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, 12-14 Septembre 2011

2. 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

3. Introduction 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Dispersion of hydrogen (helium) jets from high pressure sources (i.e P 0 > 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...

4. 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

5. 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

6. Short background : Major properties of near-field 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Streamwise stationary (Taylor-Görtler) vortices in 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)

7. 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 – K air > K helium by 15%

8. 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Validation : BOS experiments, initial conditions Kodak ES 1.0, pixel size = 9 μm, 1008x1018px PR = 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, helium P 0 = 30 – 120 bar De = 1, 2 and 3mm T 0 = 295 – 300 K Ue = 316 – 892 m/s Me = 1. 1) Conditions in tank and at orifice 2) Positioning of instrumentation 3) Camera, FOVs and RESOLUTION Dubois (2010) – PhD at Aix Marseilles, France

9. 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”

10. Modelling: Governing equations – shear stress tensor – mass fractions of helium– mass fractions of air – energy flux 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 – diffusion velocity– total energy and enthalpy,

11. 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

12. Modelling: computational grids and BC We consider 2 grids : Coarse: 50x50x100 Fine: 64x64X176 Mixing region cell size: Rad / 64 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Thus, ¼ domain simulations were used to speed-up the solutions. IC : P 0 = 30 bar T 0 = 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

13. 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

14. 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

15. 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Helium – Air results : Density 27 De Three FOV are employed

16. 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)

17. 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Helium – Air ; Air – Air results : Velocity ~ 27 De

18. 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

19. 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Helium – Air results : Density and Mass fractions To calculate Y he - need local pressure, temperature and density distributions Xp (max) ~ 33 De Y he – inversely proportinal to temperature and density 1) Xp ~ (27 – 33) De 2) Use K ghelium for FOV1,2

20. 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

21. 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 De Width = 0.08 De Total (4) blockage ratio ~ 6% Zaman et al (1994) ”Control of axisymetric jet using vortex Generators” Phys. Fluids 6 (2), February 1994

22. 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Helium – Air results : modified IC, vorticity Mach disk location Stationary streamwise vortices at Z / De = 3, with Xm / De > 3

23. 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Helium – Air results : modified IC, mass fractions Z / De ~ 3 Z / De ~ 7 With TabsNo Tabs

24. 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)

25. Conclusions a) Density (BOS) and streamwise velocity (IRS/PIV) b) Potential and subsonic core lengthes c) Xp_uj (at P 0 = 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).