We have examined three problems involving steady flows of Navier-Stokes fluids. In each problem non-classical effects are considered. In the first two problems, we consider fluids which have bulk viscosities which are much larger than their shear viscosities. In the last problem, we examine steady supersonic flows of a Bethe-Zel'dovich-Thompson (BZT) fluid over a thin airfoil or turbine blade. BZT fluids are fluids in which the fundamental derivative of gasdynamics changes sign during an isentropic expansion or compression. In the first problem we consider the effects of large bulk viscosity on the structure of the inviscid approximation using the method of matched asymptotic expansions. When the ratio of bulk to shear viscosity is of the order of the square root of the Reynolds number we find that the bulk viscosity effects are important in the first corrections to the conventional boundary layer and outer inviscid flow. At first order the outer flow is found to be frictional, rotational, and non-isentropic for large bulk viscosity fluids. The pressure is found to have first order variations across the boundary layer and the temperature equation is seen to have two additional source terms at first order when the bulk viscosity is large. In the second problem, we consider the reflection of an oblique shock from a laminar flat plate boundary layer. The flow is taken to be two-dimensional, steady, and the gas model is taken to be a perfect gas with constant Prandtl number. The plate is taken to be adiabatic. The full Navier-Stokes equations are solved using a weighted essentially non-oscillatory (WENO) numerical scheme. We show that shock-induced separation can be suppressed once the bulk viscosity is large enough. In the third problem, we solve a quartic Burgers equation to describe the steady, two-dimensional, inviscid supersonic flow field generated by thin airfoils. The Burgers equation is solved using the WENO technique. Phenomena of interest include the partial and complete disintegration of compression shocks, the formation of expansion shocks, and the collision of expansion and compression shocks. / Ph. D.

Les écoulements turbulents de gaz denses, qui sont d’un grand intérêt pour un large éventail d'applications, sont le siège de phénomènes physiques encore peu connus et difficiles à étudier par des approches expérimentale. Dans ce travail, nous étudions pour la première fois l’influence des effets de gaz denses sur la structure de la turbulence compressible à l’aide de simulations numériques. Le fluide considéré est le PP11, un fluorocarbure lourd, dont le comportement thermodynamique a été représenté à l’aide de différentes lois d’état, afin de quantifier la sensibilité des solutions aux choix de modélisation. Nous avons considéré d’abord la décroissance d’une turbulence homogène isotrope compressible. Les fluctuations de température sont négligeables, alors que celles de la vitesse du son sont importantes à cause de leur forte dépendance de la densité. Le comportement particulier de la vitesse du son modifie de manière significative la structure de la turbulence, conduisant à la formation de shocklets de détente. L’analyse de la contribution des différentes structures à la dissipation d’énergie et à la génération d’enstrophie montre que, pour un gaz dense, les régions de forte dilatation jouent un rôle similaire à celles de forte compression, contrairement aux gaz parfaits, dans lesquels le comportement est fortement dissymétrique. Ensuite, nous avons mené des simulations numériques pour une configuration de canal plan en régime supersonique, pour plusieurs valeurs des nombres de Mach et de Reynolds. Les résultats confirment la validité de l’hypothèse de Morkovin. L’introduction d’une loi d’échelle semi-locale prenant en compte le variations de densité et viscosité, permet de comparer les profils des grandeurs turbulentes (contraintes de Reynolds, anisotropie, budgets d’énergie) avec ces observés en gaz parfait. Les variables thermodynamiques, quant à elles, présentent une évolution très différente pour un gaz parfait et pour un gaz dense, la chaleur spécifique élevée de ce dernier conduisant à un découplage des effets dynamiques et thermiques et à un comportement proche de celui d’un fluide incompressible avec des propriétés variables. / Dense gas turbulent flows, of great interest for a wide range of engineering applications, exhibit physical phenomena that are still poorly understood and difficult to reproduce experimentally. In this work, we study for the first time the influence of dense gas effects on the structure of compressible turbulence by means of numerical simulations. The fluid considered is PP11, a heavy fluorocarbon, whose thermodynamic behavior is described by means of different equations of state to quantify the sensitivity of solutions to modelling choices. First, we considered the decay of compressible homogeneous isotropic turbulence. Temperature fluctuations are found to be negligible, whereas those of the speed of sound are large because of the strong dependence on density. The peculiar behavior of the speed of sound significantly modifies the structure of the turbulence, leading to the occurrence of expansion shocklets. The analysis of the contribution of the different structures to energy dissipation and enstrophy generation shows that, for a dense gas, high expansion regions play a role similar to high compression ones, unlike perfect gases, in which the observed behaviour is highly asymmetric. Then, we carried out numerical simulations of a supersonic turbulent channel flow for several values of Mach and Reynolds numbers. The results confirm the validity of the Morkovin' hypothesis. The introduction of a semi-local scaling, taking into account density and viscosity variations across the channel, allow to compare the wall-normal profiles of turbulent quantities (Reynolds stresses, anisotropy, energy budgets) with those observed in ideal gases. Nevertheless, the thermodynamic variables exhibit a different evolution between perfect and dense gases, since the high specific heats of the latter lead to a decoupling of dynamic and thermal effects, and to a behavior close to that of variable property incompressible fluids.