Mahesh V Panchagnula

The characteristic features of sprays pose unique challenges to multiphase flow methods that are used to model and simulate their behavior. This article reviews the principal modeling challenges posed by sprays, and discusses the capabilities of different modeling approaches by classifying them according to the basis for their statistical representation and the level of closure. The article goes on to provide guidelines for their comparative assessment and also a perspective on the outlook for spray modeling. Multiphase flow simulation approaches that are used for spray computations are classified according to scale, accuracy, computational cost and problem complexity. The requirements of a simulation method to be successfully used for spray computation are then discussed. The review concludes with a perspective on the outlook for spray simulation methods.

Pulmonary drug delivery systems rely on inhalation of drug-laden aerosols produced from aerosol generators such as inhalers, nebulizers etc. On deposition, the drug molecules diffuse in the mucus layer and are also subjected to mucociliary advection which transports the drugs away from the initial deposition site. The availability of the drug at a particular region of the lung is, thus, determined by a balance between these two phenomena. A mathematical analysis of drug deposition and retention in the lungs is developed through a coupled mathematical model of aerosol transport in air as well as drug molecule transport in the mucus layer. The mathematical model is solved computationally to identify suitable conditions for the transport of drug-laden aerosols to the deep lungs. This study identifies the conditions conducive for delivering drugs to the deep lungs which is crucial for achieving systemic drug delivery. The effect of different parameters on drug retention is also characterized for various regions of the lungs, which is important in determining the availability of the inhaled drugs at a target location. Our analysis confirms that drug delivery efficacy remains highest for aerosols in the size range of 1-5 μm. Moreover, it is observed that amount of drugs deposited in the deep lung increases by a factor of 2 when the breathing time period is doubled, with respect to normal breathing, suggesting breath control as a means to increase the efficacy of drug delivery to the deep lung. A higher efficacy also reduces the drug load required to be inhaled to produce the same health effects and hence, can help in minimizing the side effects of a drug.

Human lung is known to be an asymmetric dichotomously branched network of bronchioles. Existing literature on the relation between anatomy and air-flow physics in the tracheobronchial trees has discussed the results of asymmetry. We discuss a secondary (but an important) lung function to seek asymmetry: to protect the acinus from a high pathogen load. We build morphometric parameter-based mathematical models of realistic bronchial trees to explore the structure-function relationship. We observe that maximum surface area for gas exchange, minimum resistance and minimum volume are obtained near the symmetry condition. In contrast, we show that deposition of inhaled foreign particles in the non-terminal airways is enhanced by asymmetry. We show from our model, that the optimal value of asymmetry for maximum particle filtration is within 10% of the experimentally measured value in human lungs. This structural trait of the lung aids in self-defence of the host against pathogen laden aerosols. We explain how natural asymmetric design of typical human lungs makes a sacrifice away from gas exchange optimality to gain this protection. In a typical human lung, when compared to most optimal condition (which is associated with symmetric branching), the fluidic resistance is 14% greater, the gas exchange surface area is about 11% lower, the lung volume is about 13% greater to gain an increase of 4.4% protection against foreign particles. This afforded protection is also robust to minor variations in branching ratio or variation in ventilation, which are both crucial to survival.

In the present study, we investigate the phenomenon of transition of a thermoacoustic system involving two-phase flow, from aperiodic oscillations to limit cycle oscillations. Experiments were performed in a laboratory scale model of a spray combustor. A needle spray injector is used to generate a droplet spray having one-dimensional velocity field. This simplified design of the injector helps in keeping away the geometric complexities involved in the real spray atomizers. We investigate the stability of the spray combustor in response to the variation of the flame location inside the combustor. Equivalence ratio is maintained constant throughout the experiment. The dynamics of the system is captured by measuring the unsteady pressure fluctuations present in the system. As the flame location is gradually varied, self-excited high-amplitude acoustic oscillations are observed in the combustor. We observe the transition of the system behavior from low-amplitude aperiodic oscillations to large amplitude limit cycle oscillations occurring through intermittency. This intermittent state mainly consists of a sequence of high-amplitude bursts of periodic oscillations separated by low-amplitude aperiodic regions. Moreover, the experimental results highlight that during intermittency, the maximum amplitude of bursts, near to the onset of intermittency, is as much as three times higher than the maximum amplitude of the limit cycle oscillations. These high-amplitude intermittent loads can have stronger adverse effects on the structural properties of the engine than the low-amplitude cyclic loading caused by the sustained limit cycle oscillations. Evolution of the three different dynamical states of the spray combustion system (viz., stable, intermittency, and limit cycle) is studied in three-dimensional phase space by using a phase space reconstruction tool from the dynamical system theory. We report the first experimental observation of type-II intermittency in a spray combustion system. The statistical distributions of the length of aperiodic (turbulent) phase with respect to the control parameter, first return map and recurrence plot (RP) techniques are employed to confirm the type of intermittency.

An Eulerian/Eulerian multiphase flow model coupled with a population balance model is used as the basis for numerical simulation of atomization in swirling flows. The objective of this exercise is to develop a methodology capable of predicting the local point-wise drop size distribution in a spray, such as would be measured by the Phase Doppler Particle Analyzer (PDA). Model predictions are compared to experimental measurements of particle size distributions in an airblast atomizer spray to demonstrate good qualitative and quantitative agreement. It is observed that the dependence of velocity on drop size inherent in a multiphase description of the drop cloud appears necessary to capture some features of the experimental data. Using this model, we demonstrate the relative contributions of secondary atomization and transport to the variation observed in the downstream spray drop size distribution.

Droplet atomization and evaporation in dense sprays is relevant to several physical applications. We report a population balance model wherein these processes are handled simultaneously. The model is implemented in an Eulerian-Eulerian multiphase framework wherein the drop phase is itself modeled as multiple continua. The continuum model of the drop phase allows us to incorporate a stress field which naturally arises in a collision dominated dense spray. The utility of the model is first demonstrated on a uniform flow evaporator, wherein the mean droplet surface area is shown to exhibit a similarity scaling in terms of a nondimensional parameter that characterizes the competition between atomization and evaporation. The model is then generalized to a computational fluid dynamics (CFD) situation wherein a plug flow atomizer/evaporator is studied. The continuous variation of Sauter mean diameter (SMD) in the flow is presented wherein atomization processes cause the SMD to decrease while evaporation processes cause the SMD to locally increase. This is due to the preferential disappearance of the smaller size drops. Finally, the utility of the model for studying dense droplet ensemble atomization, evaporation, and combustion is discussed. © 2013 by Begell House, Inc.

We investigate the effect of the Schmidt number (Sc) on phase separation dynamics of two immiscible fluids in a two-dimensional periodic box using dissipative particle dynamics. The range of Sc investigated spans liquid-liquid separation processes. Phase separation is characterized by a domain size r(t), which typically follows a power law tβ in time t, where β is a characteristic exponent corresponding to the coarsening mechanism at play. The phase separation dynamics is studied for strongly (deep quench) separating mixtures. We consider cases of critical (φ ∼0.5) and off-critical (φ < 0.5) mixtures of fluids A and B for both ScA = ScB and ScA ≠ ScB. In all cases, the growth dynamics slow down with the increasing Schmidt number of either fluid. We observe the power law exponent β = 0.5 for symmetric (ScA = ScB) critical mixtures and β = 0.33 for all other cases. However, for off-critical mixtures, the exponent is 0.33 irrespective of the Schmidt number ratio of the two fluids. We explain these results from an analysis of the competition between diffusive effects vis-á-vis dynamical forces.

A nonlinear stability model for the breakup of annular liquid sheets subject to inner and outer gases of negligible inertia was developed. Using this model, we demonstrate the effect of viscosity and advection velocity on the breakup process. The formulation used is similar to that of Eggers and Dupont (1994) and involves expanding the flow field variables as asymptotic expansions of a "thin" variable and then solving the one-dimensional equations using the Galerkin finite element framework. Onedimensional (paravaricose) disturbances were assumed and the long wave ansatz was employed. We show that a nonzero mean axial velocity allows convection of disturbances downstream and can cause disturbance waves that are linearly stable to grow in time and eventually lead to sheet breakup (if the initial disturbance amplitude is greater than a critical value). We also show that the annular sheet could form satellite rings (analogous to the satellite drops that have been observed when cylindrical jets break up) under certain conditions. Model predictions show that increasing the Ohnesorge number yields the expected stabilization of the sheet. Finally, we show that the effect of the annular sheet thickness is counterintuitive, in that thicker sheets tend to break up faster.

This paper describes the three-dimensional destabilization characteristics of an annular liquid sheet when subjected to the combined action of Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) instability mechanisms. The stability characteristics are studied using temporal linear stability analysis and by assuming that the fluids are incompressible, immiscible and inviscid. Surface tension is also taken into account at both the interfaces. Linearized equations governing the growth of instability amplitude have been derived. These equations involve time-varying coefficients and have been analysed using two approaches - direct numerical time integration and frozen-flow approximation. From the direct numerical time integration, we show that the time-varying coefficients evolve on a slow time scale in comparison with the amplitude growth. Therefore, we justify the use of the frozen-flow approximation and derive a closed-form dispersion relation from the appropriate governing equations and boundary conditions. The effect of flow conditions and fluid properties is investigated by introducing dimensionless numbers such as Bond number (Bo), inner and outer Weber numbers (Wei, Weo) and inner and outer density ratios (Qi, Qo). We show that four instability modes are possible - Taylor, sinuous, flute and helical. It is observed that the choice of instability mode is influenced by a combination of both Bo as well as Wei and Weo. However, the instability length scale calculated from the most unstable wavenumbers is primarily a function of Bo. We show a regime map in the Bo; Wei; Weo parameter space to identify regions where the system is susceptible to three-dimensional helical modes. Finally, we show an optimal partitioning of a given total energy (ζ) into acceleration-induced and shear-induced instability mechanisms in order to achieve a minimum instability length scale (Ⅎ∗m). We show that it is beneficial to introduce at least 90% of the total energy into acceleration induced RT instability mechanism. In addition, we show that when the RT mechanism is invoked to destabilize an annular liquid sheet, Ⅎ∗m ∼ ζ-3/5.

We describe a novel nonintrusive velocimetry technique for measuring the instantaneous velocity field on a liquid sheet. Short wavelength corrugations are naturally formed on the surface of a liquid sheet when the sheet interacts with ambient air. This method, called feature correlation velocimetry (FCV), relies on cross-correlation of such short wavelength corrugations visualized on the liquid sheet surface when captured using a high-speed camera. An experimental setup was created for producing a liquid sheet of known thickness and velocity. After imaging the liquid sheet with a high-speed camera, cross-correlation was employed at various spatial locations on the liquid sheet. To examine the fidelity of the method, laser Doppler velocimetry (LDV) measurements were obtained for a range of flow rates at the same spatial locations and were compared with the FCV values. The FCV values were found to be consistently within 7% of the LDV readings with the FCV measurements being consistently less than those from the LDV. In order to examine the cause of the bias error, a theoretical model of the liquid sheet has been developed. Based on the model predictions, the bias error was observed to scale as U3/2, where U is the local instantaneous liquid sheet velocity. After correcting for this bias error, a good match was observed between the FCV and the LDV readings. As an application of the FCV method, the near-nozzle region of an annular sheet exiting a spray injector has been characterized.