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

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

Introduction


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


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


1) Xm and Dm

2) Ls – subsonic core

3) Xp – potential core

Short background : Major properties of near-field


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)


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%


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


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


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.


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


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


Results


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


Helium – Air results : Density

27 De

Three FOV are employed


Helium – Air results : Mach number

Ls ~ 6.2 De

Ls ~ 6.5 De – from correlation (3)


Helium – Air ; Air – Air results : Velocity

~ 27 De


Helium – Air results : Temperature and Pressure

Temperature decreases from 12 De up to 25 De

Pressure is +/- 10% vs 1atm after Z / De = 6


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


Helium – Air results : modified initial conditions

Modelling: modified initial conditions


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


Helium – Air results : modified IC, vorticity

Mach disk location

Stationary streamwise vorticesat Z / De = 3, with Xm / De > 3


Helium – Air results : modified IC, mass fractions

Z / De ~ 3

Z / De ~ 7

With Tabs No Tabs


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:


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).

Documents

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