Spatiotemporal instability of a variable-density Batchelor vortex

2012 ◽  
Vol 703 ◽  
pp. 49-59 ◽  
Author(s):  
Bastien Di Pierro ◽  
Malek Abid
Keyword(s):  
Velocity Ratio ◽  
Density Ratio ◽  
Three Dimensional ◽  
Laboratory Frame ◽  
Variable Density ◽  
Constant Density ◽  
Azimuthal Mode ◽  
Linear Framework ◽  
High Reynolds ◽  
Absolute Transition

AbstractLinear and nonlinear impulse responses are computed, using three-dimensional numerical simulations, for an incompressible and variable density (inhomogeneous) Batchelor vortex at a moderately high Reynolds number, $\mathit{Re}= 667$. In the linear framework, the computed wavepacket is decomposed into azimuthal modes whose growth rates are determined along each spatiotemporal ray, in the laboratory frame. It is found that the Batchelor vortex undergoes a convective/absolute transition when the density ratio (inner/ambient), $s$, is varied solely (there is no need for an external counter flow to trigger this transition like that needed in the constant density case). More precisely, it is shown that the transition occurs for heavy vortices when the density ratio reaches a critical value, ${s}_{c} \simeq 1. 08$. For light vortices ($s\lt 1$) no transition was found. It is also shown that the first azimuthal mode that transits have an azimuthal wavenumber $m= \ensuremath{-} 2$ and the transition occurs for a swirl number (a measure of the azimuthal to axial velocity ratio), $q= 0. 57$. It is followed by $m= \ensuremath{-} 1$, then by $m= \ensuremath{-} 3$. When nonlinearities are allowed, it is found that they saturate the amplitude within the linear-response wavepacket, leaving the wavepacket fronts unaffected. The conclusions should thus be the same as those obtained in the linear case: the linear convective/absolute transition should coincide with the nonlinear one for the variable-density Batchelor vortex.

The effect of air swirl profile on the instability of a viscous liquid jet

2000 ◽  
Vol 424 ◽  
pp. 1-20 ◽  
Author(s):  
Y. LIAO ◽  
S. M. JENG ◽  
M. A. JOG ◽  
M. A. BENJAMIN
Keyword(s):  
Viscous Liquid ◽  
Growth Rates ◽  
Axial Velocity ◽  
Weber Number ◽  
Velocity Ratio ◽  
Density Ratio ◽  
Three Dimensional ◽  
Interfacial Instability ◽  
Liquid Jet ◽  
Axisymmetric Mode

A temporal linear stability analysis has been carried out to predict the instability of a viscous liquid jet surrounded by a swirling air stream with three-dimensional disturbances. The effects of flow conditions and fluid properties on the instability of the liquid jet are investigated via a parametric study by varying axial Weber number axial velocity ratio of the gas to liquid phase, swirl Weber numbers, density ratio and the Ohnesorge number. It is observed that the relative axial velocity between the liquid and gas phases promotes the interfacial instability. As the axial Weber number increases, the growth rates of unstable waves, the most unstable wavenumber and the unstable range of wavenumbers increase. Meanwhile, the increasing importance of helical modes compared to the axisymmetric mode switches the breakup regime from the Rayleigh regime to the first wind-induced regime and on to the second wind-induced regime. The predicted range of wavenumbers in which the first helical mode has higher growth rates than the axisymmetric mode agrees very well with experimental data. Results show that the destabilizing effects of the density ratio and the axial Weber number are nearly the same. Liquid viscosity inhibits the disintegration process of the liquid jet by reducing the growth rate of disturbances and by shifting the most unstable wavenumber to a lower value. Moreover, it damps higher helical modes more significantly than the axisymmetric mode. Air swirl has a stabilizing effect on the liquid jet. As air swirl strength increases, the growth rates of helical modes are reduced more significantly than that of the axisymmetric mode. The air swirl profile is found to have a significant effect on the instability of the liquid jet. The global, as well as local, effects of the swirl profile are examined in detail.

Local stability analysis of an inviscid transverse jet

2007 ◽  
Vol 581 ◽  
pp. 401-418 ◽  
Author(s):  
LEONARDO S. de B. ALVES ◽  
ROBERT E. KELLY ◽  
ANN R. KARAGOZIAN
Keyword(s):  
Stability Analysis ◽  
Growth Rates ◽  
Near Field ◽  
Velocity Ratio ◽  
Three Dimensional ◽  
Constant Density ◽  
Jet Instability ◽  
Transverse Jet ◽  
Free Jet ◽  
Local Stability Analysis

A local linear stability analysis is performed for a round inviscid jet with constant density that is injected into a uniform crossflow of the same density. The baseflow is obtained from a modified version of the inviscid transverse jet near-field solution of Coelho & Hunt (J. Fluid Mech.vol. 200, 1989, p. 95) which is valid for small values of the crossflow-to-jet velocity ratio λ. A Fourier expansion in the azimuthal direction is used to couple the disturbances with the three-dimensional crossflow. The spatial growth rates of the modes corresponding to the axisymmetric and first helical modes of the free jet as λ → 0 increase as λ increases. The diagonal dominance of the dispersion relation matrix is used as a quantitative criterion to estimate the range of velocity ratios (0 < λ < λc) within which the transverse jet instability can be considered to have a structure similar to that of the free jet. Further, we show that for λ>0 positive and negative helical modes have different growth rates, suggesting an inherent weak asymmetry in the transverse jet.

scholarly journals Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 2. Nonlinear simulations

2013 ◽  
Vol 721 ◽  
pp. 295-323 ◽  
Author(s):  
M. O. John ◽  
R. M. Oliveira ◽  
F. H. C. Heussler ◽  
E. Meiburg
Keyword(s):  
Oil Recovery ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Viscous Fingering ◽  
Variable Density ◽  
Taylor Instability ◽  
Constant Density ◽  
Streamwise Vorticity ◽  
Miscible Displacements ◽  
Rayleigh Taylor Instability

AbstractDirect numerical simulations of the variable density and viscosity Navier–Stokes equations are employed, in order to explore three-dimensional effects within miscible displacements in horizontal Hele-Shaw cells. These simulations identify a number of mechanisms concerning the interaction of viscous fingering with a spanwise Rayleigh–Taylor instability. The dominant wavelength of the Rayleigh–Taylor instability along the upper, gravitationally unstable side of the interface generally is shorter than that of the fingering instability. This results in the formation of plumes of the more viscous resident fluid not only in between neighbouring viscous fingers, but also along the centre of fingers, thereby destroying their shoulders and splitting them longitudinally. The streamwise vorticity dipoles forming as a result of the spanwise Rayleigh–Taylor instability place viscous resident fluid in between regions of less viscous, injected fluid, thereby resulting in the formation of gapwise vorticity via the traditional, gap-averaged viscous fingering mechanism. This leads to a strong spatial correlation of both vorticity components. For stronger density contrasts, the streamwise vorticity component increases, while the gapwise component is reduced, thus indicating a transition from viscously dominated to gravitationally dominated displacements. Gap-averaged, time-dependent concentration profiles show that variable density displacement fronts propagate more slowly than their constant density counterparts. This indicates that the gravitational mixing results in a more complete expulsion of the resident fluid from the Hele-Shaw cell. This observation may be of interest in the context of enhanced oil recovery or carbon sequestration applications.

High Reynolds Number, Unsteady, Multiphase CFD Modeling of Cavitating Flows

2002 ◽  
Vol 124 (3) ◽  
pp. 607-616 ◽  
Author(s):  
Jules W. Lindau ◽  
Robert F. Kunz ◽  
David A. Boger ◽  
David R. Stinebring ◽  
Howard J. Gibeling
Keyword(s):  
Density Ratio ◽  
Three Dimensional ◽  
Cfd Modeling ◽  
Navier Stokes ◽  
Cavitating Flows ◽  
Good Convergence ◽  
Noncondensable Gas ◽  
Flow Features ◽  
Unsteady Rans ◽  
High Reynolds

A preconditioned, homogeneous, multiphase, Reynolds Averaged Navier-Stokes model with mass transfer is presented. The model is preconditioned in order to obtain good convergence and accuracy regardless of phasic density ratio or flow velocity. Engineering relevant validative unsteady two and three-dimensional results are given. A demonstrative three-dimensional, three-field (liquid, vapor, noncondensable gas) transient is also presented. In modeling axisymmetric cavitators at zero angle-of-attack with 3-D unsteady RANS, significant asymmetric flow features are obtained. In comparison with axisymmetric unsteady RANS, capture of these features leads to improved agreement with experimental data.

A semi-Lagrangian direct-interaction closure of the spectra of isotropic variable-density turbulence

2019 ◽  
Vol 876 ◽  
pp. 186-236 ◽  
Author(s):  
David J. Petty ◽  
C. Pantano
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Density Ratio ◽  
Direct Interaction ◽  
Variable Density ◽  
Constant Density ◽  
Velocity Spectrum ◽  
Variable Density Flow ◽  
Density Flow ◽  
Variable Density Turbulence

A study of variable-density homogeneous stationary isotropic turbulence based on the sparse direct-interaction perturbation (SDIP) and supporting direct numerical simulations (DNS) is presented. The non-solenoidal flow considered here is an example of turbulent mixing of gases with different densities. The spectral statistics of this type of flow are substantially more difficult to understand theoretically than those of the similar solenoidal flows. In the approach described here, the nonlinearly coupled velocity and scalar (which determine the density of the fluid) equations are expanded in terms of a normalised density ratio parameter. A new set of coupled integro-differential SDIP equations are derived and then solved numerically for the first-order correction to the incompressible equations in the variable-density expansion parameter. By adopting a regular expansion approach, one obtains leading-order corrections that are universal and therefore interesting in their own right. The predictions are then compared with DNS of forced variable-density flow with different density contrasts. It is found that the velocity spectrum owing to variable density is indistinguishable from that of constant-density turbulence, as it is supported by a wealth of indirect experimental evidence, but the scalar spectra show significant deviations, and even loss of monotonicity, as a function of the type and strength of the large-scale source of the mixing. Furthermore, the analysis helps clarify what may be the proper approach to interpret the power spectrum of variable-density turbulence.

scholarly journals Vorticity dynamics in a spatially developing liquid jet inside a co-flowing gas

2019 ◽  
Vol 877 ◽  
pp. 429-470
Author(s):  
A. Zandian ◽  
W. A. Sirignano ◽  
F. Hussain
Keyword(s):  
Liquid Velocity ◽  
Velocity Ratio ◽  
Density Ratio ◽  
Three Dimensional ◽  
Upstream Region ◽  
Inertia Force ◽  
Liquid Jet ◽  
Viscous Forces ◽  
Surface Deformations ◽  
Axial Acceleration

A three-dimensional transient round liquid jet within a low-speed coaxial outer gas flow is numerically simulated and analysed via vortex dynamics ($\unicode[STIX]{x1D706}_{2}$ analysis). Two types of surface deformations are distinguished, which are separated by a large indentation on the jet stem. First, there are those inside the recirculation zone behind the leading cap – directly affecting the cap dynamics and well explained by the local vortices. Second, deformations upstream of the cap are mainly driven by the Kelvin–Helmholtz (KH) instability, unaffected by the vortices in the behind-the-cap region (BCR), and are important in the eventual atomization process. Different atomization mechanisms are identified and are delineated on a gas Weber number ($We_{g}$) versus liquid Reynolds number ($Re_{l}$) map based on the relative gas–liquid velocity. In a frame moving with the liquid velocity, this result is consistent with prior temporal studies. A simpler and clearer portrait of similarity of the atomization domains is shown by using the relative gas–liquid axial velocity, i.e. $We_{r}$ and $Re_{r}$, and avoiding the widely used velocity ratio as a third key parameter. A detailed comparison of vorticity along the axis in an Eulerian frame versus a frame fixed to a surface wave reveals that the vortex development and surface deformations are periodic in the upstream region, but this periodicity is lost closer to the BCR. In the practical range of the density ratio and for early times in the process, axial vorticity is mainly generated by baroclinicity while streamwise vortex stretching becomes more important at later times and only at lower relative velocities when pressure gradients are reduced. The inertia, vortex, pressure, viscous and surface tension forces are analysed to delineate the dominant causes of the three-dimensional instability of the axisymmetric KH structure due to surface acceleration in the axial, radial and azimuthal directions. The inertia force related to the axial gradient of kinetic energy is the main cause of the axial acceleration of the waves, while the azimuthal acceleration is mainly caused by the pressure and viscous forces. The viscous forces are negligible in the radial direction and away from the nozzle exit in the axial direction. It is interesting to note that azimuthal viscous forces are important even at high $Re_{l}$, indicating that inertia is not totally dominant in this instability occurring early in the atomization cascade.

EXPERIMENTAL INVESTIGATION OF FLOW RESPONSE TO STATIONARY DISTURBANCE IN ROTATING-DISK FLOW

2019 ◽  
Vol XVI (2) ◽  
pp. 13-22
Author(s):  
Muhammad Ehtisham Siddiqui
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Careful Analysis ◽  
Laboratory Frame ◽  
Transition To Turbulence ◽  
Turbulent Regime ◽  
Mean Velocity ◽  
Layer Flow

Three-dimensional boundary-layer flow is well known for its abrupt and sharp transition from laminar to turbulent regime. The presented study is a first attempt to achieve the target of delaying the natural transition to turbulence. The behaviour of two different shaped and sized stationary disturbances (in the laboratory frame) on the rotating-disk boundary layer flow is investigated. These disturbances are placed at dimensionless radial location (Rf = 340) which lies within the convectively unstable zone over a rotating-disk. Mean velocity profiles were measured using constant-temperature hot-wire anemometry. By careful analysis of experimental data, the instability of these disturbance wakes and its estimated orientation within the boundary-layer were investigated.

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