Evolution and breakup of viscous rotating drops

We study the evolution of a viscous fluid drop rotating about a fixed axis at constant angular velocity $Omega$ or constant angular momentum L surrounded by another viscous fluid. The problem is considered in the limit of large Ekman number and small Reynolds number. The analysis is carried out by combining asymptotic analysis and full numerical simulation by means of the boundary element method. We pay special attention to the stability/instability of equilibrium shapes and the possible formation of singularities representing a change in the topology of the fluid domain. When the evolution is at constant $Omega$, depending on its value, drops can take the form of a flat film whose thickness goes to zero in finite time or an elongated filament that extends indefinitely. When evolution takes place at constant L and axial symmetry is imposed, thin films surrounded by a toroidal rim can develop, but the film thickness does not vanish in finite time. When axial symmetry is not imposed and L is sufficiently large, drops break axial symmetry and, depending on the value of L, reach an equilibrium configuration with a 2-fold symmetry or break up into several drops with a 2- or 3-fold symmetry. The mechanism of breakup is also described

Laser Shock Microformingof Thin Metal Sheets with ns Lasers

Continuous and long-pulse lasers have been used for the forming of metal sheets in macroscopic mechanical applications. However, for the manufacturing of micro-electromechanical systems (MEMS), the use of ns laser pulses provides a suitable parameter matching over an important range of sheet components that, preserving the short interaction time scale required for the predominantly mechanical (shock) induction of deformation residual stresses, allows for the successful processing of components in a medium range of miniaturization without appreciable thermal deformation.. In the present paper, the physics of laser shock microforming and the influence of the different experimental parameters on the net bending angle are presented.

Development of Robotized Laser Welding Applications for Joining Thin Sheets

Laser Welding (LW) is more often used in manufacturing due to its advantages, such as accurate control, good repeatability, less heat input, opportunities for joining of special materials, high speed, capability to join small dimension parts etc. LW is dedicated to robotized manufacturing, and the fabrication cells are using various level of flexibility, from specialized robots to very flexible setups. This paper features several LW applications using two industrially-scaled manufacturing cells at UPM Laser Centre (CLUPM) of Polytechnical University of Madrid (Universidad Politécnica de Madrid). The one dedicated to Remote Laser Welding (RLW) of thin sheets for automotive and other sectors uses a CO2 laser of 3500 W. The second has a high flexibility, is based on a 6-axis ABB robot and a Nd:YAG laser of 3300 W, and is meant for various laser processing methods, including welding. After a short description of each cell, several LW applications experimented at CLUPM and recently implemented in industry are briefly presented: RLW of automotive coated sheets, LW of high strength automotive sheets, LW vs. laser hybrid welding (LHW) of Double Phase steel thin sheets, and LHW of thin sheets of stainless steel and carbon steel (dissimilar joints). The main technological issues overcame and the critical process parameters are pointed out. Conclusions about achievements and trends are provided.

Bubble growth by injection of gas into viscous liquids in cylindrical and conical tubes.

The laminar low Mach number flow of a gas in a tube is analyzed for very small and very large values of the inlet-to-wall temperature ratio. When this ratio tends to zero, pressure forces confine the cold gas to a thin core around the axis of the tube. This core is neatly bounded by an ablation front that consumes it at a finite distance from the tube inlet. When the temperature ratio tends to infinity, the temperature of the gas increases smoothly from the wall to the axis of the tube and the shear stress and heat flux are positive at the wall despite the fact that the viscosity and thermal conductivity of the gas scaled with their inlet values tend to zero at the wall.

Numerical simulation of the evolution of viscous rotating drops

In this contribution we simulate numerically the evolution of a viscous fluid drop rotating about a fixed axis at constant angular velocity ? or constant angular momentum L, surrounded by another viscous fluid. The problem is considered in the limit of large Ekman number and small Reynolds number. In the lecture we will describe the numerical method we have used to solve the PDE system that describes the evolution of the drop (3D boundary element method). We will also present the results we have obtained, paying special attention to the stability/instability of the equilibrium shapes.

Theoretical analysis and numerical verification of the consistency of viscous smoothed-particle-hydrodynamics formulations in simulating free-surface flows

The theoretical formulation of the smoothed particle hydrodynamics (SPH) method deserves great care because of some inconsistencies occurring when considering free-surface inviscid flows. Actually, in SPH formulations one usually assumes that (i) surface integral terms on the boundary of the interpolation kernel support are neglected, (ii) free-surface conditions are implicitly verified. These assumptions are studied in detail in the present work for free-surface Newtonian viscous flow. The consistency of classical viscous weakly compressible SPH formulations is investigated. In particular, the principle of virtual work is used to study the verification of the free-surface boundary conditions in a weak sense. The latter can be related to the global energy dissipation induced by the viscous term formulations and their consistency. Numerical verification of this theoretical analysis is provided on three free-surface test cases including a standing wave, with the three viscous term formulations investigated.

Laser Shock Microforming of Thin Metal Sheets with Q-Switched ns Lasers

The increasing demands in MEMS fabrication are leading to new requirements in production technology. Especially the packaging and assembly require high accuracy in positioning and high reproducibility in combination with low production costs. Conventional assembly technology and mechanical adjustment methods are time consuming and expensive. Each component of the system has to be positioned and fixed. Also adjustment of the parts after joining requires additional mechanical devices that need to be accessible after joining.

Numerical prediction of residual stresses fields induced in thin Al2024-T351 sheets by laser shock processing

Outline: • Introduction • Numerical model SHOCKLAS© • Single LSP pulses • Overlapped LSP pulses • Discussion and Outlook

Laser Shock Microforming of Thin Metal Sheets: Physical Principles, Modelling and Experimental Implementation

The increasing demands in MEMS fabrication are leading to new requirements in production technology. Especially the packaging and assembly require high accuracy in positioning and high reproducibility in combination with low production costs. Conventional assembly technology and mechanical adjustment methods are time consuming and expensive. Each component of the system has to be positioned and fixed. Also adjustment of the parts after joining requires additional mechanical devices that need to be accessible after joining. Accurate positioning of smallest components represents an up-to-date key assignment in micro-manufacturing. It has proven to be more time and cost efficient to initially assemble the components with widened tolerances before precisely micro-adjusting them in a second step.

Dynamic interactions between solids and viscous liquids with free surface = Interacciones dinámicas entre sólidos y líquidos viscosos con superficie libre

En esta tesis se investiga la interacción entre un fluido viscoso y un cuerpo sólido en presencia de una superficie libre. El problema se expresa teóricamente poniendo especial atención a los aspectos de conservación de energía y de la interacción del fluido con el cuerpo. El problema se considera 2D y monofásico, y un desarrollo matemático permite una descomposición de los términos disipativos en términos relacionados con la superficie libre y términos relacionados con la enstrofía. El modelo numérico utilizado en la tesis se basa en el método sin malla Smoothed Particle Hydrodynamics (SPH). De manera análoga a lo que se hace a nivel continuo, las propiedades de conservación se estudian en la tesis con el sistema discreto de partículas. Se tratan también las condiciones de contorno de un cuerpo que se mueve en un flujo viscoso, implementadas con el método ghost-fluid. Se ha desarrollado un algoritmo explícito de interacción fluido / cuerpo. Se han documentado algunos casos de modo detallado con el objetivo de comprobar la capacidad del modelo para reproducir correctamente la disipación de energía y el movimiento del cuerpo. En particular se ha investigado la atenuación de una onda estacionaria, comparando la simulación numérica con predicciones teóricas. Se han realizado otras pruebas para monitorizar la disipación de energía para flujos más violentos que implican la fragmentación de la superficie libre. La cantidad de energía disipada con los diferentes términos se ha evaluado en los casos estudiados con el modelo numérico. Se han realizado otras pruebas numéricas para verificar la técnica de modelización de la interacción fluido / cuerpo, concretamente las fuerzas ejercidas por las olas en cuerpos con formas simples, y el equilibrio de un cuerpo flotante con una forma compleja. Una vez que el modelo numérico ha sido validado, se han realizado simulaciones numéricas para obtener una comprensión más completa de la física implicada en casos (casi) realistas sobre los había aspectos que no se conocían suficientemente. En primer lugar se ha estudiado el el flujo alrededor de un cilindro bajo la superficie libre. El estudio se ha realizado con un número de Reynolds moderado, para un rango de inmersiones del cilindro y números de Froude. La solución numérica permite una investigación de los patrones complejos que se producen. La estela del cilindro interactúa con la superficie libre. Se han identificado algunos inestabilidades características. El segundo estudio se ha realizado sobre el problema de sloshing, tanto experimentalmente como numéricamente. El análisis se restringe a aguas poco profundas y con oscilación horizontal, pero se ha estudiado un gran número de condiciones, lo que lleva a una comprensión bastante completa de los sistemas de onda involucradas. La última parte de la tesis trata también sobre un problema de sloshing pero esta vez el tanque está oscilando con rotación y hay acoplamiento con un sistema mecánico. El sistema se llama pendulum-TLD (Tuned Liquid Damper - con líquido amortiguador). Este tipo de sistema se utiliza normalmente para la amortiguación de las estructuras civiles. El análisis se ha realizado analíticamente, numéricamente y experimentalmente utilizando líquidos con viscosidades diferentes, centrándose en características no lineales y mecanismos de disipación. ABSTRA C T The subject of the present thesis is the interaction between a viscous fluid and a solid body in the presence of a free surface. The problem is expressed first theoretically with a particular focus on the energy conservation and the fluid-body interaction. The problem is considered 2D and monophasic, and some mathematical development allows for a decomposition of the energy dissipation into terms related to the Free Surface and others related to the enstrophy. The numerical model used on the thesis is based on Smoothed Particle Hydrodynamics (SPH): a computational method that works by dividing the fluid into particles. Analogously to what is done at continuum level, the conservation properties are studied on the discrete system of particles. Additionally the boundary conditions for a moving body in a viscous flow are treated and discussed using the ghost-fluid method. An explicit algorithm for handling fluid-body coupling is also developed. Following these theoretical developments on the numerical model, some test cases are devised in order to test the ability of the model to correctly reproduce the energy dissipation and the motion of the body. The attenuation of a standing wave is used to compare what is numerically simulated to what is theoretically predicted. Further tests are done in order to monitor the energy dissipation in case of more violent flows involving the fragmentation of the free-surface. The amount of energy dissipated with the different terms is assessed with the numerical model. Other numerical tests are performed in order to test the fluid/body interaction method: forces exerted by waves on simple shapes, and equilibrium of a floating body with a complex shape. Once the numerical model has been validated, numerical tests are performed in order to get a more complete understanding of the physics involved in (almost) realistic cases. First a study is performed on the flow passing a cylinder under the free surface. The study is performed at moderate Reynolds numbers, for various cylinder submergences, and various Froude numbers. The capacity of the numerical solver allows for an investigation of the complex patterns which occur. The wake from the cylinder interacts with the free surface, and some characteristical flow mechanisms are identified. The second study is done on the sloshing problem, both experimentally and numerically. The analysis is restrained to shallow water and horizontal excitation, but a large number of conditions are studied, leading to quite a complete understanding of the wave systems involved. The last part of the thesis still involves a sloshing problem but this time the tank is rolling and there is coupling with a mechanical system. The system is named pendulum-TLD (Tuned Liquid Damper). This kind of system is normally used for damping of civil structures. The analysis is then performed analytically, numerically and experimentally for using liquids with different viscosities, focusing on non-linear features and dissipation mechanisms.