In this study we highlight the influence of mean dilatation and mean density gradient on the Reynolds stress modeling of compressible, heat-releasing and supercritical turbulent flows.Firstly, the modeling of the rapid pressure-strain correlation has been extended to self-consistently account for the influence of mean dilatation.Secondly, an algebraic model for the turbulent density flux has been developed and coupled to the tensor equationfor Reynolds stress anisotropy via a 'local mean acceleration',a generalization of the buoyancy force. We applied the resulting differential Reynolds stress model (DRSM) and the corresponding explicit algebraic Reynolds stress model (EARSM) to homogeneously sheared and compressed or expanded two-dimensional mean flows. Both formulations have shown that our model preserves the realizability of the turbulence, meaning that the Reynolds stresses do not attain unphysical values, unlike earlier approaches. Comparison with rapid distortion theory (RDT) demonstrated that the DRSM captures the essentials of the transient behaviour of the diagonal anisotropies and gives good predictions of the turbulence kinetic energy. A general three-dimensional solution to the coupled EARSM  has been formulated. In the case of turbulent flow in de Laval nozzle we investigated the influence of compressibility effects and demonstrated that the different calibrations lead to different turbulence regimes but with retained realizability. We calibrated our EARSM against a DNS of combustion in a wall-jet flow. Correct predictions of turbulent density fluxes have been achieved and essential features of the anisotropy behaviour have been captured.The proposed calibration keeps the model free of singularities for the cases studied. In addition,  we have applied the EARSM to the investigation of supercritical carbon dioxide flow in an annulus. The model correctly captured mean enthalpy, temperature and density as well as the turbulence shear stress. Hence, we consider the model as a useful tool for the analysis of a wide range of compressible flows with large density variation. / <p>QC 20160314</p>

In dieser Arbeit werden zwei Klassen von Evolutionsgleichungen in einem Matrixraum-Setting studiert: Hyperbolische Erhaltungsgleichungen und aktive skalare Gleichungen. Für erstere wird untersucht, wann man Oszillationen mit Hilfe polykonvexen Maßen ausschließen kann; für Zweitere wird mit Hilfe von Oszillationen gezeigt, dass es unendlich viele periodische schwache Lösungen gibt.

Orientador: Lucas Catão de Freitas Ferreira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-24T12:47:02Z (GMT). No. of bitstreams: 1 Lima_LidianedosSantosMonteiro_D.pdf: 2071234 bytes, checksum: 6370d2ea978f96792562cdc2e2406365 (MD5) Previous issue date: 2014 / Resumo: Nesta tese consideramos uma família de EDPs dissipativas do tipo escalar ativo cujos campos velocidades são acoplados aos escalares através de operadores multiplicadores de Fourier que podem ser de alta ordem. Na primeira parte, provamos boa-colocação global, decaimento de normas Lp, e algumas propriedades de simetria, para dados iniciais no espaço de Lebesgue crítico e sem assumir condição de pequenez. Na segunda parte, introduzimos os espaços de Fourier-Besov-Morrey, o qual parece ser novo na analise de EDPs, com o objetivo de encontrar soluções auto-similares e considerar uma classe maior de acoplamentos e dados iniciais. Condições de pequenez na norma do espaço são assumidas para estes resultados. Além disso, mostramos um resultado de estabilidade assintótica e obtemos uma classe de soluções assintoticamente auto-similares / Abstract: In this thesis we consider a family of dissipative active scalar equations whose velocity fields are coupled by means of multiplier operators that can be of high-order. In the first part, we prove global well-posedness, decay of Lp's norms and some symmetry properties of solutions for initial data in the critical Lebesgue space and without smallness condition. In the second part, we introduce the Fourie-Besov-Morrey spaces, which seems to be new in the analysis of PDEs in order to find self-similar solutions and to consider a larger class of couplings and initial data. Smallness conditions on the norm of the space are assumed for these results. Furthermore, we show an asymptotic stability result and obtain a class of asymptotically self-similar solutions / Doutorado / Matematica / Doutora em Matemática

In dieser Arbeit werden zwei Klassen von Evolutionsgleichungen in einem Matrixraum-Setting studiert: Hyperbolische Erhaltungsgleichungen und aktive skalare Gleichungen. Für erstere wird untersucht, wann man Oszillationen mit Hilfe polykonvexen Maßen ausschließen kann; für Zweitere wird mit Hilfe von Oszillationen gezeigt, dass es unendlich viele periodische schwache Lösungen gibt.