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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