In this study, the behavior of pressure in the Rapid Distortion Limit, along with its
concomitant modeling, are addressed. In the first part of the work, the role of pressure in
the initiation, propagation and suppression of flow instabilities for quadratic flows is
analyzed. The paradigm of analysis considers the Reynolds stress transport equations to
govern the evolution of a dynamical system, in a state space composed of the Reynolds
stress tensor components. This dynamical system is scrutinized via the identification of
the invariant sets and the bifurcation analysis. The changing role of pressure in quadratic
flows, viz. hyperbolic, shear and elliptic, is established mathematically and the
underlying physics is explained. Along the maxim of "understanding before prediction", this allows for a deeper insight into the behavior of pressure, thus aiding in its modeling.
The second part of this work deals with Rapid Pressure Strain Correlation modeling in
earnest. Based on the comprehension developed in the preceding section, the classical
pressure strain correlation modeling approaches are revisited. Their shortcomings, along
with their successes, are articulated and explained, mathematically and from the
viewpoint of the governing physics. Some of the salient issues addressed include, but are not limited to, the requisite nature of the model, viz. a linear or a nonlinear structure,
the success of the extant models for hyperbolic flows, their inability to capture elliptic
flows and the use of RDT simulations to validate models. Through this analysis, the
schism between mathematical and physical guidelines and the engineering approach, at
present, is substantiated. Subsequently, a model is developed that adheres to the classical
modeling framework and shows excellent agreement with the RDT simulations. The
performance of this model is compared to that of other nominations prevalent in
engineering simulations. The work concludes with a summary, pertinent observations
and recommendations for future research in the germane field.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2010-05-8018 |
| Date | 2010 May 1900 |
| Creators | Mishra, Aashwin A. |
| Contributors | Girimaji, Sharath S. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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