Instability of an annular viscous liquid jet

Summary A linear analysis has been carried out for the temporal instability of an annular viscous liquid jet moving in an inviscid gas medium, which includes three limiting cases of a round liquid jet, a gas jet and a plane liquid sheet. It is found that there exist two independent unstable modes, which become the well-known sinuous and varicose modes for plane liquid sheets as annular jet radii approach to infinity. Hence, they are named as para-sinuous and para-varicose. It is shown that an ambient gas medium always enhances the annular jet instability. The curvature effects in general increase the disturbance growth rate, and may not be neglected for the breakup process of an annular or conical liquid sheet. An annular jet with a sufficiently small thickness tends to break up much faster than the corresponding plane liquid sheet, in accordance with existing experimental observations. Liquid viscosity has complicated dual effects on the instability. It is also found that there exists a critical Weber number below which surface tension is the source of instability. Whereas above it, instability is suppressed by surface tension effect and it promoted by aerodynamic interaction between the liquid and gas phase. For the practical importance of large Weber numbers such as related to liquid atomization, the para-sinuous mode is always predominant.     

On the instability of plane liquid sheets in two gas streams of unequal velocities

Summary This paper reports a linear stability analysis of plane liquid sheets in gas streams of unequal velocities. It is found that there exist two independent unstable modes, named herein as para-sinuous and para-varicose. They resemble, but certainly differ from, the well-known sinuous and varicose modes found for equal gas velocities. The gas velocity difference may increase or decrease the growth rate for the para-varicose mode, and for the para-sinuous mode at high Weber numbers. At Weber numbers slightly larger and less than unity, gas velocity enhances significantly the degree of instability for the para-sinuous mode. For the practical interest of large Weber numbers such as related to liquid atomization, the para-sinuous mode is always more unstable. Liquid viscosity has complicated dual effects on the instability, and surface tension is always stabilizing. Long and short wavelength approximations indicate that instability is due to the velocity jump across the two liquid-gas interfaces and from one gas stream to the other, hence is related to the classical Kelvin-Helmholtz instability, and from the disturbance energy equation that the mechanism of instability is due to the interfacial pressure fluctuations.     

Effect of liquid and air swirl strength and relative rotational direction on the instability of an annular liquid sheet

Summary Instability of a swirling annular liquid sheet in swirling inner and outer air streams has been investigated by a temporal linear stability analysis. The effects of the swirling and axial motion of the liquid and the air streams, as well as the effects of relative inner and outer air swirl orientation with respect to the liquid swirl direction on the instability have been investigated. Results show that for a non-swirling liquid sheet axial inner air stream is more effective than axial outer air stream in enhancing the sheet instability. This is opposite of a swirling liquid sheet where axial outer air is more effective in promoting sheet instability compared to axially moving inner air stream. The liquid swirl has a destabilizing effect at the outer interface but has a stabilizing effect at the inner interface. At high liquid swirl Weber number, the outer air (with axial and swirl velocity components) is more effective in enhancing sheet instability compared to the inner air (with axial and swirl velocity components). To understand the effect of air swirl orientation with respect to liquid swirl direction, four possible combinations with both swirling air streams with respect to the liquid swirl direction have been considered. Results show that at high liquid swirl Weber number a combination of counter-rotating-inner air stream and co-rotating-outer air stream has the largest most unstable wave number. However, at low liquid swirl, co-inner/counter-outer combination has the largest most unstable wave number. The combination of inner and the outer air stream co-rotating with the liquid has the highest growth rate. In many combustion applications, the liquid sheet is injected in high pressure environment where the effect of high ambient pressure results in increased aerodynamic interaction due to high air density. Hence the effect of high ambient pressure is studied in terms of the dimensionless parameter of air-to-liquid density ratio. Results show significantly higher disturbance growth rates at high air pressure. However, the qualitative sheet stability behavior is similar to that at atmospheric pressure.     

Nonlinear spatial instability of an annular swirling viscous liquid sheet

Instability and breakup of a viscous annular liquid sheet that is exposed to co-flowing inner and outer gas streams have been investigated using a nonlinear spatial stability analysis. A perturbation expansion method is used with the initial amplitude of the disturbance as the perturbation parameter. The evolution of the two gas–liquid interfaces is tracked until the sheet breaks up and the breakup length is determined. The model is validated by comparison with available experimental data. The effects of liquid swirl strength, gas-to-liquid density ratio, radius of curvature ratio, and liquid viscosity on the sheet instability and breakup have been studied. The results show that at very low values of liquid swirl, it has a stabilizing effect on sheet breakup, but as the swirl strength increases, it strongly destabilizes the sheet. Also, with increasing swirl strength, the occurrence of the large surface deformations moves from the inner interface to the outer interface. The sheet breakup length increases slightly and then decreases rapidly with an increase in liquid swirl strength. Without liquid swirl, the axisymmetric mode is the dominant instability mode. However, with increasing liquid swirl strength, the higher helical modes become dominant and the breakup becomes increasingly asymmetric. When the undisturbed liquid sheet has a purely axial motion, the inner gas stream is more effective in sheet breakup than the outer gas stream. In the presence of liquid swirl, the outer gas stream is more disruptive than the inner gas stream. The breakup length becomes shorter as gas-to-liquid density ratio and the radius of curvature ratio increases. Increase in liquid viscosity tends to slow the disturbance growth and increases the sheet breakup length.     

Domain-adaptive finite difference methods for collapsing annular liquid jets

A domain-adaptive technique which maps a time-dependent, curvilinear geometry into a unit square is used to determine the steady state mass absorption rate and the collapse of annular liquid jets. A method of lines is used to solve the one-dimensional fluid dynamics equations written in weak conservation-law form, and upwind differences are employed to evaluate the axial convective fluxes. The unknown, time-dependent, axial location of the downstream boundary is determined from the solution of an ordinary differential equation which is nonlinearly coupled to the fluid dynamics and gas concentration equations. The equation for the gas concentration in the annular liquid jet is written in strong conservation-law form and solved by means of a method of lines at high Peclet numbers and a line Gauss-Seidel method at low Peclet numbers. The effects of the number of grid points along and across the annular jet, time step, and discretization of the radial convective fluxes on both the steady state mass absorption rate and the jet's collapse rate have been analyzed on staggered and non-staggered grids. The steady state mass absorption rate and the collapse of annular liquid jets are determined as a function of the Froude, Peclet and Weber numbers, annular jet's thickness-to-radius ratio at the nozzle exit, initial pressure difference across the annular jet, nozzle exit angle, temperature of the gas enclosed by the annular jet, pressure of the gas surrounding the jet, solubilities at the inner and outer interfaces of the annular jet, and gas concentration at the nozzle exit. It is shown that the steady state mass absorption rate is proportional to the inverse square root of the Peclet number except for low values of this parameter, and that the possible mathematical incompatibilities in the concentration field at the nozzle exit exert a great influence on the steady state mass absorption rate and on the jet collapse. It is also shown that the steady state mass absorption rate increases as the Weber number, nozzle exit angle, gas concentration at the nozzle exit, and temperature of the gases enclosed by the annular liquid jet are increased, but it decreases as the Froude and Peclet numbers, and annular liquid jet's thickness-to-radius ratio at the nozzle exit are increased. It is also shown that the annular liquid jet's collapse rate increases as the Weber number, nozzle exit angle, temperature of the gases enclosed by the annular liquid jet, and pressure of the gases which surround the jet are increased, but decreases as the Froude and Peclet numbers, and annular liquid jet's thickness-toradius ratio at the nozzle exit are increased. It is also shown that both the ratio of the initial pressure of the gas enclosed by the jet to the pressure of the gas surrounding the jet and the ratio of solubilities at the annular liquid jet's inner and outer interfaces play an important role on both the steady state mass absorption rate and the jet collapse. If the product of these ratios is greater or less than one, both the pressure and the mass of the gas enclosed by the annular liquid jet decrease or increase, respectively, with time. It is also shown that the numerical results obtained with the conservative, domain-adaptive method of lines technique presented in this paper are in excellent agreement with those of a domain-adaptive, iterative, non-conservative, block-bidiagonal, finite difference method which uncouples the solution of the fluid dynamics equations from that of the convergence length.     

Instability of cylindrical compressible gas jets in viscous liquid streams

Summary A linear stability study of cylindrical compressible gas jets in a moving incompressible viscous liquid medium subject to varicose disturbances is described. It was found that the gas jet is always unstable for a range of wavenumbers at any flow condition. When the gas and liquid velocity are not equal, temporal instability is enhanced by surface tension effects for small Weber numbers, and by aerodynamic interaction between the gas and liquid phase for high Weber numbers (where surface tension has a stabilizing influence). Increasing liquid viscosity always reduces the growth rate and the dominant wavenumber, whereas increasing gas density always increases gas jet instability. It was also found that the relative, rather than the absolute, velocity of the gas and liquid controls temporal instability. Increasing gas compressibility always increases the maximum growth rate and dominant wavenumber. On the other hand, for equal gas and liquid velocities, increasing surface tension always destabilizes, while increasing gas density always stabilizes, the gas jet. For absolute and spatial (or convective) instability, it was shown that the critical Weber number, separating the region of absolute from that of spatial instability, decreases monotonically as the liquid velocity is increased. For a stationary liquid medium, the gas jet is always absolutely unstable, and spatial instability does not exist, in contrast to liquid jets in a stationary gas medium. For sufficiently large liquid velocities, the gas jet is spatially unstable, whereas absolute instability disappears. Further, the absolute velocity of gas and liquid flow controls not only the growth of unstable disturbances, but also the characteristics of the instability. Increasing viscous effects tends to suppress absolute instability, while increasing both gas density and compressibility promotes absolute instability for small liquid velocities (however, their effect diminishes as liquid velocity is increased).     

Experimental investigation of spray characteristics of kerosene and ethanol-blended kerosene using a gas turbine hybrid atomizer

Gas turbines have wide application as prime movers in transportation and power generating sectors, most of which are driven by fossil fuels like kerosene. The conventional fuels are associated with problems of air pollution, and the fuel reserves are getting depleted gradually. Addition of ethanol in kerosene leads to better spraying characteristics. The present work deals with the spray characteristics of pure kerosene and 10%-ethanol-blended (by volume) kerosene using a novel gas-turbine hybrid atomizer. Here the inner air and outer air enter in the same and opposite directions, respectively, with respect to the fuel flow direction into the atomizer and a high swirling effect occurs outside the nozzle. The fuel stream is sandwiched between two annular air streams and the flow rate of inner and outer air is varied continuously. Various spray stages like distorted pencil, onion, tulip and fully developed spray regimes have been observed. The breakup length, cone angle and sheet width of the fuel stream are analysed directly from backlit imaging for different fuel and air flow rates. From the image processing, it is observed that breakup occurs at an early stage for 10%-ethanol-blended kerosene due to low viscosity of ethanol. It is also observed that at higher air flow rate, breakup occurs at an early stage due to turbulent nature of the fuel stream.     

Axisymmetric waves in electrohydrodynamic flows

The formation of nonlinear axisymmetric waves on inviscid irrotational liquid jets in the presence of radial electric fields is considered. Gravity is neglected but surface tension is considered. Electrohydrodynamic waves of arbitrary amplitude and wavelength are computed using finite-difference methods. Particular attention is paid to nonlinear traveling waves. In the first class of problems, an electric field generated by placing the liquid jet inside a hollow cylindrical electrode held at constant voltage, its axis coinciding with that of the jet, is studied. The jet is assumed to be a perfect conductor whose free surface is stressed by the electric field acting in the hydrodynamically passive annulus. In the second class of problems, the annular gas is a perfect conductor that transmits a constant voltage onto the liquid/gas surface. The liquid axisymmetrically wets a constant-radius cylindrical rod electrode placed coaxially with respect to the hollow outer electrode, and held at a different constant voltage. The fluid dynamics and electrostatics need to be addressed simultaneously in the inner region. Axisymmetric interfacial waves influenced by surface tension and electrical stresses are computed in both cases. The computations are capable of following highly nonlinear solutions and predict, for certain parameter values, the onset of interface pinching accompanied with the formation of toroidal bubbles. For given wave amplitudes, the results suggest that, for the former case, the electric field delays bubble formation and reduces wave steepness, while for the latter case the electric field promotes bubble formation, all other parameters being equal.     

Gasdynamic stimulation of combustion of lean fuel mixtures. 1. experimental study

We studied combustion modes experimentally for a lean fuel mixture of propane-air, including combustion of a quiescent mixture, combustion with annular gas swirling, and combustion stimulated by the jets of a burning gas that are injected into the combustion chamber (pulsed jet combustion — PJC). It is shown that, in providing a maximum combustion rate, the PJC mode has an obvious advantage in initiation of combustion of extremely lean fuel mixtures over other gasdynamic combustion modes. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 2, pp. 302–308, March–April, 2000.     

Linear-stability Analysis of Thermocapillary Flow in an Annular Two-layer System with Upper Rigid Wall

The linear-stability analysis of thermocapillary flow in the annular immiscible two-layer system of 5cSt silicone oil and HT-70 with a radial temperature gradient was carried out. The annular two-layer system is heated at the outer cylindrical wall and cooled at the inner wall, the bottom and top surfaces are bounded by two rigid and heat-insulated walls. The influences of the liquid layer depth and radius ratio between the cold inner wall and the hot outer wall on stability are thoroughly investigated. The critical Marangoni number, critical wave number and critical phase velocity are obtained. In addition, the mode of bifurcation for the hydrothermal wave is predicted at different liquid layer depth, and the temperature disturbance pattern of hydrothermal wave at interface is also exhibited.     

Hydrodynamic instability of the axisymmetric flow of an ideal fluid with an interphase

We study the instability under simultaneous rotational and translational flow of a fluid and ambient medium in the cases of a cylindrical annular jet, capillary jet, and cylindrical fluid layers on the inner and outer surfaces of a cylinder.     

液体射流扰动控制方程边界条件及稳定性分析

本文针对粘性气体中的粘性不可压缩液体射流的分裂与雾化过程边界条件,进行了扰动分析,并对其进行线性化及无量纲化,得到了射流扰动控制方程无量纲线化边界条件。最后对射流分裂与雾化过程的不稳定性做了数值分析,其结果与实际观测到的射流边界面变化规律一致。     

Instability and fragmentation of expanding liquid systems

This analysis pursues the underlying physics governing the expansion, dispersal and breakup of a thin walled steel right circular cylinder filled with liquid after being impacted by a high velocity aluminum sphere. The impact generates a radially expanding coherent thin shell of liquid which stays together to at least a diameter 8 times that of the original cylinder. An instability criterion is proposed and developed based on the opposing forces of stabilizing inertial pressures and destabilizing viscous resistance. This criterion is compared to test data where possible in order to ascertain its ability to predict liquid breakup of the shell. The breakup theory developed here predicts the extensive expansion of the unthickened liquid prior to fragmentation as observed in the experiments. This result lends some credence to the underlying physics pursued here and its ability to predict the onset of liquid fragmentation.     

Two-dimensional modeling of viscous liquid jet breakup

A two-dimensional computational model has been developed to study the evolution and breakup of a viscous laminar liquid jet, using a boundary-fitted curvilinear coordinate system. A system of elliptic partial differential equations for coordinate transformations has been developed to map the moving boundaries’ physical domain of the jet to a simple rectilinear computational domain. The equations developed for the model comprise the transformed two-dimensional unsteady Navier–Stokes equations for the liquid jet, grid velocity equations, kinematic boundary conditions, and the Geometric Conservation Law. The resulting systems of equations are solved using an implicit finite difference scheme. Effects of inflow oscillation magnitude, wave number, Weber number, and Reynolds number on the breakup process of jets have been studied. The model predicts the instantaneous shape of the jet surface, formation of the main and satellite drops, and the breakup length and time. These results are compared with available experimental data. The comparisons show a good agreement between measured and computed values of drop sizes and breakup lengths for different Reynolds and Weber numbers. However, at a relatively high Reynolds number of 1,254, the model slightly overpredicts the main drop sizes and underpredicts the satellite drop sizes at a wave number of 0.4. At a low Reynolds number of 587, the model overpredicts the main drop sizes at a lower wave number of 0.3. Moreover, the model underpredicts the satellite drop sizes at a lower wave number of about 0.4 and overpredicts the satellite drop sizes at a wave number of 0.8.     

Velocity measurements in a strongly swirling natural gas flame

The present study was focused on the turbulent velocity field of a central annular natural gas jet which penetrated a strongly swirling air flow. Due to the high swirl number S=0.95 and the high momentum ratio, the fuel jet was almost immediately integrated into the air stream. High rates of shear resulted in an intensive turbulent mixing process between natural gas and air. The central hub of the fuel exit annulus stabilized the reverse flow zone at a fixed location. The present nozzle configuration resulted in a very stable and symmetric flame.     

On the failure of a brittle material by high velocity gas jet impact

Failure of brittle solid bodies due to the impingement of a high velocity air jet on the body surface is studied, experimentally and theoretically. Using the linear elastic theory and stress distribution analysis, a general criterion for the failure of brittle materials impacted by a gas jet is derived. Several special cases of jet–solid body interaction including failure of thin and thick layers and cylindrical objects immersed in a crossflow gas stream are investigated and proper material failure criteria are developed. These criteria correlate the minimum jet peak impact pressure (PIP) required to break the material to the material's tensile strength and Poisson's ratio. A series of experiments were performed using a laboratory-scale apparatus. Gypsum cast on steel tubes forming cylindrical samples was used as the model brittle material. Experimental data and high-speed breakup movies are employed to understand the gas jet–solid body interaction and to validate the theoretical criteria developed for the material failure. It is deduced that the failure of cylindrical samples impacted by a gas jet is by the formation and propagation of cracks. However, when the impact jet diameter is small, the cracks cannot propagate, and the material is failed due to localized surface pitting. One of the practical applications of this research is in Kraft recovery boilers, where high velocity supersonic steam jets are employed to remove deposits accumulated on the outer surfaces of the steam tubes.     

Monodisperse breakup of liquid jets

The monodisperse breakup of liquid jets with various physical properties is investigated experimentally and theoretically over a wide range of jet breakup parameters.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 3, pp. 413–418, September, 1988.     

An analysis of the equilibrium configurations of charged cylindrical jets of a conducting liquid

A region of physical parameters is found where the equilibrium configurations of charged cylindrical jets of a conducting liquid can exist; these configurations correspond to the azimuthal mode n=2 of the surface deformations of a round jet. A critical value of the jet linear charge is determined for which the jet splits into two. It is shown that such instability is excited in a soft regime.     

The evolution of instabilities in gas microjets under acoustic action

The results of an experimental investigation of the effect of external acoustic perturbations on the stability of millimeter- and submillimeter-scale gas jets flowing out into the atmosphere are presented. Data on flow visualization by the shadow method and the instantaneous velocity fields of the flow by the PIV method are obtained. The sound effect in the jet is shown to lead to the asymmetric mode of instability. The growth of this mode downstream leads to flow bifurcation. Frequency characteristics of the effect for jets of different geometries and jets of different gases are compared.