Some Studies on Control Theory Involving Schrodinger Group

In this M.Sc. project we have discussed and obtained some results related to optimal control and stability properties on Schrodinger grou

Particle-laden two-dimensional elastic turbulence

The aggregation properties of heavy inertial particles in the elastic turbulence regime of an Oldroyd-B fluid with periodic Kolmogorov mean flow are investigated by means of extensive numerical simulations in two dimensions. Both the small and large scale features of the resulting inhomogeneous particle distribution are examined, focusing on their connection with the properties of the advecting viscoelastic flow. We find that particles preferentially accumulate on thin highly elastic propagating waves and that this effect is largest for intermediate values of particle inertia. We provide a quantitative characterization of this phenomenon that allows to relate it to the accumulation of particles in filamentary highly strained flow regions producing clusters of correlation dimension close to 1. At larger scales, particles are found to undergo turbophoretic-like segregation. Indeed, our results indicate a close relationship between the profiles of particle density and fluid velocity fluctuations. The large-scale inhomogeneity of the particle distribution is interpreted in the framework of a model derived in the limit of small, but finite, particle inertia. The qualitative characteristics of different observables are, to a good extent, independent of the flow elasticity. When increased, the latter is found, however, to slightly reduce the globally averaged degree of turbophoretic unmixing.Comment: 12 pages, 9 figures. Submitted to EPJ

Enhanced heat transfer in a 2D serpentine micro-channel using elastic polymers

In the presence of elastic forces, even dilute polymer suspensions can exhibit erratic flow fluctuations even when the viscous forces dominate over the inertial forces, which occur at vanishing-low Reynolds numbers (Re). This phenomenon is called Elastic Turbulence (ET). ET can be generated in small-scale laboratory settings and is relevant to enhancing mixing efficiency and heat transfer in microfluidic devices. In this study, we investigate the hydraulic and thermal properties of a dilute polymer solution under ET conditions characterized by inflow conditions of vanishing Re and high Weissenberg numbers (Wi). We carry out extensive direct numerical simulations of the 2D curvilinear channel flow of an Oldroyd-B viscoelastic fluid using Rheotool. We analyze the variations of friction factor and Nusselt numbers along the serpentine channel to reveal the global and local characteristics of ET. Based on Wi, we identify three regimes. First, for 0 < Wi < 3, we observe roughly 10% heat transfer enhancement accompanied by roughly 5% reduction of friction factor compared to laminar flow, known as polymer-induced thermal conductivity enhancement. Second, for 3 < Wi < 5, we observe a sharp linear increase of heat transfer (roughly 30%) at the cost of up to 15% enhanced friction factor. Finally, in the fully developed elastic turbulence regime (Wi > 5), we observe up to 60% heat transfer enhancement accompanied by reduced friction factor. The substantial enhancement of heat transfer with increasing Wi is mainly attributed to the increasing intensity of the elastic instability resulting from the balance between normal stresses and streamlined curvatures

Numerical simulation of two-phase flow in gas diffusion layer and gas channel of proton exchange membrane fuel cells

Liquid water within the cathode Gas Diffusion Layer (GDL) and Gas Channel (GC) of Proton Exchange Membrane Fuel Cells (PEMFCs) is strongly coupled to gas transport properties, thereby affecting the electrochemical conversion rates. In this study, the GDL and GC regions are utilized as the simulation domain, which differs from previous studies that only focused on any one of them. A volume-of-fluid method is adopted to numerically investigate the two-phase flow (gas and liquid) behavior, e.g., water transport pattern evolution, water coverage ratio as well as local and total water saturation. To obtain GDL geometries, an in-house geometry-based method is developed for GDL reconstruction. Furthermore, to study the effect of GDL carbon fiber diameter, the same procedure is used to reconstruct three GDL structures by varying the carbon fiber diameter but keeping the porosity and geometric dimensions constant. The wall wettability is introduced with static contact angles at carbon fiber surfaces and channel walls. The results show that the GDL fiber microstructure has a significant impact on the two-phase flow patterns in the cathode field. Different stages of two-phase flow pattern evolution in both cathode domains are observed. Due to the difference in wettability, the water coverage of the GDL/GC interface is smaller than that of the channel side and top walls. It is also found that the water saturation inside the GDLs stabilizes after the water breakthrough, while local water saturation at the interface keeps irregular oscillations. Last but not the least, a water saturation balance requirement between the GDL and GC is observed. In terms of varying fiber diameter, a larger fiber diameter would result in less water saturation in the GDL but more water in the GC, in addition to faster water movement throughout the total domain

Large Eddy Simulations of Fully-Developed Turbulent Pipe Flows At Moderate-To-High Reynolds Numbers

Despite the high relevance of wall-bounded turbulence for engineering and natural science applications, many aspects of the underlying physics are still unclear. In particular, at high Re close to many real-life scenarios, the true nature of the flow is partially masked by the inability of numerical simulations to resolve all turbulent scales adequately. To overcome this issue, we aim to numerically investigate fully-developed turbulent pipe flows at moderate-to-high Re ($361 \leq Re_\tau \leq 6,000$), employing LES. A grid convergence study, using the WALE subgrid stress model, is presented for $Re_\tau=361$. Additionally, the prediction accuracy of distinct subgrid-scale stress models, such as WALE, SMG, OEEVM, LDKM, and DSEM, is examined using a range of statistical measures. The results infer, as expected, that SMG and OEEVM are too dissipative, whereas WALE, LDKM, and, more surprisingly, DSEM perform rather well compared to experiments and results from DNS. Moreover, LES utilizing WALE are performed and investigated in detail for six different Reynolds numbers in the interval from $Re_\tau = 361$ to $6,000$ with gradually refined grids. These computations allow an insight into what turbulence information is retained when LES with a wall model is applied to such high Reynolds numbers in the limit of a relatively coarse grid. Second-order statistics for all values of $Re_\tau$ exhibited excellent agreement with the DNS data in the outer region. Surprisingly, results also revealed a dramatic deviation from the DNS data in the sub-viscous layer region irrespective of the $Re_\tau$, attributed to the considered scaling for mesh refinement. Overall, the WALE model enabled accurate numerical simulations of high-Reynolds-number wall-bounded flows at a fraction of the cost incurred if the inner layer was temporally and spatially resolved

Turbulence élastique inhomogène chargée de particules

Les expériences de laboratoire montrent que, même dans des solutions très diluées, l’interaction des polymères avec des écoulements fluides peut modifier considérablement les propriétés des écoulements turbulents ou, si l’écoulement est laminaire, peut déclencher un nouveau type de mouvement irrégulier appelé «turbulence élastique». Les écoulements dans un tel régime dynamique sont prometteurs pour améliorer l'efficacité du mélange dans les applications microfluidiques, qui impliquent souvent la présence d'impuretés de taille finie en suspension, telles que des particules solides petites et lourdes. La compréhension de la dispersion des particules dans les écoulements à grand nombre de Reynolds des fluides newtoniens et non newtoniens a déjà été abordée dans des études antérieures, qui ont mis en évidence des effets à la fois à grande et à petite échelle et est un sujet d'intérêt à la fois fondamental et pour des applications environnementales ou industrielles par exemple. Cependant, la dynamique des particules dans les écoulements élastiques et turbulents reste encore peu explorée. L’étude ici vise à étudier les propriétés d’agrégation de particules matérielles ponctuelles (plus lourdes que le fluide porteur) dans les fluides viscoélastiques dans des conditions de turbulence élastique (c’est-à-dire dans le cas de faible inertie du fluide et de grande élasticité). Nous effectuons des simulations numériques directes bi-dimensionelles d’écoulements périodiques avec cisaillement moyen de Kolmogorov avec des solutions de polymères dilués décrites par le modèle Oldroyd-B. Les caractéristiques à petite et grande échelle de la distribution résultante inhomogène de particules sont examinées, en se concentrant sur leur connexion avec la structure sous-jacente de l’écoulement . Notre analyse révèle que les particules sont préférentiellement regroupées dans des régions où les polymères sont instantanément maximalement étirés. L’intensité d’un tel phénomène dépend de l’interaction paramétrée par le nombre de Stokes, entre l’inertie des particules et l’échelle de temps typique associée à l’écoulement de turbulence élastique, et est la plus grande pour des valeurs intermédiaires d’inertie de particules. En particulier, il est montré que la concentration préférentielle de suspensions de particules inertielles dans de tels écoulements ressemblant à la turbulence découle de la nature dissipative de leurs dynamiques. Nous établissons une caractérisation quantitative de ce phénomène (utilisant la corrélation et la dimension de Kaplan-Yorke) qui permet de le relier à l’accumulation de particules dans des régions de l’écoulement filamenteuses fortement déformées produisant des grappes de dimension fractale faiblement supérieure à 1. À plus grande échelle, les particules subissent une ségrégation de type turbophorétique dans la direction non-homogéne de l'écoulement. En effet, nos résultats indiquent que la distribution des particules est fortement liée aux structures moyennes de l’écoulement de type turbulent. En raison de la turbophorèse, les profils de densité moyenne atteignent leur maximum dans les régions où la diffusivité turbulente est la plus faible. L'inhomogénéité à grande échelle de la distribution des particules est interprétée dans le cadre d'un modèle dérivé dans la limite d'inertie des particules, petite mais finie. Les caractéristiques qualitatives de différents observables (telles que L'écart quadratique moyen de la distribution des particules par rapport à la distribution uniforme) sont, dans une large mesure, indépendantes de l'élasticité du l’écoulement. Quand celle-ci est augmentée, on constate cependant que cette dernière diminue légèrement le degré global moyen de mélange turbophorétique.Laboratory experiments show that, even in very dilute solutions, the interaction of polymers with fluid flows can dramatically change the properties of turbulent flows or, if the flow is laminar, can trigger a new sort of irregular motion named “elastic turbulence”. Flows in such a dynamical regime are promising for enhancing mixing efficiency in microfluidic applications, which often involve the presence of suspended finite-size impurities, like small and heavy solid particles. The understanding of particle dispersion in high-Reynolds number flows of Newtonian, as well as non-Newtonian, fluids were addressed by previous investigations, and it is a subject of interest both at a fundamental level and for applications, e.g., environmental or industrial ones. However, the dynamics of particles in elastic turbulent flows are still quite unexplored.The present study aims at investigating the aggregation properties of pointlike material particles (heavier than the carrying fluid) in viscoelastic fluids in elastic turbulence conditions (i.e. in the limit of vanishing fluid inertia and large elasticity). We carry out extensive direct numerical simulations of the periodic Kolmogorov mean shear flow of two-dimensional dilute polymer solutions described by the Oldroyd-B model. Both the small- and large-scale features of the resulting inhomogeneous particle distribution are examined, focusing on their connection with the underlying flow structure. Our analysis reveals that particles are preferentially clustered in regions of instantaneously maximally stretched polymers. The intensity of such a phenomenon depends on the interplay, parametrized by the Stokes number, between the particle inertia and the typical time scale associated with the elastic turbulence flow, and is the largest for intermediate values of particle inertia.In particular, it is shown that the preferential concentration of inertial particle suspensions in such turbulent-like flows follow from the dissipative nature of their dynamics. We provide a quantitative characterization of this phenomenon (using correlation and Kaplan-Yorke dimension) that allows to relate it to the accumulation of particles in filamentary highly strained flow regions producing clusters of fractal dimension slightly above 1.At larger scales, particles are found to undergo turbophoretic-like segregation along the non-homogeneity direction of the flow. Indeed, our results indicate that the particle distribution is strongly related to the mean turbulent-like structures of the flow. As an effect of turbophoresis, average density profiles peak in the regions of lowest turbulent eddy diffusivity. The large-scale inhomogeneity of the particle distribution is interpreted in the framework of a model derived in the limit of small, but finite, particle inertia. The qualitative characteristics of different observables (such as root-mean-square deviation of the particle distribution, relative to the uniform one) are, to a good extent, independent of the flow elasticity. When increased, the latter is found, however, to slightly reduce the globally averaged degree of turbophoretic unmixing

Large eddy simulations of fully developed turbulent flows over additively manufactured rough surfaces

In the last decade, with the growing demand for efficient and more sustainable products that reduce our CO2 footprint, progresses in Additive Manufacturing (AM) have paved the way for optimized heat exchangers, whose disruptive design will heavily depend on predictive numerical simulations. Typical AM rough surfaces show limited resemblance to the artificially constructed rough surfaces that have been the basis of most prior fundamental research on turbulent flow over rough walls. Hence, current wall models used in steady and unsteady three-dimensional (3D) Navier-Stokes simulations do not consider such characteristics. Therefore, a high-fidelity Large Eddy Simulation (LES) database is built to develop and assess novel wall models for AM. This article investigates the flow in rough pipes built from the surfaces created using AM techniques at Siemens based on Nickel Alloy IN939 material. We developed a code to generate the desired rough pipes from scanned planar surfaces. We performed high-fidelity LES of turbulent rough pipe flows at Reynolds number, Re = 11 700, to reveal the influence of roughness parameters on turbulence, mainly the average roughness height and the effective slope. The equivalent sand-grain roughnesses, ks, of the present AM rough surfaces are predicted using the Colebrook correlation. The main contributors to the skin friction coefficient are found to be turbulence and drag forces. In the present study, the existence of a logarithmic layer is marked even for high values of ks. The mean flow, the velocity fluctuations, and the Reynolds shear stresses show turbulence's strong dependence on the roughness topography. Profiles of turbulence statistics are compared by introducing an effective wall-normal distance defined as zero-plane displacement. The effective distance collapses the shear stresses and the velocity fluctuations outside the roughness sublayer; thus, Townsend's similarity of the streamwise mean velocity is marked for the present roughnesses. Furthermore, a mixed scaling is introduced to improve the collapse of turbulence statistics in the roughness sublayer. In addition, an attempt to investigate the impact of surface roughness on flow physics using the acquired LES results based on quadrant analysis of the Reynolds shear stresses and anisotropy of turbulence is made