This thesis presents an analysis method for determining the whipping response of a hull girder to underwater explosion (UNDEX) bubble pulse loading. A potential flow-based UNDEX bubble model capable of calculating the behavior of a migrating bubble for up to three pulses is developed. An approximate vertical plane ship vibration model is derived using fundamental beam theory by representing the ship as a free-free beam with varying cross-sectional properties along its length. The fluid-structure interaction is approximated using strip theory and the distant flow assumption. The most severe predicted whipping load conditions are applied to a MAESTRO finite element model of the ship as a quasi-static load case to determine the response of the structure to the whipping loads. The calculated hull girder bending moments are compared to the ultimate bending strength of the hull girder to determine if the girder will collapse. The analysis method is found to be a useful method for determining preliminary UNDEX-induced whipping design load cases for early-stage ship design. However, more detailed and accurate data is needed to validate and verify the predicted whipping responses. It is found that the most severe whipping loads occur as the result of an UNDEX event that occurs under the keel near midship and produces a bubble with a pulsation frequency similar to the natural vibration frequency of the ship in its third mode. Significant damage to the ship structure and hull girder collapse is possible as a result of these loads. / Master of Science

This thesis describes and assesses a simplified tool for modeling underwater explosion shock effects during early naval ship concept design. A simplified fluid model using Taylor flat-plate theory is incorporated directly into the OpenFSI module code in Nastran and used to interface with the structural solver in Nastran to simulate a far-field shockwave impacting the hull. The kick-off velocities and the shock spectra captured in this computationally efficient module is compared to results from a high-fidelity CASE (Cavitating Acoustic Spectral Element) fluid model implemented with the ABAQUS/Nastran structural solver to validate the simplified framework and assess the sufficiency of this very simple but, fast approach for early stage ship design. / Master of Science / This thesis describes and assesses a simplified tool for modeling underwater explosion shock effects during early-stage naval ship design. Far-field explosions have a significant effect in terms of damage to equipment and mission capability of a ship. A simplified fluid-structure interaction model using the concept “Taylor flat-plate theory” is developed to simulate a far-field shockwave impacting the hull. This model is directly incorporated inside ‘OpenFSI’, a module used to couple an external code with the Nastran structural solver software. The initial peak velocity in the time-history and the shock spectra characteristics captured in this computationally efficient module is compared to results from a high-fidelity “CASE” (Cavitating Acoustic Spectral Element) fluid-structure interaction model. The “CASE” model implemented with the ABAQUS/Nastran structural solver is used to validate the simplified framework and assess the sufficiency of this very simple, but fast approach for early stage ship design.

Recently, the use of thermite-based pressure waves for applications in cellular transfection and drug delivery have shown significant improvements over previous technologies. In the present study, a new technique for producing thermite-generated pressure pulses using fully-dense nano-scale thermite mixtures was evaluated. This was accomplished by evaluation of a stoichiometric mixture of aluminium (Al) and copper(II)-oxide (CuO) prepared by mechanical alloying. Flame propagation speeds, constant-volume pressure characteristics and underwater pressure characteristics of both a micron-scale and mechanically alloyed mixture were measured experimentally and compared with conventional nano-scale thermites. It was determined that mechanically alloyed mixtures are capable of attaining flame propagation speeds on the same order as nano-scale mixtures, with flame speeds reaching as high as approximately 100 m/s. Constant-volume pressure experiments indicated that mechanically alloyed mixtures result in lower pressurization rates compared with conventional nano-scale mixtures, however, an improvement by as much as an order of magnitude was achieved compared with micron-scale mixtures. Thermochemical equilibrium predictions for pressures observed in constant-volume reactions were found to capture relatively well the equilibrium pressure for both low and high values of relative density. Generally, the predictions over-estimated the measured pressures by approximately 60%. Results from underwater experiments indicated that the mechanically alloyed samples produced peak shock pressures and waveforms similar to those for a nano-scale Al-Bi2O3 mixture reported by Apperson et al. (2008). In an effort to model the pressure signal obtained from the underwater reaction, calculations were performed based on the rate of expansion of the high pressure gas sphere. Predicted pressures were found to agree fairly well in terms of both the peak pressure and pressurization rate. The present study has thus identified the ability for mechanically alloyed thermite mixtures to produce underwater pressure profiles that may be conducive for applications in cellular transfection and drug delivery. Récemment, l'utilisation d'ondes de pression produite par des mélanges de thermite pour des applications dans la transfection cellulaire et l'administration de médicaments ont démontré des améliorations importantes par rapport aux technologies précédentes. Dans l'étude ci jointe, une nouvelle technique pour produire des impulsions de pression générée par un mélange thermite, soumit a de l'alliage mécanique, a été évaluée. Ceci a été accompli par l'évaluation d'un mélange stoechiométrique d' aluminium (Al) et de l'oxyde de cuivre(II) (CuO), préparé par mécanosynthèse. Les vitesses de propagation de la flamme, les caractéristiques de pression pour la combustion à volume constant et les caractéristiques de pression pour la combustion sous l'eau ont été mesurées expérimentalement et comparés avec les thermites conventionnel à l'échelle nano. Nous avons déterminé que les mélanges alliés mécaniquement sont capables d'atteindre des vitesses de propagation de flamme du même ordre que les mélanges à l'échelle nanométrique, atteignant jusqu'à environ 100 m/s. Les expériences de combusition à volume constant, indique que les mélanges alliés mécaniquement induit des taux de pressurisation inférieures à celles des mélanges de nano-échelle conventionnel, cependant, une amélioration de près d'un ordre de grandeur a été atteint par rapport aux mélanges d'échelle micronique. Prédictions thermochimiques des pression de compbustion se sont révélés capable de relativement bien saisir les valeurs observées dans les expériences à volume constant. En règle générale, les prévisions sur-estimé les pressions mesurées par environ 60%. Les résultats des expériences sous-marines ont indiqué que les échantillons alliés mécaniquement ont produit des pressions et des profils d'onde similaires à celles produit par un mélange de Al-Bi2O3 de nano-échelle, comme indiqué par Apperson et al. (2008). Pour modéliser les pressions obtenues dans les expériences sous-marines, des calculs basés sur le taux d'expansion de la bulle de gaz à haute pression ont été obtenus. Les pressions prédites ont été trouvés d'être relativement en accord avec la pression maximale et le taux de pressurisation observé. Cette étude a ainsi identifié la possibilité pour l'utilisation des mélanges de thermites alliés mécaniquement pour produire des profils de pression sous l'eau propices pour des applications de transfection cellulaire et l'administration de médicaments.

Recently, the use of thermite-based pressure waves for applications in cellular transfection and drug delivery have shown significant improvements over previous technologies. In the present study, a new technique for producing thermite-generated pressure pulses using fully-dense nano-scale thermite mixtures was evaluated. This was accomplished by evaluation of a stoichiometric mixture of aluminium (Al) and copper(II)-oxide (CuO) prepared by mechanical alloying. Flame propagation speeds, constant-volume pressure characteristics and underwater pressure characteristics of both a micron-scale and mechanically alloyed mixture were measured experimentally and compared with conventional nano-scale thermites. It was determined that mechanically alloyed mixtures are capable of attaining flame propagation speeds on the same order as nano-scale mixtures, with flame speeds reaching as high as approximately 100 m/s. Constant-volume pressure experiments indicated that mechanically alloyed mixtures result in lower pressurization rates compared with conventional nano-scale mixtures, however, an improvement by as much as an order of magnitude was achieved compared with micron-scale mixtures. Thermochemical equilibrium predictions for pressures observed in constant-volume reactions were found to capture relatively well the equilibrium pressure for both low and high values of relative density. Generally, the predictions over-estimated the measured pressures by approximately 60%. Results from underwater experiments indicated that the mechanically alloyed samples produced peak shock pressures and waveforms similar to those for a nano-scale Al-Bi2O3 mixture reported by Apperson et al. (2008). In an effort to model the pressure signal obtained from the underwater reaction, calculations were performed based on the rate of expansion of the high pressure gas sphere. Predicted pressures were found to agree fairly well in terms of both the peak pressure and pressurization rate. The present study has thus identified the ability for mechanically alloyed thermite mixtures to produce underwater pressure profiles that may be conducive for applications in cellular transfection and drug delivery. Récemment, l'utilisation d'ondes de pression produite par des mélanges de thermite pour des applications dans la transfection cellulaire et l'administration de médicaments ont démontré des améliorations importantes par rapport aux technologies précédentes. Dans l'étude ci jointe, une nouvelle technique pour produire des impulsions de pression générée par un mélange thermite, soumit a de l'alliage mécanique, a été évaluée. Ceci a été accompli par l'évaluation d'un mélange stoechiométrique d' aluminium (Al) et de l'oxyde de cuivre(II) (CuO), préparé par mécanosynthèse. Les vitesses de propagation de la flamme, les caractéristiques de pression pour la combustion à volume constant et les caractéristiques de pression pour la combustion sous l'eau ont été mesurées expérimentalement et comparés avec les thermites conventionnel à l'échelle nano. Nous avons déterminé que les mélanges alliés mécaniquement sont capables d'atteindre des vitesses de propagation de flamme du même ordre que les mélanges à l'échelle nanométrique, atteignant jusqu'à environ 100 m/s. Les expériences de combusition à volume constant, indique que les mélanges alliés mécaniquement induit des taux de pressurisation inférieures à celles des mélanges de nano-échelle conventionnel, cependant, une amélioration de près d'un ordre de grandeur a été atteint par rapport aux mélanges d'échelle micronique. Prédictions thermochimiques des pression de compbustion se sont révélés capable de relativement bien saisir les valeurs observées dans les expériences à volume constant. En règle générale, les prévisions sur-estimé les pressions mesurées par environ 60%. Les résultats des expériences sous-marines ont indiqué que les échantillons alliés mécaniquement ont produit des pressions et des profils d'onde similaires à celles produit par un mélange de Al-Bi2O3 de nano-échelle, comme indiqué par Apperson et al. (2008). Pour modéliser les pressions obtenues dans les expériences sous-marines, des calculs basés sur le taux d'expansion de la bulle de gaz à haute pression ont été obtenus. Les pressions prédites ont été trouvés d'être relativement en accord avec la pression maximale et le taux de pressurisation observé. Cette étude a ainsi identifié la possibilité pour l'utilisation des mélanges de thermites alliés mécaniquement pour produire des profils de pression sous l'eau propices pour des applications de transfection cellulaire et l'administration de médicaments.

In this study a modern hydrocode, blastFoam, that was designed for multi-phase compressible flow problems with applications suited for high-explosive detonation was investigated for underwater explosion (UNDEX) events. The problem of over-prediction for long-term UNDEX bubble behavior in modern hydrocodes that is known to be due to neglected secondary energy-loss mechanisms is evaluated. A single secondary energy-loss mechanism is established as the most significant loss mechanism that is being disregarded in current hydrocodes. The leading secondary energy-loss mechanism is formulated into a computational model that modifies the Jones-Wilkins-Lee (JWL) equation of state (EOS). Explanation and guidance for implementing the model in an Finite Volume Method (FVM) Eulerian-based hydrocode is provided. Through this research this thesis aims to improve long-term UNDEX bubble behavior prediction. Which is apart of a larger effort to improve numerical and computational predictions of UNDEX-induced structural ship response. / M.S. / Predicting the bubble dynamics of an underwater explosion (UNDEX) event is of great importance for the survivability of America’s warships. Shock waves from high-energy explosives are destructive to anything and everything nearby. Therefore, the design and development of military machinery rely on the accurate predictions of computational simulations. Computational solvers must be able to simulate the initial propagating shock waves from an underwater explosion, as well as the smaller following shock waves from the oscillating UNDEX bubble. Current incompressible solvers neglect the important compressible effects needed to predict the behavior for the UNDEX bubble oscillation cycle. If America’s Navy cannot predict the long-term damaging effects that a warship may encounter from an UNDEX bubble, then America’s warships and crew could not survive at battle. This study considers the assumptions used to simplify current UNDEX computational solvers in order to investigate and organize a compressible long-term simulation model. This model improves the multi-pulse bubble dynamic predictions for an UNDEX event, and will in return help design a long-term battle-ready warship for America’s future warfare.

The far-field underwater explosion (UNDEX) problem is a complicated problem dominated by two phenomena: the shock wave traveling through the fluid and the cavitation in the fluid. Both of these phenomena have a significant effect on the loading of ship structures subjected to UNDEX. An approach to numerically modeling these effects in the fluid and coupling to a structural model is using cavitating acoustic finite elements (CAFE) and more recently cavitating acoustic spectral elements (CASE). The use of spectral elements in CASE has shown to offer the greater accuracy and reduced computational expense when compared to traditional finite elements. However, spectral elements also increase spurious oscillations in both the fluid and structural response. This dissertation investigates the application of CAFE, CASE, and a possible improvement to CAFE in the form of a finite element flux-corrected transport algorithm, to the far-field UNDEX problem by solving a set of simplified UNDEX problems. Specifically we examine the effect of increased oscillations on structural response and the effect of errors in cavitation capture on the structural response which have not been thoroughly explored in previous work. The main contributions of this work are a demonstration of the problem dependency of increased oscillations in the structural response when applying the CASE methodology, the demonstration of how the sensitivity of errors in the structural response changes with changes in the structural model, a detailed explanation of how error in cavitation capture influences the structural response, and a demonstration of the need to accurately capture the shape and magnitude of cavitation regions in the fluid in order to obtain accurate structural response results. / Ph. D.

This thesis investigates the use of the numerical modeling tools LS-DYNA and USA in modeling general far-field underwater explosions (UNDEX) by modeling a three-dimensional box barge that is subjected to a far-field underwater explosion. Past UNDEX models using these tools have not been validated by experiment and most are limited to very specific problems because of the simplifying assumptions they make. USA is a boundary element code that requires only the structural model of the box barge. LS-DYNA is a dynamic finite element code and requires both the structural model and the surrounding fluid model, which is modeled with acoustic pressure elements. Analysis of the box barge problem results finds that the program USA is a valid tool for modeling the initial shock response of surface ships when cavitation effects are not considered. LS-DYNA models are found to be very dependent on the accuracy of the fluid mesh. The accuracy of the fluid mesh is determined by the ability of the mesh to adequately capture the peak pressure and discontinuity of the shock wave. The peak pressure captured by the model also determines the accuracy of the cavitation region captured in the fluid model. Assumptions made in the formulation of the fluid model causes potential inaccurate fluid-structure interaction and boundary condition problems cause further inaccuracies in the box barge model. These findings provide a base of knowledge for the current capabilities of UNDEX modeling in USA and LS-DYNA from which they can be improved in future work. / Master of Science

The vulnerability of a ship to the impact of underwater explosions (UNDEX) and how to incorporate this factor into early-stage ship design is an important aspect in the ship survivability study. In this dissertation, attention is focused on the cost-efficient simulation of the ship response to a far-field UNDEX which involves fluid shock waves, cavitation, and fluid-structural interaction. Traditional fluid numerical simulation approaches using the Finite Element Method to track wave propagation and cavitation requires a high-level of mesh refinement to prevent numerical dispersion from discontinuities. Computation also becomes quite expensive for full ship-related problems due to the large fluid domain necessary to envelop the ship. The burden is aggravated by the need to generate a fluid mesh around the irregular ship hull geometry, which typically requires significant manual intervention. To accelerate the design process and enable the consideration of far-field UNDEX vulnerability, several contributions are made in this dissertation to make the simulation more efficient. First, a Cavitating Acoustic Spectral Element approach which has shown computational advantages in UNDEX problems, but not systematically assessed in total ship application, is used to model the fluid. The use of spectral elements shows greater structural response accuracy and lower computational cost than the traditional FEM. Second, a novel fully automatic all-hexahedral mesh generation scheme is applied to generate the fluid mesh. Along with the spectral element, the all-hex mesh shows greater accuracy than the all-tetrahedral finite element mesh which is typically used. This new meshing approach significantly saves time for mesh generation and allows the spectral element, which is confined to the hexahedral element, to be applied in practical ship problems. A further contribution of this dissertation is the development of a surrogate non-numerical approach to predict structural peak responses based on the shock factor concept. The regression analysis reveals a reasonably strong linear relationship between the structural peak response and the shock factor. The shock factor can be conveniently employed in the design aspects where the peak response is sufficient, using much less computational resources than numerical solvers. / Doctor of Philosophy / The vulnerability of a ship to the impact of underwater explosions (UNDEX) and how to incorporate this factor into early-stage ship design is an important aspect in the ship survivability study. In this dissertation, attention is focused on the cost-efficient simulation of the ship response to a far-field UNDEX which involves fluid shock waves, cavitation, and fluid-structural interaction. Traditional fluid numerical simulation approaches using the Finite Element Method to track wave propagation and cavitation requires a highly refined mesh to deal with large numerical errors. Computation also becomes quite expensive for full ship-related problems due to the large fluid domain necessary to envelop the ship. The burden is aggravated by the need to generate a fluid mesh around the irregular ship hull geometry, which typically requires significant manual intervention. To accelerate the design process and enable the consideration of far-field UNDEX vulnerability, several contributions are made in this dissertation to make the simulation more efficient. First, a Cavitating Acoustic Spectral Element approach, which has shown computational advantages in UNDEX problems but not systematically assessed in total ship application, is used to model the fluid. The use of spectral elements shows greater structural response accuracy and lower computational cost than the traditional FEM. Second, a novel fully automatic all-hexahedral mesh generation scheme is applied to generate the fluid mesh. Along with the spectral element, the all-hex mesh shows greater accuracy than the all-tetrahedral finite element mesh which is typically used. A further contribution of this dissertation is the development of a non-numerical approach which can approximate peak structural responses comparable to the numerical solution with far less computational effort.

Underwater explosions pose a significant threat to waterborne infrastructure though destructive pressure waves that can travel significant distances through the water. However, the use of bubble screens can attenuate the peak pressure and energy flux created by explosions to safe levels. This study investigates the prediction of pressure wave characteristics based on accumulated data, the damage potential of underwater explosions based on applied loads and effective material strength, and the bubble screen parameters required to prevent damage. The results were compiled to form a procedure for the design and implementation of a bubble screen the protection of waterborne infrastructure.

A coupled solution approach is presented for numerically simulating a near-field underwater explosion (UNDEX). An UNDEX consists of a complicated sequence of events over a wide range of time scales. Due to the complex physics, separate simulations for near/far-field and early/late-time are common in practice. This work focuses on near-field early-time UNDEX simulations. Using the assumption of compressible, inviscid and adiabatic flow, the fluid flow is governed by a set of Euler fluid equations. In practical simulations, we often encounter computational difficulties that include large displacements, shocks, multi-fluid flows with cavitation, spurious waves reflecting from boundaries and fluid-structure coupling. Existing methods and codes are not able to simultaneously consider all of these characteristics. A robust numerical method that is capable of treating large displacements, capturing shocks, handling two-fluid flows with cavitation, imposing non-reflecting boundary conditions (NRBC) and allowing the movement of fluid grids is required. This method is developed by combining numerical techniques that include a high-order accurate numerical method with a shock capturing scheme, a multi-fluid method to handle explosive gas-water flows and cavitating flows, and an Arbitrary Lagrangian Eulerian (ALE) deformable fluid mesh. These combined approaches are unique for numerically simulating various near-field UNDEX phenomena within a robust single framework. A review of the literature indicates that a fully coupled methodology with all of these characteristics for near-field UNDEX phenomena has not yet been developed. A set of governing equations in the ALE description is discretized by a Runge Kutta Discontinuous Galerkin (RKDG) method. For multi-fluid flows, a Direct Ghost Fluid (DGF) Method coupled with the Level Set (LS) interface method is incorporated in the RKDG framework. The combination of RKDG and DGF methods (RKDG-DGF) is the main contribution of this work which improves the quality and stability of near-field UNDEX flow simulations. Unlike other methods, this method is simpler to apply for various UNDEX applications and easier to extend to multi-dimensions. / Ph. D.