Mahesh V Panchagnula

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.

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.

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 behaviour from low amplitude aperiodic oscillations to large amplitude limit cycle oscillations occurring through intermittency. This intermittent state mainly consists of a sequence of highamplitude periodic bursts separated by low amplitude aperiodic regions. Moreover, the experimental results highlight that during intermittency, the maximum amplitude of bursts oscillations, 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) are 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 techniques are employed to confirm the type of intermittency.

Understanding the breakup morphology of an expelled respiratory liquid is an emerging interest in diverse fields to enhance the efficacious strategies to attenuate disease transmission. In this paper, we present the possible hydrodynamic instabilities associated with expelling the respiratory liquid by a human. For this purpose, we have performed experiments with a cylindrical soap film and air. The sequence of the chain of events was captured with high-speed imaging. We have identified three mechanisms, namely, Kelvin-Helmholtz (K-H) instability, Rayleigh-Taylor (R-T) instability, and Plateau-Rayleigh (P-R) instability, which are likely to occur in sequence. Furthermore, we discuss the multiple processes responsible for drop fragmentation. The processes such as breakup length, rupture, ligament, and drop formation are documented with a scaling factor. The breakup length scales with We-0.17, and the number of ligaments scales as Bo. In addition, the thickness of the ligaments scales as We-0.5. Here, We and Bo represent the Weber and Bond numbers, respectively. It was also demonstrated that the flapping of the liquid sheet is the result of the K-H mechanism, and the ligaments formed on the edge of the rim appear due to the R-T mechanism, and finally, the hanging drop fragmentation is the result of the P-R instability. Our study highlights that the multiple instabilities play a significant role in determining the size of the droplets while expelling a respiratory liquid. This understanding is crucial to combat disease transmission through droplets.

The destabilization of a two-fluid interface is of interest in various applications ranging from spray formation to ocean-wave currents. In most practical spray systems, instabilities that occur on the interface lead to form fragments. Among such instabilities, those caused due to the radial motion of the interface in a cylindrical configuration (Rayleigh-Taylor) are of current interest. We study the instability characteristics of a cylindrical bubble surrounded by an infinite medium of liquid. Linear stability analysis is used as a tool to understand the mechanics. A general dispersion relation has been derived for an inviscid, immiscible and incompressible pair of fluids. This dispersion relation is used to predict the most unstable wavenumber as well as the dominant instability growth rate. It was found that the Bond number is a primary determinant of the most unstable wavenumbers, dominant instability growth rate as well as the neutral stability points. Surprisingly, it was also found out that radial velocity alone (in the absence of radial acceleration) is sufficient to destabilize a cylindrical interface, unlike in the case of either planar or spherical polar configurations.

The effect of competing Rayleigh–Taylor and Kelvin–Helmholtz mechanisms of instability applied to a cylindrical two-fluid interface is discussed. A three-dimensional temporal linear stability model for the instability growth is developed based on the frozen time approximation. The fluids are assumed to be inviscid and incompressible. From the governing equations and the boundary conditions, a dispersion relation is derived and analyzed for instability. Four different regimes have been shown to be possible, based on the most unstable axial and circumferential wavenumbers. The four modes are the Taylor mode, the sinuous mode, the flute mode and long and short wavelength helical modes. The effect of Bond number, Weber number, and density ratio are investigated in the context of the mode chosen. It is found that Bond number is the primary determinant of the neutral stability while Weber number plays a key role in identifying the instability mode that is manifest. A regime map is presented to delineate the modes realized for a given set of flow parameter values. From this regime map, a short wavelength helical mode is identified which is shown to result only when both the Rayleigh–Taylor and Kelvin–Helmholtz instability mechanisms are active. A scaling law for the magnitude of the wavenumber vector as a function of Bond number and Weber number are also developed. A length scale is defined to characterize the interface distortion. Using this length scale, the set of conditions where the interface exhibits a maximum in surface area creation is identified. With the objective of achieving the smallest characteristic length scale of interface distortion, a criterion to optimally budget mean flow energy is also proposed.

The stability of a cylindrical interface separating two incompressible, inviscid and immiscible fluids under the action of radial motion is studied. Linear stability analysis is employed to understand the destabilization characteristics of the two fluid interface.Three-dimensional as well as two-dimensional (axisymmetric and azimuthal) disturbances are separately considered in the presence of surface tension. A dispersion relation governing this problem is taken from literature and analyzed. The relevant dimensionless parameters governing this study are Bond number, radial Weber number and density ratio. This dispersion relation permits the consideration of two different scenarios: (1) density of the inner fluid being greater than the outer fluid and (2) density of the inner fluid being lesser than the outer fluid. It is found out that the surface tension restricts and aids the destabilization for the former and latter case, respectively. It is also observed that the interface is unstable when even at a constant radial velocity. This is contrary to our common understanding of Rayleigh–Taylor instability where acceleration is required. Three destabilization modes are identified namely Taylor (axial) mode, flute (azimuthal) mode and helical (three-dimensional) mode for a range of parameters. It is found that three-dimensional modes are more susceptible to destabilization than the two-dimensional modes when the radial Weber number is close to zero. Regime maps are created in the Bond number, radial Weber number and density ratio space to establish the regimes where different modes occur. For a given density ratio, the destabilization starts from one mode to another two-dimensional disturbance through three-dimensional disturbances. The second and utmost finding of this study reveals that radial Weber number alone (albeit the Bond number) is sufficient to destabilize a cylindrical interface.