Rayleigh-Taylor Driven Mixing in a Multiply Stratified

Environment

Andrew Lawrie & Stuart Dalziel,Andrew Lawrie & Stuart Dalziel,Department of Applied Mathematics and Theoretical PhysicsDepartment of Applied Mathematics and Theoretical Physics

University of Cambridge, UKUniversity of Cambridge, UK

Outline

• Molecular mixing in the early stages of RT

• LIF with passive tracers

• MILES/ILES simulation

• Implications for Front-Tracking schemes

Prior Work

• Experimental setup– Dalziel et al. (1999) JFM

• Multiple stratifications– Jacobs & Dalziel (2005) JFM

• Incompressible Simulation– Almgren et al. (1998) JCP

Experimental Setup

Atwood No. = 0.0037

Passive Tracer Transport

LIF with Passive Tracers

• Chemically benign tracer

• Chemically reactive tracer

Chemically Reactive Tracer

Calibration

Numerical Approaches

• Front-Tracking

• Spectral

• TVD-Finite Volume

• Mass diffusion affects 2Agth (George et al. 2002)

Simulation

• Incompressible

• Immiscible

• Boussinesq

0.

0.

0.

1. 2

U

CUtC

Ut

kgUpUUtU

Comparison

Fractal Dimension

dimension fractal

size1)size(nboxes

Mixing Surface

Mixed Volume

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0Nondimensional Simulation Time

0.0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5Fr

actio

nal a

rea

ExperimentSimulation

Conclusions

• Molecular mixing in the early stages of RT has been directly visualised with LIF

• Arguments based on growth rate used to justify accuracy of Front-Tracking schemes are shown to be inaccurate

• MILES simulations appear to provide a reasonable approximation to the mixing behaviour

Further Work• Turbulent Diffusion over stable density interface

• Isolated vortex |ring impingement on stable density interface

• Influence of interfacial shear on turbulent diffusion

Prior Research• Experimental setup

– eg. Self-similarity and internal structure of turbulence induced by Rayleigh-Taylor instability (1999) Dalziel, S. B.,Linden, P. F., Youngs, D. L. Journal of Fluid Mechanics

• Multiple stratifications– Rayleigh-Taylor Instability in Complex Stratifications (2005) Jacobs, J. W. Dalziel, S.B.

Journal of Fluid Mechanics

• Incompressible Simulation– A Conservative Adaptive Projection Method for the Variable Density Incompressible

Navier-Stokes Equations (1998) Almgren, A.S., Bell J.B.,Collela, P., Howell, L.H., Welcome, M.L. Journal of Computational Physics

• Front Tracking Simulation– A comparison of experimental theoretical an numerical simulation rayleigh-taylor mixing

rates. (2002) George, E., Glimm, J., Li, X.-L., Marchese, A., Xu, Z.-L. Proc. Natl. Acad. Sci.

Laboratory

• Acridine +Alcohol

• 2,3,5,6, - dibenzopyridine