Browsing by Subject "rapid distortion theory"
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Item A Dynamical Systems Approach Towards Modeling the Rapid Pressure Strain Correlation(2011-08-08) Mishra, Aashwin A.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.Item Charecterization of inertial and pressure effects in homogeneous turbulence(Texas A&M University, 2005-11-01) Bikkani, Ravi KiranThe objective of the thesis is to characterize the linear and nonlinear aspects of inertial and pressure effects in turbulent flows. In the first part of the study, computations of Navier-Stokes and 3D Burgers equations are performed in the rapid distortion (RD) limit to analyze the inviscid linear processes in homogeneous turbulence. By contrasting the results of Navier- Stokes RD equations and Burgers RD equations, the effect of pressure can be isolated. The evolution of turbulent kinetic energy and anisotropy components and invariants are examined. In the second part of the thesis, the velocity gradient dynamics in turbulent flows are studied with the help of inviscid 3D Burgers equations and restricted Euler equations. The analytical asymptotic solutions of velocity gradient tensor are obtained for both Burgers and restricted Euler equations. Numerical computations are also performed to identify the stable solutions. The results are compared and contrasted to identify the effect of pressure on nonlinear velocity gradient dynamics. Of particular interest are the sign of the intermediate principle strain-rate and tendency of vorticity to align with the intermediate principle strain-rate. These aspects of velocity gradients provide valuable insight into the role of pressure in the energy cascade process.Item Rapidly Sheared Compressible Turbulence: Characterization of Different Pressure Regimes and Effect of Thermodynamic Fluctuations(2011-10-21) Bertsch, Rebecca LynneRapid distortion theory (RDT) is applied to compressible ideal-gas turbulence subjected to homogeneous shear flow. The study examines the linear or rapid processes present in turbulence evolution. Specific areas of investigation include:(i) characterization of the multi-stage flow behavior,(ii) changing role of pressure in the three-regime evolution and (iii) influence of thermodynamic fluctuations on the different regimes. Preliminary investigations utilizing the more accurate Favre-averaged RDT approach show promise however, this approach requires careful validation and testing. In this study the Favre-averaged RDT approach is validated against Direct Numerical Simulation (DNS) and Reynolds-averaged RDT results. The three-stage growth of the flow field statistics is first confirmed. The three regime evolution of turbulence is then examined in three different timescales and the physics associated with each regime is discussed in depth. The changing role of pressure in compressible turbulence evolution shows three distinct stages. The physics of each stage is clearly explained. Next, the influence of initial velocity and thermodynamic fluctuations on the flow field are investigated. The evolution of turbulence is shown to be strongly dependent on the initial gradient Mach number and initial temperature fluctuations which tend to delay the onset of the second regime of evolution. The initial turbulent Mach number, which quantifies velocity fluctuations in the flow, influences turbulence evolution only weakly. Comparison of Reynolds-averaged RDT against Favre-averaged RDT for simulations of nonzero initial flow field fluctuations shows the higher fidelity of the latter approach.Item Selected problems in turbulence theory and modeling(Texas A&M University, 2004-09-30) Jeong, Eun-HwanThree different topics of turbulence research that cover modeling, theory and model computation categories are selected and studied in depth. In the first topic, "velocity gradient dynamics in turbulence" (modeling), the Lagrangian linear diffusion model that accounts for the viscous-effect is proposed to make the existing restricted-Euler velocity gradient dynamics model quantitatively useful. Results show good agreement with DNS data. In the second topic, "pressure-strain correlation in homogeneous anisotropic turbulence subject to rapid strain-dominated distortion" (theory), extensive rapid distortion calculation is performed for various anisotropic initial turbulence conditions in strain-dominated mean flows. The behavior of the rapid pressure-strain correlation is investigated and constraining criteria for the rapid pressure-strain correlation models are developed. In the last topic, "unsteady computation of turbulent flow past a square cylinder using partially-averaged Navier-Stokes method" (model computation), the basic philosophy of the PANS method is reviewed and a practical problem of flow past a square cylinder is computed for various levels of physical resolution. It is revealed that the PANS method can capture many important unsteady flow features at an affordable computational effort.