Three dimensional adaptive method for compressible multi-fluids flows

In this paper, a hexahedral-mesh based solution adaptive algorithm for the simulation of compressible multi-fluid flows is proposed. The data structure, the refinement and coarsening process, and the solution adaptive method are described. The cells with different levels are stored in different lists. This avoids the recursive calculation of solution of mother (non-leaf) cells. Besides, the faces are separated stored into two lists: one for leaf faces and another for non-leaf faces. Thus, high efficiency is obtained due to these features. Numerical results show that there is no oscillation of pressure and velocity across the interface and it is feasible to apply it to solve compressible multi-fluid flows with large density ratio (1000) and strong shock wave interaction with the interface

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 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

Numeričke simulacije stlačivih strujanja sa slobodnom površinom

U ovom radu je prikazan novi numerički pristup za rješavanje kompresibilnih strujanja sa slobodnom površinom. Prikazan je izvod modi ciranih Navier-Stokesovih jednadžbi koje su implementirane u programski paket OpenFOAM. Kao dopunske jednadžbe korištene su izotermalna i izentropska jednadžba stanja za proračun svojstava pojedinih faza. Korišten je volumni udio kako bi se razlikovale pojedine faze. Za praćenje slobodne površine korištena je metoda VOF ("Volume of Fluid"). Također je prikazana diskretizacija jednadžbi matematičkog modela metodom kontrolnih volumena. Kako bi se izračunale primitivne varijable (volumni udio, brzina, dinamički tlak) korišten je odvojeni (eng. "segregated") algoritam koji je baziran na tlaku (eng. "pressure-based"). Odvojeni algoritam se naziva PIMPLE te je dan detaljan pregled njegove implementacije u OpenFOAM-u. Simulacije strujanja sa slobodnom površinom kod kojih se u obzir uzima kompresibilnost jedne ili više faza predstavljaju izazov za numeričko modeliranje. Podvodne eksplozije zasigurno spadaju u tu kategoriju. U tim slučajevima omjer gustoća izmeđžu plinova nakon eksplozije i okolnog fluida su tipično reda veličine O (10 ), a omjeri tlakova mogu biti jednako toliko veliki. U svrhu testiranja robustnosti rješavača u prisutnosti vrlo velikih diskontinuiteta u tlaku i gustoći bilo je potrebno provesti validacijske proračune i utvrditi njihove parametre. Ti proračuni obuhvaćaju duboku eksploziju, eksploziju pod krutom pločom i eksploziju pod slobodnom površinom. Dobiveni rezultati su usporeženi s eksperimentima odnosno drugim numeričkim simulacijama. Kako bi se rješavač dodatno provjerio odabran je slučaj ubrizgavanja tekućeg metala u zatvoreni kalup te su rezultati uspoređeni s literaturom

Numerical Simulations of Bubble Dynamics Near Viscoelastic Media

Cavitation-induced damage occurs in a wide range of applications, including in naval hydrodynamics, medicine, and the Spallation Neutron Source. Local transient pressure decreases in liquid flow may give rise to explosive bubble growth and violent collapse, with shock waves produced at collapse interacting with neighboring solids. Although the mechanisms of erosion to hard, metallic solids can be predicted in relatively simple geometries, damage to soft materials (e.g., elastomeric coatings, soft tissue) or in confined geometries is less well understood. In such problems, the constitutive models describing the medium are non-trivial and include effects such as (nonlinear) elasticity, history (relaxation effects) and viscosity. As a result, the influence of the shock on the material and the response of the material to the shock are poorly understood. To gain fundamental insights into cavitation-induced damage to both soft objects and rigid materials, we develop a novel Eulerian approach for numerical simulations of wave propagation in heterogeneous viscoelastic media. We extend the five-equations multiphase, interface-capturing model, based on the idea that all the materials (gases, liquids, solids) obey the same equation of state with spatially varying properties, to incorporate the desired constitutive relation. We consider problems in which the deformations are small, such that the substances can be described by linear viscoelastic constitutive relations. One difficulty is the calculation of strains in an Eulerian framework, which we address by using a hypoelastic model in which an objective time derivative (Lie derivative) of the constitutive relation is taken to evolve strain rates. The resulting numerical framework is a solution-adaptive, high-order interface-capturing approach for compressible, multiphase flows involving linear viscoelasticity at all speeds. We then utilize this numerical framework to gain fundamental insights into cavitation damage (i) in a confined geometry, (ii) in shock wave lithotripsy, and (iii) to rigid objects covered by an elastomeric coating. We examine the maximum stresses, pressures, and temperatures along/in rigid/compliant objects. We quantify the effect of confinement on an inertially collapsing bubble and determine the appropriate scaling governing the maximum pressures can predicted on the surfaces. We investigate the stresses produced to a model kidney stone due to a shock wave by examining the amplification of tensile stresses in the stone when a gas bubble is present. The impact loads on a polymeric coating relevant to naval engineering applications by shock-induced bubble collapse indicate how pitting and coating material ejection may take place by repeated cavitation events near the surface.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147536/1/mrdz_1.pd

A time splitting projection scheme for compressible two-phase flows. Application to the interaction of bubbles with ultrasound waves

This paper is focused on the numerical simulation of the interaction of an ultrasound wave with a bubble. Our interest is to develop a fully compressible solver in the two phases and to account for surface tension effects. As the volume oscillation of the bubble occurs in a low Mach number regime, a specific care must be paid to the effectiveness of the numerical method which is chosen to solve the compressible Euler equations. Three different numerical solvers, an explicit HLLC (Harten–Lax–van Leer-Contact) solver [48], a preconditioning explicit HLLC solver [14] and the compressible projection method , and , are described and assessed with a one dimensional spherical benchmark. From this preliminary test, we can conclude that the compressible projection method outclasses the other two, whether the spatial accuracy or the time step stability are considered. Multidimensional numerical simulations are next performed. As a basic implementation of the surface tension leads to strong spurious currents and numerical instabilities, a specific velocity/pressure time splitting is proposed to overcome this issue. Numerical evidences of the efficiency of this new numerical scheme are provided, since both the accuracy and the stability of the overall algorithm are enhanced if this new time splitting is used. Finally, the numerical simulation of the interaction of a moving and deformable bubble with a plane wave is presented in order to bring out the ability of the new method in a more complex situation