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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-12-7301 |
| Date | 2009 December 1900 |
| Creators | Suman, Sawan |
| Contributors | Girimaji, Sharath |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | application/pdf |
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