QC 20100726

The main goal of this work was to develop numerical models for studying the behaviour of fibres in an accelerated flow. This is of special interest for e.g. papermaking. The early stage of the paper manufacturing process determines most of the final properties of a paper sheet. The complexity of studying the flow of fibre suspensions both experimentally and numerically emphasises a need for new ideas and developments. By means of solving the evolution of a convective-dispersion equation, i.e. the Fokker-Planck equation, a fully 3D approach with respect to the position and the two fibre angles, polar and azimuthal angles, following a streamline is presented. As an input to the fibre orientation model the turbulent flow field is solved by Computational Fluid Dynamics (CFD) with second-order closure in the turbulence model. In this work two new hypotheses have been presented for the variation of the non-dimensional rotational diffusivity with non-dimensional fibre length, Lf /η and the Reynolds number based on the Taylor micro-scale of the turbulence, Reλ Parameters for the two new hy- potheses and earlier models are determined with the aim of achieving a general relation and a value of the rotational dispersion coeffcient of stiff fibres in an anisotropic turbulent fluid flow. Earlier modelling work has been focused on solving the planar approach, i.e. assuming all fibres to be in one plane. This planar approach is discussed and compared with the fully 3D approach and its validity is evaluated. The optimization of parameters for the different hypotheses correlated on a central streamline, showed a good agreement with an independent experimental result in the undisturbed region. Moreover, it is particularly interesting that the boundary layer region and the wake region are predicted fairly well and the phenomena are well described, which has not been the case earlier. It seems that the new hypothesis based on the variation of the non-dimensional fibre length, Lf /η gives the best correlation in these shear-layer regions. Further- more it was established that the planar approach fails to predict shear layers, i.e. the boundary layer and the wake regions. As emphasized in the theory section, the planar formulation is strictly valid only if all fibres are oriented in one plane, which is not the case in the shear layers. In the undisturbed region, the 3D and the planar approaches, agree in their results. This leads to the conclusion that both approaches are suitable when shear layers are not studied. / QC 20100812

Behavior of particles in buoyancy driven turbulent flow at Ra ≈ 10º is investigated experimentally. The volume fraction of the particles is low enough for the inter particle influence to be neglected, the mass loading of particle is low enough that the turbulence as not modified, and the particles Reynolds numbers (Re p ) st are small enough that the wake effect can be neglected. The buoyancy driven turbulent flow is created by maintaining an unstable density difference, using NaCl dissolved in water, across the ends of a long vertical tube. There is no mean flow and the turbulence is axially homogeneous. A method for uniform introduction of the particles was devised. Glass particles (S.G=2.4-2.5) of different diameter ranges (50-400 µm) are introduced into this flow. The sizes of particles considered are less than the Kolmogrov length scale corresponding to the turbulence level. The turbulence intensity level was varied in order to match its characteristic time and velocity scale to those of the particles. The ratio of the timescales, the Stokes number; is in the range (0.01-0.55); Stokes number is defined as a ratio of the viscous relaxation time of the particle and a turbulent time scale, and represents the effect of the particle inertia in the interaction with the turbulence, Stk =τp/τk. Another important non-dimensional parameter is the velocity ratio, the k ratio of the particle settling velocity in still fluid to a characteristic turbulence velocity. The flow field is illuminated by a continuous Argon-ion laser and a PHOTRON high- speed digital camera is used for imaging. The raw images are processed to evaluate particle centers followed by their velocity measurements. The objective of the experiment is to check for the effect of the turbulent flow on the sedimentation rate of the heavy particles. This sedimentation rate is compared with the settling velocity obtained in still water. It is expected that within a certain range of Stokes numbers and velocity ratios the sedimentation rate would be substantially changed, and the spatial concentration distribution of the particles may become patchy implying that turbulence may actually inhibit rather than enhance mixing of particles. By varying the turbulence level and particle mean diameter we achieved a set of values for the particle parameters, namely St k. ≈ 0.01, 0.1, 0.14, 0.55 and velocity ratios[[Wp ] St]]≈ 0.2, .0, 0.5, 2.25 respectively. The w rms velocity ratio [[Wp ] St /wf defined as a ratio between the article terminal velocity [Wp ] St and a suitable flow velocity scale; it is a measure of the residence time of the particle in an eddy, in eddy turnover time units. In this study we have considered the turbulence r.m.s velocity for the flow velocity scale.The particle Reynolds number (Re p)st corresponding to these 4 cases were 0.2, 31.5, 4.0, 31.5. Some preliminary quantitative measurements were made only for the 150-200 µm particles and turbulence level w rms ≈ 4.0 cm/s,corresponding to Stk ≈0.14 [[Wp ] St] = 0.5. A quantitative picture was obtained for the other cases. Streak pictures for these four different groups of particles revealed that Stk and the velocity ratio [[Wp ] St ] were important in influencing the particle- w rms turbulence interaction not the Stk alone. The r.m.s velocity fluctuations of particles in both the lateral (utp) and vertical direction (wtp) measured were found to be different from those obtained in still-water case.(For equations, pl see the pdf file)

The two-dimensional depth-averaged shallow water equations have attracted considerable attentions as a practical way to solve flows with free surface. Compared to three-dimensional Navier-Stokes equations, the shallow water equations give essentially the same results at much lower cost. Solving the shallow water equations by the Godunov-type finite volume method is a newly emerging area. The Godunov-type finite volume method is good at capturing the discontinuous fronts in numerical solutions. This makes the method suitable for solving the system of shallow water equations. In this dissertation, both the shallow water equations and the Godunov-type finite volume method are described in detail. A new surface flow routing method is proposed in the dissertation. The method does not limit the shallow water equations to open channels but extends the shallow water equations to the whole domain. Results show that the new routing method is a promising method for prediction of watershed runoff. The method is also applied to turbulence modeling of free surface flow. The κ - ε turbulence model is incorporated into the system of shallow water equations. The outcomes prove that the turbulence modeling is necessary for calculation of free surface flow. At last part of the dissertation, a total load sediment transport model is described and the model is tested against 1D and 2D laboratory experiments. In summary, the proposed numerical method shows good potential in solving free surface flow problems. And future development will be focusing on river meandering simulation, non-equilibrium sediment transport and surface flow - subsurface flow interaction.

Aerodynamic shape optimization and multidisciplinary optimization algorithms have the potential not only to improve conventional aircraft, but also to enable the design of novel configurations. By their very nature, these algorithms generate and analyze a large number of unique shapes, resulting in high computational costs. In order to improve their efficiency and enable their use in the early stages of the design process, a fast and robust flow solution algorithm is necessary. This thesis presents an efficient parallel Newton-Krylov-Schur flow solution algorithm for the three-dimensional Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model. The algorithm employs second-order summation-by-parts (SBP) operators on multi-block structured grids with simultaneous approximation terms (SATs) to enforce block interface coupling and boundary conditions. The discrete equations are solved iteratively with an inexact-Newton method, while the linear system at each Newton iteration is solved using the flexible Krylov subspace iterative method GMRES with an approximate-Schur parallel preconditioner. The algorithm is thoroughly verified and validated, highlighting the correspondence of the current algorithm with several established flow solvers. The solution for a transonic flow over a wing on a mesh of medium density (15 million nodes) shows good agreement with experimental results. Using 128 processors, deep convergence is obtained in under 90 minutes. The solution of transonic flow over the Common Research Model wing-body geometry with grids with up to 150 million nodes exhibits the expected grid convergence behavior. This case was completed as part of the Fifth AIAA Drag Prediction Workshop, with the algorithm producing solutions that compare favourably with several widely used flow solvers. The algorithm is shown to scale well on over 6000 processors. The results demonstrate the effectiveness of the SBP-SAT spatial discretization, which can be readily extended to high order, in combination with the Newton-Krylov-Schur iterative method to produce a powerful parallel algorithm for the numerical solution of the Reynolds-averaged Navier-Stokes equations. The algorithm can efficiently solve the flow over a range of clean geometries, making it suitable for use at the core of an optimization algorithm.

Aerodynamic shape optimization and multidisciplinary optimization algorithms have the potential not only to improve conventional aircraft, but also to enable the design of novel configurations. By their very nature, these algorithms generate and analyze a large number of unique shapes, resulting in high computational costs. In order to improve their efficiency and enable their use in the early stages of the design process, a fast and robust flow solution algorithm is necessary. This thesis presents an efficient parallel Newton-Krylov-Schur flow solution algorithm for the three-dimensional Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model. The algorithm employs second-order summation-by-parts (SBP) operators on multi-block structured grids with simultaneous approximation terms (SATs) to enforce block interface coupling and boundary conditions. The discrete equations are solved iteratively with an inexact-Newton method, while the linear system at each Newton iteration is solved using the flexible Krylov subspace iterative method GMRES with an approximate-Schur parallel preconditioner. The algorithm is thoroughly verified and validated, highlighting the correspondence of the current algorithm with several established flow solvers. The solution for a transonic flow over a wing on a mesh of medium density (15 million nodes) shows good agreement with experimental results. Using 128 processors, deep convergence is obtained in under 90 minutes. The solution of transonic flow over the Common Research Model wing-body geometry with grids with up to 150 million nodes exhibits the expected grid convergence behavior. This case was completed as part of the Fifth AIAA Drag Prediction Workshop, with the algorithm producing solutions that compare favourably with several widely used flow solvers. The algorithm is shown to scale well on over 6000 processors. The results demonstrate the effectiveness of the SBP-SAT spatial discretization, which can be readily extended to high order, in combination with the Newton-Krylov-Schur iterative method to produce a powerful parallel algorithm for the numerical solution of the Reynolds-averaged Navier-Stokes equations. The algorithm can efficiently solve the flow over a range of clean geometries, making it suitable for use at the core of an optimization algorithm.

Im Rahmen dieser Dissertation werden eine Serie von Grundlagenexperimenten zur Ablagerung (Deposition) und Remobilisierung (Resuspension) von Aerosolpartikeln in turbulenten Strömungen beschrieben. Die Kernmotivation stellt die Quelltermanalyse von Druckentlastungsstörfällen von Hochtemperaturreaktoren (HTR) dar. Im Primärkreislauf früherer HTR-Forschungsanlagen wurden größere Mengen an radiologisch belastetem Graphitstaub gefunden. Dieser Staub scheint größtenteils durch Abrieb zwischen den graphitischen Kernstrukturen entstanden zu sein und verteilte sich während des fortlaufenden Reaktorbetriebs über sämtliche Oberflächen des Primärkreislaufs. Während eines Druckentlastungsstörfalls kann dieser Staub durch die Gasströmung remobilisiert und aus dem Primärkreislauf ausgetragen werden. Eine Quelltermanalyse solch eines Störfallszenarios erfordert die Kenntnis über die Menge und die räumliche Verteilung des Staubs, die radiologische Belastung sowie das Remobilisierungsverhalten in Bezug auf die zu erwartenden Strömungstransienten. Nach dem heutigen Stand von Wissenschaft und Technik kann die räumlich-zeitliche Verteilung des Staubs im Primärkreislauf für stationären Reaktorbetrieb unter Verwendung eindimensionaler Systemcodes abgeschätzt werden. Jedoch ist unbekannt, welcher Anteil des Staubinventars durch die Gasströmung remobilisiert und aus dem Primärkreislauf ausgetragen werden würde. Zur systematischen Untersuchung des Staubtransportverhaltens in turbulenten Strömungen wurden zwei kleinskalige Versuchsanlagen entwickelt und eine Serie von Depositions- und Resuspensionsexperimenten durchgeführt. Die partikelbeladene Strömung in der Heißgasumgebung des HTR-Primärkreislaufs wurde über die Verwendung von Ähnlichkeitskennzahlen auf eine Luftströmung bei Umgebungsbedingungen herunterskaliert. Die Strömung und die Partikel wurden mittels hochauflösender, bildgebender und nichtinvasiver Messverfahren räumlich und zeitlich vermessen, um eine umfangreiche Datenbasis für die Analyse der Partikeltransportprozesse zu erstellen. Inhaltlich lassen sich die durchgeführten Untersuchungen in drei Teile gliedern. Der erste Teil besteht aus zwei Studien über die Deposition und Resuspension monodisperser, sphärischer Einzelpartikel in einer ungestörten, horizontalen Kanalströmung. Die systematische Variation experimenteller Randbedingungen wie der Partikelgröße, der Oberflächenrauheit und der Strömungsgeschwindigkeit ermöglichte die Quantifizierung der einzelnen Einflussgrößen. Im zweiten und dritten Teil der Dissertation wurden die Deposition und Resuspension einer mehrschichtigen Ablagerung (Partikel-Multilayer) zwischen periodischen Stufen und in einer Kugelschüttung untersucht, um die komplexe Interaktion zwischen der turbulenten Strömung und der Multilayer-Ablagerung weiter zu erforschen. Die gewonnenen Erkenntnisse leisten einen Beitrag für die Quelltermanalyse des Staubtransports im HTR-Primärkreislauf und können für die Weiterentwicklung numerischer Strömungssimulationen des Partikeltransports in turbulenten Strömungen verwendet werden. / Aerosol particle deposition and resuspension experiments in turbulent flows were performed to investigate the complex particle transport phenomena and to provide a database for the development and validation of computational fluid dynamics (CFD) codes. The background motivation is related to the source term analysis of an accidental depressurization scenario of a High Temperature Reactor (HTR). During the operation of former HTR pilot plants, larger amounts of radio-contaminated graphite dust were found in the primary circuit. This dust most likely arose due to abrasion between the graphitic core components and was deposited on the inner wall surfaces of the primary circuit. In case of an accident scenario, such as a depressurization of the primary circuit, the dust may be remobilized and may escape the system boundaries. The estimation of the source term being discharged during such a scenario requires fundamental knowledge of the particle deposition, the amount of contaminants per unit mass as well as the resuspension phenomena. Nowadays, the graphite dust distribution in the primary circuit of an HTR can be calculated for stationary conditions using one-dimensional reactor system codes. However, it is rather unknown which fraction of the graphite dust inventory may be remobilized during a depressurization of the HTR primary circuit. Two small-scale experimental facilities were designed and a set of experiments was performed to investigate particle transport, deposition and resuspension in turbulent flows. The facility design concept is based on the fluid dynamic downscaling of the helium pressure boundary in the HTR primary circuit to an airflow at ambient conditions in the laboratory. The turbulent flow and the particles were recorded by high-resolution, non-invasive imaging techniques to provide a spatio-temporal insight into the particle transport processes. The different investigations of this thesis can be grouped into three categories. Firstly, the deposition and resuspension of monodisperse single particles in a horizontal turbulent channel flow was studied. The systematic variation of the experimental boundary conditions allows for the quantification of the influences of particle size, surface roughness, and fluid velocity. In the second and third part of this thesis, the deposition and resuspension of a particle multilayer between periodic steps and in a pebble bed was studied to explore the complex interaction between the turbulent flow and the particles, respectively. The findings of this thesis are a contribution to the source term analysis of HTR related accidental depressurizations. Furthermore, the database can be applied to CFD code developments for the numerical simulation of particle transport processes in turbulent flows.

Turbulent jet flows issuing from rectangular nozzles are used in many technological and practical applications. Understanding their development and mechanics is important to the design and performance improvement of these applications. Therefore, rectangular jets have been studied extensively over the past decades. Previous investigations have extensively studied the effects of various initial and boundary conditions such as nozzle type, nozzle aspect ratio, nozzle exit turbulence intensity, jet exit Reynolds number. Nozzle type (e.g. smooth contraction nozzle, channel, radially contoured nozzle) has been found to affect the development of these jets. While varying Reynolds number affects the mixing of the jet with its ambient either in the near field or in the far field. Nozzle aspect ratio is also an important boundary condition. It has been experimentally shown that aspect ratio influences the dimensionality of flow field, and hence entrainment between the jet and its ambient. Some of these investigations have used sidewalls (two parallel plates attached to the nozzle short sides) to improve the two-dimensionality of the flow fields, and/or endplate (a wall flush at the nozzle exit) to prevent mixing upstream of the nozzle. Despite this fact very few investigators have specifically considered the effect of endplate or sidewalls on jet development. In the present investigation, the effects of endplates and/or sidewalls on turbulent jets issuing from a rectangular of aspect ratio, AR= 15 have been studied. The mean streamwise and lateral velocity and turbulent characteristics of four different rectangular jets, namely, 1. jet with no endplate and no sidewalls, NENS, 2. jet with endplate and no endplate, WENS, 3. jet without endplate and with sidewalls, NEWS and 4. jet with endplate and with sidewalls, WEWS, have been measured, with x-sensor hot wire anemometry, up to an axial distance of 35 D under identical inlet conditions. Centreline measurements for the four configurations have been collected for three Reynolds number, ReD=10,000, 20,000 and 30,000. For ReD=20,000 measurements in the transverse direction were collected at 13 different downstream locations in the range of x= (0, 1, 2, 2.5, 3, 4, 5, 10, 15, 20, 25, 30 and 35) nozzle widths. The jet with no endplate and no sidewalls (NENS) and the jet with endplate and no sidewalls (WENS) produce nearly similar mean and turbulent velocity profiles indicating insignificant effect of the endplates on their development in the absence of the sidewalls. At Re=20,000, larger mean streamwise velocity values were observed at the edges of the jets (NEWS or WEWS) at distances from nozzle in the range of x/D=3-30 whereas the presence of the endplate has an insignificant effect. The presence or absence of sidewalls is also key factor determining the distributions of the lateral mean velocity component. The presence of sidewalls is associated with lower outward velocities within the edges of the jets and higher inward ones outside the edges. The absence of sidewalls makes the presence of the endplate insignificant and the lateral velocity attains outside the edges low negative values of almost the same level in both cases (NENS, WENS) The presence of an endplate has again some significance only when the sidewalls are present alleviating their effect. Absence of the endplate in jet with sidewalls, leads to lowest spread rate compared to the case with endplates (comparing jet with no endplate and with sidewalls, NEWS and jet with endplate and with sidewalls, WEWS). The presence of an endplate in the absence of sidewalls has again insignificant effect on the jet’s spread rate (comparing jet with no endplate and no sidewalls, NENS and jet with endplate and no sidewalls, WENS). The effects of endplates and/or sidewalls on the decay rates have been investigated for ReD=10,000, 20,000 and 30,000. The presence of the endplate in jets with no sidewalls has insignificant effect on decay rate as was observed for all Reynolds numbers. The presence of the endplate in jet with sidewalls, leads to higher decay rates for all Re tested compared to all cases. The decay rates of the jets with no sidewalls in the presence and absence of the endplate (NENS, WENS) seem to reach their asymptotic values at around ReD=20,000. But the jets with sidewalls have not reached an asymptotic behaviour even at the highest Re tested. The implementation of sidewalls has been found to lead to a decrease of the streamwise turbulent velocity, u′, at the exit shear layer. Current results indicate that the presence of an endplate has an insignificant effect and the estimates for the root mean square of the streamwise velocity fluctuation u′, at the exit shear layer can be grouped according to the absence or presence of sidewalls (3.8% of the mean centreline velocity for NENS and WENS, and 3.1% for NEWS and WEWS). For all turbulent terms, the presence of the endplate has an effect in the presence of sidewalls and the nondimensional streamwise turbulent velocity attains always higher values in its presence (comparing WEWS with NEWS). The profiles of the streamwise turbulent velocity, u′ profiles for the jet with no endplate and no sidewalls, (NENS) and the jet with endplate and no sidewalls, (WENS) are almost indistinguishable in the range x/D=15-35 but the profiles of the jet with no endplate and with sidewalls, (NESWS) and jet with endplate and with sidewalls, (WEWS) indicate a monotonic increase of the values in the central area of the jets. This indicates that the observed trends are mainly due to the presence of the sidewalls and presence or absence endplate has insignificant effect. / Οι επίπεδες τυρβώδεις δέσμες εκροής ανήκουν στην κατηγορία των απλών ροών που παρουσιάζουν μεγάλο ενδιαφέρον για τη ρευστομηχανική και για το λόγο αυτό αποτέλεσαν θέμα μελέτης και έρευνας εδώ και πολλά χρόνια με θεωρητικά, πειραματικά και υπολογιστικά εργαλεία. Οι αρχικές διερευνήσεις επικεντρώθηκαν στη μελέτη του μέσου και τυρβώδους πεδίου της ταχύτητας ή κάποιου παθητικού ρυπαντή προσπαθώντας να αναδείξουν κυρίως τα κοινά χαρακτηριστικά αυτοομοιότητας που αναπτύσσουν οι δέσμες εκροής κυρίως στο απομακρυσμένο πεδίο. Κατά τις τελευταίες δεκαετίες και με δεδομένη τη σημασία που έχουν οι τυρβώδεις ορθογωνικές δέσμες εκροής σε πολλές πρακτικές εφαρμογές (συστήματα καύσης, ψύξη επιφανειών, έλεγχος άντωσης, έλεγχος θορύβου κλπ) η έρευνα προσανατολίστηκε στην επίδραση των αρχικών και συνοριακών συνθηκών (γεωμετρικά χαρακτηριστικά και διαμόρφωση του ακροφυσίου εκροής, αριθμό Reynolds, ένταση τύρβης στην έξοδο) στη διαμόρφωση του εγγύς και του μέσου πεδίου. Σε αρκετές από τις προηγούμενες διερευνήσεις έχουν χρησιμοποιηθεί πλευρικά τοιχώματα (sidewalls) που επεκτείνουν τις στενές πλευρές του ακροφυσίου στη διεύθυνση της ροής ή/και τοίχωμα εκροής (endplate) με στόχο την επίτευξη διδιάστατης ροής. Η σημασία της παρουσίας αυτών των τοιχωμάτων, η οποία έχει μελετηθεί ελάχιστα στο παρελθόν, αποτελεί το στόχο διερεύνησης της παρούσας διατριβής. Η επίδραση των πλευρικών τοιχωμάτων και του τοιχώματος εκροής μελετήθηκαν πειραματικά με τη χρήση ενός ακροφυσίου ομαλής σύγκλισης με λόγο πλευρών 15 με τη χρήση διατάξεων που υλοποιούσαν τέσσερεις τύπους συνοριακών συνθηκών και συγκεκριμένα: 1. Ελεύθερη δέσμη εκροής χωρίς τοίχωμα εκροής - χωρίς πλευρικά τοιχώματα (No endplate - no sidewalls, NENS), 2. Δέσμη εκροής με τοίχωμα εκροής - χωρίς πλευρικά τοιχώματα (With endplate - no sidewalls, WENS), 3. Δέσμη εκροής χωρίς τοίχωμα εκροής - με πλευρικά τοιχώματα (No endplate - with sidewalls, NEWS), 4. Δέσμη εκροής με τοίχωμα εκροής - με πλευρικά τοιχώματα (With endplate - with sidewalls, WEWS). Η πειραματική διερεύνηση έγινε με την χρήση ανεμομετρίας θερμού σύρματος (Hot wire anemometry, HWA) με αισθητήρα τύπου Χ για τη μέτρηση της διαμήκους και της εγκάρσιας συνιστώσας της ταχύτητας. Πραγματοποιήθηκαν μετρήσεις και για τις τέσσερεις διατάξεις επάνω στον άξονα εκροής για τρείς διαφορετικούς αριθμούς Reynolds, ReD = 10,000, 20,000 και 30,000 σε αποστάσεις μέχρι 35 πλάτη ακροφυσίου, D, από το σημείο εκροής. Για ReD = 20000 καταγράφηκαν επίσης οι εγκάρσιες κατανομές των δύο συνιστωσών της ταχύτητας σε δεκατρείς σταθμούς σε αποστάσεις από την έξοδο x/D = 0, 1, 2, 2.5, 3, 4, 5, 10, 15, 20, 25, 30 και 35. Τα αποτελέσματα του μέσου όσο και του τυρβώδους πεδίου καταδεικνύουν ότι η παρουσία των πλευρικών τοιχωμάτων έχει σημαντική επίδραση στην ανάπτυξη του ροϊκού πεδίου. Αντίθετα η παρουσία του τοιχώματος εκροής διαφοροποιεί τα αποτελέσματα μόνο στην περίπτωση που υπάρχουν ήδη τα πλευρικά τοιχώματα.

This research extends the capabilities of Non-oscillatory Forward-in-Time (NFT) solvers operating on unstructured meshes to allow for accurate simulation of incompressible turbulent flows. This is achieved by the development of Large Eddy Simulation (LES) and Detached Eddy Simulation (DES) turbulent flow methodologies and the development of parallel option of the flow solver. The effective use of LES and DES requires a development of a subgrid-scale model. Several subgrid-scale models are implemented and studied, and their efficacy is assessed. The NFT solvers employed in this work are based on the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) that facilitates novel implicit Large Eddy Simulation (ILES) approach to treating turbulence. The flexibility and robustness of the new NFT MPDATA solver are studied and successfully validated using well established benchmarks and concentrate on a flow past a sphere. The flow statistics from the solutions are compared against the existing experimental and numerical data and fully confirm the validity of the approach. The parallel implementation of the flow solver is also documented and verified showing a substantial speedup of computations. The proposed method lays foundations for further studies and developments, especially for exploring the potential of MPDATA in the context of ILES and associated treatments of boundary conditions at solid boundaries.

Este Trabalho apresenta novas soluções exatas para as equações de Navier – Stokes transientes tridimensionais para escoamentos viscosos incompressíveis. Estas soluções são obtidas por meio de Split e Transformações Auto-Bäcklund. O procedimento de Split desacopla as equações de Navier – Stokes em dois sistemas de equações diferenciais parciais, um linear e outro não-linear, ambos não-homogêneos. O sistema linear, que contém somente termos viscosos e derivadas temporais, é resolvido via Transformações Auto-Bäcklund induzidas por relações de comutação, fornecendo o campo de velocidades. Os componentes do vetor velocidade são então substituídos no sistema não-linear a fim de obter o correspondente campo de pressões. A resolução do sistema não-linear para a pressão pode ser obtida tanto numericamente (via integração direta) quanto analiticamente, empregando a equação de Helmholtz. O objetivo do presente trabalho é encontrar expressões analíticas para o campo de velocidades e obter resultados numéricos para o campo de pressão associado. O caráter híbrido das soluções proporciona uma redução significativa do tempo de processamento requerido para a simulação de escoamentos viscosos, o qual praticamente se reduz ao tempo demandado para a tarefa de pós-processamento. Com esse objetivo em mente, foi desenvolvida uma formulação tridimensional escalar para a função corrente, a fim de reduzir o tempo requerido na tarefa mais dispendiosa de pós-processamento, a saber, o traçado das linhas de corrente em torno de corpos submersos de formato arbitrário. Neste estágio de desenvolvimento, esta formulação é empregada para produzir mapas de linhas de corrente para escoamentos viscosos em torno de uma esfera para números de Reynolds elevados. / This work presents new exact solutions to the unsteady three dimensional Navier-Stokes equations for incompressible viscous flows. These solutions are obtained by means of split and auto-Bäcklund transformations. The splitting procedure decouples the Navier-Stokes equations into a linear and a nonlinear inhomogeneous system of partial differential equations. The linear system, which contains only viscous terms and time derivatives, is solved via auto-Bäcklund transformations induced by commutation relations, furnishing the velocity field. The components of the velocity vector are then replaced into the nonlinear system to obtain the corresponding pressure field. The solution of the nonlinear system for the pressure variable can be carried out either numerically (by direct integration) or analytically, using the Helmholtz equation . The aim of the proposed work is to find analytical expressions for the velocity field and to obtain numerical results to the associated pressure field. The hybrid character of the solutions provides a significant reduction on the time processing required to simulate viscous flows, which virtually reduces to the time demanded to execute post-processing tasks. Taking this fact in mind, a three dimensional scalar formulation for the streamfunction was developed in order to simplify the most time-consuming post-processing task required, e.g., plotting the streamlines around arbitrary shaped bodies. At this stage of development, this formulation is employed to produce streamline maps for viscous flows around a sphere for high Reynolds numbers.