Research Activities

Here are the abstracts the major projects I have done:

1. One-dimensional model of Microscale Compressible Flows with Friction, Heat Transfer and Slip through Constant Area Ducts.

The current study is an extension of the classical one-dimensional treatment on compressible flows of ideal gases through microchannels. Most of the reported  analytical studies on compressible flows ignore the effect of slip at the walls and also the substantiality of the viscous dissipation. However, several aspects of the present study make it disctinctive as compared to the other studies reported in the literature.

The only notable analytical studies reported on compressible microchannel flows consider very low Mach number regimes, and hence are unable to offer physical insights on the implications of microscale effects on various flow transitions taking place around the Mach number of unity. The present study aims to overcome the constraints by deriving a generalized theoretical framework for assessing the implications of interfacial slip and viscous dissipation on the significant physical characteristics of microscale gas flows, with a provision of accounting for fluid friction and wall heat transfer effects.

Considering cross-sectionally averaged quantities, equations of mass, momentum and energy conservation are suitably invoked in conjunction with the closure relationships depicting the equation of state as well as the extent of compressibility of the flow medium. The effect of fluid friction is accounted for in the one-dimensional theoretical framework by considering an approximate velocity profile consistent with the wall slip conditions. This leads to an axially varying friction coefficient, by virtue of continuous variation of the Knudsen number along that direction. This is in sharp contrast with the traditional treatment that routinely presumes a constant friction factor by virtue of operating in the turbulent regime, whereas the regime of operation in the microscale is mostly laminar. In addition, these velocity profiles are utilized to estimate the consequences of viscous dissipation, which unlike classical flow do not turn out to be trivially negligible for microfluid transport.  Moreover, the energy dissipation on account of work done due to pressure gradients is also considered in the one-dimensional formalism. With these considerations, the alterations in the choking length due to microscale effects are aptly pinpointed under the conditions of the specified inlet Mach number, temperature and pressure.

These studies are subsequently extended to the cases of non-adiabatic walls with heat rejections. Interestingly and non-trivially, it is revealed that such boundary heat flows may reverse the effects of friction and heat transfer as established in the classical compressible flow theory. This effect is investigated in details, leading to an optimum value of the wall heat flux consistent with the specified inlet conditions to avoid choking.

2. Modeling of One Dimensional Spherical Implosion in a Thermo-nuclear Device

Multiphase and multiscale problems such as flows with shocks, interfacial flows, shocks interacting with an interface, and flows with contact discontinuities are critical in fusion research, and as a result in meeting the energy challenges in our future. An implosion device such as an Inertial Confinement Fusion capsule consists of a fuel material surrounded by a spherical metal shell. During the implosion of these devices, triggered by laser bombardment, the turbulent mixing that occurs between the layers is of paramount importance, largely affecting the performance of the device. The current study aims at developing mathematical models to simulate this process of turbulent mixing.

A one-dimensional model in spherical geometry is considered which consists of two layers of different densities and having a time-dependent pressure applied across them. A shock occurs at the interface of these two layers which keeps moving with time as the effect of pressure and in due course gets reflected from the inner and outer boundaries as well. The movement and the reflection of this interface is clearly demonstrated along with the variation of pressure and density along the radius of the device which also pinpoints the location of the shock at a certain time interval and its movement.

The results obtained from these simulations can be used for validating the existing engineering models and in designing control strategies to maximize performance of fusion fuel capsules. This also eliminates the need for the expensive actual testing of the device. The turbulent mixing studied here also occurs prominently in supernova formation, where it is regarded as the primary mechanism of detonation.

3. Application of the Schlieren Photography Technique to determine the Frequency of Turbulence in and the Distribution of Temperature in air surrounding a Heat Source

Although, the high speed imaging and cinematography has an important application in various research fields and in detection of firearms and explosions, the required optical equipment is generally not available for such research due to the small aperture and delicacy of the optics and the expense and expertise required to implement high-speed optical methods. The Schlieren imaging technique serves this purpose well. It uses a shadow phenomenon to capture the images with the help of a high speed camera, thus protecting the camera lens from the negative effects of very bright light. The shadowgraph and schlieren methods are generally regarded as items of laboratory apparatus for visualizing inhomogeneities in transparent media.

In the current study, using a typical schlieren setup using a heat source such as a candle, the turbulence in the surrounding air is analyzed. A video of the shadowgraph and the schlieren image due to the disturbance by the heat source is taken which records images at a high frame rate. The individual frames are then observed and the variation of intensity across a particular point across the frames is observed to determine the variation of properties in the air at that point. The pattern of the variation of intensity with time at a particular point is obtained which can be used to determine the frequencies of the turbulence.

Another interesting application is to determine the temperature field around the disturbance which is a heat source.  This is done by preparing displacing the knife edge used in the schlieren technique and recording images at its various locations. A calibration curve of intensity is prepared in absence of the disturbance with which the intensity in presence of the disturbance is compared to arrive at the temperature field distribution.

4. Modeling of Non-Equilibrium Phenomena across a Liquid-Vapor Interface during Evaporation

The current study aims on developing a fundamental model of the process of evaporation from the kinetic control point of view. The model is used to determine the thermal characteristics across the liquid and vapor phases during the process of evaporation, while also investigating the temperature jump that occurs at the interface of the liquid and vapor layers.

Both planar and spherical settings are considered. For either cases, a model is developed that describes the variation of temperature in the liquid and vapor phases. The boundary temperatures are specified and depending upon the variation, the temperatures at the interface are arrived at. The two important parameters associated with the process of evaporation are the mass flux and the energy flux. These parameters are obtained from the knowledge of the condensation and the evaporation coefficients. The dependence of these coefficients on the physical properties is investigated. For calculation of the mass flow rate, some valid assumptions are made.