<div><br></div><div> Today, autoinjectors are developed for more viscous drug solutions, which require larger forces for actuating the syringe and impose larger stresses on the drug solution during the administration of autoinjectors. We developed experimentally validated high-fidelity simulations to investigate the liquid jet formation, liquid slosh and cavitation during the insertion process of an autoinjector. </div><div> </div><div> The jet formed due to an acceleration-deceleration motion of syringe is found to be governed by the interplay between inertial, viscous, surface tension and gravitational forces. A scaling for the jet velocity and a criterion for the jet breakup in a simplified geometry are proposed.</div><div> </div><div> When the syringe accelerates and decelerates during the insertion, liquid slosh occurs and there is a vehement motion of the air-liquid interface. Here, we quantified the area of air-liquid interface and hydrodynamic strain rate, which increase with the air gap size, syringe velocity, tilt angle and inner wall hydrophobicity, and decrease with the solution viscosity and hardly change with the liquid column height and surface tension. The strain rate is not sufficient to unfold the protein and the air-liquid interface is more likely to cause protein aggregation.</div><div> </div><div> In a spring-driven autoinjector, the plunger is actuated by the impact of a driving rod, which generates a strong pressure wave and can cause cavitation inception. The cavtiation bubbles can be impeded by the syringe walls and form a re-entrant jet shooting toward the syringe wall. During the process, the protein molecules are focused in the jet, pushed toward the syringe wall and spread across the wall, which can be the reason for the protein aggregation and adsorption on the syringe walls. The impedance effects of the wall decreases with the wall distance and increases with the maximum bubble size. The maximum bubble radius also increases with the liquid column size and nucleus size and decreases with the air gap pressure. Since inertia effects dominate in the cavitation process, the liquid viscosity and surface tension hardly changes the cavitation bubble dynamics. Small bubbles can also form in the bulk, which may generate aggregates in the bulk solution. Bubbles in the cavitation bubble cloud may coalesce with nearby bubbles and induce a higher pressure at the collapse (up to 1000 bar). This high pressure can potentially generate hydroxyl radicals that oxidize the protein molecules.</div><div> </div><div> The current study presents a detailed picture of fluid flows in autoinjectors and provide recommendations for mitigating the liquid slosh and cavitation generated in syringes. The results can be combined with future experiments to understand the implications of fluid flows on protein drugs and the performance of autoinjectors.</div>

Liquid sloshing with unrestrained free surface in a moving container is associated with various engineering problems, such as tankers on highways, liquid oscillations in large storage tanks caused by earthquakes, sloshing of liquid cargo in ocean-going vessels, and the motion of liquid fuel in aircraft and spacecraft. The purpose of this study is to develop a three-dimensional (3D) numerical wave tank with or without internal structures to investigate the mechanism of liquid sloshing and the interaction between the fluid and internal structures. The developed 3D time-independent finite difference method is applied on solving liquid sloshing in tanks with or without the influence of baffles under the ground motion of six-degrees of freedom. The 3D Navier-Stokes equations were solved and transformed to a tank-fixed coordinate system, and the fully nonlinear kinematic and dynamic free surface boundary conditions for fluid sloshing in a rectangular tank with a square base were considered. The fluid is assumed incompressible in this study. The complicated interaction in the vicinity of the fluid-structure interface was solved by implementing one dimensional ghost cell approach and the stretching grid technique near the fluid-structure boundaries were used to catch the detailed evolution of local flow field. A PC-cluster was established by linking several single computers to reduce the computational times due to the implementation of the 3D numerical model. The Message Passing Interface (MPI) parallel language and MPICH2 software were utilized to code the computer codes and to carry out the circumstance of parallel computation, respectively. The developed numerical scheme was verified by rigorous benchmark tests. Not only the reported analytical, numerical and experimental studies were compared with the present numerical results, the experimental investigation was also involved in the present work to further validate the accuracy of the numerical scheme. All the benchmark tests of this study showed excellent accuracy of the developed numerical scheme. For a tank without internal structures, the coupled motions of surge and sway are simulated with various excitation angles, excitation frequencies and water depths. The characteristics of sloshing waves are dissected in terms of the classification of sloshing wave types, sloshing amplitude, beating phenomenon, sloshing-induced forces and energy transfer of sloshing waves. Six types of sloshing waves, named single-directional, diagonal, square-like, swirling-like, swirling and irregular waves, were found and classified in the present study and the occurrence of these waves are tightly in connection with the excitation frequency of the tank. The effect of excitation angle on the characteristics of sloshing waves is explored and discussed, especially for swirling waves. The spectral analyses of sloshing displacement of various sloshing waves are examined and a clear evidence of the correlation between sloshing wave patterns and resonant modes of sloshing waves are demonstrated. The mechanism of switching direction of swirling waves is discussed by investigating the situation of circulatory flow, the instantaneous free surface, the gravitational effect and the instantaneous direction of external forcing. The coupling effects of heave, surge and sway motions were also included in this study and the result showed an unstable influence of heave motion on the kinematic and dynamic characteristics of sloshing waves when the vertical excitation frequency of the tank is twice as large as the fundamental natural frequency. Except irregular waves, the other types of sloshing waves are converted into swirling waves due to the effect of heave motion. The study related to tuned liquid damper (TLD) in 2D and 3D tanks were considered. A comprehensive investigation for a 2D tank with vertically tank bottom-mounted baffles (baffled tank) are demonstrated and discussed with respect to the influence of baffle height on the natural mode of the tank, the evolution of vortices and vortex shedding phenomenon, the relationship between the vortex shedding frequency and the excitation frequency of the tank, the vortex size generated in the vicinity of the baffle tip, the interaction of vortices inside the tank. The baffle height shows a significant influence on the shift of the first natural frequency of the baffled tank and the liquid depth also plays an important part in determining this influence. In other words, the shift of the first natural mode due to various baffle height is varied with water depths. The design of two baffles separated by 0.2 times the tank breadth is an efficient tool to not only reduce the sloshing amplitude but switch the first natural frequency of the tank. The sloshing displacement is affected distinctly by different numbers of baffles mounted vertically on the tank bottom. The more baffles mounted onto the tank bottom, the smaller the sloshing displacement is presented in both the transient and steady-state periods. The processes of the evolution of vortices near the baffle tip are categorized into four phases: the formation of separated shear layer and generation of vortices, the formation of a vertical jet and shedding of vortices, the interaction between shedding vortices and sloshing flow (the generation of snaky flow) and the interaction between snaky flow and sloshing waves. Vortex shedding phenomenon due to stronger vertical jets occurs when the excitation frequency is close to the first natural mode of the baffled tank. The size of the vortex generated near the baffle tip is discussed and the vortex size is closely correlated with the baffle height. Two types of 3D tuned liquid dampers, a vertically tank bottom-mounted baffle and a vertical plate, are discussed for a tank under coupled surge-sway motions. The wave types of diagonal and single-directional waves switch to the swirling type due to the influence of the baffle. The phenomenon of square-like waves or irregular waves coexisting with swirling waves is found in the baffled tank under diagonal excitation. The baffle and the vertical plate mounted parallel to the east (west) wall of the tank can effectively reduce the sloshing amplitude when the excitation angle is between 0 degree and 10 degree and the corresponding sloshing displacement in the sway (z) direction becomes more dominant with the increase of the excitation angle. The shift of the first natural mode of the baffled tank due to various baffle heights in the x direction is dominated in this design of baffled tank. The length of the plate can cause a significant influence on not only the variation of the natural frequencies but the type of the sloshing waves. The influence of the vertical plate on the irregular waves is insignificant and several peaks appear in the spectral analysis of the sloshing displacement for the irregular waves and the numbers of peaks are more than that of the baffled tank.

<p> Tuned Liquid Dampers (TLDs) are increasingly being used to suppress the dynamic vibration of tall buildings. An equivalent mechanical model is essential for rapid analysis and design of a TLD. The most common TLD tank geometries are circular, annular and rectangular. Rectangular tanks are utilized for 1-D and 2-D TLDs, whereas circular and annular are usually applied to axisymmetric structures. The amount of fluid that participates in the sloshing motion is directly influenced by the tank geometry. Although not commonly used, a TLD having a curved-bottom tank is expected to perform more effectively due to its relatively large value of effective mass. The main objective of this study is to develop mechanical models for seven TLDs with different tank geometries including the curved-bottom case, and to theoretically investigate the performance of rectangular, vertical-cylindrical and horizontal-cylindrical TLDs.</p> <p> Potential flow theory, linear long wave theory, Lagrange's equations and virtual work method are employed to develop the equivalent mechanical model parameters of TLDs with rectangular, vertical-cylindrical, horizontal-cylindrical, hyperboloid, triangular, sloped-bottom, and parabolic tank geometries. A rectangular, vertical-cylindrical and horizontal-cylindrical TLD are selected for further study using a single-degree-of-freedom (SDOF) model and a two degree of freedom structure-TLD system model applying the derived equivalent mechanical parameters.</p> <p> The dynamic characteristics of the TLDs as a SDOF system are investigated. The mechanical model is verified by comparing calculated values with experimental results for a rectangular TLD. The free surface motion, sloshing force and energy dissipation are found to be dependent upon the excitation amplitude. Analytical results also indicate that the horizontal-cylindrical TLD possesses the greatest normalized sloshing force and energy dissipation among the TLDs considered.</p> <p> The performances of various TLDs installed in a structure are studied in terms of effective damping, efficiency and robustness. Tuning ratio, structural response amplitude, mass ratio and liquid depth are adjusted to investigate their affect on the performance of the studied TLDs. Performance charts are developed and subsequently used to present the results. It is found that small liquid depth ratio and large mass ratio can lead to a robust structure-TLD system with small relative motion ratio between the structure and the vibration absorber. Comparisons of performance between the three TLDs are made and it can be concluded that the horizontal-cylindrical TLD is the most robust and effective device with the smallest relative motion ratio.</p> / Thesis / Master of Applied Science (MASc)

The purpose of this study is to perform an investigation of the numerical methods that may contribute to the design and analysis of liquid containers. The study examines several of these methods individually, namely Computational Fluid Dynamics (CFD) analysis of sloshing and Finite Element Methods (FEM) analysis of impact, to evaluate their contribution to the design cycle. Techniques that enhance the use of the various methods are presented and examined to demonstrate effectiveness. In the case of sloshing analysis, experimental tests performed add to the understanding of the phenomena at hand and qualifies the validity of the numerical method used (CFD). As a final contribution, the study presents a method of utilising impact analysis tools, FEM, and CFD in a Multidisciplinary Design Optimisation (MDO) environment. This is an introductory attempt at demonstrating a single coupled multidisciplinary method of designing liquid containers. The results of the study demonstrate a number of valuable numerical techniques that may be used in the design of liquid containers. The presented Total Deviation Value (TDV) proves to be an effective single quantification of sloshing performance and the CFD tools used to determine the value demonstrate sufficient ability to reproduce the sloshing event itself. More advanced experimental facilities would provide a more in-depth understanding of the limitations of the CFD analysis. The use of numerical optimisation adds a valuable dimension to the use of numerical simulations. Significant design improvements are possible for several design variables without performing exhaustive studies and provide interesting information about design trends. Finally, the use of multiple disciplines, FEM and CFD, in conjunction with the available numerical optimisation routines offers a powerful multidisciplinary design tool that can be adapted to any base geometry and is capable of finding optimal trade offs between the two disciplines according to the designer’s needs. This study provides a platform for further investigations in the use and coupling of sloshing and impact analysis in the design of industrial liquid container applications. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2006. / Mechanical and Aeronautical Engineering / unrestricted