The knowledge how an object withstand an underwater detonation is critical within the defense industry. This is mostly done today with physicals test which are both time consuming and connected with high costs. The aim of this thesis is to provide recommendations and guidelines on how to model and analyze a structural response of underwater detonations. This investigation are focused on firstly investigate several theoretical simulation methods and thereafter develop a model of the chosen method.  The simulation method was decided to be the Multi-Material Arbitrary Lagrangian Euler(MMALE) using the software LS-Dyna. To receive a model with functionality to simulate an explosion a method of six steps is developed to increase the complexity. The final step is to be able to analyze a structural response of an object.  The validation phase contained several convergence studies of the two Equations of states and a varying element size compared to analytical equations. The plan was to perform a validation test but because of travel restrictions due to the Covid-19 situation an alternative validation method was used. This method involved two external reports with specified measurement data.  The aim to develop a model is reached as the model performs well against the cylinder in the validation phase, however the element size is the most important parameter in an accurate model. The developed model shows good agreement regarding the structural response of an object when compared to well defined and reported experiments.

Currently shock effects on surface ships can be determined by full scale shock trials, Finite Element Analysis or semi empirical methods that reduce the analytical problem to a limited number of degrees of freedom and include hull configurations, construction methods and materials in an empirical way to determine any debilitating effects that an explosion may have on the ship. This research has been undertaken to better understand the effect of hull shape on surface ships' shock response to external underwater explosions (UNDEX). The study is within the semi empirical method category of computations. A set of simple closed-form equations has been developed that accurately predicts the magnitude of dynamic excitation of different 2- D rigid-hull shapes subject to far-field UNDEX events. This research was primarily focused on the affects of 2-D rigid hull shapes and their contribution to global ship motions. A section of the thesis,

This thesis investigates the characteristics of a close proximity underwater explosion and its effect on a ship-like structure. Finite element model tests are conducted to verify and validate the propagation of a pressure wave generated by an underwater explosion through a fluid medium, and the transmission of the pressure wave in the fluid to a structure using the Multi-Material Arbitrary Lagrangian/Eulerian method. A one dimensional case modeling the detonation of a spherical TNT charge underwater is investigated. Three dimensional cases modeling the detonation of an underwater spherical TNT charge, and US Navy Blast Test cases modeling a shape charge and a circular steel plate, and a shape charge and a Sandwich Plate System (SPS) are also investigated. This thesis provides evidence that existing tools and methodologies have some capability for predicting early-time/close proximity underwater explosion effects, but are insufficient for analyses beyond the arrival of the initial shock wave. This thesis shows that a true infinite boundary condition, a modified Gruneisen equation of state near the charge, and the ability to capture shock without a very small element size is needed in order to provide a sufficient means for predicting early-time/close proximity underwater explosion effects beyond the arrival of the initial shock wave. / Master of Science

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.

Approved for public release; distribution is unlimited / In 2001 the USS WINSTON CHURCHILL (DDG-81) was subjected to three underwater explosions as part of a ship shock trial. Using the actual trial data from experiment and three-dimensional dynamic models of the ship and surrounding fluid very successful comparisons of the vertical motion have been achieved. On average, the magnitude of the vertical motion is three to four times the magnitude of athwartship motion. Previous simulations of this athwartship motion have been less accurate than the vertical motion simulations. This thesis examines recent efforts attempted to improve the simulation results of the athwartship motion including shock spectra analysis, and the reasons behind the disparities that exist between the simulated values and the actual trial data. / Lieutenant, United States Coast Guard

Approved for public release, distribution is unlimited / Evaluations, otherwise known as ship shock trials, have been conducted in order to determine the seaworthiness of each new class of ship commissioned in the U.S. Fleet. While beneficial in determining the overall survivability of a ship and its mission essential equipment in a severe shock environment, these Navy-mandated tests pose serious danger to the crew, ship and environment. As an alternative to these labor intensive, costly and time consuming at-sea tests, the recent advances in computer processing power have made it possible to employ finite element methods involving complex geometries in the modeling and simulation of shock response for the ship and surrounding fluid. This thesis examines the accuracy of shock simulation predictions as compared to the ship shock trials conducted on USS WINSTON S. CHURCHILL (DDG-81). An investigation of the effects of sensor location, damping and shot geometry is presented as validation of the Naval Postgraduate School modeling and simulation methodology. / Lieutenant, United States Navy

Modelling the full event of an underwater explosion (UNDEX) is complex and requires advanced modelling methods in order to achieve accurate responses. The process of an UNDEX includes a series of events that has to be considered. When a detonation is initiated, a shock-wave propagates and the rest products from the explosive material creates a gaseous bubble with high pressure which pulsates and impacts the surroundings. Reflections of the initial shock-wave can also appear if it hits the sea floor, water surface or other obstacles. There are different approaches how to numerically model the impact of an UNDEX on a structure, some with analytical approaches without a water domain and others where a water domain has to be modelled. This master’s thesis focuses on two modelling methods that are available in the finite element software LS-DYNA. The simpler method is called Sub-Sea Analysis (SSA) and does not require a water domain, thus it can be beneficial to use in an early design stage, or when only approximated responses are desired. To increase the accuracy, a more complex method called S-ALE can be used. By implementing this method, the full process of an UNDEX can be studied since both the fluid domain and explosive material are meshed. These methods are studied separately together with a combination of them. Another important aspect to be considered is that oscillations of a structure submerged in water differs from the behavior it has in air. Depending on the numerical method used, the impact of the water can be included. Natural frequencies of structures submerged in water are studied, how it changes and how the methods takes this into account. To verify the numerical models, experiments were executed with a cylindrical test object where the distance and weight of charge were altered through out the test series. It was found that multiple aspects affects the results from the experiments, that are not captured in the numerical models. These aspects have for instance to do with reflections, how accurate the test object is modelled and the damping effects of the water. It is concluded that the numerical models are sensitive when small charges and fragile structures are studied. High frequency oscillations were not triggered in the experiment but found for both methods. It should be further investigated if the methods are more accurate for larger charges and stronger structures. Experiments with larger water domain would also be beneficial to reduce effects from reflections, as well as a more accurate model of the cylinder in the simulations.