Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence

We report direct numerical simulation (DNS) and large-eddy simulation (LES) of statistically stationary buoyancy-driven turbulent mixing of an active scalar. We use an adaptation of the fringe-region technique, which continually supplies the flow with unmixed fluids at two opposite faces of a triply periodic domain in the presence of gravity, effectively maintaining an unstably stratified, but statistically stationary flow. We also develop a new method to solve the governing equations, based on the Helmholtz–Hodge decomposition, that guarantees discrete mass conservation regardless of iteration errors. Whilst some statistics were found to be sensitive to the computational box size, we show, from inner-scaled planar spectra, that the small scales exhibit similarity independent of Reynolds number, density ratio and aspect ratio. We also perform LES of the present flow using the stretched-vortex subgridscale (SGS) model. The utility of an SGS scalar flux closure for passive scalars is demonstrated in the present active-scalar, stably stratified flow setting. The multi-scale character of the stretched-vortex SGS model is shown to enable extension of some second-order statistics to subgrid scales. Comparisons with DNS velocity spectra and velocity-density cospectra show that both the resolved-scale and SGS-extended components of the LES spectra accurately capture important features of the DNS spectra, including small-scale anisotropy and the shape of the viscous roll-off

Modeling Artificial Boundary Conditions for Compressible Flow

We review artificial boundary conditions (BCs) for simulation of inflow, outflow, and far-field (radiation) problems, with an emphasis on techniques suitable for compressible turbulent shear flows. BCs based on linearization near the boundary are usually appropriate for inflow and radiation problems. A variety of accurate techniques have been developed for this case, but some robustness and implementation issues remain. At an outflow boundary, the linearized BCs are usually not accurate enough. Various ad hoc models have been proposed for the nonlinear case, including absorbing layers and fringe methods. We discuss these techniques and suggest directions for future modeling efforts

The Extended Görtler-Hämmerlin Model For Linear Instability of Three-Dimensional Incompressible Swept Attachment-Line Boundary Layer Flow

A simple extension of the classic Görtler–Hämmerlin (1955) (GH) model, essential for three-dimensional linear instability analysis, is presented. The extended Görtler–Hämmerlin model classifies all three-dimensional disturbances in this flow by means of symmetric and antisymmetric polynomials of the chordwise coordinate. It results in one-dimensional linear eigenvalue problems, a temporal or spatial solution of which, presented herein, is demonstrated to recover results otherwise only accessible to the temporal or spatial partial-derivative eigenvalue problem (the former also solved here) or to spatial direct numerical simulation (DNS). From a numerical point of view, the significance of the extended GH model is that it delivers the three-dimensional linear instability characteristics of this flow, discovered by solution of the partial-derivative eigenvalue problem by Lin & Malik (1996a), at a negligible fraction of the computing effort required by either of the aforementioned alternative numerical methodologies. More significant, however, is the physical insight which the model offers into the stability of this technologically interesting flow. On the one hand, the dependence of three-dimensional linear disturbances on the chordwise spatial direction is unravelled analytically. On the other hand, numerical results obtained demonstrate that all linear three-dimensional instability modes possess the same (scaled) dependence on the wall-normal coordinate, that of the well-known GH mode. The latter result may explain why the three-dimensional linear modes have not been detected in past experiments; criteria for experimental identification of three-dimensional disturbances are discussed. Asymptotic analysis based on a multiple-scales method confirms the results of the extended GH model and provides an alternative algorithm for the recovery of three-dimensional linear instability characteristics, also based on solution of one-dimensional eigenvalue problems. Finally, the polynomial structure of individual three-dimensional extended GH eigenmodes is demonstrated using three-dimensional DNS, performed here under linear conditions

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

On the wave-cancelling nature of boundary layer flow control

International audienceThis work deals with the feedforward active control of Tollmien–Schlichting instability waves over incompressible 2D and 3D boundary layers. Through an extensive numerical study, two strategies are evaluated; the optimal linear–quadratic–Gaussian (LQG) controller, designed using the Eigensystem realization algorithm, is compared to a wave-cancellation scheme, which is obtained using the direct inversion of frequency-domain transfer functions of the system. For the evaluated cases, it is shown that LQG leads to a similar control law and presents a comparable performance to the simpler, wave-cancellation scheme, indicating that the former acts via a destructive interference of the incoming wavepacket downstream of actuation. The results allow further insight into the physics behind flow control of convectively unstable flows permitting, for instance, the optimization of the transverse position for actuation. Using concepts of linear stability theory and the derived transfer function, a more efficient actuation for flow control is chosen, leading to similar attenuation of Tollmien–Schlichting waves with only about 10% of the actuation power in the baseline case

Fully nonlinear dynamics of parallel wakes

International audienceThe fully nonlinear theory of global modes in open flows, proposed in recent analyses of amplitude equations, is extended to the case of Navier-Stokes equations using direct numerical simulations. The basic flow under consideration is a parallel wake in a finite domain generated by imposing the wake profile at the inlet boundary and by adding a body force to compensate the basic flow diffusion. The link between the global bifurcation, the absolute or convective nature of the local linear instability, and the theory of speed selection for the front separating an unperturbed domain of the flow from a fully saturated solution is elucidated. In particular, thanks to the parallelism of the flow, the bifurcation scenario and the associated scaling laws for the frequency, the healing length, and the slope at the origin predicted by a previous analysis of amplitude equations are recovered with great precision