Spontaneous Collapse Mechanism of World Trade Center Twin Towers and Progressive Collapse in General
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Damage produced by repeated bubble collapse to neighboring rigid objects in hydraulic systems is an important consequence of cavitation. Although bubble collapse near a single wall has received significant attention in the past, few studies exist on the dynamics of bubbles collapsing near a corner, i.e., two flat rigid surfaces intersecting at a right angle. In this work we quantify the pressure fields produced by a single bubble collapsing near two perpendicular rigid walls. Using a high-order accurate shock- and interface-capturing method to solve the three-dimensional compressible Navier-Stokes equations for gas and liquid flows, we simulate the dynamics of a single bubble collapsing at different initial stand-off distances from the two walls. In contrast to a bubble collapsing near a single wall, the collapse of bubbles within a critical stand-off distance is not symmetric about the bisecting plane due to the interaction between the bubble and the second wall. The second wall affects the pressure produced during the collapse in the following ways: (i) For bubbles initially located sufficiently close to both walls, the reentrant jet produced during collapse no longer points in the direction normal to the closest wall but at an angle toward the corner, (ii) the part of the emitted shock with the highest amplitude propagates in line with the jet, and (iii) the bubble migrates in that same direction during its collapse with a dependence on the stand-off distance, consistent with predictions made using Kelvin impulse. The location of maximum pressure along the walls is measured for the different initial stand-off distances. Using acoustic arguments, we find a semiempirical relationship to predict the initial stand-off distances for which the maximum pressure occurs in the corner. Here we find that when the bubble is sufficiently close to equidistant from each boundary, the maximum pressure is observed in the corner due to the water-hammer and implosion shocks reflecting off the boundaries and intersecting in the corner. We also show that when bubbles are initially attached to either wall the wall pressure produced can be significantly increased compared to bubbles detached from either wall.
One of the major technical problems associated with cryogenic liquid propellant systems used to supply rocket engines and their subassemblies and components is the phenomenon of propellant tank pressurant and ullage gas collapse. This collapse is mainly caused by heat transfer from ullage gas to tank walls and interfacing propellant, which are both at temperatures well below those of this gas. Mass transfer between ullage gas and cryogenic propellant can also occur and have minor to significant secondary effects that can increase or decrease ullage gas collapse. Pressurant gas is supplied into cryogenic propellant tanks in order to initially pressurize these tanks and then maintain required pressures as propellant is expelled from these tanks. The net effect of pressurant and ullage gas collapse is increased total mass and mass flow rate requirements of pressurant gases. For flight vehicles this leads to significant and undesirable weight penalties. For rocket engine component and subassembly ground test facilities this results in significantly increased facility hardware, construction, and operational costs. "Collapse Factor" is a parameter used to quantify the pressurant and ullage gas collapse. Accurate prediction of collapse factors, through analytical methods and modeling tools, and collection and evaluation of collapse factor data has evolved over the years since the start of space exploration programs in the 1950 s. Through the years, numerous documents have been published to preserve results of studies associated with the collapse factor phenomenon. This paper presents a summary and selected details of prior literature that document the aforementioned studies. Additionally other literature that present studies and results of heat and mass transfer processes, related to or providing important insights or analytical methods for the studies of collapse factor, are presented.
In the subject of planetesimal formation, several mechanisms have been identified that create dense particle clumps in the solar nebula. The present work is concerned with the gravitational collapse of such clumps, idealized as being spherically symmetric. Fully nonlinear simulations using the two-fluid model are carried out (almost) up to the time when a central density singularity forms. We refer to this as the collapse time. The end result of the study is a parametrization of the collapse time, in order that it may be compared with timescales for various disruptive effects to which clumps may be subject in a particular situation. An important effect that determines the collapse time is that as the clump compresses, it also compresses the gas due to drag. This increases gas pressure, which retards particle collapse and can lead to oscillation in the size and density of the clump. In the limit of particles perfectly coupled to the gas, the characteristic ratio of gravitational force to gas pressure becomes relevant and defines a two-phase Jeans parameter, J{sub t}, which is the classical Jeans parameter with the speed of sound replaced by an effective wave speed in the coupled two-fluid medium. The parameter J{sub t} remains useful even away from the perfect coupling limit because it makes the simulation results insensitive to the initial density ratio of particles to gas (Φ{sub 0}) as a separate parameter. A simple ordinary differential equation model is developed. It takes the form of two coupled non-linear oscillators and reproduces key features of the simulations. Finally, a parametric study of the time to collapse is performed and a formula (fit to the simulations) is developed. In the incompressible limit J{sub t}→0, collapse time equals the self-sedimentation time, which is inversely proportional to the Stokes number. As J{sub t} increases, the collapse time decreases with J{sub t} and eventually becomes approximately equal to the dynamical time. Values of collapse time versus clump size are given for a minimum-mass solar nebula. Finally, the timescale of clump erosion due to turbulent strain is estimated.
Molecular dynamics simulations in the microcanonical ensemble are performed to study the collapse of a bubble in liquid water using the single-site mW and the four-site TIP4P/2005 water models. To study system size effects, simulations for pure water systems are performed using periodically replicated simulation boxes with linear dimensions, L, ranging from 32 to 512 nm with the largest systems containing 8.7 × 10 6 and 4.5 × 10 9 molecules for the TIP4P/2005 and mW water models, respectively. The computationally more efficient mW water model allows us to reach converging behavior when the bubble dynamics results are plotted in reduced units, and the limiting behavior can be obtained through linear extrapolation in L –1 . Qualitative differences are observed between simulations with the mW and TIP4P/2005 water models, but they can be explained by the models’ differences in predicted viscosity and surface tension. Although bubble collapse occurs on time scales of only hundreds of picoseconds, the system sizes used here are sufficiently large to obtain bubble dynamics consistent with the Rayleigh–Plesset equation when using the models’ thermophysical properties as input. For the conditions explored here, extreme heating of the interfacial water molecules near the time of collapse is observed for the larger mW water systems (but the model underpredicts the viscosity), whereas heating is less pronounced for the TIP4P/2005 water systems because its larger viscosity contribution slows the collapse dynamics. The presence of nitrogen within the bubble only starts to affect bubble dynamics near the very end of the initial collapse, leading to an incomplete collapse and strong rebound for the mW water model. Although nitrogen is non-condensable at 300 K, it becomes highly compressed and reaches a liquid-like density near the collapse point. We find that the dissolution of nitrogen is much slower than the movement of the collapsing water front, and the re-expansion of the dense nitrogen droplet gives rise to bubble rebound. The incompatibility of the collapse and dissolution time scales should be considered for continuum-scale modeling of bubble dynamics. Finally, we also confirm that the diffusion coefficient for dissolved nitrogen is insensitive to pressure as the liquid transitions from a compressed to a stretched state.
Ice shelf collapse reduces buttressing and enables grounded glaciers to contribute more rapidly to sea-level rise in a warming climate. The abrupt collapses of the Larsen A (1995) and B (2002) ice shelves on the Antarctic Peninsula (AP) occurred, at least for Larsen B, when long-period ocean swells damaged the calving front and the ice shelf was inundated with melt lakes that led to large-scale hydrofracture cascades. During collapse, field and satellite observations indicate föhn winds were present on both ice shelves. Here we use a regional climate model and machine learning analyses to evaluate the contributory roles of föhn winds and associated melt events prior to and during the collapses for ice shelves on the AP. Föhn winds caused about 25 % ± 3 % of the total annual melt in just 9 d on Larsen A prior to and during collapse and were present during the Larsen B collapse, which helped form extensive melt lakes. At the same time, the off-coast wind direction created by föhn winds helped melt and physically push sea ice away from the ice shelf calving fronts that allowed long-period ocean swells to reach and damage the front, which has been theorized to have ultimately triggered collapse. Collapsed ice shelves experienced enhanced surface melt driven by föhn winds over a large spatial extent and near the calving front, whereas SCAR inlet and the Larsen C ice shelves are affected less by föhn-wind-induced melt and do not experience large-scale melt ponds. These results suggest SCAR inlet and the Larsen C ice shelves may be less likely to experience rapid collapse due to föhn-driven melt so long as surface temperatures and föhn occurrence remain within historical bounds.
Ullage collapse predictions made using Computational Fluid Dynamics (CFD) were validated then made for an in-space cryogenic propellant unsettling application. Ullage collapse is the decrease in propellant tank pressure due to cooling of the ullage gas, which can be significant for cryogenic propulsion systems. Vehicles may be developed that are robust to temperature and pressure changes caused by heat leaks, e.g., propellant tanks with high maximum operation pressures, technologies yielding active thermal conditioning, and systems with ample pressurant for conditioning. These methods are robust because additional mass, cost, and complexity are used to address cryogenic fluid management (CFM). As vehicles are optimized for increased payload capacity, tracking of events such as ullage collapse and self-pressurization in tanks will become increasingly important for propellant inventory calculations. Some ullage collapse events can be studied through ground experimentation, but propellant unsettling in and around in-space coast mission phases must be studied in the absence of an acceleration field. Computational Fluid Dynamics is a powerful tool to address this need, enabling prediction of complex physics prior to flight. Validation of the chosen CFD tool and modeling methodology was done using data from a previously conducted subscale slosh-induced ullage collapse ground test performed in part by the Japan Aerospace Exploration Agency (JAXA). A small tank was partially filled with liquid nitrogen and pressurized with gaseous nitrogen at various temperatures. The tank was oscillated laterally to induce high amplitude slosh dynamics resulting in wave breakup. Successful qualitative validation of slosh wave dynamics and quantitative validation of ullage collapse promoted confidence in extending ullage collapse predictions to a flight application. Mechanisms of ullage collapse caused by main engine cutoff while in-space were identified. Both slosh dynamics leading to engine shutdown and body dynamics following shutdown were shown to contribute to propellant unsettling and ullage collapse.
Magnetic fields are important contributors to the dynamics of collapsing molecular cloud cores, and can have a major effect on whether collapse results in a single protostar or fragmentation into a binary or multiple protostar system. New models are presented of the collapse of magnetic cloud cores using the adaptive mesh refinement code Enzo2.0. The code was used to calculate the ideal magnetohydrodynamics (MHD) of initially spherical, uniform density, and rotation clouds with density perturbations, i.e., the Boss and Bodenheimer standard isothermal test case for three-dimensional (3D) hydrodynamics codes. After first verifying that Enzo reproduces the binary fragmentation expected for the non-magnetic test case, a large set of models was computed with varied initial magnetic field strengths and directions with respect to the cloud core axis of rotation (parallel or perpendicular), density perturbation amplitudes, and equations of state. Three significantly different outcomes resulted: (1) contraction without sustained collapse, forming a denser cloud core; (2) collapse to form a single protostar with significant spiral arms; and (3) collapse and fragmentation into binary or multiple protostar systems, with multiple spiral arms. Comparisons are also made with previous MHD calculations of similar clouds with a barotropic equations of state. These results for the collapse of initially uniform density spheres illustrate the central importance of both magnetic field direction and field strength for determining the outcome of dynamic protostellar collapse.
Observational evidence from local star-forming regions mandates that star formation occurs shortly after, or even during, molecular cloud formation. Models of molecular cloud formation in large-scale converging flows have identified the physical mechanisms driving the necessary rapid fragmentation. They also point to global gravitational collapse driving supersonic turbulence in molecular clouds. Previous cloud formation models have focused on turbulence generation, gravitational collapse, magnetic fields, and feedback. Here, we explore the effect of structure in the flow on the resulting clouds and the ensuing gravitational collapse. We compare two extreme cases, one with a collision between two smooth streams, and one with streams containing small clumps. We find that structured converging flows lead to a delay of local gravitational collapse ({sup c}ore formation{sup )}. Hence, the cloud has more time to accumulate mass, eventually leading to a strong global collapse, and thus to a high core formation rate. Uniform converging flows fragment hydrodynamically early on, leading to the rapid onset of local gravitational collapse and an overall low core formation rate. This is also mirrored in the core mass distribution: the uniform initial conditions lead to more low-mass cores than the clumpy initial conditions. Kinetic (E{sub k} ) and gravitational energy (E{sub g} ) budgets suggest that collapse is only prevented for E{sub k} >> E{sub g} , which occurs for large scales in the smooth flow, and for small scales for the clumpy flow. Whenever E{sub k} ≈ E{sub g} , we observe gravitational collapse on those scales. Signatures of chemical abundance variations evolve differently for the gas phase and for the stellar population. For smooth flows, the forming cloud is well mixed, while its stellar population retains more information about the initial metallicities. For clumpy flows, the gas phase is less well mixed, while the stellar population has lost most of the information about its origin.
The direct collapse model of supermassive black hole seed formation requires that the gas cools predominantly via atomic hydrogen. To this end we simulate the effect of an anisotropic radiation source on the collapse of a halo at high redshift. The radiation source is placed at a distance of 3 kpc (physical) from the collapsing object and is set to emit monochromatically in the center of the Lyman-Werner (LW) band. The LW radiation emitted from the high redshift source is followed self-consistently using ray tracing techniques. Due to self-shielding, a small amount of H{sub 2} is able to form at the very center of the collapsing halo even under very strong LW radiation. Furthermore, we find that a radiation source, emitting >10{sup 54} (∼ 10{sup 3} J{sub 21}) photons s{sup –1}, is required to cause the collapse of a clump of M ∼ 10{sup 5} M {sub ☉}. The resulting accretion rate onto the collapsing object is ∼0.25 M {sub ☉} yr{sup –1}. Our results display significant differences, compared to the isotropic radiation field case, in terms of the H{sub 2} fraction at an equivalent radius. These differences will significantly affect the dynamics of the collapse. With the inclusion of a strong anisotropic radiation source, the final mass of the collapsing object is found to be M ∼ 10{sup 5} M {sub ☉}. This is consistent with predictions for the formation of a supermassive star or quasi-star leading to a supermassive black hole.
Here, coarse-grained molecular dynamics enhanced by free-energy sampling methods is used to examine the roles of solvophobicity and multivalent salts on polyelectrolyte brush collapse. Specifically, we demonstrate that while ostensibly similar, solvophobic collapsed brushes and multivalent-ion collapsed brushes exhibit distinct mechanistic and structural features. Notably, multivalent-induced heterogeneous brush collapse is observed under good solvent polymer backbone conditions, demonstrating that the mechanism of multivalent collapse is not contingent upon a solvophobic backbone. Umbrella sampling of the potential of mean-force (PMF) between two individual brush strands confirms this analysis, revealing starkly different PMFs under solvophobic and multivalent conditions, suggesting the role of multivalent “bridging” as the discriminating feature in trivalent collapse. Structurally, multivalent ions show a propensity for nucleating order within collapsed brushes, whereas poor-solvent collapsed brushes are more disordered; this difference is traced to the existence of a metastable PMF minimum for poor solvent conditions, and a global PMF minimum for trivalent systems, under experimentally relevant conditions.