A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes

In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii) flow in the left ventricle of the heart with either a mechanical or a natural valve. Both examples have in common the two-way interaction of the flow with a deformable interface or a membrane. The interaction potential approach (de Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura, Computational Biomechanics, 2016) with minor modifications can be used to capture the deformation dynamics in both classes of problems. We show that the approach can be used to replicate the deformation dynamics of liquid-liquid interfaces through the use of ad-hoc elastic constants. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as deforming drop in a shear flow or a cross flow. We show that the same potential approach can also be used to study the flow in the left ventricle of the heart. The flow imposed into the ventricle interacts dynamically with the mitral valve (mechanical or natural) and the ventricle which are simulated using the same model. Results from these simulations are compared with ad- hoc in-house experimental measurements. Finally, a parallelisation scheme is presented, as parallelisation is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies on hundreds of distributed memory computing processors

Physical mechanisms governing drag reduction in turbulent Taylor-Couette flow with finite-size deformable bubbles

The phenomenon of drag reduction induced by injection of bubbles into a turbulent carrier fluid has been known for a long time; the governing control parameters and underlying physics is however not well understood. In this paper, we use three dimensional numerical simulations to uncover the effect of deformability of bubbles injected in a turbulent Taylor-Couette flow on the overall drag experienced by the system. We consider two different Reynolds numbers for the carrier flow, i.e. $Re_i=5\times 10^3$ and $Re_i=2\times 10^4$; the deformability of the bubbles is controlled through the Weber number which is varied in the range $We=0.01 - 2.0$. Our numerical simulations show that increasing the deformability of bubbles i.e., $We$ leads to an increase in drag reduction. We look at the different physical effects contributing to drag reduction and analyse their individual contributions with increasing bubble deformability. Profiles of local angular velocity flux show that in the presence of bubbles, turbulence is enhanced near the inner cylinder while attenuated in the bulk and near the outer cylinder. We connect the increase in drag reduction to the decrease in dissipation in the wake of highly deformed bubbles near the inner cylinder

A study of nucleate boiling and critical heat flux with EHD enhancement

The paper describes results from an experimental and theoretical study of the effect of an electric field on nucleate boiling and the critical heat flux (CHF) in pool boiling of R123 at atmospheric pressure on a horizontal wall with a smooth surface. Two designs of electrode (parallel rods and wire mesh) were used. The experimental data exhibit some differences from the data obtained by other researchers in similar experiments on a wall with a different surface finish and with a slightly different design of wire mesh electrode. The hydrodynamic model for EHD enhancement of CHF cannot reconcile the differences. A theoretical model has been developed for the growth of a single vapour bubble on a superheated wall in an electric field, leading to a numerical simulation based on the level-set method. The model includes matching of sub-models for the micro- and macro- regions, conduction in the wall, distortion of the electric field by the bubble, the temperature dependence of electrical properties and free-charge generation. In the present form of the model, some of these effects are realised in an approximate form. The capability to investigate dry-spot formation and wall temperature changes that might lead to CHF has been demonstrated

A General, Mass-Preserving Navier-Stokes Projection Method

The conservation of mass is common issue with multiphase fluid simulations. In this work a novel projection method is presented which conserves mass both locally and globally. The fluid pressure is augmented with a time-varying component which accounts for any global mass change. The resulting system of equations is solved using an efficient Schur-complement method. Using the proposed method four numerical examples are performed: the evolution of a static bubble, the rise of a bubble, the breakup of a thin fluid thread, and the extension of a droplet in shear flow. The method is capable of conserving the mass even in situations with morphological changes such as droplet breakup.Comment: Submitted to Computer Physics Communication

Flow and air-entrainment around partially submerged vertical cylinders

In this study, a partially submerged vertical cylinder is moved at constant velocity through water, which is initially at rest. During the motion, the wake behind the cylinder induces free-surface deformation. Eleven cylinders, with diameters from $D=1.4$ to 16 cm, were tested at two different conditions: (i) constant immersed height $h$ and (ii) constant $h/D$. The range of translation velocities and diameters are in the regime of turbulent wake with experiments carried out for $4500<Re<240 \,000$ and $0.2<Fr<2.4$, where $Re$ and $Fr$ are the Reynolds and Froude numbers based on $D$. The focus here is on drag force measurements and relatively strong free-surface deformation up to air-entrainment. Specifically, two modes of air-entraiment have been uncovered: (i) in the cavity along the cylinder wall and (ii) in the wake of the cylinder. A scaling for the critical velocity for air-entrainment in the cavity has been observed in agreement with a simple model. Furthermore, for $Fr>1.2$, the drag force varies linearly with $Fr$

Numerical simulation of bubbles and drops in complex geometries by using dynamic meshes

CFD techniques are important tools for the study of multiphase flows, because most of the physical phenomena of these flows often happen on space and time scales where experimental methodologies are impossible in practice. Notwithstanding, numerical approaches are limited by the computational power of the present computers. In this sense, small improvements in the efficiency of the simulations can make the difference between an approachable problem and an unapproachable one. The proposal of this doctoral thesis is focused on developing numerical algorithms to optimize the simulations of multiphase solvers based on single fluids formulations, applied on three-dimensional unstructured meshes, in the context of a finite-volume discretization. In particular, the methods developed in the context of this PhD thesis use a conservative level set technique to deal with the multiphase domain. The work has been organized in five chapters and four appendices. The first chapter constitutes an introduction to the multiphase flows and the different approaches used to study them. The core work of the of this PhD thesis is explained throughout chapters two, three, and four. In those chapters, the improvements performed on the multiphase DNS techniques are addressed in detail, providing results comparisons and discussions on the obtained outcomes. After developing the main ideas of the thesis, a final concluding chapter is presented, summarizing the main findings of this research, and pointing out some future work. Finally, the appendices includes some material that can be useful to understand in depth some specific parts of the thesis but, conversely, they are not essential to follow the main thread. As said before, the core work of this thesis is presented throughout chapters two, three and four. In chapter two, four domain optimization methods are formulated and tested. By using these techniques, small domains can be used in rising bubble simulations, thus saving computational resources. These methods have been implemented in a conservative level set framework. Some of these methods require the use of open boundaries. Therefore, a careful treatment of both inflow and outflow boundaries has been carried out. This includes the development of a new outflow boundary condition as a variation of the classical convective outflow. At this point, a study about the sizing of the computational domain has been conducted, paying special attention to the placement of the inflow and outflow boundaries. Additionally, once the methods are formulated, several validation cases are run to discuss the applicability and robustness of each method. The third chapter present a physical study of a challenging problem: the Taylor bubble. By using the most promising technique from those presented in the previous chapter (i.e. the moving mesh method), the problem of an elongated bubble rising in stagnant liquid is addressed here. A transient study on the velocity field of the problem is provided. Moreover, the study also includes sensitivity analyses with respect to the initial shape of the bubble, the initial volume of the bubble, the flow regime and the inclination of the channel. Chapter number four presents an extension of the developed method to simulate bubbles and drops evolving in complex geometries. The use of an immersed boundary method allows to deal with intricate geometries and to reproduce internal boundaries within an ALE framework. The resulting method is capable of dealing with full unstructured meshes. Different problems are studied here to assert the proposed formulation, both involving constricting and non-constricting geometries. In particular, the following problems are addressed: a 2D gravity-driven bubble interacting with a highly-inclined plane, a 2D gravity-driven Taylor bubble turning into a curved channel, the 3D passage of a drop through a periodically constricted channel, and the impingement of a 3D drop on a flat plate.La Mecánica de Fluidos Computacional (CFD) es una importante disciplina para el estudio de flujos multifase. Esto se debe a que, en este tipo de flujos, la mayor parte de los fenómenos físicos ocurren en escalas de tiempo y espacio imposibles de detectar mediante una metodología experimental. Sin embargo, los enfoques numéricos están limitados por la potencia de cálculo de los ordenadores actuales. En este sentido, pequeñas mejoras en la eficiencia de las simulaciones pueden marcar la diferencia entre un problema que puede resolverse mediante CFD o uno que no. En la presente tesis doctoral se propone el desarrollo de varios algoritmos numéricos para optimizar simulaciones de flujos multifase basadas en formulaciones "single fluids", aplicadas en mallas no estructuradas y tridimensionales, en el contexto de discretizaciones "finite-volume". El trabajo se ha organizado en cinco capítulos y cuatro apéndices. El primer capítulo constituye una introducción a los flujos multifase y a los distintos enfoques usados para estudiarlos. El trabajo nuclear de la presente tesis reside en los capítulos tres, cuatro y cinco. En dichos capítulos se presentan las mejoras realizadas en las técnicas de resolución de flujos multifase mediante una metodología "DNS", aportando comparaciones de resultados y discusiones críticas de los resultados obtenidos. Después de desarrollar las ideas centrales de la tesis, se presenta un capítulo final con las conclusiones destacadas de este trabajo, señalando posibles líneas de trabajo futuro. Finalmente, se incluyen varios apéndices con material complementario que puede ser útil para profundizar en algún aspecto concreto del desarrollo, pero que a su vez no es esencial para entender las ideas principales del texto. Como se explica anteriormente, el trabajo central de la tesis se ha desarrollado a lo largo de los capítulos dos, tres y cuatro. En el segundo capítulo se formulan y prueban cuatro métodos de optimización de dominios de cálculo. Mediante la utilización de estos métodos se hace posible usar dominios de cálculo pequeños en problemas de burbujas ascendentes, ahorrando así recursos computacionales. Algunos de estos métodos requieren el uso de fronteras abiertas, por lo que se propone un estudio detallado de las condiciones de contorno de entrada y salida. Esto incluye el desarrollo de una nueva condición tipo "outflow". A continuación se estudia en profundidad el dimensionamiento del dominio de cálculo, prestando una atención especial a la posición de las fronteras de entrada y de salida. Con todo esto, el capítulo se cierra con una comparativa del rendimiento de los distintos métodos propuestos en varios problemas de burbujas ascendentes. El tercer capítulo presenta un estudio físico de un problema clave: la burbuja de Taylor. Usando la técnica con mejor rendimiento del capítulo anterior (es decir, la técnica de malla móvil), se aborda el problema de una burbuja alargada moviéndose en un fluido en reposo. Se lleva a cabo un estudio transitorio de la velocidad del campo fluido. Además, se realizan varios estudios de sensibilidad con respecto a la forma inicial de la burbuja, su volumen inicial, el régimen de flujo y la inclinación del canal. Por último, en el cuarto capítulo se presenta una extensión del método desarrollado para simular gotas y burbujas evolucionando en geometrías complejas. El uso de un método "Immersed Boundary" permite tratar geometrías complejas y reproducir fronteras internas en métodos que utilicen mallas móviles. En este punto, se estudian diversos problemas para validar la formulación propuesta, tanto en geometrías constrictivas como en no constrictivas. En particular, se han resuelto los siguientes problemas: una burbuja 2D interaccionando con un plano inclinado, una burbuja de Taylor 2D girando en un tubo curvo, el ascenso de una gota 3D dentro de un canal corrugado, y el impacto de una gota 3D contra una plaformaPostprint (published version

A simple model of ultrasound propagation in a cavitating liquid. Part II: Primary Bjerknes force and bubble structures

In a companion paper, a reduced model for propagation of acoustic waves in a cloud of inertial cavitation bubbles was proposed. The wave attenuation was calculated directly from the energy dissipated by a single bubble, the latter being estimated directly from the fully nonlinear radial dynamics. The use of this model in a mono-dimensional configuration has shown that the attenuation near the vibrating emitter was much higher than predictions obtained from linear theory, and that this strong attenuation creates a large traveling wave contribution, even for closed domain where standing waves are normally expected. In this paper, we show that, owing to the appearance of traveling waves, the primary Bjerknes force near the emitter becomes very large and tends to expel the bubbles up to a stagnation point. Two-dimensional axi-symmetric computations of the acoustic field created by a large area immersed sonotrode are also performed, and the paths of the bubbles in the resulting Bjerknes force field are sketched. Cone bubble structures are recovered and compare reasonably well to reported experimental results. The underlying mechanisms yielding such structures is examined, and it is found that the conical structure is generic and results from the appearance a sound velocity gradient along the transducer area. Finally, a more complex system, similar to an ultrasonic bath, in which the sound field results from the flexural vibrations of a thin plate, is also simulated. The calculated bubble paths reveal the appearance of other commonly observed structures in such configurations, such as streamers and flare structures