocity until detonation occurs, and the sudden change in velocity at the shock quickly separates the shock wave, or detonation wave, from the deflagration combustion products.

Then, the shock burns additional combustion products in the wake of the shock wave as the shock travels at a supersonic velocity back upstream from the point of detonation. This secondary burning process is known as a retonation wave that ignites unburned combustion products.

Compression and Autoignition

When flammable gases are compressed, they are heated and pressurized to autoignition and explosion. Such processes may occur in gas-filled pipes as well as liquid-filled pipes with gas pockets. Since parallel research investigates gas pipelines, liquid-filled pipes are considered here.

Figures 9 and 10 provide insights into the light spectrum during hydrogen explosions. A literature review determined various emission frequencies, which are discussed herein. Also, of the hydrogen–oxygen combustion species, O+ is the emitter for ultraviolet light/violet light, since O+, H2O2, and HO2 have different frequencies of light, where O+ has numerous emitted frequencies of light (Fig. 11) [8].

Water Hammer Ignition Mechanism.

Specifically, fluid transients, or water hammers, compress trapped flammable gases in pipes when flowrates are changed by pump or valve operations. Explosions do not occur during many operations, but some conditions ignite explosions. Appropriate oxygen is required to ignite an explosion between the explosion limits. The magnitude of the explosion depends on the amount of flammable gas present and the energy release of that gas, where hydrogen releases significantly more energy on explosion than carbon compounds.

Water hammer-induced explosions can be small with negligible damage, can be of larger magnitude to blast pipes apart, or can be even more significant to ignite nuclear power plant explosions, such as Fukushima Daiichi and Three Mile Island.

In fact, explosions at those plants prompted this investigation of light and explosions. Threads to extensive, detailed discussions of water hammers, nuclear power plant explosions, and exploded piping are available in a companion paper [3]. Below in this paper, the Piper Alpha water hammer explosions are evalauted as a case study.

A Water Hammer Explosion Example.

Also, there are other industrial explosions that were caused—and continue to be caused—by water hammers, where this theory was first published in 2011. That is, deflagrations to detonations have been considered by others to be the cause of some industrial explosions, but compression and autoignition ignited some of those explosions.

For example, a nuclear power plant piping explosion in Hamaoka, Japan, proves this reasoning, where radiolysis generated explosive hydrogen and oxygen in the piping to create explosive conditions. An incorrect theory contends that a chemical catalyst ignited hydrogen and oxygen in the piping and further contends that water splashing on that chemical resulted in a deflagration to detonation, but splashing water on a catalyst does not cause ignition. A 6-in., Schedule 40 pipe exploded in that nuclear power plant, and theory proven earlier in this research is that water hammer compressed the hydrogen to blow up the piping to ignite the gases and shred the piping like a paper firecracker [3]. The following discussion experimentally proves that water hammers ignite explosions in gas-filled piping.

Water Hammer Explosion Tests

Coronel et al. [9] performed a series of tests to investigate explosions of hydrogen–oxygen–nitrogen mixtures in a 50 mm-by-178 mm test section, where water slug velocities were required to exceed 28 m/s to impact the gas volume to ignite explosions for specific test conditions. The assembly consisted of a gas-driven projectile that struck a cylinder in the end of a pipe to induce a water hammer into that water-filled pipe, which had a vertical gas-filled test section. The test sections were filled with air to investigate water hammer and gas pockets in piping, or sections contained flammable hydrogen and oxygen to investigate explosions of flammable hydrogen and oxygen, where some hydrogen tests were augmented to investigate nitrogen effects to prevent ignition.

Their work proved that white light explosions ignited during water hammer compressions, where the visible light was dispersed across a range of frequencies (Fig. 9). Comparatively, Norrish and Porter [10] performed tests to identify light frequencies during species formation. Coronel et al. documented pressures in their tests for both nonexplosive conditions and explosive test conditions (Figs. 12 and 13).

A Coronel Test Evaluation.

Coronel’s tests impacted a projectile on the volume of a water-filled, U-shaped, stainless steel tubing assembly, which contained stoichiometric hydrogen and oxygen at the end of the tube opposite the impact. Although a constant pressure was not achieved, these tests clearly proved that water hammers ignite explosions, i.e., explosions were observed following water hammer impacts.

An important observation is that pressures are significantly reduced below theoretical expectations in the gas volume during tests. Coronel noted that o-rings leaked in the assembly, but leaks do not explain discrepancies between theory and experiment, and an alternate explanation is provided here.

Coronel measured pressures at various points in a pipe used for water hammer explosion testing, as shown in Fig. 16. Measured pressures in Coronel’s experiments can be affected by the data collection frequency, reflected pressure waves at the location where tubing exits the test section; splashing, vortices, and pressure losses due to entrance effects for the pressure gauge tubing, along with reflected pressures in gases near the tube entrance where explosions ignite.

Pressure losses for the piping due to friction occur primarily at elbows. Flow rates in the attached tubing to the pressure gauge may also induce pressure losses due to flow, where gas flows into the tube from the gas in the test chamber and on to the pressure gauge (Fig. 15). A flush mounted pressure gauge may have improved pressure measurements for gases.

Of particular interest, vortices in the piping significantly affect pressure readings. A common practice is to ensure that there is at least a 10-pipe-diameter distance of straight pipe downstream of an elbow to ensure that pressure gauges operate properly. Otherwise, vortices affect pressure measurements. For this design, the distance between elbows and gauges is less than 6 pipe diameters, and pressures are significantly affected.

Coronel performed 33 nonreactive tests with air and initial velocities between 6.5 and 6.7 m/s, where the tests are basically the same, but the results varied significantly. The pressures at P1 and P2 in Fig. 15 varied between 6.52 and 9.56 MPa, where the expected water hammer pressure was 9 MPa. At P3 and P4 after the first elbow, the pressures varied from 2.13 to 9.12 MPa, which is a greater pressure variation. In the cell, after the second elbow and the sharp-edged entrance to the cell, the pressures varied from 0.20 to 15.01 MPa, which is an even greater pressure variation. To accommodate these pressure swings in the test cell, a disc was inserted in the cell, which partially inhibited liquid surface instabilities.

Coronel also performed 74 tests with combinations of stoichiometric hydrogen, sometimes augmented with nitrogen—some tests with discs and some without. Again, a variation in pressure was observed due to vortices. For example, three nonreactive tests performed at 22.2 m/s yielded pressures of 9.5, 9.9, and 12.2 MPa with the disc installed.

To further consider some of these statements, predicted pressures are first considered in the absence of ignition delay considerations.

Combustion and Autoignition.

Figure 14 6 depicts the stoichiometric H2–O2 autoignition curve, where explosions autoignite as a function of temperature and pressure. Considering experimental conditions and assuming adiabatic conditions, the ideal gas temperatures and pressures to initiate explosions are related by
Tfinal=Tinitial(PfinalPinitial)(1.41)/1.4
(1)
where T = temperature and P = pressure.

The isentropic expansion coefficient k = 1.4 for oxygen, hydrogen, or a hydrogen–oxygen mixture. As temperatures increase, k decreases, which in turn decreases the predicted final temperature. A constant k = 1.4 approximation is used in this work. This decision effectively underpredicts the gas temperature for autoignition, where the error for explosion temperature calculations used in this article are less than 4%, and where this variation in k was determined using k values at 20 °C and 400 °C, which is the approximate range of interest for hydrogen–oxygen autoignition. That is, if Eq. (1) and Fig. 14 predict an explosion, an explosion is expected. However, an explosion may still be possible if Eq. (1) and Fig. 14 do not predict an explosion, and the calculated temperature is near the autoignition curve.

By using an adiabatic assumption and trial and error with the explosion limit curve of Fig. 14, autoignition conditions due to compression from standard atmospheric conditions are found to be
Pautoignition=2.93MPa
(2)
Tautoignition=425C
(3)
Pexplosion,predicted=18.56Pautoignition=18.562.93=54.4MPa(4)
(4)

In other words, a water hammer pressure of 2.9 MPa will ignite an explosion if the ignition delay time is neglected. From Coronel’s data, explosions occur at some pressure above 20 MPa. Consequently, the ignition delay time is important to autoignition in these tests.

For example, pressures to cause ignition were significantly higher for one test. From Fig. 12,
Pexplosion,experimental=49.4MPa
(5)

Even though this measurement is within 10% of the calculated pressure in Eq. (4), this result is misleading, and this water hammer explosion test is far more complicated. This estimate would be adequate for a water hammer that lasts for a period of time that is longer than the delay time. However, these Coronel tests were performed with a sharp pressure spike caused by a projectile impact, and this pressure spike significantly increases the importance of the ignition delay.

A consideration of water hammer pressures provides further insight along with the following observations:

  • For explosion conditions, the basic physics is confirmed here.

  • Pile-up occurs during explosions at the ends of pipes and at changes in piping geometry, where reflected explosion pressures increase [11,12]. Pressures in fluids change significantly at abrupt dimensional changes (Fig. 15) [13].

  • Pile-up will exacerbate explosion pressure measurements and pressure anomalies between experiment and theory.

  • Note that explosions ignited near the tubing exit from the test cell, where pile-up and fluid anomalies cause this effect. In fact, choked flow is expected in the instrumentation tubing, since flowrates will exceed the speed of sound at the tubing entrance.

  • Ignition delay has a significant effect on autoignition as discussed later in this article.

Water Hammer Theory.

During sudden water hammer events such as valve closures, pressures increase to a constant pressure for milliseconds or longer. In such cases, the ignition delay to ignite an explosion is exceeded since ignition delays of hydrogen are on the order of microseconds to milliseconds.

From the study by Leishear [14], the predicted water hammer pressure for trapped gas at the end of a pipe is expressed as follows:7
ΔP=DLFρaV
(6)
where a is the pressure wave speed in a pipe, DLF is the dynamic load factor that varies between 0 and 2, ΔP is the change in pressure, V is the initial liquid velocity, and ρ is the density of liquid.
To evaluate Coronel’s test results, reflected pressure waves are required. Transmitted pressure factors, s, at changes in diameter and material are simplified as follows:
s=2A1a1A1a1+A2a2
(7)
where A is the area and subscripts 1 and 2 represent upstream and downstream tubing sections, respectively. Note that Eq. (7) yields the DLF = 2 in Eq. (7) at the end of a pipe, where pressure waves are reflected.

Using Eqs. (3), (6), and (7), the predicted gas pressure due to a projectile impact at 28.85 m/s equals 28.3 MPa, which is significantly higher than pressures shown in Fig. 12. The DLF was estimated as DLF = 2 since the pressure oscillates slightly with the change in volume. These water hammer pressure estimates differ from one experiment to another due to friction pressure losses and vortices in the fluid flow, as discussed earlier.

Also as shown in Fig. 14, measured water hammer conditions are well above the explosion limits for stoichiometric hydrogen and oxygen. Accordingly, ignition delay times and unstable, liquid interface splashing are considered to be controlling factors for these explosions.

Ignition Delays.

Coronel’s data, while impressive, have much variation, and similarities between test conditions are problematic to perform a comparative evaluation of ignition delays. Specifically, available data were selected to approximate conditions as shown in Fig. 14. That is, experimental explosion pressures are plotted for a 23.4 m/s initial velocity; experimental water hammer pressures are plotted for 22.9 m/s; and the autoigition pressure was selected as the average of these two pressures as 23.15 m/s.

An ignition delay can be estimated from Fig. 12. The time to the 2.1 MPa autoignition condition and the time to explosion are shown for two similar nonreactive tests. These tests were chosen to estimate an ignition time from nonreactive data, where detonation times are unavailable from Coronel’s test results. At the time of ignition, the measured pressure is d = 78% times the maximum pressure, where d is an ignition delay factor, and s is the transmission factor for the change in steel to clear plastic piping. As an approximation from Eq. (7), s = 71%, such that
ΔPestimated,ignitionpressure=sdDLFρaV=0.710.7821000kg/m31380m/s23.15m/s=35.4MPa
(8)
Testimated,ignitiontemperature=1230.0C
(9)

Although uncertainties of Eqs. (8) and (9) are unknown, the results are reasonable. As shown in Fig. 14, the autoignition temperature is within 4% of the experimental water hammer pressure required for detonation, which is a necessary and sufficient condition for an explosion to detonate. Note that the calculated detonation pressure is well above the experimental explosion pressure, as discussed earlier.

Even so, the limitations of this calculation bear consideration. Input pressures are approximate, and the selected pressures were selected for high-pressure magnitudes from Coronel’s tests. The fact is that vortices in pipes produce pressure measurements that are either equal to or less than the measured pressure. This issue is discussed for vortices in an elbow [14]. The ignition delay is approximate, where an ignition delay from a pressure spike test was used, and delays may be dependent on the rate of temperature and pressure change. In short, the basic physics of water hammer autoignition are confirmed for explosion conditions, but additional research is required.

Nitrogen Effects on Detonation.

Detonations occurred at 0% and 25% nitrogen, but 50% nitrogen prevented ignition for the given conditions. In Fig. 14, a nitrogen curve is shown, where extrapolation of that curve nearly intersects the estimated values for explosions to occur. That is, nitrogen concentrations have an effect near the explosive limit for nitrogen.

However, nitrogen will not stop H2–O2 explosions in molten nuclear reactor cores, and nitrogen will not stop explosions when high-temperature combustion products pass into a H2–O2–N2 mixture. That is, Fig. 14 shows explosion limit data for a dilute 1% H2–O2 mixture in nitrogen, and nondilute H2–O2 mixture data yield the same explosion limit [15]. In other words, the extended explosion limit for nitrogen effects on hydrogen explosions is far less than available ignition temperatures from combustion products or a molten core.

Although additional research is recommended to fully understand water hammer-induced explosions, these tests and the body of research to date conclusively prove that water hammers ignite explosions in pipes filled with flammable gases when appropriate oxygen concentrations are available for ignition. This research is consistent with observations that “Water Hammers Exploded the Nuclear Power Plants at Fukushima Daiichi” and further supports the investigations and observations that water hammers caused explosions at Three Mile Island and Hamaoka.

Hydrogen Explosions and Light Emissions

Although explosion light emissions internal to industrial piping systems have not been examined, nuclear power plant explosions shed light on this topic. Again, white light occurs due to complex chemical reactions, yellow light occurs due to ignition of organics, and blue light occurs due to hydrogen ignition [3].

Photos for the Fukushima Daiichi nuclear power plant explosions were carefully examined to prove that blue light hydrogen explosions were followed by yellow light from organic explosions. Initial white light explosions are assumed to be present inside nuclear power plants [3].

To support this opinion with respect to white light explosions, Chernobyl videos were carefully examined. Clearly, a white light explosion was followed by a yellow organic explosion (Fig. 16).8 That is, a thermolytic explosion is the major explosion cause, where the possibility of a steam explosion is now dismissed. This decision bears discussion.

Light From Water/Hydrogen Reactions and Steam Explosions.

Phase changes in water are accompanied by discrete light transmissions and not white light transmissions. For example, Ravichandran et al. [16] showed that water emits infrared light during nucleate boiling (Fig. 17). As another example, Chakravarty and Walton [17] (Fig. 18) showed that narrow-band light in the visible light range was emitted, even though this light was not visible in a dark room. Also, audible explosions waves occurred during bubble collapse of superheated steam in water, where bubble collapse explosions created a “raucous metallic sound” for some tests. This sound is similar to cavitation bubble collapse that occurs when bubbles form in pipes at low pressures to later collapse with shock waves that scour metal from pipe surfaces as cavitation erosion. Basically, cavitation is a steam implosion that turns steam into water. Note in Fig. 20 that cavitation bubble collapse implosions did not form steep fronted shock waves.

In addition, the discrete light frequencies from bubble collapses were found to be in the blue to orange light range (360–600 nm). The exact frequencies were indeterminate in their tests since the photomultiplier process did not visibly differentiate light frequencies, but this process did identify a specific range of frequencies. That is, Fig. 18 shows white dots in lieu of colored dots. However, during hydrogen explosion tests discussed later, measured orange light was emitted, which is attributed to phase changes of steam.

Given that infrared light is emitted for both boiling and condensation phase changes at low pressures, expectations are that discrete visible light emissions are expected for high-temperature flashing, cavitation, bubble collapse, and condensation. At atmospheric conditions, light emissions are infrared.

The observation that water phase changes emit discrete light frequencies is critical to explain white light hydrogen explosions. In particular, specific light frequencies are generated as photons emit from water atoms, and there is no reason to expect that this photon process will change at larger scales, higher temperatures, and higher pressures. That is, only the frequencies change at higher temperatures, but the fact is that discrete frequencies do not change with conditions for phase change processes.

Steam Explosions and Detonations.

Essentially, steam explosions are a boiling process, where water suddenly flashes to steam, while detonations are initiated as shock waves. One such test is shown in Fig. 19, where a detonation wave was measured in a steam separator that was used during testing [18].

With respect to light frequencies, no light was reported for this small detonation in undimmed lighting conditions. If light was emitted, the time may have been too short to see with the naked eye since the eye photoreceptors act every 0.1–0.2 s, and measurements for these tests had 2 μs rise times. Even so, a large detonation was not observed. Again, more research is required.

Cavitation.

Basically, cavitation turns water into steam when pressures are lowered sufficiently to cause vaporization. Upon subsequent vapor collapse, or implosion, of steam bubbles, high pressures are created. For cavitation created by ultrasound, such pressures are shown in Fig. 20 [19]. Schreiner et al. [20] also performed cavitation tests.

For shock waves, the width of the shock is several molecular diameters, which ensures a nearly instantaneous pressure increase at the shock. Note that shock waves are not present for cavitation bubble formation as indicated by the sloping pressure increases for various recorded steam explosions, even though pressure magnitudes are sufficient to induce shock waves.

Steam Explosions and Light Frequencies.

For steam explosions, discrete frequency light explosions rather than white light explosions are expected for steam explosions. This finding concludes that Chernobyl white light explosions must then be thermolytic explosions to ignite hydrogen, along with steam flashing and radiolysis during this criticality accident.

The proportions are indeterminate for each contributing factor of thermolysis, radiolysis, and steam explosions for the total energy release at Chenobyl. Even so, the flash of white light was not from steam formation. Steam at a molten reactor core may emit visible light since the steam may be superheated, but steam in the air above an exploding nuclear reactor emits infrared light at atmospheric pressures. To better support these statements, large-scale hydro-volcanic explosions are considered with respect to light emissions.

Nuclear Plant Explosion Magnitudes

Explosion magnitudes are an important aspect of nuclear power plant explosions. Half of the 3800-MW Three Mile Island (TMI) reactor melted down, the reactor vessel was not breached, explosions occurred, and buildings were not exploded. All of the 3579-MW Fukushima Daiichi reactor fuel melted, and the reactor core was breached to ignite subsequent building explosions. The 3200-MW Chernobyl reactor spiked to 500 times the operating power due to uncontrolled nuclear reactions, and the reactor building was demolished. In short, the magnitude of the explosion is related to the energy release during a meltdown. Although fatalities occurred due to meltdown related explosions, the fatalities fall far short of the potential tens of thousands of deaths predicted in television accounts of nuclear accidents.

Hydro-Volcanic Explosions

Concluding that steam explosions emit discrete light frequencies affects an understanding of hydro-volcanic explosions, where white light has been observed during lava collapse into water (Fig. 21) [21]. Hydro-volcanic chemistry includes molten alumina that chemically explodes on contact with water, and hydrogen and oxygen are also formed during acid formation chemical reactions [22]. That is, chemical explosion conditions are available at the time of white light chemical explosions, and white light proves the presence of chemical explosions. Once the steam plume forms, light is infrared (Fig. 22) [23]. That is, when water changes to steam, both infrared light and white light are distinctly emitted and observed, and the amount of white light depends on the process that creates this light. For example, boiling water does not emit visible white light, while volcanic explosions emit significant white light.

Vapor Collapse Water Hammers

The high pressures during vapor collapse (steam hammer or condensate-induced water hammer) can cause considerable structural damage to piping from bursting and bending (Fig. 23). Subsequent explosive damages that burst from piping ruptures can be significant, as seen for one of the multiple New York steam system explosions (Figs. 24 and 25) [14,24].

With respect to light emissions, infrared light is expected for vapor collapse water hammers since water vapors are not significantly superheated. If there is an interest in video recording these hammers inside of pipes, note that plastic piping is typically opaque to infrared light, and glass piping would be required for infrared imaging. From investigative experience of this author, temperatures sufficient to generate hydrogen are not expected during vapor collapse.

Other than steam explosions, there are no other known explosion causes for violent releases of steam into the air from piping systems. These findings also conclude that visible nonwhite light occurs during radiolysis near a nuclear reactor core, which occurs in parallel to boiling and flashing processes.

Nuclear Explosions

As another example, a photo of a nuclear weapon explosion exemplifies the fact that chemical explosions are white (Fig. 26).9 Innumerable chemical and radiation reactions emit photons at a wide spectrum of electromagnetic frequencies to form visible white light, gamma rays, etc. (Fig. 10). Note that yellow light is seen in some mushroom clouds, where carbon in the soil or environment burns from the heat of explosion. Other colors that have been observed during atomic bomb blasts are red or orange, depending on the chemical composition of the initial chemistry for the unburned combustion products of the soil, buildings, or other chemicals at the bomb detonation site. For example, copper burns blue, lithium and radium burn red, strontium and calcium burn orange, iron and sodium burn yellow, aluminum and barium burn green, and chemical compounds also have distinct colors. Such nuclear reactions and chemical explosions are far more complex than chemical hydrogen explosions in nuclear power plants.

Piper Alpha Off-Shore Oil Rig Explosions

The research presented here provides new findings for the 1988 Piper Alpha explosions that killed 165 of 226 on board personnel, west of Scotland (Fig. 27). Technology moved forward since this disaster, and a comprehensive 1990 investigation is updated here [2530]. Water hammer ignited Piper Alpha explosions.

A water hammer occurred that ignited a module C piping explosion, and module B piping ruptured as the explosion blasted into the module B piping of the oil rig. Air to support the explosion entered the pipe between the time that a pipe flange was removed and replaced for a safety valve recertification. Condensate boiled off and vented when exposed to air, and buoyant methane gas lifted into the air to be replaced by air (small concentrations of heavier hydrocarbons like propane would have remained in the pipe). Methane condensate boils off in a vertical pipe at a rate as high as 2 in. per second for about the first 20 s, and then reduces at 0.2 in. per second [31]. The amount of air in the piping is not known, but bomb-like conditions were created.

When a gas operated valve (GOV) was opened at the condensate injection pump a detonation ignited in module C piping. Internal piping combustion and water hammer explosions are endorsed here, where combustion inside the pipeline ruptured that piping to ignite two explosions in module C. There were 7 major Piper Alpha explosions. Six gas detonations ignited for certain, and a probable oil tank explosion detonated as well. These explosions are summarized here, and a more detailed description of this explosion cascade is available [30]. Richardson et al. falsely claimed that detonations did not occur, and therefore the actual combustion and detonation sequence was not investigated at all.

The Explosion Sequence.

Two initial audible explosions—separated by 2–3 s—were heard and seen by different witnesses, where both explosions ignited detonation waves. A first audible detonation ignited inside module C condensate injection pump piping (Fig. 28). The water hammer explosion, or first detonation (Explosion 1), was ignited in a 4-in. pipe in module C by the startup of a condensate pump, which was located on another deck below Module A.

A second explosion ignited in module C (Explosion 2), and a subsequent deflagration emitted observed blue flames from hydrocarbon combustion in module C. The blue flames were observed to move away from the explosion site at the burst pipe, and then the blue flames moved back to the explosion site. That is, the liquid methane erupted from the pipe and flowed outward onto the floor while it evaporated and burned. As the methane fuel was consumed by combustion, the blue flames flowed out of the platform into the air, and then the blue flames retracted back toward the explosion source, or 4-in. piping.

Explosion vibrations were felt from this second explosion, but not heard, on a 2,645 gross ton, 72-m-long ship, which was located 25 m from the oil rig. This second explosion shook the platform and knocked workers to the floor, There is no doubt that a detonation wave impacted the ship to vibrate such a large structure, i.e., otherwise fire would shake surrounding buildings, which does not occur for any fire. Such a conclusion was incorrect at the time of the original reports and is incorrect today.

The first two explosions in module C contributed to the next two explosions in module B and acted as the catalyst for other explosions. Since the condensate piping routed from module A to B to C, shockwaves inside the piping system blasted from the initial water hammer explosion to crack a 20-in. diameter pipe in module B. This cracked pipe in module B provided fuel to ignite an explosion and sustain a fire (Explosion 3). The fourth detonation (Explosion 4) probably burst from oil tanks in module B. These third and fourth audible detonations were followed by a smoke cloud and observed yellow fires in module B and above the platform (Fig. 29). Water hammer initiated explosions also ignited piping pressure blasts to also crack an 18-in. diameter pipe (Explosion 5). Explosion 5 burst from an 18-in. pipe to fuel the fire that blazed across most of the platform (Fig. 30). The sixth and seventh detonations (Explosions 6 and 7) utterly destroyed the Piper Alpha platform, and most of the platform sunk into the North Sea near Scotland. These last two explosions created the largest fires on the Piper Alpha oil rig as multiple sources fueled the fire.

Cullen concluded that the first explosion was unproven. Claiming that the first water hammer piping explosion was not heard, that explosion was dismissed. The second explosion was not heard by everyone, and even the third and fourth explosions were not heard by everyone. All four explosions were reported by witnesses, even though witnessing a sound is not the condition for the presence of an explosion. Important to new findings, the explosion shockwave from the bursting pipe in module C was heard at the time of that explosion. Cullen falsely concluded that there were no detonations for the first and second explosions. The third detonation ignited due to a ruptured pipe in module B. Due to flaws in Cullen’s report, there are many other errors as well. In fact, Cullen’s technical explanation of how the piping system initially failed completely missed the water hammer explosion, where technology to effectively do so has since been developed by this author, i.e., water hammer exploded the module C piping. That is, Cullen [27] concluded that detonations did not occur even though numerous witnesses heard and felt the shock waves from detonations. As a new finding, a water hammer explosion exceeded the natural gas autoigition temperature to initiate Piper Alpha detonations.

In an earlier Three Mile Island investigation, thermocouples were too slow to record detonations, and investigators errantly concluded from those inadequate temperature recording devices that fires rather than explosions occurred. Similarly, using standard pressure transducers inside the pipes to falsely claim that a detonation, rather than an explosion, did not ignite in module C was like closing your eyes for a minute while watching an 8 second drag race. You do not see the race, and similarly an explosion was not recorded. Pressure measurements in pipelines did not, and could not, measure explosions. Piper Alpha thermocouples for motor overheating and other temperature measurements were also inadequate to respond to momentary explosion temperatures.

Detrimental similarities between TMI and Piper investigations were the facts that engineers reached conclusions and misused available data. When data was misunderstood, false conclusions were published.

Pertinent Piping Design and Operations.

The explosion ignited in a 4-in. diameter pipe that was connected to the 46.2 bara system through a 4-in. piped, positive displacement pump (the condensate injection pump), which in turn was connected to an 8-in. GOV. A temporary flange was installed at the downstream dead end of the pipe—at a local high point in the system—where a pressure safety valve (PSV) had been removed for recertification.

Standard practice to operate the condensate injection pump was to open the GOV valve and then proceed to the control room to turn on the pump. Cullen concluded that the operator jagged the valve or cycled the valve open and closed the valve, where that operator was also killed. Nobody saw that operator open the valve, but they saw him walking away from the valve when they heard the explosion. That is, he was not at the valve, jagging that valve. If he was no longer near the valve, and the explosion ignited, the valve was still open.10

Flange Damages.

Earlier analyses and tests were performed for a comparable flange at the assumed 46.2 bara pressure, i.e., an incorrect test pressure was used as discussed here. Similar flange connections were tested, and leaks were not observed for hand-tight conditions with wrenches and flogging conditions that were torqued to higher values. Leaks were observed during tests for finger tight conditions where no wrenches were used, but the consensus of opinions were that finger tightening of the bolted PSV flange did not occur, since such an action “would be severely dealt with.”

Blamed for improper bolt tightening, the mechanic who installed the flange was killed. At the 46.2 bara pressure, the flange was not expected to fail when bolts were tightened properly. The following discussion provides technology updates to explain the generation of much higher explosion pressures to burst the piping.

Water Hammer Pressures.

Critical to findings presented here, this author’s earlier research proved that reflected pressures within a gas pocket are double the applied pressure, when that gas pocket is present at the dead end of a pipe [14]. Richardson et al. and Cullen previously concluded that the pressure of the water hammer was limited to 46.2 bara, and this new finding changes many of their statements, calculations, and conclusions. Calculated water hammer pressures below are as high as 628 bara.

This maximum water hammer pressure of 628 bara was well in excess of the 46.2 bara leak test pressure for the flanges. Explosion pressures further exceeded “The maximum allowable pressure for a 900 lb flange assembly was 150 bar (2160 psig) and for a 1500 lb assembly 250 bar (3600 psig),” where there was uncertainty about the type of the installed flange.

Accordingly, water hammer pressures, or an explosion, damaged the flange or pipe to leak and caused the “high-pitched, hissing sound” that operators heard just prior to Explosion 1.11 High pressures were sufficient to damage the flange or to cause a leak through the flange gasket. Preliminary jagging operations of a condensate pump are considered to be a source of lower transient pressures to damage the flange or pipe. Subsequent operation of the pump with higher flow rates and higher dead-head pressures generated sufficient pressure to ignite flammable gases in the pipe to burst the pipe.

Water hammer pressures were approximated as follows, where the DLF < 2 since the trapped air pocket at the flange acted like a spring subjected to a suddenly applied pressure [14]. By way of comparison, when a force is suddenly applied to a spring, the maximum force is twice the applied force.

Water Hammer Calculations.

In Cullen’s report, Richardson et al. assumed a 30% throttled valve and a 133 m/s flowrate, which will be assumed here as well. Presumably, there is a limit on GOV % opening in the plant that is not mentioned in published reports, since this liquid methane velocity was the crux of all pressure calculations and conclusions for the Cullen report. Accordingly,
V4in.piping=133m/s(436.35ft/s)
(10)

As the valve opened, the initial velocity would have been sonic since the air and residual methane in the piping were at atmospheric pressure. Sonic velocity occurs when the pressure differential equals 0.5283 for methane or air. The pressure change from 46.2 bara to one atmosphere ensured cavitating flow conditions as the valve first opened and liquid methane partially flashed to a vapor. The physics of valve opening, cavitation, flashing, and re-condensation are complex, to say the least. However, the trapped air, or bubble, at the high-point, damaged flange was noncondensable and stratified with respect to the initial residual methane.

Accordingly, the 133 m/second fluid velocity also ensured that any trapped air in the repaired piping responded as a single degree-of-freedom oscillator, when the valve was opened to pressurize the air in the piping. That is, the air bubble acted as a single degree-of-freedom system. In this case, the final pressure was twice the value of the suddenly applied water hammer pressure. For this example, the methane would have re-condensed, and the pressure can be approximated by the basic water hammer equation.

Then, the maximum pressure in the gas at the dead end of the 4-in. piping then equaled,
ΔP=DLFρaV=2ρaV=(220.269psf2381.79ft/s436.35ft/s)/32.174=9093.54psig(62.7MPa)
(11)
where the wave speed, a, is a variable function of temperature and pressure with respect to the bulk modulus and density of the condensate.

The bulk modulus and other properties were assumed at equilibrium and at 20 MPa, which are an available condition in AFT Impulse. Properties were obtained for AFT Impulse from data of the National Institute of Standards and Technology. Specifically, methane properties for Eq. (11) were obtained from AFT Impulse [31].

Closed-form equations were used here to determine maximum water hammer pressures, since AFT does not model systems that are initialized with steady-state cavitation conditions. Since the wave speed, a, increases with decreasing temperature, this assumption yielded a conservative estimate for the maximum air pressure to cause autoignition.

Note that the use of the water hammer equation to describe slug flow water hammer pressures was first experimentally validated in 1993 and again in 2003, and this particular use of the DLF was first used in 2003 [14]. That is, these findings were developed after the 1990 Piper Alpha explosion investigation.

Condensate Evaporation and Venting.

Although condensate evaporates and cools when approaching atmospheric pressure, water hammer pressures condense and heat the gas. In fact, the liquid interface may initially boil off at a rate as high as 2 in./s when exposed to atmospheric air [32]. Energy losses from vaporizing and condensing gas in the piping were neglected, where Cullen [27] predicted a 30 °C decrease in condensate temperature within the pump, where boiling was minimal, i.e., boiling is offset by increasing pressures as the air fuel mixture compresses in the piping.

More importantly, if the piping system had been directly vented to atmosphere for repairs, the high-pressure liquid methane in the piping would have cavitated as the methane gas exited the piping, where both vapor and liquid exited the piping. In such a situation, autoignition and explosion may be possible. Accordingly, venting of piping sections for repair should be controlled to prevent this danger.

Explosion Temperatures and Pressures.

Using revised higher liquid and gas pressures, the adiabatic temperature for gas compression exceeded the natural gas autoignition temperatures.12 The gas temperature for piping primarily filled with air equaled 1568 °C, and autiognition sparked an explosion on the Piper Alpha. Both the autoignition temperature and the compressed gas temperature at the dead end were required to reach this conclusion and are discussed using Eqs. (11) and (12).

The autoignition temperatures for different fuel concentrations of natural gas vary between 1168 °C and 1250 °C, in air at atmospheric pressures [33]. For these tests, fuel and air were forced onto hot surfaces to imitate industrial conditions. As operating pressures decrease, the autoignition temperature decreases. By using methane test data, this temperature decrease is approximated as 120 °C [34]. Accordingly, autoignition temperatures for the given conditions are in the range of 1048 °C to 1130 °C.

To calculate the maximum air temperature in the piping, where initial temperature conditions are assumed to equal 20 °C:
Tfinal=Tinitial(PfinalPinitial)(1.41)/1.4=293.15K(62.7MPa0.101MPa)1.41/1.4=1568C>1130C=Autoignitionandexplosion
(12)

Although there may be some uncertainty for autoignition temperatures in the 4-in. piping, these calculated values provide new data to better estimate explosion conditions. Even if the DLF is neglected, the predicted temperature is 1237 °C, which is above the 1130 °C autoignition temperature that is required to ignite an explosion in the piping.

DLFs require additional discussion. For very short duration pressure application, the DLF can be less than 2 or even less than 1. Damping has some effects, but in models by this author, damping effects were minor, and a DLF = 2 provides an upper bounding limit for these calculations [14].

Also, adiabatic conditions are assumed for temperature calculations since the time for filling the piping is less than 2 s, and the pulsations of air in the piping will be on the order of tenths of seconds to seconds [14]. Such short times ensured that negligible heat was lost through the pipe walls. Also, these pulsation frequencies ensured that even shorter duration ignition delay times were exceeded to autoignite gases in the piping.13

Flange Damages.

Water hammer pressures of 9094 psig were well above the 3600 psig (20.68 MPa < 24.82 MPa) allowable pressure of the flange, where pressures certainly exceeded the pressures expected for a leak of properly tightened flange bolts. The water hammer, alone, exerted sufficient pressures to cause the hissing sound from the flange as the pressure at the dead end increased. The pressure inside the piping increased by a factor near 30 after the first explosion ignited. Such pressures were sufficient to burst the piping to flood flammable condensate into the modules (Fig. 31).

The extent of damage was dictated by the amount of air inside the piping at the time of explosion. The longer the piping was opened during maintenance, the greater the amount of methane evaporation, and the larger the explosion when the GOV was open. That is, an explosion was expected after every time that maintenance was performed, but smaller explosions were contained inside the piping, following earlier PSV recertifications. Actions to improve safety inadvertently spiraled into a disaster that took many lives.

Preventive Actions.

If the GOV at Piper Alpha had been opened slower, pressures would have been lower, and explosions would not have occurred. Slow-acting valves should be used in lieu of fast-acting valves for conditions where water hammers may occur.

In addition, water hammer analyses need to be performed to prevent ongoing oil rig explosions. The technology is here to stop these ongoing oil rig explosions, but authorities fail to act. If actions are not implemented, fatalities and environmental disasters will continue. Stop oil rig explosions.

Furthermore, oxygen concentrations inside pipes should be measured to ensure that explosion conditions are not present inside pipes, following repairs or other access to the system, which allow air entry into the pipes.

Conclusions

Evaluations of light emissions and explosion autoignition provide new insights into explosions.

For example, water hammer ignited the Piper Alpha explosions that killed 167 workers. For another example, steam explosions have significant damage consequences. However, the work summarized here clearly demonstrates that explosions involving water cannot always be simplified as steam explosions alone.

For different nuclear processes, radiolysis and thermolysis contribute hydrogen detonations to complex explosion processes. For other processes, such as oil rig explosions and volcanoes, chemical reactions contribute to detonations.

These different processes were examined here in terms of light emissions to explain conclusions. The importance of each explosive process requires further investigation. Even so, important understandings are concluded from this essay and companion papers [3,29,30].

  • Analysis of experimental data further proves that water hammers autoignite explosions in flammable gas-filled piping (Leishear explosion theory).

  • Calculations are sufficient to predict that flammable gas water hammer explosions will occur in piping systems. However, ignition delay data are required to theoretically analyze pressure transients. By using available ignition delay times, a method was presented to find the pressure required to ignite and detonate flammable gases. Available theory serves to determine the probability of a piping explosion due to water hammer, where additional research is required.

  • Three Mile Island, Fukushima Daiichi, Brunsbuttel, and Hamaoka experienced water hammer-induced hydrogen explosions in piping.

  • Chernobyl, Three Mile Island, and Fukushima Daiichi experienced hydrogen explosions at the molten reactor cores.

  • Actions to prevent imminent water hammer explosions in nuclear power plants have been dismissed by government authorities [3537]. Stop nuclear power plant explosions!

  • Nitrogen will stop some explosions, but nitrogen blankets will not stop explosions in reactor cores or stop other explosions that are initiated elsewhere in nuclear reactor systems.

  • Hydro-volcanic explosions are composed of chemical and steam explosions.

  • Vapor collapse water hammers are not explosions and may occur at system high points, where pressures drop to the vapor pressures of the contained liquid.

  • Condensate-induced water hammers are not detonations, but they may cause explosions.

  • Phase changes emit discrete infrared and visible light photon frequencies due to singular phase processes.

  • Chemical explosions release white light due to multiple chemical reactions and the emission of multiple photon light frequencies.

  • The Piper Alpha oil rig explosions were ignited by water hammer pressures, and other oil rig explosions are also affected by water hammer explosions.14

  • Since water hammer explosions were not evaluated by others, appropriate corrective actions were not performed, following the Piper Alpha explosions to prevent water hammer explosions on oil rigs. Such inaction continues as oil rig explosions continue to cost lives and cause environmental damage. Stop oil rig explosions!

  • Water hammers killed 167 men during the Piper Alpha oil rig explosions – 165 oil rig workers and 2 rescuers.

The primary goal of my ongoing research is to explain and stop industrial explosions and nuclear power plant explosions. However, the tentacles of this research reach into gas pipeline explosions, water main breaks, earthquake technology, and even volcanoes. Striking new theory into reality demands a leap from the status quo. Accepting old ideas forges the chains of the status quo. This continuing research refuses to accept those shackles that hinder saving lives and the environment. That is, I refuse to accept mediocrity in place of new ideas.

Footnotes

6

Figure 14 along with these calculations and observations represents new research conclusions in the literature.

7

This equation describes the maximum pressure at the end of a pipe where the incident pressure is doubled due to reflected pressure wave effects. As discussed by Leishear [14], DLFs or DMFs (dynamic magnification factors) may be applied to either pressures or stresses to determine their effects. DLFs for stresses near the dead end of a pipe are far more complicated and outside the scope of this work. DLFs are used in this research to describe the amplification of stresses or pressures by applied pressures exerted by water hammer in piping systems. This amplification refers to the increase, or ratio, of stresses or pressures to the expected pressures if dynamic effects from sudden loadings are not considered.

10

Cullen concluded that if the operator was not seen operating the valve, there was no proof that the valve was operated.

11

Cullen noted that a screaming sound was heard for as long as minutes before the explosion, while other witnesses mentioned that a hissing sound lasted for seconds before the explosion. Apparently, there were two different sounds, and the reasons for the differences between their lengths of time were not determined. The high-pitched screaming sound was likely associated with a bound-up drive shaft of the failed condensate injection pump that necessitated the use of the condensate injection pump connected to the blind flange, which was overlooked during GOV operation.

12

Richardson et al. [25] cited numerous deficiencies in autoignition data that inhibited explosion analysis. Even though more experimentation would be beneficial, significant autoignition research has been completed since 1990 to understand the Piper Alpha explosions. That is, sufficient autoignition data are now available to prove the methane autoignition conclusions that are presented here.

13

Richardson et al. also asserted that the gas temperature would be cut nearly in half by heat losses through the wall and that the process would be isothermal. However, this assertion was not based on high-frequency water hammer pulsations, where they dismissed water hammer. New facts yield new results.

14

The US Bureau of Science and Environmental Engineering stated that they had “other, more relevant safety research that we are considering,” as a 2014 response to water hammer explosion, safety communications, which stated “stop explosions, deaths and oil spills at offshore oil rigs.” Oil rig explosions continue.

Acknowledgment

As always, thanks go to Janet Leishear for making this work happen and proofing this article for clarifications and better communications.

Conflict of Interest

There are no conflicts of interest. This article does not include research in which human participants were involved. Informed consent not applicable. This article does not include any research in which animal participants were involved.

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Nomenclature

a =

pressure wave speed in a pipe

d =

ignition delay factor

s =

transmission factor

A =

area

T =

temperature

V =

fluid velocity in a pipe

ΔP =

pressure change

ρ =

density

DLF =

dynamic load factor

DMF =

dynamic magnification factor

GOV =

gas operated valve

PSV =

pressure safety valve

TMI =

Three Mile Island

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