Numerical study of the near-field of highly under-expanded gas jets A. Velikorodny and S. Kudriakov...
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Transcript of Numerical study of the near-field of highly under-expanded gas jets A. Velikorodny and S. Kudriakov...
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, 12-14 Septembre 2011
Outline
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
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
Introduction
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Dispersion of hydrogen (helium) jets from high pressure sources (i.e P0 > 10 bar )
Simplifying methods:
1) « 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...
Objectives
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
1) 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
Short background : Major properties of near-field
From Wilke et al. (2006). Images obtained using PLIF
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
1) Xm and Dm
2) Ls – subsonic core
3) Xp – potential core
Short background : Major properties of near-field
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Streamwise stationary (Taylor-Görtler) vorticesin the near-field of under-expanded jet
1) Entrain external fluid and change concentration
2) Their strength can be increased: roughness elements
Zapryagaev et al. (1990)
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
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%
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Validation : BOS experiments, initial conditions
Kodak ES 1.0, pixel size = 9 μm, 1008x1018pxPR = 21.3, 108.2, 201.5 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
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
Injected Gas = Air, heliumP0 = 30 – 120 barDe = 1, 2 and 3mm T0 = 295 – 300 KUe = 316 – 892 m/sMe = 1.
1) Conditions in tank and at orifice
2) Positioning of instrumentation
3) Camera, FOVs and RESOLUTION
Dubois (2010) – PhD at Aix Marseilles, France
• Dimensional analysis
• Subsonic core length
• Yuceil (2003) IRS/PIV data (air-air) Limited to first 7 exit diameters
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Validation : Other studies
(1)
(2)
(3)Glotov, G.F. (1998) “Local subsonic zones in supersonic jet flows”
Modelling: Governing equations
– shear stress tensor
Y 1– mass fractions of helium Y 2=1−Y 1
– mass fractions of air
– energy flux
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Vk– diffusion velocity
q
et– total energy and enthalpyht,
Modelling: discretization and turbulence
Consider entrainment for high Re number turbulent jet flow
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.
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Convergence with increasing resolution
From Boris et al. (1992)
2nd-order accurate VLH, AUSM+ schemes used in present work
Complementary study : effective (numerical) viscosity generated by grids and schemes in high-speed shear flows
Modelling: computational grids and BC
We consider 2 grids :Coarse: 50x50x100Fine: 64x64X176Mixing region cellsize: Rad / 64
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Thus, ¼ domain simulations were used to speed-up the solutions.
IC : P0 = 30 bar T0 = 300 K
Size of the domain :10 x 35 x 48 exit diameters (De)
Explicit simulations with CFL = 0.5 required time steps as small as 10e-8
Simulations of the one- and two-component(Air– Air and Helium – Air) gas jets
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Results
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Helium – Air results : Initial transients
Simulations were continued until t* = 540 and the steady-state was obtained
Top : at t*=270, bottom : at t*=225
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Helium – Air results : Density
27 De
Three FOV are employed
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Helium – Air results : Mach number
Ls ~ 6.2 De
Ls ~ 6.5 De – from correlation (3)
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Helium – Air ; Air – Air results : Velocity
~ 27 De
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Helium – Air results : Temperature and Pressure
Temperature decreases from 12 De up to 25 De
Pressure is +/- 10% vs 1atm after Z / De = 6
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Helium – Air results : Density and Mass fractions
To calculate Yhe - need local pressure, temperature and density distributions
Xp (max) ~ 33 De
Yhe – inversely proportinalto temperature and density
1) Xp ~ (27 – 33) De
2) Use Kghelium for FOV1,2
Amplification of the perturbations at the nozzle exit by a curved barrel shock structure
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Helium – Air results : modified initial conditions
Modelling: modified initial conditions
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
¼ domain simulations with symmetry conditions.
Vortex generators (delta tabs) :Height = 0.17 DeWidth = 0.08 DeTotal (4) blockage ratio ~ 6%
Zaman et al (1994) ”Control of axisymetric jet using vortexGenerators”Phys. Fluids 6 (2), February 1994
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Helium – Air results : modified IC, vorticity
Mach disk location
Stationary streamwise vorticesat Z / De = 3, with Xm / De > 3
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Helium – Air results : modified IC, mass fractions
Z / De ~ 3
Z / De ~ 7
With Tabs No Tabs
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
Helium – Air results : modified IC, density
25% density increase at Z / De ~ 30 (where temp. and press. are ~ equal)
Conclusions
a) Density (BOS) and streamwise velocity (IRS/PIV) b) Potential and subsonic core lengthes c) Xp_uj (at P0 = 30 bar) ~ 15 * Xp_sj.
The highly under-expanded jet was simulated using conservative schemes without any compressibility-corrected turbulence models. Combined experimental/numerical data suggests that:
4th International Conference on Hydrogen Safety, 12-14 Septembre 2011
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
1) Present numerical model (both in the air-air and helium-air scenarios ) is in general agreement with experimental data :
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).