A code for direct numerical simulation of turbulent boundary layers at high Reynolds numbers in BG/P supercomputers

A new high-resolution code for the direct numerical simulation of a zero pressure gradient turbulent boundary layers over a flat plate has been developed. Its purpose is to simulate a wide range of Reynolds numbers from Reθ = 300 to 6800 while showing a linear weak scaling up to 32,768 cores in the BG/P architecture. Special attention has been paid to the generation of proper inflow boundary conditions. The results are in good agreement with existing numerical and experimental data sets.

Direct numerical simulation of statistically stationary and homogeneous shear turbulence and its relation to other shear flows

Statistically stationary and homogeneous shear turbulence (SS-HST) is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, long-term simulations of HST are “minimal” in the sense of containing on average only a few large-scale structures. It is found that the main limit is the spanwise box width, Lz, which sets the length and velocity scales of the turbulence, and that the two other box dimensions should be sufficiently large (Lx ≳ 2Lz, Ly ≳ Lz) to prevent other directions to be constrained as well. It is also found that very long boxes, Lx ≳ 2Ly, couple with the passing period of the shear-periodic boundary condition, and develop strong unphysical linearized bursts. Within those limits, the flow shows interesting similarities and differences with other shear flows, and in particular with the logarithmic layer of wall-bounded turbulence. They are explored in some detail. They include a self-sustaining process for large-scale streaks and quasi-periodic bursting. The bursting time scale is approximately universal, ∼20S−1, and the availability of two different bursting systems allows the growth of the bursts to be related with some confidence to the shearing of initially isotropic turbulence. It is concluded that SS-HST, conducted within the proper computational parameters, is a very promising system to study shear turbulence in general.

Computation of nonlinear streaky structures in boundary layer flow

En esta tesis se integran numéricamente las ecuaciones reducidas de Navier Stokes (RNS), que describen el flujo en una capa límite tridimensional que presenta también una escala característica espacial corta en el sentido transversal. La formulación RNS se usa para el cálculo de “streaks” no lineales de amplitud finita, y los resultados conseguidos coinciden con los existentes en la literatura, obtenidos típicamente utilizando simulación numérica directa (DNS) o nonlinear parabolized stability equations (PSE). El cálculo de los “streaks” integrando las RNS es mucho menos costoso que usando DNS, y no presenta los problemas de estabilidad que aparecen en la formulación PSE cuando la amplitud del “streak” deja de ser pequeña. El código de integración RNS se utiliza también para el cálculo de los “streaks” que aparecen de manera natural en el borde de ataque de una placa plana en ausencia de perturbaciones en la corriente uniforme exterior. Los resultados existentes hasta ahora calculaban estos “streaks” únicamente en el límite lineal (amplitud pequeña), y en esta tesis se lleva a cabo el cálculo de los mismos en el régimen completamente no lineal (amplitud finita). En la segunda parte de la tesis se generaliza el código RNS para incluir la posibilidad de tener una placa no plana, con curvatura en el sentido transversal que varía lentamente en el sentido de la corriente. Esto se consigue aplicando un cambio de coordenadas, que transforma el dominio físico en uno rectangular. La formulación RNS se integra también expresada en las correspondientes coordenadas curvilíneas. Este código generalizado RNS se utiliza finalmente para estudiar el flujo de capa límite sobre una placa con surcos que varían lentamente en el sentido de la corriente, y es usado para simular el flujo sobre surcos que crecen en tal sentido. Abstract In this thesis, the reduced Navier Stokes (RNS) equations are numerically integrated. This formulation describes the flow in a three-dimensional boundary layer that also presents a short characteristic space scale in the spanwise direction. RNS equations are used to calculate nonlinear finite amplitude “streaks”, and the results agree with those reported in the literature, typically obtained using direct numerical simulation (DNS) or nonlinear parabolized stability equations (PSE). “Streaks” simulations through the RNS integration are much cheaper than using DNS, and avoid stability problems that appear in the PSE when the amplitude of the “streak” is not small. The RNS integration code is also used to calculate the “streaks” that naturally emerge at the leading edge of a flat plate boundary layer in the absence of any free stream perturbations. Up to now, the existing results for these “streaks” have been only calculated in the linear limit (small amplitude), and in this thesis their calculation is carried out in the fully nonlinear regime (finite amplitude). In the second part of the thesis, the RNS code is generalized to include the possibility of having a non-flat plate, curved in the spanwise direction and slowly varying in the streamwise direction. This is achieved by applying a change of coordinates, which transforms the physical domain into a rectangular one. The RNS formulation expressed in the corresponding curvilinear coordinates is also numerically integrated. This generalized RNS code is finally used to study the boundary layer flow over a plate with grooves which vary slowly in the streamwise direction; and this code is used to simulate the flow over grooves that grow in the streamwise direction.

Global instability analysis and control of three-dimensional long open cavity flow

The three-dimensional wall-bounded open cavity may be considered as a simplified geometry found in industrial applications such as leading gear or slotted flats on the airplane. Understanding the three-dimensional complex flow structure that surrounds this particular geometry is therefore of major industrial interest. At the light of the remarkable former investigations in this kind of flows, enough evidences suggest that the lateral walls have a great influence on the flow features and hence on their instability modes. Nevertheless, even though there is a large body of literature on cavity flows, most of them are based on the assumption that the flow is two-dimensional and spanwise-periodic. The flow over realistic open cavity should be considered. This thesis presents an investigation of three-dimensional wall-bounded open cavity with geometric ratio 6:2:1. To this aim, three-dimensional Direct Numerical Simulation (DNS) and global linear instability have been performed. Linear instability analysis reveals that the onset of the first instability in this open cavity is around Recr 1080. The three-dimensional shear layer mode with a complex structure is shown to be the most unstable mode. I t is noteworthy that the flow pattern of this high-frequency shear layer mode is similar to the observed unstable oscillations in supercritical unstable case. DNS of the cavity flow carried out at different Reynolds number from steady state until a nonlinear saturated state is obtained. The comparison of time histories of kinetic energy presents a clearly dominant energetic mode which shifts between low-frequency and highfrequency oscillation. A complete flow patterns from subcritical cases to supercritical case has been put in evidence. The flow structure at the supercritical case Re=1100 resembles typical wake-shedding instability oscillations with a lateral motion existed in the subcritical cases. Also, This flow pattern is similar to the observations in experiments. In order to validate the linear instability analysis results, the topology of the composite flow fields reconstructed by linear superposition of a three-dimensional base flow and its leading three-dimensional global eigenmodes has been studied. The instantaneous wall streamlines of those composited flows display distinguish influence region of each eigenmode. Attention has been focused on the leading high-frequency shear layer mode; the composite flow fields have been fully recognized with respect to the downstream wave shedding. The three-dimensional shear layer mode is shown to give rise to a typical wake-shedding instability with a lateral motions occurring downstream which is in good agreement with the experiment results. Moreover, the spanwise-periodic, open cavity with the same length to depth ratio has been also studied. The most unstable linear mode is different from the real three-dimensional cavity flow, because of the existence of the side walls. Structure sensitivity of the unstable global mode is analyzed in the flow control context. The adjoint-based sensitivity analysis has been employed to localized the receptivity region, where the flow is more sensible to momentum forcing and mass injection. Because of the non-normality of the linearized Navier-Stokes equations, the direct and adjoint field has a large spatial separation. The strongest sensitivity region is locate in the upstream lip of the three-dimensional cavity. This numerical finding is in agreement with experimental observations. Finally, a prototype of passive flow control strategy is applied.

Numerical simulation of the upward propagation of a flame in a vertical tube filled with a very lean mixture.

Upwardpropagation of a premixed flame in averticaltubefilled with a very leanmixture is simulated numerically using a single irreversible Arrhenius reaction model with infinitely high activation energy. In the absence of heat losses and preferential diffusion effects, a curved flame with stationary shape and velocity close to those of an open bubble ascending in the same tube is found for values of the fuel mass fraction above a certain minimum that increases with the radius of the tube, while the numerical computations cease to converge to a stationary solution below this minimum mass fraction. The vortical flow of the gas behind the flame and in its transport region is described for tubes of different radii. It is argued that this flow may become unstable when the fuel mass fraction is decreased, and that this instability, together with the flame stretch due to the strong curvature of the flame tip in narrow tubes, may be responsible for the minimum fuel mass fraction. Radiation losses and a Lewis number of the fuel slightly above unity decrease the final combustion temperature at the flame tip and increase the minimum fuel mass fraction, while a Lewis number slightly below unity has the opposite effect.

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.

Coupling time-stepping numerical methods and standard aerodynamics codes for instability analysis of flows in complex geometries

The development of a global instability analysis code coupling a time-stepping approach, as applied to the solution of BiGlobal and TriGlobal instability analysis 1, 2 and finite-volume-based spatial discretization, as used in standard aerodynamics codes is presented. The key advantage of the time-stepping method over matrix-formulation approaches is that the former provides a solution to the computer-storage issues associated with the latter methodology. To-date both approaches are successfully in use to analyze instability in complex geometries, although their relative advantages have never been quantified. The ultimate goal of the present work is to address this issue in the context of spatial discretization schemes typically used in industry. The time-stepping approach of Chiba 3 has been implemented in conjunction with two direct numerical simulation algorithms, one based on the typically-used in this context high-order method and another based on low-order methods representative of those in common use in industry. The two codes have been validated with solutions of the BiGlobal EVP and it has been showed that small errors in the base flow do not have affect significantly the results. As a result, a three-dimensional compressible unsteady second-order code for global linear stability has been successfully developed based on finite-volume spatial discretization and time-stepping method with the ability to study complex geometries by means of unstructured and hybrid meshes

Assessment of Narrow-Body Transport Airplane Evacuation by Numerical Simulation

This paper presents the results obtained with a new agent-based computer model that can simulate the evacuation of narrow-body transport airplanes in the conditions prescribed by the airworthiness regulations for certification. The model, described in detail in a former paper, has been verified with real data of narrow-body certification demonstrations. Numerical simulations of around 20 narrow-body aircraft, representative of current designs in various market segments, show the capabilities of the model and provide relevant information on the relationship between cabin features and emergency evacuation. The longitudinal location of emergency exits seems to be even more important than their size or the overall margin with respect to the prescribed number and type of exits indicated by the airworthiness requirements

Numerical simulation of tangling in jet engine turbines

The numerical analysis of certain safety related problems presents serious difficulties, since the large number of components present leads to huge finite elementmodels that can only be solved by using large and expensive computers or by making rough approaches to the problem. Tangling, or clashing, in the turbine of a jet engine airplane is an example of such problems. This is caused by the crash and friction between rotor and stator blades in the turbine after an eventual shaft failure. When facing the study of an event through numerical modelling, the accurate simulation of this problem would require the engineer to model all the rotor and stator blades existing in the turbine stage, using a small element size in all pieces. Given that the number of stator and rotor blades is usually around 200, such simulations would require millions of elements. This work presents a new numerical methodology, specifically developed for the accurate modelling of the tangling problem that, depending on the turbine configuration, is able to reduce the number of nodes up to an order of magnitude without losing accuracy. The methodology, which benefits from the cyclic configuration of turbines, is successfully applied to the numerical analysis of a hypothetical tangling event in a turbine, providing valuable data such as the rotating velocity decrease of the turbine, the braking torque and the damage suffered by the blades. The methodology is somewhat general and can be applied to any problem in which damage caused by the interaction between a rotating and static piece is to be analysed.

Numerical simulation of Ge solar cells using D-AMPS-1D code

A solar cell is a solid state device that converts the energy of sunlight directly into electricity by the photovoltaic effect. When light with photon energies greater than the band gap is absorbed by a semiconductor material, free electrons and free holes are generated by optical excitation in the material. The main characteristic of a photovoltaic device is the presence of internal electric field able to separate the free electrons and holes so they can pass out of the material to the external circuit before they recombine. Numerical simulation of photovoltaic devices plays a crucial role in their design, performance prediction, and comprehension of the fundamental phenomena ruling their operation. The electrical transport and the optical behavior of the solar cells discussed in this work were studied with the simulation code D-AMPS-1D. This software is an updated version of the one-dimensional (1D) simulation program Analysis of Microelectronic and Photonic Devices (AMPS) that was initially developed at The Penn State University, USA. Structures such as homojunctions, heterojunctions, multijunctions, etc., resulting from stacking layers of different materials can be studied by appropriately selecting characteristic parameters. In this work, examples of cells simulation made with D-AMPS-1D are shown. Particularly, results of Ge photovoltaic devices are presented. The role of the InGaP buffer on the device was studied. Moreover, a comparison of the simulated electrical parameters with experimental results was performed.

Numerical simulation of the transition from densely distributed to localized cracking.

8th International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS8).

Numerical simulation of group combustion of pulverized coal

A mathematical model for the group combustion of pulverized coal particles was developed in a previous work. It includes the Lagrangian description of the dehumidification, devolatilization and char gasification reactions of the coal particles in the homogenized gaseous environment resulting from the three fuels, CO, H2 and volatiles, supplied by the gasification of the particles and their simultaneous group combustion by the gas phase oxidation reactions, which are considered to be very fast. This model is complemented here with an analysis of the particle dynamics, determined principally by the effects of aerodynamic drag and gravity, and its dispersion based on a stochastic model. It is also extended to include two other simpler models for the gasification of the particles: the first one for particles small enough to extinguish the surrounding diffusion flames, and a second one for particles with small ash content when the porous shell of ashes remaining after gasification of the char, non structurally stable, is disrupted. As an example of the applicability of the models, they are used in the numerical simulation of an experiment of a non-swirling pulverized coal jet with a nearly stagnant air at ambient temperature, with an initial region of interaction with a small annular methane flame. Computational algorithms for solving the different stages undergone by a coal particle during its combustion are proposed. For the partial differential equations modeling the gas phase, a second order finite element method combined with a semi-Lagrangian characteristics method are used. The results obtained with the three versions of the model are compared among them and show how the first of the simpler models fits better the experimental results.

Time-resolved evolution of coherent structures in turbulent channels

El objetivo de esta tesis es estudiar la dinámica de la capa logarítmica de flujos turbulentos de pared. En concreto, proponemos un nuevo modelo estructural utilizando diferentes tipos de estructuras coherentes: sweeps, eyecciones, grupos de vorticidad y streaks. La herramienta utilizada es la simulación numérica directa de canales turbulentos. Desde los primeros trabajos de Theodorsen (1952), las estructuras coherentes han jugado un papel fundamental para entender la organización y dinámica de los flujos turbulentos. A día de hoy, datos procedentes de simulaciones numéricas directas obtenidas en instantes no contiguos permiten estudiar las propiedades fundamentales de las estructuras coherentes tridimensionales desde un punto de vista estadístico. Sin embargo, la dinámica no puede ser entendida en detalle utilizando sólo instantes aislados en el tiempo, sino que es necesario seguir de forma continua las estructuras. Aunque existen algunos estudios sobre la evolución temporal de las estructuras más pequeñas a números de Reynolds moderados, por ejemplo Robinson (1991), todavía no se ha realizado un estudio completo a altos números de Reynolds y para todas las escalas presentes de la capa logarítmica. El objetivo de esta tesis es llevar a cabo dicho análisis. Los problemas más interesantes los encontramos en la región logarítmica, donde residen las cascadas de vorticidad, energía y momento. Existen varios modelos que intentan explicar la organización de los flujos turbulentos en dicha región. Uno de los más extendidos fue propuesto por Adrian et al. (2000) a través de observaciones experimentales y considerando como elemento fundamental paquetes de vórtices con forma de horquilla que actúan de forma cooperativa para generar rampas de bajo momento. Un modelo alternativo fué ideado por del Álamo & Jiménez (2006) utilizando datos numéricos. Basado también en grupos de vorticidad, planteaba un escenario mucho más desorganizado y con estructuras sin forma de horquilla. Aunque los dos modelos son cinemáticamente similares, no lo son desde el punto de vista dinámico, en concreto en lo que se refiere a la importancia que juega la pared en la creación y vida de las estructuras. Otro punto importante aún sin resolver se refiere al modelo de cascada turbulenta propuesto por Kolmogorov (1941b), y su relación con estructuras coherentes medibles en el flujo. Para dar respuesta a las preguntas anteriores, hemos desarrollado un nuevo método que permite seguir estructuras coherentes en el tiempo y lo hemos aplicado a simulaciones numéricas de canales turbulentos con números de Reynolds lo suficientemente altos como para tener un rango de escalas no trivial y con dominios computacionales lo suficientemente grandes como para representar de forma correcta la dinámica de la capa logarítmica. Nuestros esfuerzos se han desarrollado en cuatro pasos. En primer lugar, hemos realizado una campaña de simulaciones numéricas directas a diferentes números de Reynolds y tamaños de cajas para evaluar el efecto del dominio computacional en las estadísticas de primer orden y el espectro. A partir de los resultados obtenidos, hemos concluido que simulaciones con cajas de longitud 2vr y ancho vr veces la semi-altura del canal son lo suficientemente grandes para reproducir correctamente las interacciones entre estructuras coherentes de la capa logarítmica y el resto de escalas. Estas simulaciones son utilizadas como punto de partida en los siguientes análisis. En segundo lugar, las estructuras coherentes correspondientes a regiones con esfuerzos de Reynolds tangenciales intensos (Qs) en un canal turbulento han sido estudiadas extendiendo a tres dimensiones el análisis de cuadrantes, con especial énfasis en la capa logarítmica y la región exterior. Las estructuras coherentes han sido identificadas como regiones contiguas del espacio donde los esfuerzos de Reynolds tangenciales son más intensos que un cierto nivel. Los resultados muestran que los Qs separados de la pared están orientados de forma isótropa y su contribución neta al esfuerzo de Reynolds medio es nula. La mayor contribución la realiza una familia de estructuras de mayor tamaño y autosemejantes cuya parte inferior está muy cerca de la pared (ligada a la pared), con una geometría compleja y dimensión fractal « 2. Estas estructuras tienen una forma similar a una ‘esponja de placas’, en comparación con los grupos de vorticidad que tienen forma de ‘esponja de cuerdas’. Aunque el número de objetos decae al alejarnos de la pared, la fracción de esfuerzos de Reynolds que contienen es independiente de su altura, y gran parte reside en unas pocas estructuras que se extienden más allá del centro del canal, como en las grandes estructuras propuestas por otros autores. Las estructuras dominantes en la capa logarítmica son parejas de sweeps y eyecciones uno al lado del otro y con grupos de vorticidad asociados que comparten las dimensiones y esfuerzos con los remolinos ligados a la pared propuestos por Townsend. En tercer lugar, hemos estudiado la evolución temporal de Qs y grupos de vorticidad usando las simulaciones numéricas directas presentadas anteriormente hasta números de Reynolds ReT = 4200 (Reynolds de fricción). Las estructuras fueron identificadas siguiendo el proceso descrito en el párrafo anterior y después seguidas en el tiempo. A través de la interseción geométrica de estructuras pertenecientes a instantes de tiempo contiguos, hemos creado gratos de conexiones temporales entre todos los objetos y, a partir de ahí, definido ramas primarias y secundarias, de tal forma que cada rama representa la evolución temporal de una estructura coherente. Una vez que las evoluciones están adecuadamente organizadas, proporcionan toda la información necesaria para caracterizar la historia de las estructuras desde su nacimiento hasta su muerte. Los resultados muestran que las estructuras nacen a todas las distancias de la pared, pero con mayor probabilidad cerca de ella, donde la cortadura es más intensa. La mayoría mantienen tamaños pequeños y no viven mucho tiempo, sin embargo, existe una familia de estructuras que crecen lo suficiente como para ligarse a la pared y extenderse a lo largo de la capa logarítmica convirtiéndose en las estructuras observas anteriormente y descritas por Townsend. Estas estructuras son geométricamente autosemejantes con tiempos de vida proporcionales a su tamaño. La mayoría alcanzan tamaños por encima de la escala de Corrsin, y por ello, su dinámica está controlada por la cortadura media. Los resultados también muestran que las eyecciones se alejan de la pared con velocidad media uT (velocidad de fricción) y su base se liga a la pared muy rápidamente al inicio de sus vidas. Por el contrario, los sweeps se mueven hacia la pared con velocidad -uT y se ligan a ella más tarde. En ambos casos, los objetos permanecen ligados a la pared durante 2/3 de sus vidas. En la dirección de la corriente, las estructuras se desplazan a velocidades cercanas a la convección media del flujo y son deformadas por la cortadura. Finalmente, hemos interpretado la cascada turbulenta, no sólo como una forma conceptual de organizar el flujo, sino como un proceso físico en el cual las estructuras coherentes se unen y se rompen. El volumen de una estructura cambia de forma suave, cuando no se une ni rompe, o lo hace de forma repentina en caso contrario. Los procesos de unión y rotura pueden entenderse como una cascada directa (roturas) o inversa (uniones), siguiendo el concepto de cascada de remolinos ideado por Richardson (1920) y Obukhov (1941). El análisis de los datos muestra que las estructuras con tamaños menores a 30η (unidades de Kolmogorov) nunca se unen ni rompen, es decir, no experimentan el proceso de cascada. Por el contrario, aquellas mayores a 100η siempre se rompen o unen al menos una vez en su vida. En estos casos, el volumen total ganado y perdido es una fracción importante del volumen medio de la estructura implicada, con una tendencia ligeramente mayor a romperse (cascada directa) que a unirse (cascade inversa). La mayor parte de interacciones entre ramas se debe a roturas o uniones de fragmentos muy pequeños en la escala de Kolmogorov con estructuras más grandes, aunque el efecto de fragmentos de mayor tamaño no es despreciable. También hemos encontrado que las roturas tienen a ocurrir al final de la vida de la estructura y las uniones al principio. Aunque los resultados para la cascada directa e inversa no son idénticos, son muy simétricos, lo que sugiere un alto grado de reversibilidad en el proceso de cascada. ABSTRACT The purpose of the present thesis is to study the dynamics of the logarithmic layer of wall-bounded turbulent flows. Specifically, to propose a new structural model based on four different coherent structures: sweeps, ejections, clusters of vortices and velocity streaks. The tool used is the direct numerical simulation of time-resolved turbulent channels. Since the first work by Theodorsen (1952), coherent structures have played an important role in the understanding of turbulence organization and its dynamics. Nowadays, data from individual snapshots of direct numerical simulations allow to study the threedimensional statistical properties of those objects, but their dynamics can only be fully understood by tracking them in time. Although the temporal evolution has already been studied for small structures at moderate Reynolds numbers, e.g., Robinson (1991), a temporal analysis of three-dimensional structures spanning from the smallest to the largest scales across the logarithmic layer has yet to be performed and is the goal of the present thesis. The most interesting problems lie in the logarithmic region, which is the seat of cascades of vorticity, energy, and momentum. Different models involving coherent structures have been proposed to represent the organization of wall-bounded turbulent flows in the logarithmic layer. One of the most extended ones was conceived by Adrian et al. (2000) and built on packets of hairpins that grow from the wall and work cooperatively to gen- ´ erate low-momentum ramps. A different view was presented by del Alamo & Jim´enez (2006), who extracted coherent vortical structures from DNSs and proposed a less organized scenario. Although the two models are kinematically fairly similar, they have important dynamical differences, mostly regarding the relevance of the wall. Another open question is whether such a model can be used to explain the cascade process proposed by Kolmogorov (1941b) in terms of coherent structures. The challenge would be to identify coherent structures undergoing a turbulent cascade that can be quantified. To gain a better insight into the previous questions, we have developed a novel method to track coherent structures in time, and used it to characterize the temporal evolutions of eddies in turbulent channels with Reynolds numbers high enough to include a non-trivial range of length scales, and computational domains sufficiently long and wide to reproduce correctly the dynamics of the logarithmic layer. Our efforts have followed four steps. First, we have conducted a campaign of direct numerical simulations of turbulent channels at different Reynolds numbers and box sizes, and assessed the effect of the computational domain in the one-point statistics and spectra. From the results, we have concluded that computational domains with streamwise and spanwise sizes 2vr and vr times the half-height of the channel, respectively, are large enough to accurately capture the dynamical interactions between structures in the logarithmic layer and the rest of the scales. These simulations are used in the subsequent chapters. Second, the three-dimensional structures of intense tangential Reynolds stress in plane turbulent channels (Qs) have been studied by extending the classical quadrant analysis to three dimensions, with emphasis on the logarithmic and outer layers. The eddies are identified as connected regions of intense tangential Reynolds stress. Qs are then classified according to their streamwise and wall-normal fluctuating velocities as inward interactions, outward interactions, sweeps and ejections. It is found that wall-detached Qs are isotropically oriented background stress fluctuations, common to most turbulent flows, and do not contribute to the mean stress. Most of the stress is carried by a selfsimilar family of larger wall-attached Qs, increasingly complex away from the wall, with fractal dimensions « 2. They have shapes similar to ‘sponges of flakes’, while vortex clusters resemble ‘sponges of strings’. Although their number decays away from the wall, the fraction of the stress that they carry is independent of their heights, and a substantial part resides in a few objects extending beyond the centerline, reminiscent of the very large scale motions of several authors. The predominant logarithmic-layer structures are sideby- side pairs of sweeps and ejections, with an associated vortex cluster, and dimensions and stresses similar to Townsend’s conjectured wall-attached eddies. Third, the temporal evolution of Qs and vortex clusters are studied using time-resolved DNS data up to ReT = 4200 (friction Reynolds number). The eddies are identified following the procedure presented above, and then tracked in time. From the geometric intersection of structures in consecutive fields, we have built temporal connection graphs of all the objects, and defined main and secondary branches in a way that each branch represents the temporal evolution of one coherent structure. Once these evolutions are properly organized, they provide the necessary information to characterize eddies from birth to death. The results show that the eddies are born at all distances from the wall, although with higher probability near it, where the shear is strongest. Most of them stay small and do not last for long times. However, there is a family of eddies that become large enough to attach to the wall while they reach into the logarithmic layer, and become the wall-attached structures previously observed in instantaneous flow fields. They are geometrically self-similar, with sizes and lifetimes proportional to their distance from the wall. Most of them achieve lengths well above the Corrsin’ scale, and hence, their dynamics are controlled by the mean shear. Eddies associated with ejections move away from the wall with an average velocity uT (friction velocity), and their base attaches very fast at the beginning of their lives. Conversely, sweeps move towards the wall at -uT, and attach later. In both cases, they remain attached for 2/3 of their lives. In the streamwise direction, eddies are advected and deformed by the local mean velocity. Finally, we interpret the turbulent cascade not only as a way to conceptualize the flow, but as an actual physical process in which coherent structures merge and split. The volume of an eddy can change either smoothly, when they are not merging or splitting, or through sudden changes. The processes of merging and splitting can be thought of as a direct (when splitting) or an inverse (when merging) cascade, following the ideas envisioned by Richardson (1920) and Obukhov (1941). It is observed that there is a minimum length of 30η (Kolmogorov units) above which mergers and splits begin to be important. Moreover, all eddies above 100η split and merge at least once in their lives. In those cases, the total volume gained and lost is a substantial fraction of the average volume of the structure involved, with slightly more splits (direct cascade) than mergers. Most branch interactions are found to be the shedding or absorption of Kolmogorov-scale fragments by larger structures, but more balanced splits or mergers spanning a wide range of scales are also found to be important. The results show that splits are more probable at the end of the life of the eddy, while mergers take place at the beginning of the life. Although the results for the direct and the inverse cascades are not identical, they are found to be very symmetric, which suggests a high degree of reversibility of the cascade process.

Numerical Simulation of the Aerodynamic Behavior of High Velocity Trains under Synthetic Crosswinds of Different Shear and Turbulence Characteristics

A numerical simulation of the aerodynamic behavior of high-speed trains under synthetic crosswinds at a 90º yaw angle is presented. The train geometry is the aerodynamic train model (ATM). Flow description based on numerical simulations is obtained using large eddy simulation (LES) and the commercial code ANSYSFluent V14.5. A crosswind whose averaged velocity and turbulence characteristics change with distance to the ground is imposed. Turbulent fluctuations that vary temporally and spatially are simulated with TurbSim code. The crosswind boundary condition is calculated for the distance the train runs during a simulation period. The inlet streamwise velocity boundary condition is generated using Taylor?s frozen turbulence hypothesis. The model gives a time history of the force and moments acting on the train; this includes averaged values, standard deviations and extreme values. Of particular interest are the spectra of the forces and moments, and the admittance spectra. For comparison, results obtained with LES and a uniform wind velocity fluctuating in time, and results obtained with Reynolds averaged Navier Stokes equations (RANS), and the averaged wind conditions, are also presented.

Numerical issues in Lagrangian tracking and topological evolution of fluid particles in wallbounded turbulent flows

The determination of the local Lagrangian evolution of the flow topology in wall-bounded turbulence, and of the Lagrangian evolution associated with entrainment across the turbulent / non-turbulent interface into a turbulent boundary layer, require accurate tracking of a fluid particle and its local velocity gradients. This paper addresses the implementation of fluid-particle tracking in both a turbulent boundary layer direct numerical simulation and in a fully developed channel flow simulation. Determination of the sub-grid particle velocity is performed using both cubic B-spline, four-point Hermite spline and higher-order Hermite spline interpolation. Both wall-bounded flows show similar oscillations in the Lagrangian tracers of both velocity and velocity gradients, corresponding to the movement of particles across the boundaries of computational cells. While these oscillation in the particle velocity are relatively small and have negligible effect on the particle trajectories for time-steps of the order of CFL = 0.1, they appear to be the cause of significant oscillations in the evolution of the invariants of the velocity gradient tensor.