Rayleigh–Taylor mixing between density stratified layers

2016 ◽  
Vol 810 ◽  
pp. 584-602 ◽  
Author(s):  
R. J. R. Williams
Keyword(s):  
Initial Conditions ◽  
Mixing Layer ◽  
Configurational Entropy ◽  
Experimental Results ◽  
Numerical Calculations ◽  
Fluid Mixing ◽  
Late Time ◽  
Density Profiles ◽  
Rayleigh Taylor Instability ◽  
Good Agreement

We have performed numerical calculations of fluid mixing driven by Rayleigh–Taylor instability for density profiles based on the stratified density experiments of Lawrie & Dalziel (J. Fluid Mech., vol. 688, 2011, pp. 507–527) and Davies Wykes & Dalziel (J. Fluid Mech., vol. 756, 2014, pp. 1027–1057). We find that the late-time mixing profiles are similar to their experimental results for similar initial conditions; we consider a range of additional initial conditions to investigate the robustness of the results. A model for the late-time structure of the mixing layer, based on the maximization of configurational entropy, is compared with the results of the numerical calculations, and shows good agreement.

scholarly journals Rayleigh-Taylor Instability: A Status Review of Experimental Designs and Measurement Diagnostics

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Arindam Banerjee
Keyword(s):  
Initial Conditions ◽  
Nonlinear Models ◽  
Imaging Techniques ◽  
Mixing Layer ◽  
Single Mode ◽  
Taylor Instability ◽  
Experimental Designs ◽  
Late Time ◽  
Buoyancy Driven Flows ◽  
Rayleigh Taylor Instability

Abstract The focus of experiments and the sophistication of diagnostics employed in Rayleigh-Taylor instability (RTI) induced mixing studies have evolved considerably over the past seven decades. The first theoretical analysis by Taylor and the two-dimensional experimental results by Lewis on RTI in 1950 examined single-mode RTI using conventional imaging techniques. Over the next 70 years, several experimental designs have been used to creating an RTI unstable interface between two materials of different densities. These early experiments though innovative, were arduous to diagnose and provided little information on the internal, turbulent structure and initial conditions of the RT mixing layer. Coupled with the availability of high-fidelity diagnostics, the experiments designed and developed in the last three decades allow detailed measurements of various turbulence statistics that have allowed broadly to validate and verify late-time nonlinear models and mix-models for buoyancy-driven flows. Besides, they have provided valuable insights to solve several long-standing disagreements in the field. This review serves as an opportunity to discuss the understanding of the RTI problem and highlight valuable insights gained into the RTI driven mixing process with a focus on low to high Atwood number (>0.1) experiments.

Viscous Dissipation in Laminar Water Flows in Micro-Tubes

2007 ◽  
Author(s):  
In-Hwan Yang ◽  
Mohamed S. El-Genk
Keyword(s):  
Experimental Data ◽  
Viscous Dissipation ◽  
Temperature Rise ◽  
Experimental Results ◽  
Numerical Calculations ◽  
Analytical Expression ◽  
Water Flows ◽  
Good Agreement

Numerical calculations are performed to investigate the effect of viscous dissipation on the temperature rise and friction numbers for laminar water flows in micro-tubes. The calculated values are compared with those determined from reported experimental data for glass and diffused silica micro-tubes (D = 16 – 101 μm and L/D = 625 – 1479). The results confirm a definite slip at the wall with slip lengths of ∼ 0.7 μm and 1.0 μm, which decrease the friction number and the temperature rise in the micro-tubes, but their effect gradually diminishes as either D or L/D increases. The friction number decreases exponentially as D decreases and, to a lesser extent, as L/D increases. The effect of L/D on the friction number is insignificant for micro-tube diameters ≤ 20 μm. For D > 400 μm, the friction number approaches that of Hagen-Posieuille of 64 for macro-tubes when L/D > 1500, but approaches higher values at smaller L/D. The dimensionless analytical expression developed for calculating the friction number and the temperature rise for water flows in micro-tubes is in good agreement with both the numerical and experimental results.

scholarly journals On the “Early-Time” Evolution of Variables Relevant to Turbulence Models for the Rayleigh-Taylor Instability

2010 ◽  
Author(s):  
Bertrand Rollin ◽  
Malcolm J. Andrews
Keyword(s):  
Turbulence Model ◽  
Initial Conditions ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Early Time ◽  
Variable Density ◽  
Taylor Instability ◽  
Turbulent Regime ◽  
Rayleigh Taylor Instability

We present our progress toward setting initial conditions in variable density turbulence models. In particular, we concentrate our efforts on the BHR turbulence model [1] for turbulent Rayleigh-Taylor instability. Our approach is to predict profiles of relevant variables before fully turbulent regime and use them as initial conditions for the turbulence model. We use an idealized model of mixing between two interpenetrating fluids to define the initial profiles for the turbulence model variables. Velocities and volume fractions used in the idealized mixing model are obtained respectively from a set of ordinary differential equations modeling the growth of the Rayleigh-Taylor instability and from an idealization of the density profile in the mixing layer. A comparison between predicted profiles for the turbulence model variables and profiles of the variables obtained from low Atwood number three dimensional simulations show reasonable agreement.

Reflexionserscheinungen bei Torsions-Alfvén-Wellen in inhomogenen Magnetfeldern/ Reflection Phenomena of Torsional Alfvén Waves in Inhomogeneous Magnetic Fields

1975 ◽  
Vol 30 (12) ◽  
pp. 1594-1599
Author(s):  
E. Räuchle ◽  
P. G. Schüller
Keyword(s):  
Magnetic Fields ◽  
Experimental Results ◽  
Numerical Calculations ◽  
Wave Frequency ◽  
Field Inhomogeneity ◽  
Cylindrical Plasma ◽  
Spatially Inhomogeneous ◽  
Strong Reflection ◽  
Order Of Magnitude ◽  
Good Agreement

Abstract The propagation of torsional Alfen waves in a cylindrical plasma is investigated. Superimposed on the plasma are various types of spatially inhomogeneous axisymmetric magnetic fields. Characteristic examples are: in the direction of propagation spatially decreasing, increasing and periodically modulated magnetic fields. The wave lengths are of the same order of magnitude as the characteristic lengths of the inhomogeneities. Strong reflection is observed which depends on wave frequency and strength of the field inhomogeneity. There exists good agreement between experimental results and numerical calculations.

scholarly journals Efficient mixing in stratified flows: experimental study of a Rayleigh–Taylor unstable interface within an otherwise stable stratification

2014 ◽  
Vol 756 ◽  
pp. 1027-1057 ◽  
Author(s):  
Megan S. Davies Wykes ◽  
Stuart B. Dalziel
Keyword(s):  
Turbulent Mixing ◽  
Laboratory Experiments ◽  
Functional Form ◽  
Salt Water ◽  
Stable Stratification ◽  
Mixing Efficiency ◽  
Final States ◽  
Density Profiles ◽  
Rayleigh Taylor Instability ◽  
Good Agreement

AbstractBoussinesq salt-water laboratory experiments of Rayleigh–Taylor instability (RTI) can achieve mixing efficiencies greater than 0.75 when the unstable interface is confined between two stable stratifications. This is much greater than that found when RTI occurs between two homogeneous layers when the mixing efficiency has been found to approach 0.5. Here, the mixing efficiency is defined as the ratio of energy used in mixing compared with the energy available for mixing. If the initial and final states are quiescent then the mixing efficiency can be calculated from experiments by comparison of the corresponding density profiles. Varying the functional form of the confining stratifications has a strong effect on the mixing efficiency. We derive a buoyancy-diffusion model for the rate of growth of the turbulent mixing region, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\dot{h} = 2 \sqrt{\alpha A g h}$ (where $A = A(h)$ is the Atwood number across the mixing region when it extends a height $h$, $g$ is acceleration due to gravity and $\alpha $ is a constant). This model shows good agreement with experiments when the value of the constant $\alpha $ is set to 0.07, the value found in experiments of RTI between two homogeneous layers (where the height of the turbulent mixing region increases as $h =\alpha A g t^2$, an expression which is equivalent to that derived for $\dot{h}$).

Numerical Calculations of Wing Tip Vortices and Effects of Suction at Wing Tip

2002 ◽  
Author(s):  
S. Okada ◽  
N. Arai ◽  
K. Hiraoka
Keyword(s):  
Three Dimensional ◽  
Turbulence Models ◽  
Experimental Results ◽  
Numerical Calculations ◽  
Analysis Software ◽  
Tip Vortices ◽  
Fluid Analysis ◽  
Induced Drag ◽  
Wing Tip ◽  
Good Agreement

In three-dimensional wing, the induced drag occurs by wing tip vortices. So it is important to study the characteristics of wing tip vortices in order to reduce the induced drag. In this paper, at first comparing the numerically calculated results of three-dimensional incompressible flow using several turbulence models and the law speed wind tunnel experimental results using a two-dimensional hot wire anemometer, the characteristics of wing tip vortices are studied. In the numerical calculations, the multipurpose fluid analysis software FLUENT and the pre-processor GAMBIT are used on popular PC. The numerical results that were obtained by using the RNG k-ε turbulence model is good agreement with the experimental results. Then controlling the flow near the wing tip by suction, the effects against wing tip vortices are studied by numerically and experimentally. It is shown by numerical calculation and experiment that the strength of wing tip vortices decrease by appropriate suction at the wing tip.

scholarly journals A Validation Study of the Compressible Rayleigh–Taylor Instability Comparing the Ares and Miranda Codes

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Thomas J. Rehagen ◽  
Jeffrey A. Greenough ◽  
Britton J. Olson
Keyword(s):  
Wave Number ◽  
Late Time ◽  
Kolmogorov Spectrum ◽  
Global Properties ◽  
Grid Convergence ◽  
Large Eddy ◽  
Convergence Study ◽  
Rayleigh Taylor Instability ◽  
Rt Instability ◽  
Good Agreement

The compressible Rayleigh–Taylor (RT) instability is studied by performing a suite of large eddy simulations (LES) using the Miranda and Ares codes. A grid convergence study is carried out for each of these computational methods, and the convergence properties of integral mixing diagnostics and late-time spectra are established. A comparison between the methods is made using the data from the highest resolution simulations in order to validate the Ares hydro scheme. We find that the integral mixing measures, which capture the global properties of the RT instability, show good agreement between the two codes at this resolution. The late-time turbulent kinetic energy and mass fraction spectra roughly follow a Kolmogorov spectrum, and drop off as k approaches the Nyquist wave number of each simulation. The spectra from the highest resolution Miranda simulation follow a Kolmogorov spectrum for longer than the corresponding spectra from the Ares simulation, and have a more abrupt drop off at high wave numbers. The growth rate is determined to be between around 0.03 and 0.05 at late times; however, it has not fully converged by the end of the simulation. Finally, we study the transition from direct numerical simulation (DNS) to LES. The highest resolution simulations become LES at around t/τ ≃ 1.5. To have a fully resolved DNS through the end of our simulations, the grid spacing must be 3.6 (3.1) times finer than our highest resolution mesh when using Miranda (Ares).

scholarly journals Three-dimensional simulations and analysis of the nonlinear stage of the Rayleigh-Taylor instability

1995 ◽  
Vol 13 (3) ◽  
pp. 423-440 ◽  
Author(s):  
J. Hecht ◽  
D. Ofer ◽  
U. Alon ◽  
D. Shvarts ◽  
S.A. Orszag ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Spherical Geometry ◽  
Taylor Instability ◽  
Three Dimensions ◽  
Type Model ◽  
Late Time ◽  
Nonlinear Stage ◽  
Rayleigh Taylor Instability ◽  
Atwood Number

The nonlinear stage in the growth of the Rayleigh-Taylor instability in three dimensions (3D) is studied using a 3D multimaterial hydrodynamic code. The growth of a single classical 3D square and rectangular modes is compared to the growth in planar and cylindrical geometries and found to be close to the corresponding cylindrical mode, which is in agreement with a new Layzer-type model for 3D bubble growth. The Atwood number effect on the final shape of the instability is demonstrated. Calculations in spherical geometry of the late deceleration stage of a typical ICF pellet have been performed. The different late time shapes obtained are shown to be a result of the initial conditions and the high Atwood number. Finally, preliminary results of calculations of two-mode coupling and random perturbations growth in 3D are presented.

scholarly journals LES of spray in crossflow – Effect of droplet distortion

2016 ◽  
Vol 9 (1) ◽  
pp. 55-70 ◽  
Author(s):  
Anubhav Sinha ◽  
RV Ravikrishna
Keyword(s):  
Initial Conditions ◽  
Spherical Shape ◽  
Experimental Results ◽  
Mass System ◽  
Large Eddy ◽  
Droplet Sizes ◽  
Experimental Values ◽  
Early Breakup ◽  
Drag Law ◽  
Good Agreement

The present investigation is focused on modeling of spray in crossflow using Large Eddy Simulations (LES). The modeling efforts are supported by experiments which are used both to provide accurate boundary and initial conditions and to evaluate droplet shapes in the near nozzle region. The droplets are modeled as Lagrangian parcels in an Eulerian continuum. Droplets in such configuration have been found to be distorted and not in perfect spherical shape from experimental results of our previous study. Droplet distortion is computed by Taylor-Analogy Breakup (TAB) distortion model. Each droplet is modelled as damped spring-mass system, where surface tension acts as a spring on the mass of the droplet and viscous dissipation provides the damping effect. The effort is to examine the effect of drag law used and the effect of this distortion on the droplet sizes produced in the flow field. Spray wind-ward trajectory and droplet sizes obtained from simulations are compared with the experimental results available. Although computational spray trajectory shows a reasonable match with experimental values, droplet sizes using the standard TAB model are found to be larger than that from experimental observation. To account for this distortion and its role in early breakup of droplets, constants of the TAB model are modified and the droplet sizes are found to be in good agreement with the experimental data.

Inducing Frictional Force to Enhance the Transient Response in Beams

2019 ◽  
Vol 22 (2) ◽  
pp. 88-93
Author(s):  
Hamed Khanger Mina ◽  
Waleed K. Al-Ashtrai
Keyword(s):  
Numerical Analysis ◽  
Transient Response ◽  
Frictional Force ◽  
Damping Ratio ◽  
Experimental Results ◽  
Damping Capacity ◽  
Tightening Force ◽  
Contact Areas ◽  
Good Agreement ◽  
Ansys Workbench

This paper studies the effect of contact areas on the transient response of mechanical structures. Precisely, it investigates replacing the ordinary beam of a structure by two beams of half the thickness, which are joined by bolts. The response of these beams is controlled by adjusting the tightening of the connecting bolts and hence changing the magnitude of the induced frictional force between the two beams which affect the beams damping capacity. A cantilever of two beams joined together by bolts has been investigated numerically and experimentally. The numerical analysis was performed using ANSYS-Workbench version 17.2. A good agreement between the numerical and experimental results has been obtained. In general, results showed that the two beams vibrate independently when the bolts were loosed and the structure stiffness is about 20 N/m and the damping ratio is about 0.008. With increasing the bolts tightening, the stiffness and the damping ratio of the structure were also increased till they reach their maximum values when the tightening force equals to 8330 N, where the structure now has stiffness equals to 88 N/m and the damping ratio is about 0.062. Beyond this force value, increasing the bolts tightening has no effect on stiffness of the structure while the damping ratio is decreased until it returned to 0.008 when the bolts tightening becomes immense and the beams behave as one beam of double thickness.

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