IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

In this work we establish a link between a Reynolds averaged turbulence modeling methodology, containing interactions up to the second order correlations between the velocity fluctuations at various scales, and a multi-objective optimization problem with the constraints expressed in terms of equality and inequality, imposed by the given boundary conditions and the positive semi-definiteness of the Reynolds stress tensor, etc. The information unavailability and uncertainty associated with the boundary conditions for the fluctuation correlations of various orders is delineated, and the information from the Navier-Stokes equations is utilized to the extent allowed by the available input data necessary for simulations; turbulence from the perspective of systems simulation is explored and some objective functions are proposed. Finally, the challenges faced by the formulation and the issues yet to be resolved are discussed. © 2009.

Department of Aerospace Engineering

World University root node

Nonlinear Analysis: Real World Applications

Turbulence modeling from a new perspective

We investigate the applicability of Poincaré's and the quantum recurrence theorems to the physical systems such as a container filled with a gas from a physical perspective. We discuss certain difficulties with regard to the definition of the Hamiltonian for such systems and the existence of one-to-one mappings as solutions to the equations of motion. We examine a typical proof of Poincaré's recurrence theorem and notice that a key part of the proof appeals to the motion of a neighborhood of finite volume in a phase space and this neighborhood possesses infinite kinetic energy, raising another question concerning the applicability of the theorem to physical systems. The same situations also present themselves in the application of Liouville's theorem. © 2008 Elsevier B.V. All rights reserved.

Communications in Nonlinear Science and Numerical Simulation

A note on the applicability of recurrence theorems

In this paper we develop a description for the mechanical response of non-dissipative solids. Unlike the classical approach, a relative deformation gradient tensor is introduced and, based on the second law of thermodynamics, the Cauchy stress is derived from a potential function for the relative deformation tensor and the preferred directions associated with the material symmetry possessed by a non-dissipative solid. The requirement of Galilean invariance and the symmetry of the Cauchy stress are then employed to restrict the form of the potential, with the help of invariance theory. Finally, the implications of the formulation are explored by considering special cases of symmetry such as isotropy, transverse isotropy and orthotropy. The difference between the present approach and the standard treatment of elasticity are discussed. © 2006 Elsevier B.V. All rights reserved.

Department Of Civil Engineering

On the response of non-dissipative solids

The increased use of heating in many medical specialties is driven by the availability of new devices, not an understanding of the underlying physics. Whereas most prior studies have quantified material response characteristics before and after thermal damage, the goal of this work is to describe changing response characteristics during a particular class of thermal damage tests-biaxial isometric tests on collagenous biomembranes. Evolution equations are derived/postulated that provide a good fit to data but more generally provide direction for future work.

Note di Matematica

A model for the kinetics of thermal damage of biological membranes

This note reexamines Biot's model for the propagation of acoustic waves in a material such as cohensionless sand, infused with a fluid, within the context of mixture theory. Instead of the standard entropy equation that is used in mixture theory, an inequality for the viscous dissipation is employed here due to a conceptual difficulty that one encounters in applying the standard equation to a mixture of sand and a fluid. The wave equations are reformulated by taking the velocity field, instead of the displacement, for the fluid as a primary quantity. By recognizing and thereby exploiting the dependence of the stored energy of the sand on the pore fluid pressure and choosing an appropriate form for the rate of dissipation, a set of governing equations are obtained which are equivalent to those derived by Biot [J. Acoust. Soc. Am. 28(1956) 168, 179; J. Appl. Phys. 33(1962) 1482]. A differential equation for the pore fluid pressure is derived and the effects of drag and virtual mass are dealt with in a unified fashion. The procedure allows us to develop generalizations to Biot's equations in a rational manner.

International Journal of Non-Linear Mechanics

On the propagation of waves through porous solids

Some basic issues in constitutive modeling are examined. The first concerns the requirement of material frame indifference, the commonly used version is analyzed under the restriction that the effect of relativity is negligible. The second deals with the entropy production inequality in the modeling of large scale motions and the uncertainty involved in formulating such an inequality as a constraint in developing constitutive relations is discussed. Finally, the use of Lagrangian frames and reference configurations and related questions concerning the development of a constitutive model for turbulent flows of a fluid, on the basis of laminar flows of that fluid, is discussed. © 2003 Elsevier B.V. All rights reserved.

Some issues in constitutive modeling

We propose a thermodynamic framework for describing the microwave drying process of aqueous dielectrics based on Maxwell-Lorentz field equations and mixture theory. Several issues are discussed such as the form of entropy equation; the constitutive relations for the macroscopic electric polarization vectors, Cauchy stresses, heat fluxes, internal momentum supplies, etc., for each component of the mixture: porous solid, water and gas in different regions; and the interfacial jump conditions between different regions in the mixture. A brief examination of the status of material frame indifference within the context of our framework is presented.

Zeitschrift fur Angewandte Mathematik und Physik

Modeling of the microwave drying process of aqueous dielectrics

This note presents a random walk formulation of small particle tracking within the framework of averaged turbulence modeling. Several issues, such as a justification for the finite number of multi-point correlations to be taken, the adoption of just one two-point correlation rather than several, and construction of specific models, are discussed. It offers a new perspective on random walk modeling of small particle dispersion and suggests some possible improvements to existing models, especially with regard to taking into account the spatial correlation explicitly. © 2002 Published by Elsevier Science B.V.

A new perspective on random walk modeling of particle dispersion

We propose a framework to describe the mechanical behavior of thermally damaged biological soft tissues based on a melding of ideas from classical continuum thermodynamics and irreversible thermodynamics. Relevant assumptions are delineated, details of the constitutive formulation are provided, and a set of interfacial conditions are derived that can be used as the boundary conditions for certain diffusion processes. The utility of the framework is illustrated by considering two problems that correspond to tractable experiments: transverse diffusion through a finitely deformed membrane, and radial diffusion in a thermally damaged cylindrical tissue. © 2001 Elsevier Science Ltd.

International Journal of Engineering Science

A mixture theory for heat-induced alterations in hydration and mechanical properties in soft tissues

Despite the intense effort expended towards obtaining a model for describing the turbulent flows of fluid, there is no model at hand that can do an adequate job. This leads us to look for a non-traditional approach to turbulence modeling. In this work we conjoin the notion of large eddy simulation with those of fuzzy sets and neural networks to describe a class of turbulent flows. In previous works we had discussed several issues concerning large eddy simulation such as filtering and averaging. Here, we discuss the use of fuzzy sets to improve the filtering procedure.

Discrete large eddy simulation

For large eddy simulation of turbulent flows, some analysis and general remarks on the filtering operation and modeling under small filtering length scales are presented.

Remarks on large eddy simulation

We propose a framework to develop turbulence models based on single-point closure through a probability distribution function. The evolution equation for the characteristic function is formed and the possible way of constructing specific models is addressed.

American Society of Mechanical Engineers, Applied Mechanics Division, AMD

A PDF formulation on turbulence modeling

International Journal of Nonlinear Sciences and Numerical Simulation

A PDF Formulation on Turbulence Modeling of Single-Point Closure

Rotor-bearing systems supported on squeeze film dampers (SFDs) show large amplitude vibratory motions when traversing critical speeds. At these operating conditions air is drawn into the damper thin film clearance generating a bubbly mixture with the lubricant and producing SFD forces not readily predictable with currently available analysis. A continuum model is proposed for describing the motion of a bubbly fluid in an open ended SFD operating with circular centered journal orbits. Computed predictions for peak-peak dynamic pressures and fluid film forces agree reasonably well with experimental measurements conducted on a SFD test rig operating with a controlled air in oil mixture. The bubbly flow model provides an initial procedure towards the reliable design of SFDs in actual operating conditions.Rotor-bearing systems supported on squeeze film dampers (SFDs) show large amplitude vibratory motions when traversing critical speeds. At these operating conditions air is drawn into the damper thin film clearance generating a bubbly mixture with the lubricant and producing SFD forces not readily predictable with currently available analysis. A continuum model is proposed for describing the motion of a bubbly fluid in an open ended SFD operating with circular centered journal orbits. Computed predictions for peak-peak dynamic pressures and fluid film forces agree reasonably well with experimental measurements conducted on a SFD test rig operating with a controlled air in oil mixture. The bubbly flow model provides an initial procedure towards the reliable design of SFDs in actual operating conditions.

Journal of Tribology

Analysis of squeeze film dampers operating with bubbly lubricants

This note presents a formulation on large eddy simulation with the idea motivated by Fourier series representation. A set of filtered equations are obtained.