Some issues and methods in particles tracking

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Some issues and methods inparticles tracking
Laurent DUMAS Université 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

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1. The Ariane V launcher 2. The ASSM program 3.
Description of the flow in the Ariane V
boosters 2.1 Experimental measurements 2.2
Qualitative behavior 2.3 Characteristic values
4. Slag deposition 4.1 The Lagrange /Euler
computations 4.2 The Euler /Euler computation 4.3
Comparison of the results 5. Pressure
oscillations 5.1 The Navier Stokes
computations 5.2 The LES computations 6.
Conclusion
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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 (2238 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.

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1. The Ariane V launcher
Schematic view of the Ariane V booster
First flight October 1997
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2. 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
• ignition
• dense phase (slag deposition, combustion)
• stability (pressure oscillations),
• etc...

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members and references of 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 dalumine 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

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3.1 Experimental measurements

• 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 t95 s
• main 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.

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3.2 Qualitative behavior of the flow in the
Ariane V boosters at t95s
Ejection of combustion products (gasAlAl2O3)
Alumina trajectories
Alumina deposition
Propellant blocks 2 and 3
1.5 m
Thermal protections
23 m
Second segment
Third segment
turbulent shear layer region giving rise to
vortex shedding
recirculation area
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Modelisation 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
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3.3 Characteristic values of the flow in the
Ariane V boosters

• 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 rp/rg 1000
• Adimensionalised numbers
• Stokes number 1 (large particles) or 1
  (small particles)
• Reynolds number 100 000
• Particle volumetric fraction (a priori
  estimate) ap 1
• ? The hypotheses of one way coupling and dilute
  phase is assumed

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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-e 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.

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Particle tracking in a Lagrangian approach

• Computation of the trajectories of
  particles by solving the ODE
• with and where

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Dispersion effects in the Lagrangian approach

• The dispersion effects due to turbulence are
  taken into account with the Gossman-Ioannides
  model
• ltuggt is replaced during a time ?t by ltuggtu
  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.

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Details of the Euler/Lagrange computations(t95s)

• 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)

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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.

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4.2 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

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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.

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4.3 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 lt M
  lt 2055 kg
• Second criterion (nose point) 1452 kg lt M lt
  3600 kg
• Eulerian approach
• 12 deposition rate for the chosen case against
  2 to 6 in the corresponding Lagrangian
  approach.

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5.1 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 Leers 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

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5.2 Pressure oscillations LES simulation(LEGI)

• Same conditions and same 2D grid.
• Extrusion of the 2D grid in the 3rd direction
  (318?31?90 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.

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6. 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.