On the modelling of impulsive pressures and residual stresses induced by cavitation peening

International audienceResidual stresses are those remaining in mechanical parts free of any external loading. They generally come from thermal effects, mechanical loading and/or metallurgical phase transformation during the manufacturing steps. When these stresses are of tensile type, they can have negative consequences on the lifetime of the component by helping cracks initiation and propagation phenomena like Stress Corrosion Cracking (SCC). In order to improve the fatigue life and avoid the premature failure of metallic components, surface treatment processes are carried out to introduce residual stresses of compression in materials and to raise the critical value of operating tensile stress. Conventional Shot Peening (SP), Ultrasonic Shot Peening (USP) and Laser Shock Peening (LSP) are some of these surface treatment methods which have been widely studied both experimentally and numerically. Water Cavitation Peening (WCP) is a similar process of surface treatment [1]. During WCP, cavitation bubbles are created by a high-speed submerged water jet directed toward the workpiece surface. The cavitation phenomenon occurs in low static pressure (lower than vapour pressure of water) zones due to the turbulence generated, at a given temperature. The collapse and/or the impact of these bubbles on the treated surface induce high loading pressures and thereby plastic deformation of the superficial layers of the material. Superficial compressive residual stresses are then introduced in the material. This process is known to provide a better surface finish with less roughness than that of the conventional shot peening because there is no solid-solid contact involved [2]. Many experimental studies have proven the efficiency of the present process to introduce compressive residual stresses into relatively high yield strength materials and enhance their fatigue strength [3]. However, the modelling of cavitation peening is very challenging, because of the complex behaviour of cavitation phenomenon. Very few studies concerning the modelling and simulation of WCP have been reported. A mechanical model based on finite element method have been proposed by Han and Hu [4] to predict the residual stress profile obtained after WCP. The authors measured experimentally the affected surface diameter. Then, they supposed a constant spatial distribution and trapezoidal temporal variation, for the loading pressure. As the above-mentioned study, most of the numerical studies about the modelling of cavitation peening employed theoretical values for pressure magnitude and pressure pulse duration with no direct link to the process parameters. The main reason and issue is the difficulty to determine the impulsive pressure distribution of cavitation peening

Numerical simulations of non-spherical bubble collapse

A high-order accurate shock- and interface-capturing scheme is used to simulate the collapse of a gas bubble in water. In order to better understand the damage caused by collapsing bubbles, the dynamics of the shock-induced and Rayleigh collapse of a bubble near a planar rigid surface and in a free field are analysed. Collapse times, bubble displacements, interfacial velocities and surface pressures are quantified as a function of the pressure ratio driving the collapse and of the initial bubble stand-off distance from the wall; these quantities are compared to the available theory and experiments and show good agreement with the data for both the bubble dynamics and the propagation of the shock emitted upon the collapse. Non-spherical collapse involves the formation of a re-entrant jet directed towards the wall or in the direction of propagation of the incoming shock. In shock-induced collapse, very high jet velocities can be achieved, and the finite time for shock propagation through the bubble may be non-negligible compared to the collapse time for the pressure ratios of interest. Several types of shock waves are generated during the collapse, including precursor and water-hammer shocks that arise from the re-entrant jet formation and its impact upon the distal side of the bubble, respectively. The water-hammer shock can generate very high pressures on the wall, far exceeding those from the incident shock. The potential damage to the neighbouring surface is quantified by measuring the wall pressure. The range of stand-off distances and the surface area for which amplification of the incident shock due to bubble collapse occurs is determined

Compressible simulations of bubble dynamics with central-upwind schemes

This paper discusses the implementation of an explicit density-based solver, that utilises the central-upwind schemes for the simulation of cavitating bubble dynamic flows. It is highlighted that, in conjunction with the Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) scheme they are of second order in spatial accuracy; essentially they are high-order extensions of the Lax–Friedrichs method and are linked to the Harten Lax and van Leer (HLL) solver family. Basic comparison with the predicted wave pattern of the central-upwind schemes is performed with the exact solution of the Riemann problem, for an equation of state used in cavitating flows, showing excellent agreement. Next, the solver is used to predict a fundamental bubble dynamics case, the Rayleigh collapse, in which results are in accordance to theory. Then several different bubble configurations were tested. The methodology is able to handle the large pressure and density ratios appearing in cavitating flows, giving similar predictions in the evolution of the bubble shape, as the reference

A compressible Lagrangian framework for the simulation of underwater implosion problems

The development of efficient algorithms to understand implosion dynamics presents a number of challenges. The foremost challenge is to efficiently represent the coupled compressible fluid dynamics of internal air and surrounding water. Secondly, the method must allow one to accurately detect or follow the interface between the phases. Finally, it must be capable of resolving any shock waves which may be created in air or water during the final stage of the collapse. We present a fully Lagrangian compressible numerical framework for the simulation of underwater implosion. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method [109]. A nodally perfect matched definition of the interface is used [57, 25] and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm), and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in addition to the shock waves traveling in the fluid domains are among the phenomena that are observed in the simulation. We then extend our framework to model the underwater implosion of a cylindrical aluminum container considering a monolithic fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data.El desarrollo de métodos eficientes para modelar la dinámica de implosión presenta varios desafíos. El primero es una representación eficaz de la dinámica del sistema acoplado de aire-agua. El segundo es que el método tiene que permitir una detección exacta o un seguimiento adecuado de la interfase entre ambas fases. Por último el método tiene que ser capaz de resolver cualquier choque que podría generar en el aire o en el agua, sobre todo en la última fase del colapso. Nosotros presentamos un método numérico compresible y totalmente Lagrangiano para simular la implosión bajo el agua. Tanto el aire como el agua se consideran compresibles y las ecuaciones Lagrangianos para la hidrodinámica del choque se estabilizan mediante un método multiescala que es variacionalmente consistente [109]. Se utiliza una definición de interfase que coincide perfectamente con los nodos [57, 25]. Ésta, nos facilita duplicar eficazmente las variables cinéticas como la presión y la densidad en los nodos de la interfase. Con el fin de obtener suficiente resolución alrededor de la interfase, la malla se genera de forma adaptativa y respetando la posición de la interfase. A continuación el método desarrollado se utiliza para simular la implosión bajo el agua de una burbuja cilíndrica del tamaño de un centímetro. Varios fenómenos se han capturado durante el colapso: un ciclo inmediato de colapso-crecimiento de la burbuja que ocurre en un espacio (0.3mm) y tiempo (0.1ms) bastante limitado, aparición de inestabilidades de tipo Rayleigh-Taylor en la interfase y formaron de varias ondas de choque que viajan tanto en el agua como en el aire. Después, seguimos el desarrollo del método para modelar la implosión bajo el agua de un contenedor metálico considerando una interacción monolítica de fluido y estructura. El cilindro de aluminio, que a su vez contiene aire a presión atmosférica y está rodeada de agua en alta presión, se modelando con elementos de lámina de tres nodos y sin grados de libertad de rotación. El cilindro se somete a deformaciones transitorias suficientemente rápidos y enormes hasta llegar a colapsar. Un nuevo modelo elástico de contacto sin considerar la fricción se ha desarrollado para detectar el contacto y calcular las fuerzas en el dominio discretizado entre las superficies medianas de las laminas. Dos esquemas temporales están considerados, uno es implícito utilizando el método de Bossak y otro es explícito utilizando Forward Euler. Al final los resultados de ambos casos se comparan con los resultados experimentales

A compressible Lagrangian framework for the simulation of underwater implosion problems

The development of efficient algorithms to understand implosion dynamics presents a number of challenges. The foremost challenge is to efficiently represent the coupled compressible fluid dynamics of internal air and surrounding water. Secondly, the method must allow one to accurately detect or follow the interface between the phases. Finally, it must be capable of resolving any shock waves which may be created in air or water during the final stage of the collapse. We present a fully Lagrangian compressible numerical framework for the simulation of underwater implosion. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method. A nodally perfect matched definition of the interface is used and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm), and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in addition to the shock waves traveling in the fluid domains are among the phenomena that are observed in the simulation. We then extend our framework to model the underwater implosion of a cylindrical aluminum container considering a monolithic fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data

A variational framework for multi-scale defect modeling in strained electronics and processing of composite materials

With the recent advances in material processing technologies and the introduction of the material genome initiative, material processing has gained an increased level of attention in the research community. Primary challenges in most material processing technologies and specifically in composite materials are the uncertainties concerning the material’s performance under loading whether it be static, dynamic or cyclic. That is due to the variabilities in these technologies that may lead to the formation of defects within the material parts at critical location during processing. This dissertation presents a deterministic defect modeling framework based on a system of variationally consistent formulations that allow for the modeling of the material processing stage and incorporate multi-physics coupling for multi-constituent materials. A stabilized and novel discontinuity capturing formulation is developed to model multi-phase flow of the materials and their defect while sharply capturing the jumps in material properties, material compressibility and kinetic reaction across the multi-phase interfaces. The method is based on employing structured non-moving meshes to solve the Navier-Stokes equations employing a finite element method (FEM) stabilized via the Variational Multiscale Method (VMS). Within VMS framework a discontinuity capturing method is derived that allows for sharp discontinuity capturing of the physical discontinuities of across phases within a single numerical element allowing for highly accurate and discrete representation of the interfacial physical phenomena. In addition, surface tension is incorporated into the formulation to discretely model jumps in the pressure field. The multi-phase interface is evolved employing a stabilized level-set method allowing for intricate motion of the two phases and the discontinuities within the Eulerian mesh. The formulation is then expanded to incorporate discontinuities in the governing system of equations allowing for modeling adjacent compressible-incompressible fluids within a unified formulation. Coupled with the thermal evolution within the constituents of the material and accounting for phase change and mass leading to mass transfer across the interface the materials, kinetic evolution of the material viscosities is modeled at the material points accounting for variability in the flow behavior as a function of kinetic curing. Finally, a previously developed isogeometric FEM method is expanded to model quantum defect evolution of strained electronics and the effect of straining on the electronic properties of these materials. Representative numerical tests involving complex multi-phase flows of physical instabilities, hydrodynamic collapse of bubbles and convective mass transfer along with electronic band-gap structures with strain effects are presented as validations and applications for the framework’s robustness. Finally, the chemo-thermo-mechanical coupling and real-life application is presented via a fully coupled problem involving processing of a composite bracket during the early curing stages

An Improved CFD Tool to Simulate Adiabatic and Diabatic Two-Phase Flows

With increasing computer capabilities, numerical modeling of two-phase flows has developed significantly over the last few years. Although there are two main categories, namely 'one' fluid and 'two' fluid methods, the 'one' fluid methods are more commonly used for tracking or capturing the interface between two fluids. Level set (LS), volume-of-fluid (VOF), front tracking, marker-and-cell (MAC) and lattice Boltzmann (LB) methods are all 'one' fluid methods. It is clear that there is no perfect method; each method has advantages and disadvantages which make it more appropriate for one kind of problem than for others. For instance, a LS method will accurately compute the curvature and the normal to the interface, but tends to loss mass which is physically incorrect. On the other hand, a VOF method will conserve mass up to machine precision, but the computation of the curvature and normal to the interface is not as accurate. In order to minimize the disadvantages of these methods, several authors have used two or more methods together to model two-phase flows. This is the case for the CLSVOF (Couple Level Set Volume Of Fluid) method, where LS and VOF are coupled together in order to better capture the interface. In CLSVOF, the level set function is used to compute the interface curvature and normal to the interface, while the volume of fluid function is used to capture the interface. For two-phase flows in microchannels, surface tension forces play an important role in determining the dynamics of bubbles whereas gravitational forces are generally negligible. Also it is very important to consider the interaction between the boundaries and the fluids by prescribing or computing the correct contact angle between them. The commercial CFD code FLUENT allows the use of static constant angles, or the use of User Defined Functions (UDF) to compute the dynamic contact angles. It is inappropriate to use a static contact angle to model cases involving moving contact lines. For such cases a dynamic contact angle scheme should be implemented. In this study, FLUENT was used to model adiabatic and diabatic, time dependent two-phase flows. Since FLUENT already contains a VOF method, a LS method was implemented and coupled with VOF into FLUENT via UDFs. Furthermore, since the LS function, used to compute the surface tension force, ceases to be a signed distance to the interface even after one time step, a re-initialization equation was solved after each time step. This involved using a fifth order WENO (Weighted Essentially Non Oscillatory) scheme to discretize the space derivatives (otherwise oscillations of the interface occurred), and a first order Euler method for the time integration. In another part of the study, a 3D dynamic contact angle model based on volume fraction, interface reconstruction, and experimentally available advancing and receding static contact angles was also developed and implemented into FLUENT via UDFs. Several validations for the developed CLSVOF method and dynamic contact angle model are presented in this thesis, these includes a static bubble, a bubble rising in a stagnant liquid for Morton numbers ranging from 102 to 10-11, droplet deformation due to a vortex flow field, droplets spreading over a wall under the gravity effect and droplets sliding over a wall due to gravity. These validations demonstrated the high accuracy and the stability of our methods for modeling these phenomena. A heat and mass transfer model was also implemented into the commercial CFD code FLUENT for simulating of boiling (and condensation) heat transfer. Several simulations were presented with water and R134a as working fluids. The influence of the contact angle and the wall superheat was also studied