This is the presentation I gave to the EUCASS 2009 conference in Versailles. http://www.eucass.eu/

1. Large‐Eddy Simula0on of Transcri0cal
Round Jets
T. Schmi<, A. Ruiz, L. Selle, B. Cuenot
July 6-9 2009 EUCASS 2009 1

2. Introduction
Solid Liquid
Pc
Pressure
Gaseous
Temperature Tc
Modeling of supercri4cal flows is challenging:
• Non linear equa0on of state (EOS)
• Complex transport phenomena (Soret and Dufour effects)
• Rapid varia0on of thermodynamic proper0es
• Large density gradients (without surface tension)
July 6-9 2009 EUCASS 2009 2

3. OUTLINE
I. Supercritical fluids
II. Flow configuration of the present simulation
III. Results

4. Supercritical Fluids
Going beyond the
cri0cal pressure
changes atomiza0on
Drops => Finger‐like
structures (no more
surface tension)
Solid Liquid
Pc
Pressure
Gaseous
Tc Oschwald, CST 2006
Temperature

5. Supercritical Fluids
From the molecular point of view:
Low-density gas : the distance between molecules is large enough
to neglect electromagnetic interactions
High-density gas: Van Der Waals forces must be taken into account
r
Toward Perfect
Gas
July 6-9 2009 EUCASS 2009 5

6. From the
mesoscopic point
of view
Peng Robinson (1976) EOS
6

7. Supercritical Fluids
“Standard” Navier‐Stokes equa0ons for
compressible flows
EOS
Molecular
transport
July 6-9 2009 EUCASS 2009 7

8. Supercritical Fluids
Transport Coefficients
RG RG
PG PG
Chung et al. (1984) method is used for predic0on of viscosity
and thermal conduc0vity
July 6-9 2009 EUCASS 2009 8

9. OUTLINE
I. Supercritical fluids
II. Flow configuration of the present simulation
III. Results

10. Flow configuration
P (bar)
Transcri4cal Reservoir
Solid
N2 at 40 bar 40
Mayer et al. (2003) Pc=33.96
Supercri4cal
Liquid
Gaseous
Tc=126.2 T (K)
140 300
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11. Flow configuration
N2 at 40 bar
Mayer et al. (2003)
Transcri0cal
Tin = 127 K
ρ = 435 kg/m3
Tamb= 300 K
5 m/s
ρ = 45 kg/m3 Supercri0cal
Tin = 137 K
ρ = 171 kg/m3
July 6-9 2009 EUCASS 2009 11

12. 250 mm
AVBP solver (CERFACS) :
2,2 mm 122 mm • Unstructured mesh
• Massively parallel
• Compressible reac0ve flows
• Explicit 3rd order scheme [1]
• WALE turbulence model [2]
• Δx = 0.1 mm
• N = 5.5 M cells
• Re = 150 000
[1] Colin and Rudgyard, J. Comp. Phys, 162, 338-371 (2000)
[2] Nicoud and Ducros, Flow Turb. Comb., 62, 183-200 (1999) 12

13. OUTLINE
I. Supercritical fluids
II. Flow configuration of the present simulation
III. Results

14. Results
1 2 3
1 –Growth of small velocity perturba0ons
2 –Vortex roll‐up. Transi0on region
3 – Fully‐developed turbulence. Self‐preserving jets ? Real‐gas
effects ?
July 6-9 2009 EUCASS 2009 14

15. Results
Transcri0cal
Mean Centerline
Simula0on
Density Exp. data
Comparison with the
experimental data of Mayer et
al. (2003) obtained with Raman
sca<ering
• Dense core length : Supercri0cal
Transcri0cal = 8 Diameters
Supercri0cal = 5 Diameters
15

16. Results
Supercri0cal
Transcri0cal
July 6-9 2009 EUCASS 2009 16

17. Results
Radial velocity perturbations along the
mixing layer 0 D 5 D
1.2
[m/s]
0.8
ur
0.4
'
TRANSCRITICAL
SUPERCRITICAL
0.0
0 5 10
x/d
July 6-9 2009 EUCASS 2009 17

18. Instantaneous Results
wrinkling of the
Surface / Volume [1/mm]
surface 12
TRANSCRITICAL
10 SUPERCRITICAL
The wrinkling of the 8
6
surface in the
4
supercri0cal case 2
enhances heat transfer 0 5 10
x/d
Supercri4cal
Transcri4cal
July 6-9 2009 EUCASS 2009 18

19. Enstrophy budget
Stretching Dilatation Baroclinic torque Dissipation
Transcri4cal Supercri4cal
3
3
Budget / (uinj/d)
Budget / (uinj/d)
6 6
4 4
2 2
0 0
-2 -2
-4 -4
0.6 0.8 1.0 1.2 1.4 1.6 0.6 0.8 1.0 1.2 1.4 1.6
y / rinj y / rinj
19

20. Fully developped
turbulence
Normaliza0on by effec0ve
diameters
1 ( [1])
1.4 ( [1])
4 ( Present)
8 ( [2])
10 ( Present)
[1] Chassaing, PhD dissertation, INP Toulouse (1979)
[2] Zong, PhD dissertation, Penn. State University (2005)
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21. Fully developped Results
turbulence
• Density and velocity
profiles are self-
preserving as in low
pressure jets.
Different behaviour than
in Zong (2005)
1.4 ( [1])
4 ( Present)
8 ( [2])
10 ( Present)
July 6-9 2009 EUCASS 2009 21

22. Conclusions
• Derivation of the LES framework for supercritical flows
• Implementation in the AVBP unstructured parallel LES
solver
• Application to an experimental setup
• Quantitative agreement with available experimental
data for a nitrogen jet
• Similarity of centerline velocity and density as in low-
pressure jets
July 6-9 2009 EUCASS 2009 22

23. Thank you for your a<en0on
July 6-9 2009 EUCASS 2009
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