Ghobad Amini

Capillary instability of elliptic liquid jets

Instability of a liquid jet issuing from an elliptic nozzle in Rayleigh mode is investigated and its behavior is compared with a circular jet. Mathematical solution of viscous free-surface flow for asymmetric geometry is complicated if 3-D analytical solutions are to be obtained. Hence, one-dimensional Cosserat (directed curve) equations are used which can be assumed as a low order form of Navier-Stokes equations for slender jets. Linear solution is performed using perturbation method. Temporal dispersion equation is derived to find the most unstable wavelength responsible for the jet breakup. The obtained results for a circular jet (i.e., an ellipse with an aspect ratio of one) are compared with the classical results of Rayleigh and Weber for inviscid and viscous cases, respectively. It is shown that in the Rayleigh regime, which is the subject of this research, symmetric perturbations are unstable while asymmetric perturbations are stable. Consequently, spatial analysis is performed and the variation of growth rate under the effect of perturbation frequencies for various jet velocities is demonstrated. Results reveal that in comparison with a circular jet, the elliptic jet is more unstable. Furthermore, among liquid jets with elliptical cross sections, those with larger ellipticities have a larger instability growth rate.

Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis

The instability dynamics of inviscid liquid jets issuing from elliptical orifices is studied, and effects of the surrounding gas and the liquid surface tension on the stability behavior are investigated. A dispersion relation for the zeroth azimuthal (axisymmetric) instability mode is derived. Consistency of the analysis is confirmed by demonstrating that these equations reduce to the well-known dispersion equations for the limiting cases of round and planar jets. It is shown that the effect of the ellipticity is to increase the growth rate over a large range of wavenumbers in comparison to those of a circular jet. For higher Weber numbers, at which capillary forces have a stabilizing effect, the growth rate decreases with increasing ellipticity. Similar to circular and planar jets, increasing the density ratio between gas and liquid increases the growth of disturbances significantly. These theoretical investigations are complemented by experiments to validate the local linear stability results. Comparisons of predicted growth rates with measurements over a range of jet ellipticities confirm that the theoretical model provides a quantitatively accurate description of the instability dynamics in the Rayleigh and first wind-induced regimes.

Jet Noise Receptivity to Nozzle-upstream Perturbations in Compressible Heated Jets

E ects of nozzle-upstream entropy perturbations on the acoustic radiation from heated jets are investigated. For this, a model problem is considered, in which a gas-turbine combustor discharges reaction products through a converging nozzle into the ambient environment. The turbulent reacting ow eld in the combustor is computed using large-eddy simulation (LES), and the unsteady oweld at the combustor exit is extracted to provide realistic in ow conditions to the jetow simulation. To study the indirect coupling process, arising from the interaction of the combustion-generated entropy uctuations with the adverse pressure gradient through the nozzle, a linearized Euler formulation is employed. Parametric studies are performed to investigate e ects of frequency and amplitude of the nozzle-upstream entropy perturbations on the jet instability and the jet noise directivity. Simulation results show that the directivity is dependent on the perturbation frequency. Excitation near the preferred shear-layer instability leads to strong acoustic radiation in the 45 forward direction, and the radiation angle decreases with decreasing excitation frequency.

Capillary Instability of Liquid Jets Issuing From Elliptic Nozzles

Breakup of a liquid jet issuing from an orifice is one of the classical problems in fluid dynamics due to its theoretical and practical importance. The main application of the process is in spray and droplet formation, which is of interest in the combustion in liquid-fuelled engines, ink-jet printers, coating systems, medical equipment, and irrigation device. The complexity of the breakup mechanism is due to the large number of parameters involved such as the design of injection nozzle, and thermodynamic states of both liquid and gas. In addition, different combinations of surface tension, inertia, and aerodynamic forces acting on the jet, define main breakup regimes. Effects of nozzle geometry on the behavior of liquid jets have been overlooked in the literature. Elliptic jets have never been investigated theoretically since mostly circular jets or liquid sheets have been analyzed; while experiments have shown that by using elliptical nozzles, entrainment and air mixing of fuel in combustion will be increased. In this article, instability of an elliptic liquid jet under the effect of inertia, viscous, and surface tension forces has been studied using temporal linear analyses. The effects of the gravity and the surrounding gas have been neglected. 1-D Cosserat equation (directed curve) has been used which can be considered as simplified form of Navier-Stokes equations. Results are comparable with classical Rayleigh mode of circular jet when the aspect ratio (ratio of major to minor axis) is one. Growth rate of instability on an elliptic liquid jet under various conditions has been compared with those of a circular jet. Results show that in comparison with a circular jet, the elliptic jet is more unstable and by increasing the aspect ratio the instability grows faster. In addition, similar to the circular case, the effect of viscosity is diminishing the growth rate for the elliptic jet.Copyright

Liquid Jet Instability Under Gravity Effects

The effect of gravity on the onset and growth rate of absolute and convective instabilities in viscous liquid jets is studied. To this end, a spatial linear stability analysis of the Cosserat’s equations is performed. A multiscale expansion technique is employed and dispersion relation and expressions for the perturbation amplitude are derived to evaluate the growth rate of axisymmetric disturbances. Model-results for zero gravity are compared with classical results of hydrodynamic instability, confirming the validity of this approach. It is shown that gravity increases both the instability growth rate and the cutoff frequency below which disturbances are spatially amplified and above which they are damped. The critical Weber number, demarcating the transition between convective and absolute instability is determined as function of Reynolds and Froude numbers. It is found that, by increasing the acceleration of gravity, the critical Weber number decreases. This result explains the reason for shifting the transition between dripping and jetting to lower Weber numbers in the case of increasing gravity.

Breakup of Liquid Jets Emerging From Elliptic Orifices

Passive control can result in increasing fuel efficiency and reducing combustion instabilities of gas turbine spray combustors. Through the use of geometric modifications of the conventional circular nozzles, this method potentially enhances mixing which is responsible for entraining the bulk air necessary for combustion. Several studies show that elliptic jets have higher mass entrainment and spreading rate compared to the equivalent circular jets [1]. The majority of these works have been limited to gaseous jets. The present study focuses on a liquid spray discharging into still ambient air from a single-hole injector with elliptic cross-section. The primary breakup is investigated using a theoretical approach. Characteristics of elliptic orifice jet are compared with circular orifice jet under different breakup regimes and various nozzle geometries.Copyright