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 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, 12-14 Septembre 2011

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 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... 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 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 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 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, 12-14 Septembre 2011

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 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

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

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 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, 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 3) Camera, FOVs and RESOLUTION 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 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) 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 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, 12-14 Septembre 2011

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 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 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. 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Results  Simulations of the one- and two-component (Air– Air and Helium – Air) gas jets 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 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 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

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

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

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

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

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 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 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Helium – Air results : modified initial conditions Amplification of the perturbations at the nozzle exit by a curved barrel shock structure 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 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. 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

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

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 Helium – Air results : modified IC, mass fractions With Tabs No Tabs Z / De ~ 3 Z / De ~ 7 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

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) 4th International Conference on Hydrogen Safety, 12-14 Septembre 2011

4th International Conference on Hydrogen Safety, 12-14 Septembre 2011 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, 12-14 Septembre 2011