The evolution and interaction of two shock-accelerated, unstable gas - - PowerPoint PPT Presentation

The evolution and interaction of two shock-accelerated, unstable gas cylinders

Chris Tomkins, Kathy Prestridge, Paul Rightley, Mark Marr-Lyon, Robert Benjamin Summer students: James Doyle and Michael Schneider

Dynamic Experimentation Division, Los Alamos National Laboratory

Peter Vorobieff

Department of Mechanical Engineering, University of New Mexico

Cindy Zoldi

Applied Physics Division, Los Alamos National Laboratory

Gas cylinders

suction air air

D Y N

PIV PIV IC

SF6

Fog generator Fog generator

Experimental setup: shock tube

Overview

• Examine interaction of planar shock with 2 gas cylinders,

separated spanwise.

• S = 1.2D to 2.0D.

(D = cylinder diameter)

• Goal: Investigate the evolution of the interacting,

RM-unstable cylinders. Issues of interest include:

• What is the effect of the interaction on the resulting

flow morphologies? On the initial vorticity deposition? On the post-shock vortex development?

• How sensitive is the flow evolution to the initial

separation S? Shock S D

Single shock-accelerated cylinder

Double-cylinder “vortex blob” simulation

• 2
• 1

1 2 5 6 7 8

(c) Spanwise Streamwise

• 2
• 1

1 2 5 6 7 8

(b) Spanwise Streamwise

• 2
• 1

1 2 5 6 7 8

(a) Spanwise Streamwise

2D

Double-cylinder interaction: weak

S 2.0D Shock S 1.8D

Double-cylinder interaction: moderate

S 1.6D Shock S 1.5D

Double-cylinder interaction: strong

S 1.4D Shock S 1.2D

PIV images: double cylinder

• Two-frame cross-correlation, flow left to right, 6th pulse
• S = 2.0D. Note non-uniform seeding.

to t1 Shock

Double-cylinder velocity field: PIV

• Double-cylinder

data, 6th pulse, S = 2.0D

• Two-frame cross-

correlation (Christensen et al., 2000)

• Not smoothed
• Contours are

fluctuating velocity magnitude

Shock

2 4 6 8 10 12 2 4 6 8 10 12

40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0

x (mm) z (mm) 10 m/s

(u'

2 + v' 2) 1/2

(m/s)

Double-cylinder vorticity field

• Same realization
• Vorticity

contours

• Not smoothed
• And the ratio of

circulations is

Shock

2 4 6 8 10 12 1 2 3 4 5 6 7 8 9 10 11 12

60 48 36 24 12 6 4

• 4
• 6
• 12
• 24
• 36
• 48
• 60

x (mm) z (mm) y (1/s)

3

• inner
• uter

Correlation-based ensemble averaging

D Match one image (template) to each individual realization. Desire optimum match between template and image, i.e. minimize mean sq. error: This requires maximizing w.r.t. Do for each realization, then extract and average (Soloff, 1997) Yields cond. avg.:

• I

x x x | ) (

dA x x I x I e

t

• 2

) ( ) (

• D
• t

dA I I ) ( ) ( x x x

• x
• x

x

t

I I

This avg. becomes the new template.

Properties:

• Minimizes dependence on initial choice of

template.

• Converges quickly.

Correlation-based ensemble average

Shock S 1.2D, Ensemble average S 1.2D, Individual realization

Fluctuating intensity fields, S = 1.2D

s t

• 750
• s

t

• 470
• Total

Fluctuating Total Fluctuating

RMS of fluctuating intensity

100 200 300 400 500 600 700 800 5 10 15 20 25 30 35 40

Time after shock passage (sec)

RMS intensity, I

RMS Intensity vs. Time for several values of S/D.

S/D = 1.2 S/D = 1.4 S/D = 1.5 S/D = 1.6 S/D = 1.8 S/D = 2.0

1.2 1.4 1.6 1.8 2 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Normalized IC RMS Intensity

S/D

Mean

RMS of Initial Conditions

Small-scale activity: single cylinder

B A

2 4 6 8 10 2 4 6 8 10 12

Spanwise (mm) Streamwise (mm)

B A

1.0mm 800m

Vorticity and swirling strength

5 10 1 2 3 4 5 6 7 8 9 10 11 12

50 40 30 20 10

• 10
• 20
• 30
• 40
• 50

z

(1/s)

Spanwise (mm) Streamwise (mm)

5 10 1 2 3 4 5 6 7 8 9 10 11 12

300 200 100

• 100
• 200
• 300

ci

Spanwise (mm) Streamwise (mm)

Conclusions

• The degree of cylinder-cylinder interaction, and hence

the resulting flow morphology, is highly sensitive to the initial cylinder separation.

• Different separations may lead to weak, moderate, or strong

interactions.

• An idealized “vortex blob” simulation leads to very

different flow morphologies than experiment, suggesting that the inner vortices are weakened by interaction.

• Vorticity fields calculated from high-resolution PIV

measurements confirm that the inner vortices are significantly weaker, even for S/D = 2.0:

3 /

• inner
• uter

Conclusions

• A correlation-based ensemble averaging procedure

effectively captures the large and intermediate scales of the flow, providing confirmation of the experimental repeatability, and permitting decomposition of the density field into mean and fluctuating components.

• The RMS intensity fluctuations based on this

decomposition are substantially greater for the case of “moderate” interaction than for the “strong” or “weak” interaction cases, despite comparable initial RMS values.

• High-resolution PIV data resolves mm-scale vortices

being convected around the vortex cores.