Growth Of Unstable Waves Research Articles

Resolving the initial spray structure of fire sprinklers with a volume-of-fluid modeling

The initial spray formation process of commercial fire sprinklers was investigated with a Large-eddy simulation and a Volume-of-Fluid model. The water-supply flow rate was set to 80 L/min corresponding to the minimum required flow rate in South Korea. From the study of grid dependency, a mesh size of 62.5 μm was adopted. Using this size of the mesh, unstable wave growth on the surface of the liquid sheet was captured, which corresponds to 1/16 the size of a sprinkler droplet that was derived in a previous study to be 1 mm. Sprinkler spray consisted of horizontal sheets generated by tines and vertical sheets generated by slots. Ligaments were produced by vortices on the air-water interface and droplets were generated by both longitudinal and lateral stretching. The flow rate of the tine section was larger than that of the slot section due to the large section angle. The water at the tine section was delivered to neighboring slot sections as flowing downstream. A formula for the sheet thickness was calibrated with measured mass outflow, which showed a more accurate value than the original formula driven by the mass conservation for the plate.

A Businger Mechanism for Intermittent Bursting in the Stable Boundary Layer

AbstractHigh-resolution large-eddy simulations of the Antarctic very stable boundary layer reveal a mechanism for systematic and periodic intermittent bursting. A nonbursting state with a boundary layer height of just 3 m is alternated by a bursting state with a height of ≈5 m. The bursts result from unstable wave growth triggered by a shear-generated Kelvin–Helmholtz instability, as confirmed by linear stability analysis. The shear at the top of the boundary layer is built up by two processes. The upper, quasi-laminar layer accelerates due to the combined effect of the pressure force and rotation by the Coriolis force, while the lower layer decelerates by turbulent friction. During the burst, this shear is eroded and the initial cause of the instability is removed. Subsequently, the interfacial shear builds up again, causing the entire sequence to repeat itself with a time scale of ≈10 min. Despite the clear intermittent bursting, the overall change of the mean wind profile is remarkably small during the cycle. This enables such a fast erosion and recovery of the shear. This mechanism for cyclic bursting is remarkably similar to the mechanism hypothesized by Businger in 1973, with one key difference. Whereas Businger proposes that the flow acceleration in the upper layer results from downward turbulent transfer of high-momentum flow, the current results indicate no turbulent activity in the upper layer, hence requiring another source of momentum. Finally, it would be interesting to construct a climatology of shear-generated intermittency in relation to large-scale conditions to assess the generality of this Businger mechanism.

Coherent Capillary Wave Structure Revealed by ISS Experiments for Spontaneous Nozzle Jet Disintegration

A series of International Space Station (ISS) experiments were conducted to observe the disintegration feature of a water jet issued from an orifice/nozzle into atmospheric air. The purpose was to validate our proposal that any laminar liquid jet can spontaneously disintegrate by its own self-destabilizing loop formed along the jet. This paper reports the experiment results focusing on a water jet issued from a nozzle with a radius 0.4 mm and length 120 mm, in which the parabolic velocity profile relaxes toward that of a plug flow along the jet. As predicted in our proposal, the nozzle jet had a two-valued breakup distance in a certain jet issue speed range and exhibited hysteresis behaviors, indicating that the jet disintegration state is determined by past jet disintegration history. Analyses of video images suggest the establishment of a coherent capillary wave structure in the steady jet disintegration state. New fundamental theories were developed to examine the underlying physics involved. The short-length breakup mode was confirmed to essentially follow the same self-destabilizing mechanism as that of the plug flow jet, in which the upstream propagating capillary wave produced by the release of surface energy due to jet tip contraction or nonlinear unstable wave growth is reflected at the orifice, and becomes the unstable wave responsible for jet disintegration. In the long-length breakup mode, the velocity profile relaxation plays a role equivalent to an orifice and the average nozzle jet length is expressed as the sum of the velocity profile relaxation length and average orifice jet length at large jet issue speeds. This paper focuses on the coherent capillary wave structure of long-length breakup mode.

Linear and Non-linear Analysis of Breakup of Liquid Sheets: a Review

Atomization primarily involves interaction between liquid and surrounding gaseous medium resulting in the growth of unstable waves on a distorted liquid surface. There is a huge volume of work surrounding various models and theories involved in investigation of interface dynamics during sheet breakup. The present work summarizes the linear and nonlinear studies for different geometrical shapes of liquid sheet such as planar, annular, and swirling. The techniques involved in deriving nonlinear governing equations such as perturbation technique, multiple scales approach, and long wave approximation have been outlined. Effects of various factors on sheet instability such as viscosity, compressibility, surface temperature difference, unequal velocity, lateral waves and gas swirl have been listed. Research lacunae and scope of future work are presented in the summary.

Examination of the mechanism behind observed canopy waves

In this paper, we document the existence of wave-like motions above a forest canopy using data taken from a 138m high tower placed within a forest. Characteristics of the waves are examined in relation to their possible effects on wind energy. It is shown that when the wave signal is relatively clean, the phase lag between horizontal and vertical velocity is close to 90°, which limits the contribution of the waves to the downward momentum flux. Numerical solutions of the linear wave equations agree with measurements in terms of wave period and the vertical shape of the wave amplitude. Linear analysis show that shear instability is the cause of unstable wave growth, and that the fastest growing unstable wave number typically has a period of 10–100s. In addition to the shear instability, the linear analysis predicts that under certain conditions instabilities of the Holmboe kind can develop over forests.

Effect of velocity profile of impinging jets on sheet characteristics formed by impingement of two round liquid jets

The characteristics of a liquid sheet formed by the impingement of two round liquid jets are analyzed theoretically. Since the velocity profile of the impinging jet greatly affects the sheet characteristics, the sheet characteristics are analyzed using round impinging jets with uniform or parabolic velocity profiles. The calculated sheet shape is compared with the results of theoretical analyses reported in previous studies. The effects of the velocity profile of impinging jets on the sheet characteristics are shown theoretically. Experiments are conducted in order to verify the theoretical analysis using short and long nozzles. The sheet contour is determined by two mechanisms, i.e., the force balance at the periphery between the liquid inertia and the surface tension, and the unstable wave growth. A critical condition in which the sheet disintegrates as a result of the unstable wave growth is newly proposed. The predicted sheet shapes agree somewhat with the results of experiments using short and long nozzles. The predicted sheet breakup lengths calculated using the newly proposed critical condition agree well with the results of these experiments. The predicted sheet velocity distributions exhibit slightly smaller values compared with measurements reported in previous studies.

Experimental CFD grade data for stratified two-phase flows

Stratified two-phase flows were investigated at two test facilities with horizontal test-sections. For both, rectangular channel cross-sections were chosen to provide optimal observation possibilities for the application of optical measurement techniques. In order to show the local flow structure, high-speed video observation was applied, which delivers the high-resolution in space and time needed for CFD code validation. The first investigations were performed in the Horizontal Air/Water Channel (HAWAC), which is made of acrylic glass and allows the investigation of air/water co-current flows at atmospheric pressure and room temperature. At the channel inlet, a special device was designed for well-defined and adjustable inlet boundary conditions. For the quantitative analysis of the optical measurements performed at the HAWAC, an algorithm was developed to recognise the stratified interface in the camera frames. This allows to make statistical treatments for comparison with CFD calculation results. As an example, the unstable wave growth leading to slug flow is shown from the test-section inlet. Moreover, the hydraulic jump as the quasi-stationary discontinuous transition between super- and subcritical flow was investigated in this closed channel. The structure of the hydraulic jump over time is revealed by the calculation of the probability density of the water level. A series of experiments show that the hydraulic jump profile and its position from the inlet vary substantially with the inlet boundary conditions due to the momentum exchange between the phases. The second channel is built in the pressure chamber of the TOPFLOW test facility, which is used to perform air/water and steam/water experiments at pressures of up to 5.0 MPa and temperatures of up to 264 °C, but under pressure equilibrium with the vessel inside. In the present experiment, the test-section represents a flat model of the hot leg of the German Konvoi pressurised water reactor scaled at 1:3. The investigations focus on the flow regimes observed in the region of the elbow and of the steam generator inlet chamber, which are equipped with glass side walls. An overview of the experimental methodology and of the acquired data is given. These cover experiments without water circulation, which can be seen as test cases for CFD development, as well as counter-current flow limitation experiments, representing transient validation cases of a typical nuclear reactor safety issue.

Effects of wall temperature on boundary layer stability over a blunt cone at Mach 7.99

Effects of wall temperature on stabilities of hypersonic boundary layer over a 7° half-cone-angle blunt cone are studied by using both direct numerical simulation (DNS) and linear stability theory (LST) analysis. Four isothermal wall cases with T w / T 0 = 0.5 , 0.7 , 0.8 and 0.9 , as well as an adiabatic wall case are considered. Results of both DNS and LST indicate that wall temperature has significant effects on the growth of disturbance waves. Cooling the surface accelerates unstable Mack II mode waves and decelerates the first mode (Tollmien–Schlichting mode) waves. LST results show that growth rate of the most unstable Mack II mode waves for the cases of cold wall T w / T 0 = 0.5 and 0.7 are about 45% and 25% larger than that for the adiabatic wall, respectively. Numerical results show that surface cooling modifies the profiles of ρ du t dy n and temperature in the boundary layers, and thus changes the stability characteristic of the boundary layers, and then effects on the growth of unstable waves. The results of DNS indicate that the disturbances with the frequency range from about 119.4 to 179.1 kHz, including the most unstable Mack modes, produce strong mode competition in the downstream region from about 11 to 100 nose radii. And adiabatic wall enhances the amplitudes of disturbance according to the results of DNS, although the LST indicates that the growth rate of the disturbance of cold wall is larger. That because the growth of the disturbance does not only depend on the development of the second unstable mode.

A Predictive Model for the Initial Droplet Size and Velocity Distributions in Sprays and Comparison with Experiments

AbstractThe distribution of sizes and velocities of droplets initially formed in sprays is an important piece of information needed in the spray modelling, because it defines the initial condition of the spray droplets in the predictive calculations of the downstream two‐phase flow fields. A predictive model for the initial droplet size and velocity distributions in sprays is formulated in this study. The present model incorporates both the deterministic and the stochastic aspect of spray formation process. The deterministic aspect takes into account of the unstable wave motion before the liquid bulk breakup through the linear and nonlinear instability analysis, which provides information for the liquid bulk breakup length, the mass‐mean diameter and a prior distribution for the droplet sizes corresponding to the unstable wave growth of various wavelengths. The stochastic aspect deals with the final stage of droplet formation after the liquid bulk breakup by statistical means through the maximum entropy principle based on Bayesian entropy. The two sub‐models are coupled together by the various source terms signifying the liquid‐gas interaction, the mass mean diameter and the prior distribution based on the instability analysis. The initial droplet size and velocity distributions are measured experimentally by phase‐Doppler interferometry for sprays generated by a planar research nozzle and a practical gas turbine airblast nozzle. For the two nozzles, the liquid bulk sheet is formed before its breakup in a coflowing air stream. It is found that the model predictions are in satisfactory agreement with the experimental data for all the cases measured. Hence the present model may be applied to a variety of practical sprays to specify the initial conditions for the spray droplets formed in practical spray systems.

Nongyrotropic particle distributions in space plasmas

Abstract. In nonstationary, strong inhomogeneous or open plasmas particle orbits are rather complicated. If the nonstationary time scale is smaller than the gyration period, if the inhomogeneity scale is smaller than the gyration radius, i.e. at magnetic plasma boundaries, or if the plasma has sources and sinks in phase space, then nongyrotropic distribution functions occur. The stability of such plasma configurations is studied in the framework of linear dispersion theory. In an open plasma nongyrotropy drives unstable waves parallel and perpendicular to the background magnetic field, whereas in the gyrotropic limit the plasma is stable. In nonstationary plasmas nongyrotropy drives perpendicular unstable waves only. Temporal modulation couples a seed mode with its side lobes and thus it renders unstable wave growth more difficult. As an example of an inhomogeneous plasma a magnetic halfspace is discussed. In a layer with thickness of the thermal proton gyroradius a nongyrotropic distribution is formed which may excite unstable parallel and perpendicular propagating waves.Key words. Interplanetary physics (plasma waves and turbulence) · Ionosphere (plasma waves and instabilities) · Magnetospheric physics (plasma waves and instabilities)

Nongyrotropic particle distributions in space plasmas

In nonstationary, strong inhomogeneous or open plasmas particle orbits are rather complicated. If the nonstationary time scale is smaller than the gyration period, if the inhomogeneity scale is smaller than the gyration radius, i.e. at magnetic plasma boundaries, or if the plasma has sources and sinks in phase space, then nongyrotropic distribution functions occur. The stability of such plasma configurations is studied in the framework of linear dispersion theory. In an open plasma nongyrotropy drives unstable waves parallel and perpendicular to the background magnetic field, whereas in the gyrotropic limit the plasma is stable. In nonstationary plasmas nongyrotropy drives perpendicular unstable waves only. Temporal modulation couples a seed mode with its side lobes and thus it renders unstable wave growth more difficult. As an example of an inhomogeneous plasma a magnetic halfspace is discussed. In a layer with thickness of the thermal proton gyroradius a nongyrotropic distribution is formed which may excite unstable parallel and perpendicular propagating waves.Key words. Interplanetary physics (plasma waves and turbulence) · Ionosphere (plasma waves and instabilities) · Magnetospheric physics (plasma waves and instabilities)

Experimental studies of flooding in nearly horizontal pipes

To investigate the flooding phenomenon in nearly horizontal pipes, experimental studies are performed for air and water countercurrent flow in a test section with a length of 2160 mm, with three different inner diameters of 40, 60 and 70 mm, with different types of end geometry, and with various inclination angles. The effects of the pipe diameter, end geometry and inclination angle on flooding are examined. Two mechanisms governing the transition to flooding are proposed: inner flooding and entrance flooding. The inner flooding is initiated by unstable wave growth, i.e. slugging, at the inner location of the pipe. The entrance flooding is always observed to take place at the entrance of the water flow without slugging. The effect of the inclination angle on flooding is predominant within quite a narrow range of inclination (0° < θ < 1°). A small deviation of the inclination angle from the horizontal plane causes a large deviation of the required air flow rates for flooding. Two local void fractions are measured by parallel wire probes and a scale marked rule in two regions (sub- and super-critical regions). The local effects of the void fraction on slug formation models are investigated. It is found that the differences in the exponents of the void fraction terms of the existing slug formation models mainly result from the definition of the void fraction used. When the void fraction measured in the sub-critical region is used in the slug formation model, Mishima et al.'s model well predicts the trend of the present data. However, if the void fraction measured in the super-critical region is used, Taitel et al.'s model better predicts the present data.

Theoretical and physical interpretation of entrainment phenomenon in capillary-driven heat pipes using hydrodynamic instability theories

The entrainment phenomenon in two-phase parallel flow has been studied from the standpoint of wave instability theories, which are related to the exponential growth of unstable waves caused by viscous interaction between the two parallel flowing fluids. Instability theories related to the Kelvin-Helmholtz and the Orr-Sommerfeld problems were reviewed and applied to predict the critical air/vapor velocity at the onset of entrainment from a capillary structure. To compare the theoretical criteria with the experimental results, entrainment observed in both air-water and steam-water situations were characterized and classified into three major categories. As results of these comparisons, a modified theoretical criterion based on the results of Miles was developed and used to investigate the effect of liquid depth on the critical air/vapor velocity or corresponding Weber number for the given temperatures, and general trends of the various criteria were examined as a function of vapor temperature.

Quasilinear theory of non-resonant electromagnetic instabilities

Our quasilinear theory includes explicitly macroscopic drifts, which are then modified, together with other equilibrium quantities, by the growth of unstable waves. We study the saturation of nonresonant electromagnetic instabilities, due to streaming effects besides pressure anisotropies. The resulting equations governing the equilibrium changes can be integrated exactly, so that more precise estimates are given for the ultimate levels of magnetic field fluctuations. This is applied to the quenching of streaming low-frequency instabilities in the mass-loaded solar wind near comets.

The mean flow character of two-phase flow equations

This study examines the nature of the one-dimensional mean motion description for two-phase flows. It is conjectured that the unstable wave growth in a streaming two-phase flow with unequal phasic velocities is a result of the failure to model the correlations of the fluctuating velocity components in the momentum equations. A general functional form for these velocity correlations is derived based upon invariance and dimensional arguments. Some speculative closure models using this functional form are derived and it is shown that reasonable forms of this closure model do in fact lead to a stable mean motion description.

Baroclinic Instability of Easterly Jets with Applications to the Summer Mesosphere

Abstract anally and seasonally averaged zonal wind fields in the summer mesosphere are unstable in the Charney-Stern sense, with a primarily baroclinic component. Two-dimensional stability analyses show peaks in the unstable wave growth spectrum at zonal wavenumbers 2–4, with periods of 1.4–3 days, for a variety of basic state flows. Wavenumbers of peak growth are consistently lower for the two-dimensional analyses than for the one-dimensional analyses, with the lowest wavenumber peaks found for the basic state flows with the smallest latitudinal scale. For strongly baroclinic basic state flows, wave growth was inhibited by introducing stronger latitudinal variations in the basic state flow; however, for marginally unstable flows, stronger latitudinal variations slightly enhance the peak growth rates. The strong thermal damping in the mesosphere reduces growth rates by 20–60% of the damping rate, but has little effect on the wave structure. The primary significance of the thermal damping is that basic sta...

On Moist Quasi-Geostrophic Baroclinic Instability

Abstract The analytic theory of quasi-geostrophic baroclinic instability is generalized with the consideration of condensational heating. The heating is parameterized in terms of the vorticity field of the baroclinic wave itself, on the basis of the postulate that the baroclinically induced, low-level convergence sustains the moisture supply to the condensational processes. This heating parameterization is expressed in terms of an integral relationship between the baroclinically induced vertical velocity at a low level, say 900 mb, and the whole vorticity field. This formulation is tested with a model of baroclinic instability in its purest form. An exact characteristic equation is obtained with which all instability properties can be precisely determined. The solution reveals that as the heating intensity parameter is increased, the most unstable wave's growth rate significantly increase, its wavelength significantly decreases and its phase speed increases. The first two trends diminish as the heating in...

Propagation and evolution of waves in a self-gravitating medium

The propagation and evolution of linear waves in a self-gravitating medium are discussed in a comparatively general way. In one special case, the well-known Jeans formula is recovered; in another, an important property of unstable waves in a self-gravitating medium is obtained, namely, the equiphase surfaces of the wave are “frozen” in the moving medium. When the motion of the basic state is one of shear flow (or differential rotation), this property implies that unstable waves would evolve into a quasi-stationary state. This shows that, for a self-gravitating medium, besides the usual non-linear effects, there is a special mechanism within the linear theory which prevents the infinite growth of unstable waves. Possible relation of this effect to the origin of celestial bodies is pointed out.

Analysis of the CO2 laser transverse mode-medium instability

Large-scale temporal oscillations are observed in the output of high-energy flowing cw CO2 lasers, causing appreciable reduction in power output and optical-beam quality. The modulation is linked to wavelike disturbances in the optical cavity which propagate either along the flow axis or transverse to both optical and flow axes. These waves, caused by an unstable interaction between the radiation field and the laser medium, are referred to as the mode-medium instability. The present analysis examines transverse waves that are associated with interactions between optical resonator modes and acoustic resonator modes. The modes interact through fluctuations in gain and refractive gradients due to the heat release during lower-laser-level collisional deactivation. This can lead to unstable acoustic wave growth. Two important propagation numbers, k0 and km, emerge from the analysis. They define a region of unstable wave growth for k between k0 and km. The instability growth rate is maximum near km and is zero at k0. It appears possible to minimize the instability by adjusting the laser parameters so that k0 and km coincide.

Some stability properties of large-scale baroclinic flows with nonlinear zonal current profile

The stability properties of a baroclinic zonal current with nonlinear velocity profile are investigated. The integral method is applied to the governing eigenvalue equation having the vertical velocity as the dependent variable. Expressed in terms of the Rossby number and the Richardson number, stability criteria, unstable regions in the complexc plane, and the upper bound of the unstable wave growth rate are found. Some differences in the results are noted between the present model and the quasi-geostrophic streamfunction model, particularly in connection with the effect of the velocity profile curvature termU zz . It is conjectured in the present model that, depending on extreme behaviors ofU zz , the propagation speed of unstable waves can be greater thanU max or smaller thanU min .