1. Numerical study of the near-field of highly under-expanded gas jets
A. Velikorodny and S. Kudriakov
CEA Saclay, DEN, DANS, DM2S/SFME,
Gif-Sur-Yvette, FRANCE
4th International Conference on Hydrogen Safety, Septembre 2011

2. Outline 1) Introduction and Objectives
2) Short background on the near-field regimes and main parameters
3) Validation and Experimental methods
4) Numerical modelling
5) Results
6) Conclusions
4th International Conference on Hydrogen Safety, Septembre 2011

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Introduction
Dispersion of hydrogen (helium) jets from
high pressure sources (i.e P0 > 10 bar )
Simplifying methods:
« NOTIONAL NOZZLE » concept – defined based on the conservation laws :
2) Alternative approach is to numerically resolve complex shock-structured region and use obtained results as an inflow (e.g. Xu et al. (2005))
– Simple formulation
– Does not account for entrainment into shear layer
– Does not account for any gradients of velocity, temperature,
species etc., which exist along the notional diameter.
– etc...
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Objectives
Perform simulations and validation of the near-field of highly underexpanded gas jets taking into account :
2) Define initial conditions for simulations of the far-field
– Properties of the numerical schemes
– Turbulence treatment in compressible flows
– Computational domain and resolution of the grid
– Initial conditions
– Distance from the source
– Gas dynamic parameters at this location
– Steady vs. Transient initial conditions
– Properties of the “Far-field” solver
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Short background : Major properties of near-field
1) Xm and Dm
2) Ls – subsonic core
3) Xp – potential core
From Wilke et al. (2006). Images obtained using PLIF
4th International Conference on Hydrogen Safety, Septembre 2011

6. Short background : Major properties of near-field
Streamwise stationary (Taylor-Görtler) vortices
in the near-field of under-expanded jet
Zapryagaev et al. (1990)
1) Entrain external fluid and change concentration
2) Their strength can be increased: roughness elements
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Validation : BOS Fundamentals
1) PIV cross-corrleation IW used to obtain the light beam displacement (eps) – resolution
2) Inverse Abel transform is applied to find local index of refraction (IR) from eps – axisymmetric flow
3) IR is proportional to density through Gladstone-Dale relation –
Kair > Khelium by 15%
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Validation : BOS experiments, initial conditions
1) Conditions in tank and at orifice
Injected Gas = Air, helium
P0 = 30 – 120 bar
De = 1, 2 and 3mm
T0 = 295 – 300 K
Ue = 316 – 892 m/s
Me = 1.
2) Positioning of instrumentation
Dubois (2010) – PhD at Aix Marseilles, France
De << Zi = f+B = 52 – 60mm: distance “Lens – image plane”
Zd = 139mm: distance “backplane – jet”
Zc = Zb - Zd = 142, 649 and 1164 mm: distance “jet – lens”.
Gj = Zi / Zc : Magnification factor at the jet plane
Kodak ES 1.0, pixel size = 9 μm, 1008x1018px
PR = 21.3, 108.2, µm/px
FOV = 1) 11x9.6, 2) 70x30 and 3) 200x112 De
1) 5.9x11.8, 2) 1.15x1.85 and 3) 0.6 x 1.2 Vec / De
3) Camera, FOVs and
RESOLUTION
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Validation : Other studies
Dimensional analysis
Subsonic core length
Yuceil (2003) IRS/PIV data (air-air)
Limited to first 7 exit diameters
(1)
(2)
Glotov, G.F. (1998) “Local subsonic zones in supersonic jet flows”
(3)
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Modelling: Governing equations
– shear stress tensor
– energy flux
– diffusion velocity ,
– total energy and enthalpy
– mass fractions of helium
– mass fractions of air
4th International Conference on Hydrogen Safety, Septembre 2011

11. Modelling: discretization and turbulence
High resolution monotone CFD algorithms can provide
intrinsic ''nonlinear'' SGS model without calibrating constants
This approach was applied in complex problems :
turbulent combustion, shock-vortex interaction, etc.
Consider entrainment for high
Re number turbulent jet flow
Convergence with
increasing resolution
From Boris et al. (1992)
Complementary study : effective (numerical) viscosity generated by grids and schemes in high-speed shear flows
2nd-order accurate VLH, AUSM+
schemes used in present work
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Modelling: computational grids and BC
IC : P0 = 30 bar
T0 = 300 K
Size of the domain :
10 x 35 x 48
exit diameters (De)
We consider 2 grids :
Coarse: 50x50x100
Fine: 64x64X176
Mixing region cell
size: Rad / 64
Explicit simulations with CFL = 0.5
required time steps as small as 10e-8
Thus, ¼ domain simulations were
used to speed-up the solutions.
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Results 
Simulations of the one- and two-component
(Air– Air and Helium – Air) gas jets
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Helium – Air results : Initial transients
Top : at t*=270, bottom : at t*=225
Simulations were continued
until t* = 540 and the
steady-state was obtained
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Helium – Air results : Density
Three FOV are employed
27 De
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Helium – Air results : Mach number
Ls ~ 6.2 De
Ls ~ 6.5 De – from correlation (3)
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Helium – Air ; Air – Air results : Velocity
~ 27 De
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Helium – Air results : Temperature and Pressure
Temperature decreases
from 12 De up to 25 De
Pressure is +/- 10%
vs 1atm after Z / De = 6
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Helium – Air results : Density and Mass fractions
Yhe – inversely
proportinal
to temperature
and density
Xp (max) ~ 33 De
To calculate Yhe - need local
pressure, temperature
and density distributions
1) Xp ~ (27 – 33) De
2) Use Kghelium for FOV1,2
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Helium – Air results : modified initial conditions
Amplification of the perturbations
at the nozzle exit by a curved
barrel shock structure
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Modelling: modified initial conditions
Zaman et al (1994)
”Control of axisymetric jet using vortex
Generators”
Phys. Fluids 6 (2), February 1994
Vortex generators (delta tabs) :
Height = 0.17 De
Width = 0.08 De
Total (4) blockage ratio ~ 6%
¼ domain simulations with
symmetry conditions.
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Helium – Air results : modified IC, vorticity
Stationary streamwise vortices
at Z / De = 3, with Xm / De > 3
Mach disk location
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Helium – Air results : modified IC, mass fractions
With Tabs
No Tabs
Z / De ~ 3
Z / De ~ 7
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Helium – Air results : modified IC, density
25% density increase at Z / De ~ 30
(where temp. and press. are ~ equal)
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Conclusions
The highly under-expanded jet was simulated using conservative
schemes without any compressibility-corrected turbulence models.
Combined experimental/numerical data suggests that:
1) Present numerical model (both in the air-air and helium-air scenarios )
is in general agreement with experimental data :
a) Density (BOS) and streamwise velocity (IRS/PIV)
b) Potential and subsonic core lengthes
c) Xp_uj (at P0 = 30 bar) ~ 15 * Xp_sj.
2) Simulations with modified initial conditions (tabs) show significant
changes in the near-field concentration fields due to presence of
stationary streamwise counter-rotating vortices
3) For far-field LES simulations, the initial conditions are proposed to be
axisymmetric (a transverse cut) at a distance beyond the shock-cells,
while well prior the end of potential core. Velocity and temperature
at this location exibit strong gradients across the shear layer (supersonic).
4th International Conference on Hydrogen Safety, Septembre 2011