scholarly journals Helical modes in combined Rayleigh–Taylor and Kelvin–Helmholtz instability of a cylindrical interface

2016 ◽  
Vol 8 (4) ◽  
pp. 219-234 ◽  
Author(s):  
M Vadivukkarasan ◽  
Mahesh V Panchagnula
Keyword(s):  
Short Wavelength ◽  
Weber Number ◽  
Scaling Law ◽  
Density Ratio ◽  
Bond Number ◽  
Length Scale ◽  
Neutral Stability ◽  
Mean Flow ◽  
Helmholtz Instability ◽  
Regime Map

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.

Nonlinear instability of plane liquid sheets

2000 ◽  
Vol 406 ◽  
pp. 281-308 ◽  
Author(s):  
SEYED A. JAZAYERI ◽  
XIANGUO LI
Keyword(s):  
Weber Number ◽  
Density Ratio ◽  
Perturbation Expansion ◽  
Liquid Sheet ◽  
Fundamental Wave ◽  
Liquid Density ◽  
Initial Amplitude ◽  
Nonlinear Stability Analysis ◽  
Liquid Sheets ◽  
Breakup Time

A nonlinear stability analysis has been carried out for plane liquid sheets moving in a gas medium at rest by a perturbation expansion technique with the initial amplitude of the disturbance as the perturbation parameter. The first, second and third order governing equations have been derived along with appropriate initial and boundary conditions which describe the characteristics of the fundamental, and the first and second harmonics. The results indicate that for an initially sinusoidal sinuous surface disturbance, the thinning and subsequent breakup of the liquid sheet is due to nonlinear effects with the generation of higher harmonics as well as feedback into the fundamental. In particular, the first harmonic of the fundamental sinuous mode is varicose, which causes the eventual breakup of the liquid sheet at the half-wavelength interval of the fundamental wave. The breakup time (or length) of the liquid sheet is calculated, and the effect of the various flow parameters is investigated. It is found that the breakup time (or length) is reduced by an increase in the initial amplitude of disturbance, the Weber number and the gas-to-liquid density ratio, and it becomes asymptotically insensitive to the variations of the Weber number and the density ratio when their values become very large. It is also found that the breakup time (or length) is a very weak function of the wavenumber unless it is close to the cut-off wavenumbers.

scholarly journals Jet Formation and Evolution in Baroclinic Turbulence with Simple Topography

2010 ◽  
Vol 40 (2) ◽  
pp. 257-278 ◽  
Author(s):  
Andrew F. Thompson
Keyword(s):  
Southern Ocean ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Length Scale ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Jet Formation ◽  
Meridional Transport ◽  
Jet Behavior ◽  
Jet Variability

Abstract Satellite altimetry and high-resolution ocean models indicate that the Southern Ocean comprises an intricate web of narrow, meandering jets that undergo spontaneous formation, merger, and splitting events, as well as rapid latitude shifts over periods of weeks to months. The role of topography in controlling jet variability is explored using over 100 simulations from a doubly periodic, forced-dissipative, two-layer quasigeostrophic model. The system is forced by a baroclinically unstable, vertically sheared mean flow in a domain that is large enough to accommodate multiple jets. The dependence of (i) meridional jet spacing, (ii) jet variability, and (iii) domain-averaged meridional transport on changes in the length scale and steepness of simple sinusoidal topographical features is analyzed. The Rhines scale, ℓβ = 2πVe/β, where Ve is an eddy velocity scale and β is the barotropic potential vorticity gradient, measures the meridional extent of eddy mixing by a single jet. The ratio ℓβ /ℓT, where ℓT is the topographic length scale, governs jet behavior. Multiple, steady jets with fixed meridional spacing are observed when ℓβ ≫ ℓT or when ℓβ ≈ ℓT. When ℓβ < ℓT, a pattern of perpetual jet formation and jet merger dominates the time evolution of the system. Zonal ridges systematically reduce the domain-averaged meridional transport, while two-dimensional, sinusoidal bumps can increase transport by an order of magnitude or more. For certain parameters, bumpy topography gives rise to periodic oscillations in the jet structure between purely zonal and topographically steered states. In these cases, transport is dominated by bursts of mixing associated with the transition between the two regimes. Topography modifies local potential vorticity (PV) gradients and mean flows; this can generate asymmetric Reynolds stresses about the jet core and can feed back on the conversion of potential energy to kinetic energy through baroclinic instability. Both processes contribute to unsteady jet behavior. It is likely that these processes play a role in the dynamic nature of Southern Ocean jets.

Dynamics of Liquid Sheet Breakup in Splash Plate Atomization

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
G. Thunivumani ◽  
Hrishikesh Gadgil
Keyword(s):  
Solid Surface ◽  
Weber Number ◽  
Jet Impingement ◽  
Liquid Sheet ◽  
Force Balance ◽  
Impingement Angle ◽  
Wide Range ◽  
Perforated Sheet ◽  
Sheet Breakup ◽  
Regime Map

An experimental study was conducted to investigate the breakup of a liquid sheet produced by oblique impingement of a liquid jet on a plane solid surface. Experiments are carried out over a wide range of jet Weber number (80–6300) and various jet impingement angles (30 deg, 45 deg, and 60 deg) are employed to study the sheet dynamics. The breakup of a liquid sheet takes place in three modes, closed rim, open rim, and perforated sheet, depending upon the Weber number. The transitions across the modes are also influenced by the impingement angle with the transition Weber number reducing with increase in impingement angle. A modified regime map is proposed to illustrate the role of impingement angle in breakup transitions. A theoretical model based on force balance at the sheet edge is developed to predict the sheet parameters by taking the shear interaction between the sheet and the solid surface into account. The sheet shape predicted by the model fairly matches with the experimentally measured sheet shape. The breakup length and width of the sheet are measured and comparisons with the model predictions show good agreement in closed rim mode of breakup.

Instability and transition of a vertical ascension or fall of a free sphere affected by a vertical magnetic field

2018 ◽  
Vol 859 ◽  
pp. 33-48 ◽  
Author(s):  
Jun-Hua Pan ◽  
Nian-Mei Zhang ◽  
Ming-Jiu Ni
Keyword(s):  
Magnetic Field ◽  
Interaction Parameter ◽  
Scaling Law ◽  
Density Ratio ◽  
Vertical Magnetic Field ◽  
Streamwise Vorticity ◽  
Close Relationship ◽  
Wake Patterns ◽  
The Magnetic Field ◽  
Solid System

When the Galileo number is below the first bifurcation, the instability and transition of a vertical ascension or the fall of a free sphere affected by a vertical magnetic field are investigated numerically. A compact model is used to explain that the magnetic field can destabilize the fluid–solid system. When the interaction parameter exceeds a critical value, the sphere trajectory is transitioned from a steady vertical trajectory to a steady oblique one. Furthermore, the trajectory will remain vertical at a sufficiently large magnetic field because of a double effect of the magnetic field on the fluid–solid system. Under the influence of an external vertical magnetic field, four wake patterns at the rear of the sphere are found and the physical behaviour of the free sphere is independent of the density ratio. The wake or trajectory of the free sphere is only determined by the Galileo number $G$ and the interaction parameter $N$. A close relationship between the streamwise vorticity and the sphere motion is found. An interesting ‘agglomeration phenomenon’ is also found, which shows that the vertical velocities are agglomerated into a point for a certain magnetic field regardless of the Galileo number and satisfy a scaling law $V_{z}\sim N^{-1/4}$, when $N>1$. The principal results of the present work are summarized in a map of regimes in the $\{G,N\}$ plane.

Liquid Jets in Subsonic Air Crossflow at Elevated Pressure

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Jinkwan Song ◽  
Charles Cary Cain ◽  
Jong Guen Lee
Keyword(s):  
Weber Number ◽  
Momentum Flux ◽  
Drop Size ◽  
Density Ratio ◽  
Flux Ratio ◽  
Mie Scattering ◽  
Air Pressure ◽  
Scattering Intensity ◽  
Nozzle Orifice ◽  
Momentum Flux Ratio

The breakup, penetration, droplet size, and size distribution of a Jet A-1 fuel in air crossflow has been investigated with focus given to the impact of surrounding air pressure. Data have been collected by particle Doppler phased analyzer (PDPA), Mie-scattering with high speed photography augmented by laser sheet, and Mie-scattering with intensified charge-coupled device (ICCD) camera augmented by nanopulse lamp. Nozzle orifice diameter, do, was 0.508 mm and nozzle orifice length to diameter ratio, lo/do, was 5.5. Air crossflow velocities ranged from 29.57 to 137.15 m/s, air pressures from 2.07 to 9.65 bar, and temperature held constant at 294.26 K. Fuel flow provides a range of fuel/air momentum flux ratio (q) from 5 to 25 and Weber number from 250 to 1000. From the results, adjusted correlation of the mean drop size has been proposed using drop size data measured by PDPA as follows: (D0/D32)=0.267Wea0.44q0.08(ρl/ρa)0.30(μl/μa)-0.16. This correlation agrees well and shows roles of aerodynamic Weber number, Wea, momentum flux ratio, q, and density ratio, ρl/ρa. Change of the breakup regime map with respect to surrounding air pressure has been observed and revealed that the boundary between each breakup modes can be predicted by a transformed correlation obtained from above correlation. In addition, the spray trajectory for the maximum Mie-scattering intensity at each axial location downstream of injector is extracted from averaged Mie-scattering images. From these results, correlations with the relevant parameters including q, x/do, density ratio, viscosity ratio, and Weber number are made over a range of conditions. According to spray trajectory at the maximum Mie-scattering intensity, the effect of surrounding air pressure becomes more important in the farfield. On the other hand, effect of aerodynamic Weber number is more important in the nearfield.

scholarly journals Scaling and Similarity of the Anisotropic Coherent Eddies in Near-Surface Atmospheric Turbulence

2018 ◽  
Vol 75 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Khaled Ghannam ◽  
Gabriel G. Katul ◽  
Elie Bou-Zeid ◽  
Tobias Gerken ◽  
Marcelo Chamecki
Keyword(s):  
Scaling Laws ◽  
Velocity Structure ◽  
Scaling Law ◽  
Longitudinal Velocity ◽  
Structure Functions ◽  
Length Scale ◽  
Near Surface ◽  
Vegetation Canopies ◽  
Velocity Spectra ◽  
Attached Eddies

Abstract The low-wavenumber regime of the spectrum of turbulence commensurate with Townsend’s “attached” eddies is investigated here for the near-neutral atmospheric surface layer (ASL) and the roughness sublayer (RSL) above vegetation canopies. The central thesis corroborates the significance of the imbalance between local production and dissipation of turbulence kinetic energy (TKE) and canopy shear in challenging the classical distance-from-the-wall scaling of canonical turbulent boundary layers. Using five experimental datasets (two vegetation canopy RSL flows, two ASL flows, and one open-channel experiment), this paper explores (i) the existence of a low-wavenumber k−1 scaling law in the (wind) velocity spectra or, equivalently, a logarithmic scaling ln(r) in the velocity structure functions; (ii) phenomenological aspects of these anisotropic scales as a departure from homogeneous and isotropic scales; and (iii) the collapse of experimental data when plotted with different similarity coordinates. The results show that the extent of the k−1 and/or ln(r) scaling for the longitudinal velocity is shorter in the RSL above canopies than in the ASL because of smaller scale separation in the former. Conversely, these scaling laws are absent in the vertical velocity spectra except at large distances from the wall. The analysis reveals that the statistics of the velocity differences Δu and Δw approach a Gaussian-like behavior at large scales and that these eddies are responsible for momentum/energy production corroborated by large positive (negative) excursions in Δu accompanied by negative (positive) ones in Δw. A length scale based on TKE dissipation collapses the velocity structure functions at different heights better than the inertial length scale.

Measurement of the Mean Flow Field in a Smooth Rotating Channel With Coriolis and Buoyancy Effects

2017 ◽  
Author(s):  
Ruquan You ◽  
Haiwang Li ◽  
Zhi Tao ◽  
Kuan Wei
Keyword(s):  
Flow Field ◽  
Coriolis Force ◽  
Indium Tin Oxide ◽  
Buoyancy Force ◽  
Flow Direction ◽  
Density Ratio ◽  
Mean Flow ◽  
The Mean ◽  
Static Conditions ◽  
Rotating Channel

The mean flow field in a smooth rotating channel was measured by particle image velocimetry under the effect of buoyancy force. In the experiments, the Reynolds number, based on the channel hydraulic diameter (D) and the bulk mean velocity (Um), is 10000, and the rotation numbers are 0, 0.13, 0.26, 0.39, 0.52, respectively. The four channel walls are heated with Indium Tin Oxide (ITO) heater glass, making the density ratio (d.r.) about 0.1 and the maximum value of buoyancy number up to 0.27. The mean flow field was simulated on a 3D reconstruction at the position of 3.5<X/D<6.5, where X is along the mean flow direction. The effect of Coriolis force and buoyancy force on the mean flow was taken into consideration in the current work. The results show that the Coriolis force pushes the mean flow to the trailing side, making the asymmetry of the mean flow with that in the static conditions. On the leading surface, due to the effect of buoyancy force, the mean flow field changes considerably. Comparing with the case without buoyancy force, separated flow was captured by PIV on the leading side in the case with buoyancy force. More details of the flow field will be presented in this work.

scholarly journals Cratering for Impact of Hypervelocity Projectiles into Granite Targets within a Velocity Range of 1.91–3.99 km/s: Experiments and Analysis

2020 ◽  
Vol 10 (4) ◽  
pp. 1393
Author(s):  
Xiaofeng Wang ◽  
Jingbo Liu ◽  
Biao Wu ◽  
Defeng Kong ◽  
Jiarong Huang ◽  
...  
Keyword(s):  
Impact Velocity ◽  
Scaling Law ◽  
Density Ratio ◽  
Hypervelocity Impact ◽  
Experimental Results ◽  
Tungsten Alloy ◽  
Regression Equations ◽  
Velocity Range ◽  
Predicted Values ◽  
The Impact

To understand and analyze crater damage of rocks under hypervelocity impact, the hypervelocity impact cratering of 15 shots of hemispherical-nosed cylindrical projectiles into granite targets was studied within the impact velocity range of 1.91–3.99 km/s. The mass of each projectile was 40 g, and the length–diameter ratio was 2. Three types of metal material were adopted for the projectiles, including titanium alloy with a density of 4.44 g/cm3, steel alloy with a density of 7.81 g/cm3, and tungsten alloy with a density of 17.78 g/cm3. The projectile–target density ratio (ρp/ρt) ranged from 1.71 to 6.86. The depth–diameter ratios (H/D) of the craters yielded from the experiments were between 0.14 and 0.24. The effects of ρp/ρt and the impact velocity on the morphologies of the crater were evaluated. According to the experimental results, H/D of craters is negatively correlated with the impact velocity, whereas the correlation between H/D and ρp/ρt is weak positive. The crater parameters were expressed as power law relations of impact parameters by using scaling law analysis. The multiple regression analysis was utilized to obtain the coefficients and the exponents of the relation equations. The predicted values of the regression equations were close to the experimental results.

scholarly journals Splash wave and crown breakup after disc impact on a liquid surface

2013 ◽  
Vol 724 ◽  
pp. 553-580 ◽  
Author(s):  
Ivo R. Peters ◽  
Devaraj van der Meer ◽  
J. M. Gordillo
Keyword(s):  
Numerical Simulations ◽  
Weber Number ◽  
Threshold Value ◽  
Bond Number ◽  
Radius Of Curvature ◽  
Time Varying ◽  
Self Similar Solution ◽  
Air Cushion ◽  
Self Similar ◽  
The Impact

AbstractIn this paper we analyse the impact of a circular disc on a free surface using experiments, potential flow numerical simulations and theory. We focus our attention both on the study of the generation and possible breakup of the splash wave created after the impact and on the calculation of the force on the disc. We have experimentally found that drops are only ejected from the rim located at the top part of the splash – giving rise to what is known as the crown splash – if the impact Weber number exceeds a threshold value ${\mathit{We}}_{crit} \simeq 140$. We explain this threshold by defining a local Bond number $B{o}_{\mathit{tip}} $ based on the rim deceleration and its radius of curvature, with which we show using both numerical simulations and experiments that a crown splash only occurs when $B{o}_{\mathit{tip}} \gtrsim 1$, revealing that the rim disrupts due to a Rayleigh–Taylor instability. Neglecting the effect of air, we show that the flow in the region close to the disc edge possesses a Weber-number-dependent self-similar structure for every Weber number. From this we demonstrate that ${\mathit{Bo}}_{\mathit{tip}} \propto \mathit{We}$, explaining both why the transition to crown splash can be characterized in terms of the impact Weber number and why this transition occurs for $W{e}_{crit} \simeq 140$. Next, including the effect of air, we have developed a theory which predicts the time-varying thickness of the very thin air cushion that is entrapped between the impacting solid and the liquid. Our analysis reveals that gas critically affects the velocity of propagation of the splash wave as well as the time-varying force on the disc, ${F}_{D} $. The existence of the air layer also limits the range of times in which the self-similar solution is valid and, accordingly, the maximum deceleration experienced by the liquid rim, that sets the length scale of the splash drops ejected when $We\gt {\mathit{We}}_{crit} $.

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