Development of improved turbulence closure models for compressible fluid flow simulations requires better understanding of the effects of compressibility on various underlying processes of turbulence. Fundamental studies of turbulent velocity gradients hold the key to understanding several non-linear processes like material element deformation, energy cascading, intermittency and mixing. Experiments, direct numerical simulation (DNS) and simple mathematical models are three approaches to study velocity gradients. With the goal of furthering our understanding of the effects of compressibility on turbulent velocity gradients, this dissertation (i) employs DNS results to characterize some of the effects of compressibility on turbulent velocity gradients, and (ii) develops simple mathematical models for velocity gradient dynamics in compressible turbulence. In the first part of the dissertation, effects of compressibility on velocity gradient invariants and the local topology of compressible turbulence are characterized employing DNS results of compressible decaying isotropic turbulence. Joint statistics of second and third invariants of velocity gradient tensor and the exact probability of occurrence of associated topologies conditioned upon dilatation (degree of compression/expansion of fluid) are computed. These statistics are found to be (i) highly dependent on dilatation and (ii) substantially different from the statistics observed in incompressible turbulence. These dilatation-conditioned statistics of compressible turbulence, however, are found to be fairly independent of Mach number and Reynolds number. In the second part of the dissertation, two mathematical models for compressible velocity gradient dynamics are developed. To take into account the significant aero-thermodynamic coupling that exists in compressible flows, the models are derived explicitly using the continuity, energy and state equations, along with the momentum equation. The modeling challenge involved in the development of these models lies in capturing the inherently non-local nature of pressure and viscous effects as a function of local terms to derive a closed set of ordinary differential equations. The models developed in this dissertation are evaluated in a variety of flow regimes - incompressible limit (low Mach number); pressure-released limit (extremely high Mach number); and intermediate (sub-sonic Mach numbers) - and are shown to recover a range of known compressibility effects.

Rapid Distortion Theory is used to perform calculations of unsteadily-forced initially isotropic turbulence so that the physics of such flows can be better understood. The results of these calculations show that there are three distinct regimes of physical behavior for the kind of turbulence that we are considering: (1) turbulence that is forced at a relatively low frequency in which the kinetic energy settles down to a constant value at later times, (2) turbulence that is forced at a slightly higher frequency in which the kinetic energy value oscillates for a time, but then increases dramatically, and (3) turbulence that is forced at a relatively high frequency in which the kinetic energy evolution exhibits a periodic behavior. To better understand the role of the rapid pressure-strain correlation, these results are also compared to Inertial Model results for the same set of forcing frequencies. The results of this comparison show that the rapid pressure plays a key role in determining the stability characteristics of unsteadily-forced turbulence. The evolution equation for kinetic energy is then used to propose a model that describes the behavior approximately in terms of a time lag between applied mean strain and the Reynolds stress. This model suggests that the different responses under the different frequencies of forcing correspond to different stress-strain time lags. Overall, then the results indicate that rapid pressure serves to create a time lag between applied stress and strain, and it is the extent of this time lag that causes turbulence to respond differently under various frequencies of forcing.

Particle Image Velocimetry (PIV) and pressure measurement techniques were performed to investigate the drag reduction due to microbubble injection in the boundary layer of a fully developed turbulent channel flow. Two-dimensional full-field velocity components in streamwise-near-wall normal plane of a turbulent channel flow at Reynolds number of 5128 based on the half height of the channel were measured. The influence of the presence of microbubbles in the boundary layer was assessed and compared with single phase channel flow characteristics. A drag reduction of 38.4% was achieved with void fraction of 4.9%. The measurements were analyzed by studying the turbulence characteristics utilizing wavelet techniques. The wavelet cross-correlation and auto-correlation maps with and without microbubbles were studied and compared. The two-dimensional and threedimensional wavelet maps were used to interpret the results. The following observations were deduced from this study: 1. The microbubble injection within the boundary layer increases the turbulent energy of the streamwise velocity components of the large scale (large eddy size, low frequency) range and decreases the energy of the small scale (small eddy size, high frequency) range. 2. The wavelet cross-correlation maps of the normal velocities indicate that the microbubble presence decrease the turbulent energy of normal velocity components for both the large scale (large eddy size, low frequency) and the small scale (small eddy size, high frequency) ranges. 3. The wavelet auto-correlation maps of streamwise velocity shows that the intensities at low frequency range were increased with microbubble presence and the intensities at high frequency range were decreased. 4. The turbulent intensities for the normal fluctuating velocities at both low frequency and high frequency range were decreased with microbubble injection. This study presents the modifications in the characteristics of the boundary layer of channel flow which are attributed to the presence of microbubbles. Drag reduction studies with microbubble injections utilizing wavelet techniques are promising and are needed to understand the drag reduction phenomena.

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 179-183).

Reproduction de : Thèse de doctorat : Génie des procédés et de l'environnement : Toulouse, INPT : 2005. / Titre provenant de l'écran-titre. Bibliogr. 134 réf.

Thèse doctorat : Acoustique : Villeurbanne, INSA : 2004. / Titre provenant de l'écran-titre. Bibliogr. p. 173-177.

Reproduction de : Thèse de doctorat : Sciences de la Terre et de l'environnement : Toulouse, INPT : 2005. / Titre provenant de l'écran-titre. Bibliogr. 77 réf.

Reproduction de : Thèse de doctorat : Dynamique des fluides : Toulouse, INPT : 2005. / Titre provenant de l'écran-titre. Bibliogr. 124 réf.

Reproduction de : Thèse de doctorat : Dynamique des fluides : Toulouse, INPT : 2006. / Titre provenant de l'écran-titre. Bibliogr. 39 réf.

Reproduction de : Thèse de doctorat : Énergétique et transfert : Toulouse, INPT : 2006. / Titre provenant de l'écran-titre. Bibliogr. 104 réf.