One of the biggest unsolved problems of modern physics is the turbulence phenomena in fluid flow. The appearance of turbulence in a flow system is regularly determined by velocity and length scales of the system. If those scales are small the motion of the fluid is laminar, but at larger scales, disturbances appear and grow, leading the flow field to transition to a fully turbulent state. The prediction of transitional flow is critical for many complex fluid flow applications, such as aeronautical, aerospace, biomedical, automotive, chemical processing, heating and cooling systems, and meteorology. For example, in some cases the flow may remain laminar throughout a significant portion of a given domain, and fully turbulent simulations may produce results that can lead to inaccurate conclusions or inefficient design, due to an inability to resolve the details of the transition process. This work aims to develop, implement, and test a new model concept for the prediction of transitional flows using a linear eddy-viscosity RANS approach. The effects of transition are included through one additional transport equation for v2 as an alternative to the Laminar Kinetic Energy (LKE) framework. Here v2 is interpreted as the energy of fully turbulent, three-dimensional velocity fluctuations. This dissertation presents two new single-point, physics-based turbulence models based on the transitional methodology mentioned above. The first one uses an existing transitional model as a baseline which is modified to accurately capture the physics of fully turbulent free shear flows. The model formulation was tested over several boundary layer and free shear flow test cases. The simulations show accurate results, qualitatively equal to the baseline model on transitional boundary layer test cases, and substantially improved over the baseline model for free shear flows. The second model uses the SST k-w fully turbulent model and again the effects of transition are included through one additional transport equation for v2. An initial version of the model is presented here. Simplicity of the formulation and ease of extension to other baseline models are two potential advantages of the new method.

Axisymmetric and swirling jets are generic flows that characterize many natural and man-made flows. These include cylindrical shear layer/mixing layer flows, aircraft jets and wakes, shedding of leading edge and wing tip vortices, tornadoes, astrophysical plasma flows and flows in mechanical devices such as supersonic combustion chambers and cyclone separators. These and other applications have resulted in a high level of interest in the stability of axisymmetric and swirling jets. To date, the majority of studies on stability of axisymmetric and swirling jets have been completed under the assumption of steady flow in both axial and azimuthal (swirl) directions. Yet, flows such as the ones mentioned above can have an inherent unsteadiness. Moreover, such unsteadiness can be used to control stability and thus flow characteristics in axisymmetric and swirling jets. In this work effects of periodic variations on the temporal stability of axisymmetric and swirling jets is examined. The unsteadiness is introduced in the former as a periodic variation of the axial velocity component of the flow, and in the latter as a periodic variation of the azimuthal (swirl) velocity component of the flow. The temporal linear hydrodynamic stability of both steady inviscid axisymmetric and swirling jets is reviewed. An analytical dispersion relation is obtained in both cases and solved numerically. In the case of the steady axisymmetric jet, growth rate and celerity of unstable axisymmetric and helicalmodes are determined as functions of axial wavenumber. Results show that the inviscid axisymmetric jet is unstable to all values of axisymmetric and helical modes. In the case of the steady swirling jet, growth rate and celerity of axisymmetric modes are determined as functions of the axial wavenumber and swirl number. Results show that the inviscid swirling jet is unstable to all values of axial and azimuthal wavenumber, however, it is shown that increasing the swirl decreases the growth rate and increases the celerity of axisymmetric disturbances. The effects of periodic variations on the stability of a mixing layer is also reviewed. Results show that when the instability time scale is much smaller than the mean time scale a transformation of the time variable may be taken that, when the quasi-steady approach works, will reduce the unsteady field to that of the corresponding steady field in the new time scale. The price paid for this transformation, however, is a modulation of the amplitude and phase of the unsteady modes. Extending the results from the unsteady mixing layer, the stability of a periodically unsteady inviscid axisymmetric jet is considered. An analytical dispersion relation is obtained and results show that for the unsteady inviscid axisymmetric jet, the quasi-steady approach works. Following this, the stability of a periodically unsteady swirling jet is considered and an analytical dispersion relation is obtained. It is shown that for the unsteady inviscid swirling jet, the quasi-steady approach does not work. Resulting modulations of unsteady modes are shown via a numerical solution to the unsteady dispersion relation. In both cases, using established results for unsteady mixing layers, these results are substantiated analytically by showing that the unsteady axisymmetric jet can be reduced the the exact equational form of the steady axisymmetric jet in a new time scale, whereas the unsteady swirling jet cannot. / Master of Science

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present work is dedicated to perform the mathematical modeling and DNS and LES simulations of a three-dimensional, temporally evolving incompressible plane wake are performed, seeking to evidence differences in stability, transition and onset of both coherent and small scale structures, when the flow is subjected to random perturbations of different amplitudes. The perturbations are generated using the Random-Flow-Generator (RFG) technique, being imposed to the flow as initial conditions. The Navier-Stokes equations are solved in a prismatic domain, with periodic boundary conditions in all directions, using Fourier pseudospectral method. The invariants of the velocity gradient tensor, Q and R, are analyzed for random perturbations with magnitudes 10−3, 10−4 and 10−5, showing the onset of their characteristic teardrop correlation map. Moreover, maps of the second and third invariants of the rate-of-strain tensor, QS and RS, are shown, in order to evidence the differences in local flow strain and topological characteristics of the dissipation of kinetic energy. Isosurface plots of Q and QW, as well as vorticity contours are shown, allowing visual identification of the coherent structures and confirming patterns predicted by the invariant maps. / O presente trabalho se dedica a modelagem matemática e a simulações numéricas DNS e LES de uma esteira tridimensional, incompressível, em desenvolvimento temporal, buscando evidenciar diferenças na estabilidade, transição e no desenvolvimento de estruturas coerentes e de pequena escala, quando o escoamento é submetido a perturbações randômicas de diferentes amplitudes. As perturbações são geradas utilizando-se a técnica Random Flow Generator (RFG), sendo sobrepostas à condição inicial do escoamento. As equações de Navier-Stokes são resolvidas em um domínio prismático, com condições de contorno periódicas em todas as direções, utilizando-se o método pseudoespectral de Fourier. Os invariantes do tensor gradiente de velocidade, Q e R, são analisados para perturbações de magnitude 10−3, 10−4 and 10−5, mostrando a formação de uma correlação no formato de gota, característica da resolução das equações de Navier-Stokes. Além disso, são apresentados mapas do segundo e terceiro invariante do tensor taxa de deformação, QS e RS, a fim de evidenciar as diferenças locais no escoamento e as características topológicas na taxa de dissipação de energia cinética. Isosuperfícies de Q e QW, bem como contornos de vorticidade são apresentados, possibilitando a identificação visual das estruturas coerentes, e confirmando os padrões de estruturas previstos pelos mapas de invariância. / Mestre em Engenharia Mecânica

Tato numerická studie je zaměřená na axisymetrickou pulzní trysku při zachování relativně nízkých Reynoldsových čísel a její fyzikální podstatu, která dosud nebyla zcela vysvětlena. Hlavním cílem práce bylo prozkoumat a zhodnotit vliv přidání periodického komponentu rychlosti ke stacionární složce rychlosti. Nejdříve byl řešen stacionární případ, poté byla do simulace přidána pulzace a byla vytvořena nestacionární simulace. Numerické řešení stacionárního případu bylo ověřeno pomocí asymptotického řešení, které předložil Hermann Schlichting [44]. Přesnost tohoto analytické řešení byla opravena na základě experimentálních poznatků Andradeho a Tsiena [1]. Pomocí této korekce je zmenšena oblast singularity řešení v blízkosti počátku proudění. Z matematického pohledu se v podstatě jedná korekcí prvního řádu, což bylo dokázáno Revueltou a spol [36]. Samotné analytické řešení bylo vytvořeno v MATLABu zatímco pro numerické řešení byl použit software Ansys Fluent. Při numerické simulaci byly Navier-Stokesovi rovnice integrovány ve své plné formě za pomoci algoritmu založeném na tzv. rovnici korekce tlaku. Pulzační tryska byla poté řešena pro různé parametry tak, aby bylo možné zhodnotit vliv jednotlivých parametrů na evoluci takto modulovaného proudu. Nakonec byla posouzena možná aplikace pulzních trysek v průmyslu s ohledem na možnost snížení emisí v průběhu spalovacího procesu.