Book of Abstract: Flow and transport in porous media with - PDF document

Book of Abstract: “Flow and transport in porous media with applications” Prof. K. Muralidhar Department of Mechanical Engineering Indian Institute of Technology Kanpur; Kanpur 208106 Abstract: Flow, heat, and mass transfer in porous media are encountered in a great many fields of engineering: civil, chemical, mechanical and petroleum, to name a few. A wide variety of flow patterns can be realized in the porous medium. These are controlled by the flow regime - for example, steady or unsteady, laminar or turbulent, fluid interfaces in multi-phase flow, non-equilibrium phenomena in the transported variables such as pressure, temperature and concentration, chemical reactions, and phase change. Additionally, it is well-established that flow patterns and transport depend intricately on the variability of the pore space and the solid matrix. Strategies employed for studying transport phenomena in a non-uniform porous medium include the following: 1. Formulate the governing equations for an inhomogeneous, anisotropic region. Properties such as permeability and dispersion are interpreted here as second order tensors that have built-in dependence on spatial location. 2. Permeability and dispersion are treated as random variables with a well-defined average that can be a function of space. These are associated with appropriate statistics that account for fluctuations in the physical properties and possible spatial correlation, apart from correlations among the properties themselves. While approach 1 leads to a deterministic model that can be solved by a numerical technique, approach 2 leads to a stochastic model that must be solved several times to generate realizations of the resulting flow and scalar fields. One of the major difficulties encountered in the two approaches referred above pertains to the sensitivity of the predicted variables on the specification of pore-scale variation (deterministic or statistical). For example, a refinement of the computational grid will permit greater details of the pore structure to be prescribed and yield a completely new solution. Yet another difficulty is experienced when the model parameters have to be determined from laboratory or field-scale experiments. The scale of measurements may be such that variations on a smaller scale are completely masked. The difficulties become compounded when transport occurs over a wide range of length scales or over an extremity of pore scales. The best one can accomplish is to determine parameters in such a way that a few limited goals of the mathematical model are fulfilled, though the estimations may not strictly conform to every possible variation in the pore geometry. The subject of hierarchical modeling of transport in porous media is in its infancy. The present talk is introductory and deterministic modeling of flow and transport in porous media will be discussed. Applications relate to enhanced oil recovery, regenerators, recovery of gas hydrates, and coil embolization in medical treatment. Research directions in this field will be highlighted.

“Dynamics of a radially expanding liquid sheet” Prof. Mahesh S Tirumkudulu Department of Chemical Engineering Powai, IIT-Bombay Abstract: A fundamental understanding of the break-up of bulk liquids and subsequent drop formation is important in areas as diverse as spray coating, combustion, and in biomedical devices such nebulizers. One such route of atomization involves radial liquid sheets generated by laminar jet impingement which eventually break-up into fine droplets. Radial liquid sheets are formed by head-on impingement of liquid jets, where the liquid sheet spreads out radially in a plane perpendicular to direction of the jets. We focus on the dynamics of break-up of such liquid sheets when the point of impingement is subjected to perturbations via acoustic forcing of controlled sound intensity and frequency to identify regimes of accelerated and violent sheet break-up. Stability equations are derived from the inviscid flow equations for a radially expanding sheet that govern the time-dependent evolution of the two liquid interfaces. The analysis accounts for the varying liquid sheet thickness while the inertial effects due to the surrounding gas phase is ignored. When the sheet is excited at a fixed frequency, a small sinuous displacement introduced at the point of impingement grows as it is convected downstream suggesting that the sheet is unstable at all Weber numbers (ratio of inertia to surface tension forces) in the absence of the gas phase. Asymptotic analysis of the sinuous mode for large frequencies shows that the disturbance amplitude diverges inversely with the distance from the edge of the sheet. The varicose waves (thickness modulations), on the other hand, are neutrally stable at all frequencies and are convected at the speed of the liquid jet. To test the predictions of the theory, we used laser induced fluorescence technique (LIF) to determine the thickness variation and deflection of the sheet for varying sound pressure levels and frequencies. In the absence of the disturbance, the measured liquid sheet thickness varies inversely with radial distance from the point of impingement for the smooth sheet and matches well with theoretical predictions. When the perturbations are introduced, sheet undergoes flag like motion though the thickness modulations appear to negligible. The measured wave speed, wavelengths and growth rates of the sinuous waves match with those predicted by the theory confirming that the sinuous waves are unstable and that a simple theory that ignores the inertia of the surrounding gas phase is sufficient to capture the main aspects of the sheet dynamics.

“Effect of specimen size on strength in concrete under axial compression” Prof. ArghyaDeb Department of Civil Engineering, IIT Kharagpur Abstract: In the absence of significant plastic deformations, the effect of specimen size on nominal strength of tensile specimens is well known. In case of quasi-brittle materials such as concrete, where specimen size plays an important role in determining whether LEFM is applicable, Bazant and his collaborators have, since 1981, formulated a size-effect law for concrete specimens subjected to tensile stresses. While this law has been found to be a reasonable fit to experimental data in concrete flexural members, its extension to concrete compression members (again by Bazant and co-workers) is somewhat controversial. In this presentation, the existing state of experimental knowledge and conclusions therefrom, for unconfined concrete specimens subjected to uniaxial compression, will be summarized. Next, the case for an energetic size effect, amenable to deterministic treatment, will be presented – along with some recent numerical results. The effect of specimen size on strength in concrete columns subjected to triaxial compression will be discussed. Here, the existing experimental data seems to confirm that no size effect exists. However some recent numerical results seem to show the existence of a significant size effect in weakly confined concrete members, which however becomes insignificant as confining pressure is increased. What is also interesting is that the deterministic size effect in weakly confined systems may actually be higher than in unconfined systems. Tentative explanations for this behavior will be presented.

“Non--linear dynamics of non--smooth systems using smoothening schemes” Prof. P. Chandramouli Department of Mechanical Engineering Indian Institute of Technology Madras, Chennai 600036 Abstract: Dry friction damping is an effective way of reducing the resonant amplitudes inturbine bladed system where the inherent structural damping is very small. One method ofinducing damping in such systems is by providing shrouds at the tip of the blades. In this case,the shrouds constrain the blade motion not only along the contact plane but also along thedirection normal to the contact plane. The tangential motion along the contact plane results infriction between the contact surfaces and the interface undergoes stick slip motion. The motionnormal to the contact plane results in intermittent separation and impact of the contactingsurfaces. In this talk the nonlinear dynamics of such dry friction damped systems is investigated withapplication to the vibration damping in shrouded turbine blade systems. A contactelement proposed by Yang and Menq is used to model the contact interface, the stick slip motioninduced by friction and the intermittent separation and impact due to variable normal load. The dynamics of these systems are governed by differential equations of discontinuous naturewhich are treated as Filippov systems for smoothening the dynamics. It is shown that such smoothening enables the solution of these kind of systems for situations where even numerical integration has convergence issues. Assuming periodic motion of the interface the transition times corresponding to different states are computed and the hysteresis plots generated. A multi-harmonic balance procedure in combination with path following based on an arc length continuation is used to generate the periodic solutions.