Some issues and methods inSome issues and methods inparticles trackingparticles tracking

Laurent DUMASUniversité Paris 6 (L.AN.) & Ecole Normale supérieure (D.M.I.)

• Lecture 1 (August 19th): an academical survey

Particle methods for rarefied gas and two phase flows

• Lecture 2 (August 27th): an industrial approach

Slag deposition and pressure oscillations in Ariane V boosters

1. The Ariane V launcher

2. The ASSM program

3. Description of the flow in the Ariane V boosters2.1 Experimental measurements2.2 Qualitative behavior2.3 Characteristic values

4. Slag deposition 4.1 The Lagrange /Euler computations4.2 The Euler /Euler computation4.3 Comparison of the results

5. Pressure oscillations5.1 The Navier Stokes computations5.2 The LES computations

6. Conclusion

1. The Ariane V launcher 1. The Ariane V launcher

• Ariane V, the european space launcher has a simplified architecture which comprises the following elements:

The main cryogenic stage (158 tons of O2/H2) develops a thrust of 1140 kN in vacuum. The stage operates for 10 min.

Two boosters (2*238 tons of solid propellant), each developing a thrust of 5300 kN. They lead to the lift off of the launcher and are jettisoned at an altitude of 65 km after a burn time of 120 s.

An upper composite section made of the upper stage (10 tons of storable propellant), the equipment bay, the payload (one or two satellites of mass lesser than 6 tons) and the fairing.

1. The Ariane V launcher 1. The Ariane V launcher

First flight: October 1997

Schematic view of the Ariane V booster

2. The A.S.S.M. Program2. The A.S.S.M. Program(Aerodynamics of Solid Segmented Motors)

• Joint and long term program aimed at understanding and numerically reproducing some problems occurring in solid segmented motors with a submerged nozzle such as Ariane V boosters.

• Header: CNES

•Members: industrials (Aérospatiale, SEP, SNPE, Bertin) national organisms (ONERA, universities, etc...)

• Program divided into different axes: ignitiondense phase (slag deposition, combustion)stability (pressure oscillations), etc...

members and references ofmembers and references of the ASSM program the ASSM program

• Modeling of slag deposition in solid rocket motors”J.F. Chauvot, LD, K. Schmeisser (Aérospatiale), 31th AIAA Joint Propulsion conference, San Diego, 1995.

• “Prévision du dépot d’alumine dans les moteurs a propergol solide”P. Bellomi (BPD), LD, Y. Fabignon (ONERA), L. Jacques (SEP), G. Lavergne (ONERA), International symposium on propulsion, Paris, 1996.

• “Stochastic models to the investigation of slag accumulation”N. Cesco (ONERA), LD, Y. Fabignon (ONERA), A. Hulin (Bertin), T. Pevergne (SEP); 33th AIAA Joint Propulsion conference, Seattle, 1997.

• “Vortex shedding phenomena in solid rocket motors”: F. Vuillot (ONERA); Journal of Propulsion and Power, 1995.

• “Simulation des grandes échelles: application aux moteurs a propergol solides segmentés” J.H. Silverstrini, P. Comte, M. Lesieur (LEGI), conference on propulsive flows in space transportation, Bordeaux, 1995

Some experiments at real flight conditions have been made and have given the following results:

Slag deposition: between 2 and 2.2 tons of Alumina (Al2O3) in the chamber after flight

Pressure oscillations:amplitude: 120 mb (0.3%) at t=95 smain frequency: first acoustic mode of the combustion chamber

These two values causes a loss on the payload of the order of 400 kg. Moreover, the low frequency of pressure oscillations makes the possible coupling with the launcher structural mode a point of concern.

3.1 3.1 Experimental measurements

Propellant blocks 2 and 3Alumina deposition

Alumina trajectories

Second segment Third segment

Thermal protections

23 m

1.5 m

: recirculation area

3.2 Qualitative behavior of the flow3.2 Qualitative behavior of the flow in the Ariane V boosters at t=95s in the Ariane V boosters at t=95s

Ejection of combustion products

(gas+Al+Al2O3)

: turbulent shear layer region giving rise to vortex shedding

Modelisation of pressure oscillationsModelisation of pressure oscillations

• Coupling of vortex shedding with acoustics:

• The prediction of the stability of a motor can be achieved by means

of analytical tools but quantitative results are only available with a

full numerical approach.

Acoustic feedback

Acoustic excitation

Vortex generation

Vortex impingement

• Liquid alumina at ejection (if instantaneous combustion of Al): Bimodal diameter distribution (1micron-70 microns) Total mass of Alumina ejected: 72 tons Estimated velocity: 1 m/s Temperature: 3272 K Estimated turbulence rate: 20% Density ratio p/g~ 1000

• Adimensionalised numbers: Stokes number ~ 1 (large particles) or « 1 (small particles) Reynolds number ~ 100 000 Particle volumetric fraction (a priori estimate) p « 1

The hypotheses of one way coupling and dilute phase is assumed

3.3 3.3 Characteristic values of the flow of the flow in the Ariane V boosters in the Ariane V boosters

4.1 Slag deposition: Euler/Lagrange simulations (Aérospatiale, SEP, Bertin, ONERA)

Time, space and particle diameter discretisation.

For each discretised time (50, 66, 82, 95 and 115 s), computation of an equivalent stationary one phase flow with a Navier Stokes solver and a k- model.

Computation of particles trajectories in the previous stationary flow with (or without) dispersion effects due to turbulence.

Evaluation of the rate of entrapped particles.

Estimation of total slag deposition by space and time interpolation.

Particle tracking in a Lagrangian approachParticle tracking in a Lagrangian approach

• Computation of the trajectories of particles by solving the ODE:

with and where:

)(txt

gFmdt

dv

vdtdx

drag

1

duv

C

ggp

pp

drag

Re

)Re.(Re

.6870150124

ggdragdrag uvuvdCF 2

81

• The dispersion effects due to turbulence are taken into account with the Gossman-Ioannides model:

<ug> is replaced during a time t by <ug>+u’ where u’ is selected from a Gaussian distribution with a variance related to the turbulence energy (2k/3). t is deduced from the lifetime of the energy containing eddy and allows for the particle to pass through the eddy before it decayed.

• In this case, a sufficient number of random trajectories is computed for each class of particles and a statistical treatment has to be done.

Dispersion effects in the Lagrangian approachDispersion effects in the Lagrangian approach

Details of the Euler/Lagrange computationsDetails of the Euler/Lagrange computations(t=95s)(t=95s)

• Geometry (SNPE):extrapolation from experimental measurements.

• Aerodynamic computation (SEP, Aerospatiale):comparison of a computation on a multi-block grid (20 000 elements) and on a unstructured grid (8 000 elements).

• Particle tracking (SEP*, Aerospatiale, Onera, Bertin): comparison of the results obtained with the same aerodynamic field and the same discretisation (30 injection points located on the third block and 10 particle diameters from 1 to 140 microns).(* without dispersion effects)

4.2 Slag deposition: Euler/Euler simulation (SNPE)

Choice of a particular combustion time (95 s) and of a particular particle diameter value (35 microns).

Computation of an unstationary inviscid two phase flow on a fine grid (50 000 elements, duration of simulation: 200 ms).

Evaluation of the rate of entrapped particles.

4.2 Particle tracking in a Eulerian approach4.2 Particle tracking in a Eulerian approach

• The particles are considered as a continuum phase with a volumetric fraction p and a velocity vp at each point x and time t:

• mass conservation:

• momentum conservation:

0

).( u

xt pppp

p

gpppppp

pp uuguu

xt

u

).()(

Euler/Euler simulation: main observations

A particle high concentration zone is created at the nozzle nose, is then “pushed” at the rear end by the arrival of another curl, a part of these particles is going out, Another part is accumulating.

The particles outgoing from the end of the block are periodically deviated.

4.3 Comparison of the results4.3 Comparison of the results

• The estimation of the amount of slag deposition is very sensitive to:

The particle diameter distribution The chosen method (Euler or Lagrange, dispersion effects or not) The entrapment criterion. • Lagrangian approach:The amount of slag deposition obtained by the four different teams is: First criterion (geometrical point): 872 kg < M < 2055 kg Second criterion (nose point): 1452 kg < M < 3600 kg

• Eulerian approach : 12 % deposition rate for the chosen case against 2 to 6% in the corresponding Lagrangian approach.

5.1 Pressure oscillations: Navier Stokes simulation5.1 Pressure oscillations: Navier Stokes simulation (SNPE, ONERA, CERFACS)

• Different computations have been compared on a test case of a 2D planar chamber with a choked nozzle and a side injection along two directions (sub-scale model 1/15 of Ariane V boosters) and for the same curvilinear grid (10 000 elements).

Main conclusions of an organized workshop (1992): Second order accurate schemes needed to capture the shear layer and acoustic motion. Van Leer’s flux splitting too dissipative. Implicit schemes unapropriate. Importance of boundary conditions. Good correlations between different families of codes, once properly validated. Cell Reynolds number limitation

))1((Re OLv cellcell

cell

5.2 Pressure oscillations: LES simulation5.2 Pressure oscillations: LES simulation(LEGI)

• Same conditions and same 2D grid.• Extrusion of the 2D grid in the 3rd direction (3183190 elements)• Large Eddy Simulation with the filtered structured function model.• Duration of simulation: 13ms (75 hours on Cray C98)

Main conclusions:

Main frequency mode at 2300 Hz (Navier Stokes: 2670 Hz) Widening of the kinetic energy spectrum at low and high frequencies. Two different mechanisms of instability generating streamwise vortices.

6. Conclusions6. Conclusions

• Numerical tools have been developed which qualitatively predict the flow in the Ariane V boosters.

• Due to the complexity of the problem, some crude hypotheses have been made to estimate slag deposition. However, in the absence of more accurate experimental data (particle diameter, exact mechanism of slag deposition), the chosen level of modelisation (stationary Euler/ Lagrange) seems to be well suited.

• The numerical simulations of pressure oscillations in the Ariane V boosters are still under progress. Indeed, in this case, the level of accuracy can be improved with a better numerical modelisation.