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The role of capillary pumping on the course of cleaning porous materials containing liquid contam-inants using supercritical fluids was investigated numerically. As a specific process to be modelled, cleaning of porous membranes, contaminated with soybean oil, using supercritical carbon dioxide as the cleaning fluid (solvent) was considered. A 3D pore-network model, developed as an extension of a 2D drying model, was used for performing pore scale simulations. The influence of various process parameters, including the coordination number of the pore network, the computational domain size, and the external flow mass transfer resistance, on the strength of the capillary pumping effect was investigated. The capillary pumping effect increases with increasing domain size and decreasing ex -ter nal flow mass transfer resistance. For low coordination numbers of the pore network, the capillary pumping effect is not noticeable at macro scale, while for high coordination numbers, the opposite trend is observed - capillary pumping may influence the process at macro scale. In the investigated system, the coordination number of the pore network seems to be low, as no capillary pumping effects were observed at macro scale during experimental investigation and macro-scale modelling of the membrane cleaning process., Chemical and Process Engineering, 42 (4)

Capillaries are the prime location for oxygen and nutrient exchange in all tissues. Despite their fundamental role, our knowledge of perfusion and flow regulation in cortical capillary beds is still limited. Here, we use in vivo measurements and blood flow simulations in anatomically accurate microvascular network to investigate the impact of red blood cells (RBCs) on microvascular flow. Based on these in vivo and in silico experiments, we show that the impact of RBCs leads to a bias toward equating the values of the outflow velocities at divergent capillary bifurcations, for which we coin the term “well-balanced bifurcations”. Our simulation results further reveal that hematocrit heterogeneity is directly caused by the RBC dynamics, i.e. by their unequal partitioning at bifurcations and their effect on vessel resistance. These results provide the first in vivo evidence of the impact of RBC dynamics on the flow field in the cortical microvasculature. By structural and functional analyses of our blood flow simulations we show that capillary diameter changes locally alter flow and RBC distribution. A dilation of 10% along a vessel length of 100 μm increases the flow on average by 21% in the dilated vessel downstream a well-balanced bifurcation. The number of RBCs rises on average by 27%. Importantly, RBC up-regulation proves to be more effective the more balanced the outflow velocities at the upstream bifurcation are. Taken together, we conclude that diameter changes at capillary level bear potential to locally change the flow field and the RBC distribution. Moreover, our results suggest that the balancing of outflow velocities contributes to the robustness of perfusion. Based on our in silico results, we anticipate that the bi-phasic nature of blood and small-scale regulations are essential for a well-adjusted oxygen and energy substrate supply., PLoS Computational Biology, 15 (8), ISSN:1553-734X, ISSN:1553-7358

Data has always played an important role in the modeling and simulation of turbulent flows. In the last decade, with the advancement and abundance of measurement techniques, computational resources, and mathematical algorithms, data has been systematically used to develop and improve turbulence models. Experimental measurements, which are generally sparse or of low resolution, can be incorporated into models using mathematical techniques such as variational data assimilation to enable data-driven simulation of turbulent flows. In this project, we investigate different techniques to incorporate sparse data into the turbulence models to obtain the most accurate results possible. Such inverse problems are typically severely ill-posed and the solutions are non-unique. Therefore, in addition to sparse measurements, further information, expert knowledge, or physical constraints should be added to the problem to obtain a reconstructed solution that is smooth, accurate, and physical. We, therefore, impose the linear eddy viscosity (LEV) assumption to reduce the degrees of freedom of the problem and the constraint of positivity of the eddy viscosity. The optimization problem is defined as reducing the discrepancy between the LEV RANS model's solution and the sparse measurement data by tuning a corrective parameter field that results in an optimal eddy viscosity field. The discrete adjoint method is implemented in OpenFOAM to compute the gradients. The case study of flow over periodic hills is chosen for the investigation. We see that the LEV assumption without including further information would lead to irregular, jagged velocity profiles, due to the ill-conditioning and non-uniqueness nature of the problem. Regularization is then introduced to promote regularity and smoothness to the solution. The $L_2$, total variation, and Sobolev gradient regularization methods were employed. We find that physical velocity profiles can be reconstructed using these methods. However, we observe that with each of these regularization methods we cannot accurately reconstruct wall shear stresses, which are important quantities of interest, even if sparse wall shear stress measurement data is assimilated. Therefore, we propose a method called piecewise linear dimension reduction (PLDR). In this method, the parameter field is constrained to be piecewise linear to avoid, in a controlled way, any noise and large fluctuations in the gradients. The results suggest that the PLDR method can provide accurate and smooth velocity profiles as well as wall shear stresses. Next, we investigate a scenario where only sparse wall shear stress measurements are available. We observe that incomplete and not uniformly distributed data cannot be assimilated properly resulting in deteriorated solutions in the free shear flow region. Therefore, we augmented the available data by using the solution of a high-fidelity but computationally efficient model. A loosely coupled hybrid LES/RANS method is proposed, in which an under-resolved LES is coupled with a steady-RANS model. We show that such a method is easy to implement and that it provides an accurate velocity field with less accurate wall shear stresses. The solution of the proposed hybrid LES/RANS method in combination with the sparse wall shear stress measurements was successfully assimilated into a RANS model providing both accurate velocities and wall shear stresses. We can conclude that accurate sparse data-driven simulation is possible if the inverse problem is properly defined such that any available knowledge is incorporated, from adding data from a higher fidelity simulation, constraining the Reynolds stress tensor, and imposing a hard constraint on the positivity of the eddy viscosity, to penalizing noise and non-smoothness, etc. The project thus shows a promising path towards using sparse data-driven simulation for practical applications.

Transit systems are indispensable to the growing urban population. However, severe unforeseen and unprecedented disruptions place planners and operators in a position where typical risk mitigation and reliability improvements cease to provide manageable solutions. Instead, resilience assessment may lead the way towards an alternative perspective on handling disruptions. Firstly, it does not necessarily predispose that incidents are known or predictable. Moreover, it conceptualises that a system will undergo a number of phases during the draw-down and draw-up cycle following an adverse event, that each can be assessed and exploited for system improvements. This resilience perspective has been the premise of this thesis and drove development of computational models for the assessment of possible disruption management and decision-making strategies that remedy the impact of adverse events in transit systems. By taking resilience assessment as a key requirement, computational models need to capture the complete and dynamic draw-down and draw-up cycle during a disruption. At the same time, this thesis emphasizes that system performance ought to be, at least partly, expressed in terms of the inherent level-of-service that a transit system provides to passengers. Any evaluation or optimisation of system planning and operational rescheduling measures thus requires an explicit treatment of passengers and their interaction with the transit system supply. In addition, uncertainties related to variability of demand and supply as well as limited or lack of knowledge about current and future system conditions are prevalent. On the one hand, this means that models need to be able to capture these uncertainties. On the other hand, planning strategies and operational measures need to account and exploit these uncertainties to better cope whenever disruptions impinge on the network. In order to tackle the aforementioned challenges, this thesis starts by analyzing and reproducing the user demand patterns via the development of a static Origin-Destination (OD)-estimation problem for networked transit systems. Time series measurements of the number of passengers entering and exiting at stations are the only observable data. These data are used to infer the missing OD-coefficient matrix, where each coefficient denotes the share of passengers that enter at a specific origin station and are bound to travel to a designated destination station. The proposed solution method is a Bayesian model formulation and Markov Chain Monte Carlo (MCMC) sampling approach to find estimates of the parameter posterior distributions. The method is scalable to instances with hundreds of network nodes and superior over alternative Quadratic Programming (QP) formulations and solutions. In addition, the Bayesian model approach enables the explicit treatment and quantification of uncertainty, which not only provides a means of assessing the reliability of parameter estimates, but also has advantages in model testing and verification. The inference model is demonstrated on the New York City (NYC) subway network to showcase its advantages regarding the robustness to high-dimensional and underdetermined OD-estimation problems. Solving the OD-estimation problem efficiently is a prerequisite for many of the tasks that follow; a main objective of this thesis is to develop a predictive model of the effects of transit system disruptions that can be validated against a real-world system and further be leveraged for alternative design and operational strategy optimisation. Deriving OD-demand estimates for the NYC subway network, which is the reference network of this thesis, is thus a necessary step. This thesis then continues to delineate the development of the agent-based discrete-event simulation model to capture dynamic processes that occur during transit system disruptions. The model is a dynamic transit assignment model that emulates passengers as individual entities (i.e., agents) that interact with the transit system supply network. The agent-based simulation approach enables the generation of heterogeneous passenger agent populations and asynchronous sharing of system and timetable information with these passenger agents. Although targeted towards assessing disruption scenarios, the model is equally suitable for normal, un-disrupted (i.e., nominal) conditions. By expressing each individual passengers' en-route behavior, passenger flows emerge bottom-up, as opposed to the top-down representation of typical transit assignment approaches. The novelty of the proposed model lies with the re-routing module of passenger agents, which accounts for multiple choice options when faced with service disruptions, including the option to terminate a journey early. Moreover, the simulation programme is able to handle multiple local faults and dispatch strategies simultaneously, during which passenger agents can choose to freely re-route their journeys. Furthermore, this thesis applies the developed agent-based simulation model to the NYC subway network. The results are validated against real-world observations of passenger access and egress rates at stations during nominal and disrupted conditions. This validation step establishes is that the simulation model is able to closely capture the real-world observations of passenger egress rates. In addition, the simulation enables high-resolution predictions of passenger movement throughout the network and uncertainty estimates of these predictions. This approach therefore facilitates reliable estimates of crowding and congestion levels on-board trains and at stations. Moreover, the simulation model approximately resolves the changes in passenger access and egress rates at stations following a specific fault event and ensuing service disruption. This fault event occurred on May 9th 2017 and is due to a power outage and resulting signalling defect, halting the operations at a station in the network for one hour. Despite being an isolated local fault, the simulation model reveals that this contingency causes system-wide and long-lasting ripple effects on service level losses and timetable deviations. Therefore, this thesis underlines that demand-supply interaction during disruptions is not limited to local delays and re-routing decisions along a single line, for instance, but instead propagates across the entire network. Seemingly intact and undisrupted network components may thus become unusually stressed and face passenger demand levels that the standard (nominal) timetable and operational schedule are not designed for. By taking as reference the same aforementioned initiating fault that caused the real-world disruption event in the NYC subway network on May 9th 2017, this thesis assesses the potential of intervening rescheduling strategies to partly restore the system service level during and after the disruption. Without any rescheduling interventions, the simulation assumes that services scheduled to run along the blocked segment will stack up until the blockage is cleared. The proposed intervening rescheduling measure short-turns trains nearest to the fault location, thus maintaining train movement upstream of the fault location and covering for the missing opposite direction services. By studying the dynamic response of system-wide link flow levels over a several-hour long time horizon, this thesis points out that this strategy, on average, reduces deviations from the undisrupted link flows. However, it also identifies abnormal and unfavourably high demand levels along certain line corridors that are not directly affected by the fault or rescheduling strategy. It therefore shows that the conceptual abstraction of the resilience draw-down and draw-up cycle of the full network cannot be generalised to individual components of the network. In return, the developed simulation model and decision-making framework can support the identification of balanced intervening rescheduling measures which minimize the potential for creating abnormal conditions in the remaining operational sections of the transit system. Having established that the simulation model is suitable for predicting the immediate and hour-long aftermath of disruption events, a next step is to explore possible remedial strategies for timetable adjustment and rolling stock rescheduling through a structured simulation-based optimisation approach. This approach is deemed suitable for the medium-to-long-term tactical planning phase in railway and metro networks to preemptively assess rescheduling measures, inform contingency plans, identify potential bottlenecks, or prepare component and process redundancies to be swiftly engaged and dispatched when needed during disruptions. The developed agent-based simulation model is therefore coupled to a multi-objective simulation-based optimisation tool known as SOCEMO (Müller, 2017), and applied to a subcomponent of the NYC subway network. A benchmark standard timetable for nominal operations is determined that adjusts the dispatch headways every two hours throughout the day in order to adapt to the daily passenger peak and off-peak demand profiles. The standard timetable optimisation objectives account for level-of-service and rolling stock requirements, where level-of-service is measured in terms of the average travel time of passengers and rolling stock requirements are measured in terms of the number of allocated trains needed to fulfill the standard timetable. Once in place, the benchmark timetable is tested on a scenario that considers multiple track blockages at separate locations in the network. An optimal short-turning strategy is determined, where the set of standard timetable objective functions is extended to also account for passenger inconvenience measured in terms of the number of agents that need re-route to a new destination. The decision variables are the times and locations to short-turn trains along the affected line. The chosen Pareto-optimal short-turning strategy ensures that passengers who reach their intended destinations experience a similar level-of-service as for the standard timetable, and limits the inconvenience to passengers who need to re-route to a new destination or cut their journey short while travelling, all while reducing the number of required trains to uphold the dispatch schedule. This strategy is compared to an ad-hoc strategy of short-turning trains nearest to the fault location, which is also termed on-location short-turning. For the specific disruption scenario under study, on-location short-turning slightly increases level-of-service and reduces passenger inconvenience versus the Pareto-optimal strategy. However, it requires more trains to be dispatched. The exploratory analysis of optimal and on-location short-turning strategies shows that considerable improvements are possible to retain level-of-service and reduce passenger inconvenience, while mitigating severe deviations from the planned rolling stock circulation during a disruption. However, the computationally costly simulation-based optimisation approach is unsuitable for real-time applications. At the same time, it is conjectured that the on-location short-turning strategy is not guaranteed to always utilize available resources most efficiently. Therefore, a control methodology is proposed that is embedded into a real-time flexible rescheduling strategy, denoted as fuzzy short-turning. Under this strategy, trains are variably and flexibly short-turned upstream of a track blockage. The short-turning times and locations are determined from a fuzzy control algorithm that accounts for the incertitude regarding passenger congestion and crowding levels as well as the deviations from the planned rolling stock schedule. The assessment of multiple disruption scenarios with variable durations shows that the fuzzy short-turn control strategy generally abates passenger inconvenience more efficiently, when compared to the on-location short-turning strategy; only in few scenarios does on-location short-turning outperform fuzzy short-turning. The proposed fuzzy control approach is therefore a promising decision support system for disruption management in high-frequency urban transit networks, especially given that its underlying control rules can be verbosely formulated by professional operators. Moreover, it is poised to be compatible with mathematical optimisation formulations for timetable and rolling stock rescheduling. Overall, this thesis achieves to address the three key objectives originally set out: (1) Gaining an understanding of the (re-)distribution of transit system passenger flows during normal and disrupted conditions; (2) Facilitating experimental, close-to-reality testing of various disruptions and operational rescheduling interventions in a controlled and observable environment; and (3) Identifying suitable and tuned vehicle operation and timetable rescheduling strategies that can control the disruption draw-down and draw-up cycle under uncertainty.

Steam turbines hold the largest share of electricity production worldwide. In order to meet growing energy demands, steam turbine designers strive for increased power output, improved efficiency, and longer operational lifespan. Modern steam turbine designs employ large exit annulus area with long blades of up to 60 inches in the last stage of a low-pressure steam turbine in order to achieve these objectives. Increase in last stage blade height introduces supersonic flows in the tip span of the last stage rotor inlet. Such flows are subject to high unsteadiness induced by shock waves. In addition, condensation, droplet formation and unsteady blade loads in the rotor transonic tip region introduce a very complicated flow for numerical computations. Therefore, optimization of blade stacking in the last stage of a transonic low-pressure steam turbine is one of the most delicate and time-consuming parts of the design process. This requires design modifications including blade sweep, lean or twist. The experiments for scaled geometries are nevertheless very expensive and designers have to rely on time accurate computational fluid dynamics. The accuracy of computations is extremely critical in order to guide optimization algorithms and designers to the most viable design. The time-accurate computations are an order of magnitude more expensive than steady state. During design optimization, detailed geometrical features are excluded in order to achieve realistic computational runtime at the cost of accuracy. The geometrical features mostly excluded are hub-tip cavities, seals, part span snubbers, full span shroud, blade count modification or exclusion of upstream or downstream stages. Full-scale multi-stage model with all-inclusive geometrical features results in very large meshes of up to one billion mesh nodes. The proposed meshes must have matching block interfaces throughout the mesh in order to keep a second-order accuracy in space and time posing additional requirements of a very fine mesh in order to resolve high blade twist, shroud connections, and cavities-seals in the flow path. In the case of low-pressure steam turbines, the steam transition from superheated to condense in penultimate and last stages. This necessitates the inclusion of steam modeling at the least for the prediction of wetness as well as numerical accuracy. This results in additional computational resource requirements posing a very challenging computing problem. The recent widespread use of modern general-purpose graphics processing units (GPUs) for scientific computing provides a possibility to scale time-accurate computational fluid dynamic solvers for such challenging problems. A steady decline in graphics processing unit costs and at the same time improvements in throughput and onboard memory gradually allow hybrid high performance computing cluster as a viable option for the design engineering process. The key objective of this work is to improve the aerodynamic efficiency of a modern low-pressure steam turbine, using carefully tailored stator stacking, numerically on a cluster of GPUs and explain underlying time-resolved flow mechanisms. For this purpose, in-house Unsteady Reynolds Averaged Navier-Stokes (URANS) solver MULTI3 is developed for multi-GPU supercomputing clusters with additional equilibrium steam modeling, able to handle full-scale model. In this work, the typical scale of about 386 million mesh nodes for a full annular four-stage model running on 114 Pascal P100 GPUs with time-resolved equilibrium steam modeling is reported with a convergence run-time of less than a week. For design optimization, a typical scale of 57 million mesh nodes including tip-cavities and seals for the last two stages is achieved within a week of run-time on 17 GPUs. Last two-stage computational model of 16.9 million mesh nodes excluding tip cavities converge within 21 hours of reported runtime on two GPUs. Further, a key understanding is developed on computational accuracy versus cost with each geometrical or modeling approximation and guidelines are proposed for a suitable compromise of numerical approximation in a low-pressure steam turbine design optimization process. The results show the transonic tip region as the main source of entropy loss in the last stage of the transonic low-pressure steam turbine. The proposed stator stacking with an increase in tip axial gap (forward curved sweep) and throat-to-pitch ratio variation designs show aerodynamic total-to-total efficiency improvements of up to 1.3% and 1.1% respectively. The key improvements are seen in supersonic flow expansion in the last stage rotor tip driven by a reduction of relative inlet Mach. The flow unsteadiness in the transonic stator-rotor tip gap is primarily driven by leading edge bow shock, however as found in this work, also depends on the axial gap. Despite an increase in unsteadiness by the closing throat (stator twist design) in the last stage stator tip, a decrease in relative Mach improves efficiency by improvements in the flow expansion in the supersonic rotor tip airfoils. The control of throat-to-pitch ratio is found to be the most effective way to control reaction variation and mass flow redistribution in both the stator and rotor. The analysis shows that at least penultimate stage is compulsory in the computational model along with tip cavities and seals for the last stage optimization as any change in throat area as a result of stacking modification introduce a change in stage pressure ratio, workload, and reaction for both stages.

The fully implicit (FI) method is widely used for numerical modeling of multiphase flow and transport in porous media. It entails iterative linearization and solution of fully-coupled linear systems with mixed elliptic/hyperbolic character. However, in methods that treat the near-elliptic (flow) and hyperbolic (transport) parts separately, such as multiscale formulations (Jenny et al., JCP 2003, Møyner and Lie, JCP 2016), sequential solution strategies are used to couple the flow (pressures and velocities) and the transport (saturations / compositions). SFI schemes solve the fully coupled system in two steps: (1) Construct and solve the pressure equation (flow problem). (2) Solve the coupled species transport equations for the phase saturations and phase compositions. In SFI, each outer iteration involves this two-step sequence. Here, we propose a new SFI variant based on a nonlinear overall-volume balance equation. The first step consists of forming and solving a nonlinear pressure equation, which is a weighted sum of all the component mass conservation equations. The resulting pressure field is used to compute the total-velocity. The second step of the new SFI scheme entails introducing the overall-mass density as a degree-of-freedom, and solving the full set of component conservation equations cast in the natural-variables form (i.e., saturations and phase compositions). During the second step, the pressure and the total-velocity fields are fixed. The SFI scheme with a nonlinear pressure extends the SFI approach of Jenny et al. (JCP 2006) to multi-component compositional processes with interphase mass transfer. We analyze the `splitting errors' associated with the compositional SFI scheme, and we show how to control these errors in order to converge to the same solution as the FI method. We also show that phase-potential upwinding is incompatible with the total-velocity formulation of the fluxes, which is common in SFI schemes. We observe that in cases with strong capillary pressure or gravity, it is possible to have flow reversals. These reversals can strongly affect the convergence rate of SFI methods. We employ phase upwinding (PU) as well as a new hybrid upwinding (HU) scheme. HU determines the upwinding direction differently for the viscous, capillary pressure and buoyancy terms in the phase velocity expression. The use of HU leads to a consistent SFI scheme in terms of both pressure and compositions, and it improves the SFI convergence significantly in settings with strong capillarity and/or buoyancy. Finally, we use the multiscale restriction-smoothed basis (MsRSB) method (Møyner and Lie, JCP 2016) for the parabolic pressure operator. This sequential scheme then allows the design of robust numerical methods that are optimized for the sub-problems of flow and transport. Thus, we strongly recommend using this SFI method for sequential formulations in general, and multiscale formulations in particular.

The topic of this thesis is the analysis and parallel implementation of the Fokker-Planck-DSMC algorithm for the numerical simulation of rarefied gas flows. The most established method for this task is the Direct Simulation Monte Carlo (DSMC) technique. For gas flows in the near-continuum regime, however, its computational cost becomes intractable due to the high number of collisions of (computational) particles that need to be computed. The Fokker-Planck (FP) algorithm, on the other hand, provides accurate numerical predictions for near-continuum gas flows at computational cost independent of the number of collisions. In this method, the trajectories of the computational particles evolve independently along continuous stochastic paths. Since both DSMC and the FP algorithm are stochastic particle methods sharing the same underlying structure, they may be coupled seamlessly: the resulting FP-DSMC algorithm is capable of simulating rarefied gas flows from the near-continuum to the fully rarefied regime. One result of this thesis is a flexible, yet computationally efficient simulation software, which uses both distributed- and shared-memory parallelization to exploit state-of-the-art high-performance computer cluster technologies. It provides the means to conduct computer simulations of flows of diatomic, rarefied gases in complex domains, using many computational particles. The new implementation is used to analyze the accuracy and performance of the FP-DSMC algorithm by means of a variety of simulations. It is shown that given a limited amount of computational resources, using FP-DSMC can provide more accurate results at lower computational cost compared to pure DSMC. Further, the implementation is capable of performing automatic local mesh refinement, as well as parallel load balancing. This is achieved by choosing space-filling curves (SFCs) as a fundamental concept for the ordering of the computational mesh and particle data. SFCs not only allow for an elegant implementation of these features, but have the additional benefit of ensuring cache-friendly computations. The impact on computational performance of using different space-filling curves is analyzed numerically, and the implementation is demonstrated to deliver accurate simulation results for a relevant test case. In order to maximize the efficiency gains due to the FP-DSMC algorithm, the computational mesh should be locally adapted to the flow gradients. With this goal in mind, a general theoretical framework for the estimation of mixed partial derivatives of statistics of scattered data is developed based on the concept of kernel density estimation. The new approach allows for the computation of flow gradients locally in each cell of the mesh as a simple weighted sum of the particle states, and may prove useful beyond the scope of rarefied gas flow simulations.

Many problems in science and engineering are driven by time-periodic forces. In fluid dynamics, this occurs for example in turbines, rotors or in human blood flow. These problems are described by the Navier–Stokes equations. The traditional way to solve them is to use a time-stepping method and compute the whole transitional phase until the time-periodic steady state is reached. We are using a different approach. We model directly the steady state by using periodic boundary conditions in time. This results into time-periodic Navier–Stokes equations. We use two different ways to discretize these equations in time. One way is to use a truncated Fourier series to represent the solution. The equations are then discretized by a spectral Galerkin method. The other way is to use the finite difference method in time. Both temporal discretization are accompanied by spatial finite differences in space. We solve the resulting nonlinear space-time problem with a Picard iteration method. A linear system of equation has to be solved in each Picard iteration. This linear system is solved by preconditioned Krylov methods. We provide problem specific preconditioners. For the spectral in time method, we use a block-tridiagonal preconditioner. The (1, 1) block is a diagonal approximation of the multi-harmonic convection-diffusion matrix. The (2, 2) block is an approximation of the Schur complement based on a commutator. For the finite differences in time, we use a geometric multigrid method with a space-time box smoother. The described discretizations and solvers have been implemented in a templated C++ library. This library is very flexible and uses the message passing interface (MPI) to parallelize the space-time problems. The parallelization is done in space and time. We applied the spectral in time method to various problems. A Rayleigh streaming has been computed to test the preconditioner of the linear solvers. A Taylor–Green vortex has been computed to compare the spectral in time method with a traditional time-stepping method. A channel flow with an oscillating obstacle has been computed to evaluate the parallel performance in time. A time-periodically disturbed swept Hiemenz flow has been computed to test the solver for turbulent flows. Such turbulent flows are not purely time-periodic. Only its statistics are time-periodic.

Membrane-based processes are regarded as sustainable replacement to traditionally used energy-intensive gas separation methods. The preferred membrane material should be able to operate at harsh separation condition, demonstrate high permeance and selectivity to minimize compression energy and separation stages. Continuous research has been focused on developing more permeable, selective and durable membranes. It is a common belief that membranes facilitate better process efficiency with higher permeance, which can be possibly achieved at lower thicknesses. Developments in the nanotechnology research area enabled researchers to fabricate sub -1000 nm thick membranes. However, it is yet unclear, how gas permeance and selectivity vary in the ultra-thin materials in comparison to their bulk value, especially in the sub-100 nm regime of thickness. To date, fabrication of defective films obstructs drawing solid conclusion regarding transport phenomena in ultra-thin regime of thickness. Here, gas transport and separation are investigated through two types of ultra-thin membrane materials: 1. Dense polymers down to 20 nm thickness. 2. Porous layers as thin as single-atom-thick graphene. Gas transport is studied in semi-crystalline and fully amorphous, liquid-like polymers. In a first-time demonstration, semi-crystalline polyamide/imide nanofilms are synthesized at the vapor-liquid interface over CNT-buckypaper and also porous graphene scaffolds in a lab scale. Amorphous oligomeric layers are synthesized via stage-wise physical vapor deposition on a porous support. Gas permeance in the semi-crystalline layers is defined by Fickian diffusion and shows a maximum at the intermediate thickness of 30 nm. Reducing the thickness decreases the diffusion length, but at the same time would decrease the diameter of the diffusion path leading to formation of the maximum. In thin, amorphous, liquid-like polymer layers, the entrance event to the matrix imposes impedance as significant as Fickian diffusion through the matrix. At a certain critical length, entrance event would define completely the transport rate. Thus, the permeance might not necessary increase by reducing the thickness of the dense polymers at the ultra-thin regime. In addition to thickness, pore diameter is another influencing factor in gas transport through microporous material. Investigation of gas transport through zero-thick porous graphene revealed the pore size dependency of permeance and selectivity in the transition regime between free molecular and collective flow, explained by intermolecular collision between gases at the entrance of the pores. In a further investigation, controlled vapor deposition of amorphous polymer on the porous support enabled capturing two distinguished transitions from collective transport toward solution-diffusion mechanism. The fabricated polymer-graphene nanofilms demonstrate two orders of magnitude higher permeance than the-state-of-the-art membranes. The polymer-CNT nanofilms benefit from antiplasticization property due to the confinement of the polymer chains and interaction between the polymer and scaffold, which makes these films attractive for harsh separation condition of hydrocarbons separation. Application of the fabricated membranes is extended beyond the typical gas separation focus. The fabricated nanofilms are used to generate power through the first-time lab scale demonstration of gas osmosis physic. Fast transport through the fabricated nanofilms resulted in capturing gas phase concentration polarization phenomenon adjacent to the membrane surface, which can reduce the membrane process selectivity. This phenomenon rationalizes developing mixing strategies and membrane module design to minimize concentration polarization and gain maximum performance out of highly permeable membranes. The present thesis demonstrates novel methods to synthesize ultra-thin membranes as platforms to study gas transport and separation in the ultra-thin regime of thickness, as well as membrane films for high performance gas separation and power generation applications.

The brain is vital for every human being and consequently its functioning is a highly relevant research topic. Furthermore, it is one of the organs with the highest energy demand in the human body. To be more precise 25% of the body’s energy is consumed in the brain. This is a remarkable amount, if we keep in mind that the brain makes up for only 2% of the whole body weight. For the brain’s functioning a sustained supply of nutrients is essential. Nonetheless, the brain’s energy storage capabilities are limited and to deliver sufficient nutrients a robust perfusion with blood is crucial. Additionally, the energy demand of different brain areas is fluctuating in response to higher neuronal activity. It is well-established that the cortical vasculature is able to adapt to those changes and to locally up-regulate blood flow. However, the precise regulation mechanisms are not yet fully understood. The aim of this thesis is to improve our understanding of cerebral blood flow, its regulation as well as the underlying cortical vasculature. For this purpose a numerical framework has been developed, which simulates blood flow in realistic microvascular networks. Our approach has the specific feature that it tracks individual red blood cells and thus is a close representation of blood flow in vivo. We demonstrate that this aspect is crucial, because the red blood cell distribution strongly influences the flow field and vice versa. Our investigations are performed in realistic microvascular networks from the mouse parietal cortex. In order to improve our understanding of the flow and pressure field various network and flow characteristics are computed. Our analysis focuses on layer-specific characteristics and differences between vessel types. Moreover, the impact of vasodilations on the flow field are studied. In summary, we demonstrate how our numerical framework can be applied to perform representative simulations in realistic microvascular networks. We reveal important features of the flow in the microvasculature and point towards relevant topics for future research.

Oxygen supply to cells by the cardiovascular system involves multiple physical and chemical processes that aim to satisfy fluctuating metabolic demand. Regulation mechanisms range from increased heart rate to minute adaptations in the microvasculature. The challenges and limitations of experimental studies in vivo make computational models an invaluable complement. In this thesis, oxygen transport from capillaries to tissue is investigated using a new numerical model that is tailored for validation with experimental data. On this basis, theoretical analyses of tissue oxygenation and intravascular oxygen distribution are conducted with applications to blood flow regulation mechanisms and heterogeneity in microvascular networks. The computational model developed here employs moving red blood cells (RBCs) in the frame of reference of the tissue. This key feature enables direct result comparison to oxygen measurements in capillaries and tissue. Thus, the first model validation with micrometric-resolution measurements of oxygen partial pressure (PO2) in vivo could be performed. This novel technique is used to describe the complex relation between hemoglobin saturation and plasma PO2 which manifests itself by the presence of erythrocyte-associated transients. Dynamic regulation mechanisms of microvascular blood flow in the brain were modeled. The effect of individual pericyte-induced capillary dilations was investigated in a simple capillary network. Although a slight increase in tissue PO2 was observed, multiple dilations need to simultaneously occur to produce a response comparable to the effect of arteriolar dilations. The dependence of tissue oxygenation on hematocrit and blood velocity was also described. Based on analytical tools supported by the computational model, the relative influence of hematocrit was demonstrated to be stronger. The complex topology of microvascular networks entails a certain degree of heterogeneity in oxygen supply. Excessive variations in RBC transit times through the microvasculature have been associated to conditions such as diabetes, Alzheimer’s disease and hypertension. Their relation with hemoglobin saturation heterogeneity was modeled based on the computational and analytical tools developed here. Diffusive interaction within and between capillaries was shown to lead to a considerable reduction of hemoglobin saturation heterogeneity at the scale of neighboring capillaries. These findings may substantially affect the interpretation of RBC transit time measurements in health and disease. The state-of-the-art technique for high-resolution oxygen measurements in vivo is currently two-photon phosphorescence lifetime microscopy (2PLM). To address uncertainties related to photochemical consumption of oxygen, a numerical model for 2PLM that includes oxygen diffusion and removal by organic molecules was devised. The ensuing potential underestimation of PO2 can be quantified, thereby allowing to choose experimental parameters to avoid systematic errors and photodamage of the region of interest. This model, along with the rest of this thesis, considerably improves the synergy between theoretical modeling and experimental studies in the context of microvascular oxygen transport.

The lattice Boltzmann method (LBM) is a modern and highly successful approach to computational fluid dynamics based on a fully discrete kinetic equation and offers an attractive alternative to direct discretizations of the macroscopic continuum equations. However, the original single relaxation-time formulation (LBGK) was plagued by numerical instabilities and prevented the simulation of highly turbulent flows unless prohibitively high resolutions were employed. A number of improvements and variations of LBM attempted to alleviate this issue. In particular, the multiple relaxation-times methods (MRT) take advantage of the additional degrees of freedom in the LBM kinetic system in order to stabilize the solution and improve accuracy. However, the introduction of additional tunable constants must be chosen appropriately depending on the physics and the flow at hand and are not universal, and thus, the problem of stability could not be solved consistently. With the inception of the entropic lattice Boltzmann method (ELBM) which reintroduced the discrete-time equivalent of Boltzmann's H-theorem, the application range has grown widely not only for incompressible turbulent flows, but also for thermal flows, two-phase systems with non-ideal equations of state and has made the simulation of compressible and high Mach number flows possible. The ELBM, however, comes at the price of introducing a fluctuating viscosity. The main result of this thesis is the development of a new class of entropic MRT models which combine the salient advantages from MRT and ELBM while trying to circumvent their respective disadvantages. J. W. Gibbs' seminal prescription for constructing optimal states by maximizing the entropy under pertinent constraints is used to derive a novel lattice kinetic theory and the the notion of modifying the viscosity to stabilize sub-grid simulations is challenged in this kinetic framework. By exploiting the degrees of freedom of MRT and by compliance to the discrete-time H-theorem, the advantages of both MRT and ELBM can be retained and the problems of parameter tuning and fluctuating viscosity can be solved. The resulting models are accurate, adaptive, parameter-free, efficient and, more importantly, very stable The entropic MRT models are studied extensively for two- and three- dimensional benchmark simulations at turbulent conditions and compared to experiments, theory and other numerical methods. While the entropic MRT models yield the same results as the LBGK in the resolved limit, and converge towards the Navier-Stokes equations with second-order accuracy, sufficiently accurate results are obtained also at coarse resolutions without the use of sub-grid turbulence models. This made the simulation of high Reynolds number flows with complex boundaries possible which are most relevant for engineering applications. Due to the general nature of the entropic MRT methods, a number of extensions beyond the incompressible low Mach number regimes were explored and extensions for thermal flows and two-phase flows are presented. Moreover, a novel model for miscible binary mixtures is presented in combination with the entropic MRT collision step. The salient features of this model are the lack of interpolation and the use of thermal multi-speed lattices to account for the different sound speed of the two unequally heavy substances involved. Independent adjustment of the diffusion coefficient and kinematic viscosity of the mixture is assured and the diffusion follows the Stefan-Maxwell model. To conclude it is shown that entropy maximisation principle can be extended to multiple relaxation-time lattice Boltzmann models to create more stable and computationally efficient LBM models. This principle of entropy maximization is applied without nominal modification of viscosity and is extended to not only high Reynolds number flows but also thermal, mixture and multi-phase flows. This principle is also shown to be lattice independent and generic nature thus opening a possibility of new class of LB models that are more robust to under-resolution and have a wide range of applications.

The combustion and heat transfer characteristics of catalytic microreactors fueled by hydrogen and hydrogen-rich mixtures are investigated for power generation applications. Moreover, the fundamental hetero-/homogeneous combustion properties of such reactive mixtures are studied both experimentally and numerically. In particular, the combustion stability limits of hydrogen in platinum-coated microchannels, the onsite production of hydrogen fuel via catalytic partial oxidation (CPO) of methane for microreactors, and the hetero-/homogeneous kinetic interactions in the combustion of hydrogen over platinum are addressed. To examine the combustion and heat transfer characteristics of microreactors for power generation, a catalytic microreactor made of SiC with dimensions 30×30×4 mm^3 was designed, constructed and tested. Surface temperatures were measured with an infrared (IR) camera, exhaust compositions were analyzed with a micro gas chromatograph, while simulations were carried out with a newly built 3-D code that included conjugate heat transfer, external heat losses, and detailed hetero-/homogeneous chemistry. Fundamental kinetic studies were subsequently performed experimentally in the high-pressure optically-accessible channel flow catalytic reactor at the Combustion Fundamentals Group of Paul Scherrer Institute and numerically using a 2-D reactive CFD code with detailed hetero-/homogeneous chemical reaction schemes and transport. Raman measurements of major gas phase species concentrations assessed the heterogeneous combustion processes, while planar laser induced fluorescence (LIF) of radical species determined the onset of homogeneous ignition. Combustion of fuel lean H2/air mixtures in the catalytic microreactor was studied at equivalence ratios 0.25-0.50 and inlet velocities 15-50 m/s. Higher mass throughputs reduced the surface temperature spatial non-uniformities, while the onset of gaseous combustion lowered the catalyst surface temperatures. Different channel configurations were tested for optimum temperature uniformity. Counterflow configurations were shown superior to the coflow configuration in attaining better surface temperature spatial uniformities. Comparisons of measurements and predictions were very favorable in terms of temperature probability density function (PDF) shapes and higher distribution moments. Radiation efficiencies increased with increasing inlet velocity and equivalence ratio. Application of the microreactor to power generation systems, in conjunction with thermoelectric devices, appeared quite promising given the high values of surface temperatures (up to 1311 K, the highest reported in the literature for catalytic microreactors with sizes of a few cm) and the attained good spatial uniformity (less than 20 K standard deviations). The catalytic combustion in the microreactor was further studied using fuel lean H2/CO/air and H2/CH4/air mixtures. The diverse transport, kinetic and thermodynamic properties of the H2, CO and CH4 fuels gave rise to rich combustion phenomena. H2/CO mixtures yielded lower wall temperatures compared to undiluted H2. Although CO had a high catalytic reactivity when combusting in H2/CO mixtures, its larger than unity Lewis number did not allow for the attainment of high surface temperatures. Mixtures of H2/CH4 were the least attractive due to the substantially lower catalytic reactivity of CH4. To demarcate stable combustion operating regimes for the microreactor, the hetero-/homogeneous combustion and stability limits of fuel-lean H2/air mixtures (φ = 0.40) were investigated numerically in a platinum coated planar microchannel. Two pressures and two solid thermal conductivities were examined, while stability maps were constructed in terms of the critical extinction heat transfer coefficient h_cr versus inlet velocity U_IN (or mass throughput). For a given solid thermal conductivity, there existed a crossover mass throughput above (below) which the stability envelope was broader at 5 bar (1 bar), originating from a shift in the pressure dependence of the catalytic reactivity of H2. The stability limits of H2 were solely determined by the catalytic chemistry, as it sustained combustion at temperatures down to 320-380 K. Critical extinction heat transfer coefficients for H2 were three to four orders of magnitude higher than those reported for CH4 and C3H8 fuels. Fundamentals of H2/air combustion over platinum have been studied. The hetero-/homogeneous combustion of fuel rich H2/O2/N2 mixtures (φ = 2.5-6.5) was investigated at pressures 1-14 bar. Planar laser induced fluorescence (LIF) of OH at pressures below ~5 bar and of hot O2 at pressures above ~5 bar, was applied to determine the onset of homogeneous ignition. The agreement between measured and predicted homogeneous ignition distances validated the aptness of the employed hetero-/homogeneous chemical reaction mechanisms. Analytical homogeneous ignition criteria revealed that the catalytic reaction pathway introduced a scaling factor 1/p to the homogeneous ignition distances. Moreover, the hetero-/homogeneous combustion of fuel-lean H2/O2/N2 mixtures (φ = 0.20-0.28) was also studied in the narrow pressure range 1 to 3.5 bar where microreactors generally operate. It was found that pressures above 2 bar led to increased safety against homogeneous ignition. This pressure dependence is the opposite to the foregoing dependence at fuel-rich stoichiometries, whereby rising pressures promote the onset of homogeneous ignition. To better understand the onsite hydrogen production for microreactors via CPO of CH4, the heterogeneous and homogeneous combustion of fuel rich CH4/O2/N2/CO2 mixtures (φ = 1.8-3.5) over rhodium and platinum was investigated at 5 bar. Rh was shown superior to Pt in syngas production. The higher syngas production on Rh, and in particular of the highly reactive H2, had a drastic impact on the ensuing gas phase combustion characteristics. While vigorous homogeneous combustion was always established on Rh, it was altogether suppressed on Pt. The strong gaseous combustion on Rh considerably reduced the length of the oxidation zone in CPO reactors such that the catalytic reforming zone could be initiated farther upstream. It was also shown that homogeneous combustion did not affect the reactor thermal management and that it promoted the syngas yields at the reactor outlet. Finally, the complete oxidation of methane over rhodium (a topic not falling in the general framework of the microreactor work) was also investigated (φ = 0.3-0.4, p = 2-12 bar and catalyst temperatures 700-1250 K). Performance of detailed surface reaction mechanisms was evaluated and a one step catalytic reaction was constructed. For the investigated range, the catalytic reactivity of CH4 over Rh exhibited an overall positive pressure dependence ~p^0.30, which was weaker compared to an earlier reported pressure dependence of methane over platinum (~p^0.47). An elementary gaseous reaction mechanism was shown to reproduce the measured homogeneous ignition distances at all pressures, particularly when used in conjunction with the herein proposed one step catalytic reaction.