K. Muralidhar

Three-dimensional study of flow past a square cylinder at low Reynolds numbers

Abstract The spatial evolution of vortices and transition to three-dimensionality in the wake of a square cylinder have been numerically studied. A Reynolds number range between 150 and 500 has been considered. Starting from the two-dimensional Karman vortex street, the transition to three-dimensionality is found to take place at a Reynolds number between 150 and 175. The three-dimensional wake of the square cylinder has been characterized using indicators appropriate for the wake of a bluff body as described by the earlier workers. In these terms, the secondary vortices of Mode-A are seen to persist over the Reynolds number range of 175–240. At about a Reynolds number of 250, Mode-B secondary vortices are present, these having predominantly small-scale structures. The transitional flow around a square cylinder exhibits an intermittent low frequency modulation due to the formation of a large-scale irregularity in the near-wake, called vortex dislocation. The superposition of vortex dislocation and the Mode-A vortices leads to a new pattern, labelled as Mode-A with dislocations. The results for the square cylinder are in good accordance with the three-dimensional modes of transition that are well-known in the circular cylinder wake. In the case of a circular cylinder, the transition from periodic vortex shedding to Mode-A is characterized by a discontinuity in the Strouhal number–Reynolds number relationship at about a Reynolds of 190. The transition from Mode-A to Mode-B is characterized by a second discontinuity in the frequency law at a Reynolds number of ≈250. The numerical computations of the present study with a square cylinder show that the values of the Strouhal number and the time-averaged drag-coefficient are closely associated with each other over the range of Reynolds numbers of interest and reflect the spatial structure of the wake.

A ROBUST MART ALGORITHM FOR TOMOGRAPHIC APPLICATIONS

The present work is concerned with the development of a robust reconstruction algorithm for applications involving tomography. In an earlier study it was shown that among the ART family of algorithms, the multiplicative algebraic reconstruction algorithm (MART) was the most appropriate for tomographic reconstruction [1]. In the present work, the MART algorithm has been extended so that (a) its performance is now acceptable over a wider range of relaxation factors, (b) the time requirement for convergence to a solution is lower, and (c) its performance is less sensitive to noise in the projection data. Applications considered for evaluating the proposed algorithms are (1) a circular region with holes, (2) a three-dimensional temperature field in a differentially heated fluid layer, and (3) experimental data recorded in a differentially heated fluid layer using an interferometer. The proposed algorithms are seen to be an improvement over those presently available, for all three examples considered.

Performance of iterative tomographic algorithms applied to non-destructive evaluation with limited data

Iterative tomographic algorithms have been applied to the reconstruction of a two-dimensional object with internal defects from its projections. Nine distinct algorithms with varying numbers of projections and projection angles have been considered. Each projection of the solid object is interpreted as a path integral of the light-sensitive property of the object in the appropriate direction. The integrals are evaluated numerically and are assumed to represent exact data. Errors in reconstruction are defined as the statistics of difference between original and reconstructed objects and are used to compare one algorithm with respect to another. The algorithms used in this work can be classified broadly into three groups, namely the additive algebraic reconstruction technique (ART), the multiplicative algebraic reconstruction technique (MART) and the maximization reconstruction technique (MRT). Additive ART shows a systematic convergence with respect to the number of projections and the value of the relaxation parameter. MART algorithms produce less error at convergence compared to additive ART but converge only at small values of the relaxation parameter. The MRT algorithm shows an intermediate performance when compared to ART and MART. An increasing noise level in the projection data increases the error in the reconstructed field. The maximum and RMS errors are highest in ART and lowest in MART for given projection data. Increasing noise levels in the projection data decrease the convergence rates. For all algorithms, a 20% noise level is seen as an upper limit, beyond which the reconstructed field is barely recognizable.

EVALUATION OF RHEOLOGICAL PROPERTIES OF MEDIUM FOR AFM PROCESS

Abrasive Flow Machining (AFM) is a new non-traditional machining process used to deburr, radius, polish, and remove recast layer of components used in a wide range of applications. Material removal in AFM takes place by flowing medium (i.e. carrier/or putty mixed with abrasive particles), across the surface to be machined. The medium is the key element in the process because of its ability to precisely abrade the selected areas along its flow path. From the literature review, it is found that there is a need to study how to evaluate rheological properties of the medium in general, and viscosity in particular. Viscosity of the medium has significant effects on the AFM process performance. In the present work, effects of concentration and mesh size of abrasive particles, and temperature of medium on the medium viscosity have been studied. To determine the viscosity of the abrasive medium, a viscometer has been designed and fabricated based on the principle of capillary viscometry. Experiments have been conducted at different abrasive concentrations and mesh sizes, and medium temperatures. It is observed from the experiments that the viscosity of the medium increases with the abrasive concentration and decreases with the abrasive mesh size and medium temperature. Theoretical values obtained from mathematical model, and experimental results are compared. The results of viscosity are correlated with the process performance parameters, i.e. material removal and surface roughness. It is observed that there is an increase in material removal and decrease in surface roughness value as viscosity of the medium increases.

Dropwise Condensation Underneath Chemically Textured Surfaces: Simulation and Experiments

Experimental observations of dropwise condensation of water vapor on a chemically textured surface of glass and its detailed computer simulation are presented. Experiments are focused on the pendant mode of dropwise condensation on the underside of horizontal and inclined glass substrates. Chemical texturing of glass is achieved by silanation using octyl-decyl-tri-chloro-silane (C 18 H 37 C 13 Si) in a chemical vapor deposition process. The mathematical model is built in such a way that it captures all the major physical processes taking place during condensation. These include growth due to direct condensation, droplet coalescence, sliding, fall-off, and renucleation of droplets. The effects arising from lyophobicity, namely the contact angle variation and its hysteresis, inclination of the substrate, and saturation temperature at which the condensation is carried out, have been incorporated. The importance of higher order effects neglected in the simulation is discussed. The results of model simulation are compared with the experimental data. After validation, a parametric study is carried out for cases not covered by the experimental regime, i.e., various fluids, substrate inclination angle, saturation temperature, and contact angle hysteresis. Major conclusions arrived at in the study are the following: The area of droplet coverage decreases with an increase in both static contact angle of the droplet and substrate inclination. As the substrate inclination increases, the time instant of commencement of sliding of the droplet is advanced. The critical angle of inclination required for the inception of droplet sliding varies inversely with the droplet volume. For a given static contact angle, the fall-off time of the droplet from the substrate is a linear function of the saturation temperature. For a given fluid, the drop size distribution is well represented by a power law. Average heat transfer coefficient is satisfactorily predicted by the developed model.

Mixed convection flow in a saturated porous annulus

Mixed convective flow and heat transfer are considered in the annular region between concentric cylinders filled with fluid-saturated porous material. The inner cylinder is heated and the outer cylinder cooled. The heat transfer rate from the inner cylinder as a function of the superimposed flow is studied, allowing for possible buoyancy effects. Both horizontal and vertical annuli are included in the study. The equations governing flow are numerically solved. Results have been obtained for a range of Peclet numbers, 0 < Pe < 10 and Rayleigh numbers, 0 < Ra < 500. The mixed convection regime is expected to be predominant for this range of parameters.

Analysis of flow and heat transfer in a regenerator mesh using a non-Darcy thermally non-equilibrium model

Abstract An analysis has been made for the pulsating flow of gas and the accompanying heat transfer within a regenerator made from mesh screens. A flow model is developed taking the mesh as a non-Darcy, thermally non-equilibrium porous medium. A harmonic analysis technique is used for solving the fully developed but unsteady gas flow in the regenerator. Based on the flow solution thus obtained, slowly evolving axisymmetric unsteady thermal fields are solved numerically over a wide range of frequencies by making use of the finite volume method. Presentation is made of the friction factor and regenerator effectiveness. Effects of Reynolds number and frequency on the temperature profile and the transient behavior of the system are discussed. The importance of a thermal time constant of the system and length-to-radius ratio of the regenerator demonstrated.

Reconstruction of the concentration field around a growing KDP crystal with schlieren tomography

Salt concentration distribution around a potassium dihydrogen phosphate (KDP) crystal growing from its aqueous solution has been experimentally determined using a laser schlieren technique. The growth process is initiated by inserting a KDP seed into its supersaturated solution, followed by slow cooling of the solution. Fluid convection leads to a distribution of concentration around the growing crystal. The pattern and strength of convection are important factors for the determination of the crystal growth rate and quality. Experiments have been conducted in a beaker with a diameter of 16.5 cm and a height of 23 cm. A monochrome schlieren technique has been employed to image the concentration field from four view angles, namely, 0 degrees, 45 degrees, 90 degrees, and 135 degrees. By interpreting the schlieren images as projection data of the solute concentration, the three-dimensional concentration field around the crystal has been determined using the convolution backprojection algorithm. The suitability of the overall approach has been validated using a simulated convective field in a circular differentially heated fluid layer, where full as well as partial data are available. Experiments have been conducted in the convection-dominated regime of crystal growth. The noncircular shape of the crystal is seen to affect axisymmetry of the concentration field close to the crystal surface. The reconstructed concentration fields reveal symmetry of the flow field away from the growing crystal. The solute concentration contours show large growth rates of the side faces of the crystal in comparison with the horizontal faces. In this respect, the concentration profiles are seen to correlate with the crystal geometry.

Vortex structures and kinetic energy budget in two-dimensional flow past a square cylinder

Abstract Direct Numerical Simulation of unsteady, two-dimensional flow past a square cylinder placed centrally in a channel has been carried out using a higher order finite difference scheme. A Reynolds number of 100 has been considered in the computation. The flow in the wake is found to be unsteady with a strong periodic component. The instantaneous vorticity field at this Reynolds number is seen to be spatially coherent. Maps of stress components formed from the oscillatory components of the velocity field ũ and ṽ show double peaks in u u and u v but a single peak in v v . The maps are seen to be symmetric about the centreline of the flowspace. The results obtained in the present work are qualitatively similar to the phase-averaged plots from the experiments reported at high Reynolds numbers. Hence, the primary conclusion of the present study is that the unsteady flows with one or a few dominating frequencies (periodic or quasi-periodic) are statistically similar to a fully turbulent flow. To assess the similarity further, the energy transfer mechanism between the mean motion and the fluctuations has been studied through different terms associated with kinetic energy budget of the fluctuating velocities. The total pressure, the advection of the time-mean flow and production terms are found to be primarily responsible for the energy cascade. In contrast, diffusion and dissipation do not appear to have a significant influence on the energy transfer mechanism.

Dropwise Condensation Studies on Multiple Scales

Recent advances in nanotechnology, chemical/physical texturing and thin film coating technology generate definite possibilities for sustaining a dropwise mode of condensation for much longer durations than was previously possible. The availability of superior experimental techniques also leads to deeper understanding of the process parameters controlling the relevant transport phenomena, the distinguishing feature of which is the involvement of a hierarchy of length/time scales, proceeding from nuclei formation, to clusters, all the way to macroscopic droplet ensemble, drop coalescence, and subsequent dynamics. This paper is an attempt to connect and present a holistic framework of modeling and studying dropwise condensation at these multiple scales. After a review of the literature, discussions on the following problems are presented: (i) atomistic modeling of nucleation; (ii) droplet–substrate interaction; (iii) surface preparation; (iv) simulation of fluid motion inside sliding drops; (v) experimental determination of the local/ average heat transfer coefficient; and (vi) a macroscopic model of the complete dropwise condensation process underneath horizontal and inclined surfaces. The study indicates that hierarchal modeling is indeed the way forward to capture the complete process dynamics. The microscopic phenomena at the three-phase contact line, leading to the apparent droplet contact angle, influence the shear stress and heat transfer. The nucleation theory captures the quasi-steady-state behavior quite satisfactorily, although the early atomistic nucleation was not seen to have a profound bearing on the steady-state behavior. The latter is strongly governed by the coalescence dynamics. Visual observation of dropwise condensation provides important information for building hierarchical models.