scholarly journals Rayleigh-Taylor Instability with Finite Skin Depth

2018 ◽  
Vol 5 (3) ◽  
pp. 95-98
Author(s):  
F. E. M. Silveira
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Scaling Laws ◽  
Geometric Mean ◽  
Skin Depth ◽  
Taylor Instability ◽  
Fluid Viscosity ◽  
Viscous Effects ◽  
Rayleigh Taylor Instability ◽  
Viscous Boundary

In this work, the Rayleigh-Taylor instability is addressed in a viscous-resistive current slab, by assuming a finite electron skin depth. The formulation is developed on the basis of an extended form of Ohm’s law, which includes a term proportional to the explicit time derivative of the current density. In the neighborhood of the rational surface, a viscous-resistive boundary-layer is defined in terms of a resistive and a viscous boundary layers. As expected, when viscous effects are negligible, it is shown that the viscous-resistive boundary-layer is given by the resistive boundary-layer. However, when viscous effects become important, it is found that the viscous-resistive boundary-layer is given by the geometric mean of the resistive and viscous boundary-layers. Scaling laws of the time growth rate of the Rayleigh-Taylor instability with the plasma resistivity, fluid viscosity, and electron number density are discussed.

scholarly journals Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

2011 ◽  
Vol 671 ◽  
pp. 96-120 ◽  
Author(s):  
J. C. R. HUNT ◽  
D. D. STRETCH ◽  
S. E. BELCHER
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Lower Layer ◽  
Coupling Mechanism ◽  
Viscous Layer ◽  
Viscous Coupling ◽  
Viscous Effects ◽  
Horizontal Structure ◽  
Velocity Fluctuations ◽  
Viscous Boundary

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.

Jetting of viscous droplets from cavitation-induced Rayleigh–Taylor instability

2018 ◽  
Vol 846 ◽  
pp. 916-943 ◽  
Author(s):  
Qingyun Zeng ◽  
Silvestre Roberto Gonzalez-Avila ◽  
Sophie Ten Voorde ◽  
Claus-Dieter Ohl
Keyword(s):  
Bubble Dynamics ◽  
Stokes Equations ◽  
Droplet Surface ◽  
Taylor Instability ◽  
Bubble Collapse ◽  
Fluid Viscosity ◽  
Analytic Model ◽  
Radial Acceleration ◽  
Rayleigh Taylor Instability ◽  
Good Agreement

Liquid jetting and fragmentation are important in many industrial and medical applications. Here, we study the jetting from the surface of single liquid droplets undergoing internal volume oscillations. This is accomplished by an explosively expanding and collapsing vapour bubble within the droplet. We observe jets emerging from the droplet surface, which pinch off into finer secondary droplets. The jetting is excited by the spherical Rayleigh–Taylor instability where the radial acceleration is due to the oscillation of an internal bubble. We study this jetting and the effect of fluid viscosity experimentally and numerically. Experiments are carried out by levitating the droplet in an acoustic trap and generating a laser-induced cavitation bubble near the centre of the droplet. On the simulation side, the volume of fluid method (OpenFOAM) solves the compressible Navier–Stokes equations while accounting for surface tension and viscosity. Both two-dimensional (2-D) axisymmetric and 3-D simulations are performed and show good agreement with each other and the experimental observation. While the axisymmetric simulation reveals how the bubble dynamics results destabilizes the interface, only the 3-D simulation computes the geometrically correct slender jets. Overall, experiments and simulations show good agreement for the bubble dynamics, the onset of disturbances and the rapid ejection of filaments after bubble collapse. Additionally, an analytic model for the droplet surface perturbation growth is developed based on the spherical Rayleigh–Taylor instability analysis, which allows us to evaluate the surface stability over a large parameter space. The analytic model predicts correctly the onset of jetting as a function of Reynolds number and normalized internal bubble energy.

The Influence of Viscous Effects and Physical Scale on Cavitation Tunnel Contraction Performance

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
P. A. Brandner ◽  
J. L. Roberts ◽  
G. J. Walker
Keyword(s):  
Boundary Layer ◽  
Test Section ◽  
Maximum Pressure ◽  
Fluid Viscosity ◽  
Viscous Effects ◽  
Local Pressure ◽  
Displacement Effect ◽  
Physical Scale ◽  
Cavitation Tunnel ◽  
Cfd Analyses

The general performance of an asymmetric cavitation tunnel contraction is investigated using computational fluid dynamics (CFD) including the effects of fluid viscosity and physical scale. The horizontal and vertical profiles of the contraction geometry were chosen from a family of four-term sixth-order polynomials based on results from a CFD analysis and a consideration of the wall curvature distribution and its anticipated influence on boundary layer behavior. Inviscid and viscous CFD analyses were performed. The viscous predictions were validated against boundary layer measurements on existing full-scale cavitation tunnel test section ceiling and floor and for the chosen contraction geometry against model-scale wind tunnel tests. The viscous analysis showed the displacement effect of boundary layers to have a fairing effect on the contraction profile that reduced the magnitude of local pressure extrema at the entrance and exit. The maximum pressure gradients and minimum achievable test section cavitation numbers predicted by the viscous analysis are correspondingly less than those predicted by the inviscid analysis. The prediction of cavitation onset is discussed in detail. The minimum cavitation number is shown to be a function of the Froude number based on the test section velocity and height that incorporate the effects of physical scale on cavitation tunnel performance.

scholarly journals Acoustic Streaming Generated by Sharp Edges: The Coupled Influences of Liquid Viscosity and Acoustic Frequency

Micromachines ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 607 ◽  
Author(s):  
Chuanyu Zhang ◽  
Xiaofeng Guo ◽  
Laurent Royon ◽  
Philippe Brunet
Keyword(s):  
Boundary Layer ◽  
Scaling Laws ◽  
Acoustic Streaming ◽  
Maximal Velocity ◽  
Liquid Viscosity ◽  
Viscous Boundary Layer ◽  
Acoustic Frequency ◽  
Streaming Velocity ◽  
Viscous Boundary ◽  
Streaming Flow

Acoustic streaming can be generated around sharp structures, even when the acoustic wavelength is much larger than the vessel size. This sharp-edge streaming can be relatively intense, owing to the strongly focused inertial effect experienced by the acoustic flow near the tip. We conducted experiments with particle image velocimetry to quantify this streaming flow through the influence of liquid viscosity ν , from 1 mm 2 /s to 30 mm 2 /s, and acoustic frequency f from 500 Hz to 3500 Hz. Both quantities supposedly influence the thickness of the viscous boundary layer δ = ν π f 1 / 2 . For all situations, the streaming flow appears as a main central jet from the tip, generating two lateral vortices beside the tip and outside the boundary layer. As a characteristic streaming velocity, the maximal velocity is located at a distance of δ from the tip, and it increases as the square of the acoustic velocity. We then provide empirical scaling laws to quantify the influence of ν and f on the streaming velocity. Globally, the streaming velocity is dramatically weakened by a higher viscosity, whereas the flow pattern and the disturbance distance remain similar regardless of viscosity. Besides viscosity, the frequency also strongly influences the maximal streaming velocity.

Loss Mechanisms in Turbomachines

1993 ◽  
Author(s):  
J. D. Denton
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Axial Flow ◽  
Boundary Layer Separation ◽  
Quantitative Prediction ◽  
Prediction Methods ◽  
Viscous Effects ◽  
Mixing Processes ◽  
Loss Mechanisms

The origins and effects of loss in turbomachines are discussed with the emphasis on trying to understand the physical origins of loss rather than on reviewing the available prediction methods. Loss is defined in terms of entropy increase and the relationship of this to the more familiar loss coefficients is derived and discussed. The sources of entropy are in general: Viscous effects in boundary layers, viscous effects in mixing processes, shock waves and heat transfer across temperature differences. These are first discussed in general and then the results are applied to turbomachinery flows. Understanding of the loss due to heat transfer requires some discussion of cycle thermodynamics. Sections are devoted to discussing: Blade boundary layer and trailing edge loss, tip leakage loss, endwall loss, effects of heat transfer and miscellaneous losses. The loss arising from boundary layer separation is particularly difficult to quantify. Most of the discussion is based on axial flow machines but a separate section is devoted to the special problems of radial flow machines. In some cases, eg attached blade boundary layers, the loss mechanisms are well understood, but even so the loss can seldom be predicted with great accuracy. In many other cases, eg endwall loss, the loss mechanisms are still not clearly understood and prediction methods remain very dependent on correlations. The paper emphasises that the use of correlations should not be a substitute for trying to understand the origins of loss and suggests that a good physical understanding of the latter may be more valuable than a quantitative prediction.

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