NUMERICAL AND
EXPERIMENTAL STUDY OF A
RAYLEIGH-TAYLOR MIXING
FRONT
José M. REDONDO
Dept. de Fisica Aplicada
Universidad Politécnica de Cataluña (UPC)
NUMERICAL AND
EXPERIMENTAL STUDY OF A
RAYLEIGH-TAYLOR MIXING
FRONT
1.
2.
3.
4.
5.
Introduction
Experiments
Simulations
Fractal Dimension
Conclusions
1. INTRODUCTION
Important parameters to consider in Rayleigh
Taylor Instability study
•
•
•
•
1 -  2
The Atwood Number, A 
1   2
The width of the mixing zone, d  2cgAt²
The non-dimensional time, t-t0 
The Fractal Dimension
1
N D

log N
D
log 1 /  
 Ag / H   t
2.EXPERIMENTS ON RTI
Experiments in a Perspex tank;
H=500mm
Lx=400mm
Ly=200mm
Linden, Redondo & Youngs (1994) J. Fluid Mech. 265
Dalziel, Linden & Youngs (1997) 6th IWPCTM
Experimental Visualizations
LIF Fluoresceine Visualization – Elevation and Plane Views
3. SIMULATIONS
LES RTI
1.4
2D LES
SGS: Smagorinsky – Lilly
Unsteady, 1st-Order, Implicit
Boussinesq model
256² elements mesh
Atwood 5x10-²
1.2
64²
128²
256²
(h/H)^1/2
1
0.8
Exp
Lin Exp
Lin 64²
Lin 128²
Lin 256²
0.6
0.4
0.2
0
0
1
2
3
t
4
5
2D LES of the RT Front
max
Velocity
Magnitude
0÷0,33
Volume
of Fluid
Vorticity
Magnitude
0÷1
-106÷84
min
Experimental results vs LES
0.7
0.6
0.5
Exp1
(h/H)^1/2
Exp2
Exp3
0.4
Exp4
Exp5
LES 3D Pre
0.3
LES 2D
Lineal (LES 3D Pre)
0.2
Lineal (LES 2D)
0.1
0
0
1
2
t
3
4
The Density Variation - Mixing
998.2
1018.2
1038.2
1058.2
1078.2
0.4
0.3
0.2
h
0.1
0
-0.1
-0.2
-0.3
-0.4
0.5
1
2
3
4
1098.2

4. FRACTAL DIMENSION
Vorticity
Velocity
Volume
Magnitude
Magnitude
of Fluid
2
1.6
1.6
0
0.2
0
40
0.4
2080
0.6
120
40
60
200
160
0.8
 4.5  4.0  3.5
 3.0  2.5  2.0
1.6
1.2
1.2
1.2
0.8
0.8
D
0.8
0.4
0.4
0.4
0
00
140
400
150
80 0.1
160
120
0.2
170
160
0.3
180
200
Fractal dimension by scalar values
Overall
1.6
1.4
D
1.2
1
vof L
0.8
vel L
0.6
vor L
0.4
0.2
0
1
2
3
t
4
5
Volume of fluid and Vorticity
Vorticity
- Fractal
Dimension
Volume
of Fluid
- Fractal
dimension
1.6
1.4
D
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
vor
vof L
vor
vof M
vor
vof H
0.2
0.2
0
1
2
3
t
4
5
Fractal dimension by scalar values
Mushroom
Mush.
- Volume
of Fluid
- Fractal
Dimension
Mush.
- Vorticity
- Fractal
Dimension
1.6
1.4
D
D
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
vof
vorLL
vof
vorMM
vof
vorHH
0.2
0
0
10
1 2
2
3
tt
3
4
4
55
Fractal Dimension for the Overall,
Mushroom and Front
1.6
0
0.2
0.4
0.6
0.8
1
1.6
1.4
1.2
1.2
1
vof All
D
D
0.8
vof Mush
0.8
.
0.6
vof Front
0.4
0.2
0.4
0
1
2
3
4
5
t
0
0
40
80
120
160
200
Fractal Dimension for the
Experiments
1.6
1.4
1.2
D
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
t-t
Experimental
2
0
LES Average
2.5
3
5. CONCLUSIONS
1.6
0
0.2
0.4
0.6
0.8
1
1.2
0.8
2
1.6
0.4
1.2
0
0
40
80
120
160
200
0.8
0.4
0
0
40
80
120
160
200
Conclusions
1.
2.
3.
4.
Fractal dimension anlaysis probed that the mixing
occurs mainly at the sides of the blobs and that in the
front there is no mixing
The fractal dimension differs for the various scalar fields
even when there is presence of similar topology and
structure.
These differences seem to be related with a complex
system of cascades of direct and inverse vorticity.
The range of scales is very active and complex and in
the future the application of Fractal Analysis can be
helpful to decompose and analyse these scales.
A three dimensional simulation (even better if DNS is
used) analyzed with Fractal Analysis may give a better
approach to the experimental results.