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Simulations and experimental study of DDT behind a single obstacle. André Vagner Gaathaug Knut Vaagsaether Dag Bjerketvedt Faculty of Technology Telemark University College Norway. Setup of study. 100 x 100 m 2 quadratic cross sectional area, 3000 mm long

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simulations and experimental study of ddt behind a single obstacle
Simulations and experimental study of DDT behind a single obstacle

André Vagner Gaathaug

Knut Vaagsaether

Dag Bjerketvedt

Faculty of Technology

Telemark University College

Norway

setup of study
Setup of study
  • 100 x 100 m2quadratic cross sectional area, 3000 mm long
  • One obstacle with variable blockage ratio BR=0.5 to BR=0.9
  • Spark ignition at the closed end, open at the other
  • 5 and 6 pressure trancducers
  • 15% to 40% Hydrogen in air mixture
why this work
Why this work?
  • Not smooth channel
  • Not obstructed channel
  • Not unconfined jet
  • Earlier work by Vaagsaether and Knudsen
    • Circular geometry
    • Various blockage ratio
    • BR=Blocked area / open area
  • Investigated where DDT occur, a possibly why.
  • Challenges related to the problem
    • Driving section, the first meter
    • Investigated earlier by the authors
experimental results
Experimental results

High speed frames with sketches of their phenomena. BR=0.84, H2 conc. 30%, 30000 fps

experimental results1
Experimental results

High speed film. BR=0.84, H2 conc. 28%, 30000 fps

numerical methods
Numerical methods
  • In house code by K. Vaagsaether – FLIC
    • Flux LImited Centered scheme
    • 2D TVD method
    • Details by K. Vaagsaether and E.F. Toro
  • Euler equation with ideal gas equation of state
    • Conservation of mass
    • Conservation of momentum
    • Conservation of energy
    • Conservation of turbulent kinetic energy

1. Toro, E.F., Riemann Solvers and Numerical Methods for Fluid Dynamics:

A Practical Introduction, 1999, Springer-Verlag, Berlin, Heidelberg.

2. Vaagsaether, K., Modelling of Gas Explosions, PhD thesis, 2010,

Telemark University College – NTNU, 2010:221.

combustion model
Combustion model
  • Progress variable β is conserved and can represent a concentration.
  • β =1 are products, while β =0 are reactants
  • Progress variable α is conserved and represents induction time
  • α<1 ”not hot enough”, while α=1 auto ignite
combustion model1
Combustion model
  • The reaction rate is a maximum of two rates.
  • One turbulent reaction rate and one kinetic reaction rate.
  • Turbulent burning velocity from Flohr and Pitsch. Original from Zimont (1979), model constant A = 0.52 from Zimont and Lipatnikov (1995).
  • Flohr, P. and Pitsch, H., Centre for Turbulent Research, Proceedings
  • of the Summer Program, 2000.
  • Zimont, V. L. 1979 The theory of turbulent combustion at high
  • Reynolds numbers. Combust. Expl. and Shock Waves. 15.
  • Zimont, V. L., & Lipatnikov, A. N. 1995 A numerical model of
  • premixed turbulent combustion of gases. Chem. Phys. Reports. 14(7).
combustion model2
Combustion model
  • The kinetic model is given by Korobeinikov et.al. 2002
  • Then α is linked to the induction time τ by
  • Need model for induction time.

Korobeinikov, M.S., Levin, V.A., Markov, V.V. and Chernyi, G.G,

Propagation of Blast in a Combustible Gas, Astronautica Acta,

17, 1972, pp. 529-537.

induction time
Induction time
  • Sichel et.al. model
  • Del Alamo et.al. model

1. Sichel, M., Tonello, N.A., Oran, E.S. and Jones, D.A.,

A Two–Step Kinetics Model for Numerical Simulation

of Explosions and Detonations in H2-O2 Mixtures,

Proc. R. Soc. Lond. A, 458, 2002, pp. 49-82.

2. Del Alamo, G., Williams, F.A. and Sanchez, A.L.,

Hydrogen–Oxygen Induction Times Above Crossover

Temperatures, Combustion Science and Technology,

176, 2004, pp. 1599–1626.

reaction rates
Reaction rates
  • Turbulent reaction rate ωT is relevant for deflagrations, where diffusion and mixing is the dominante mechanism.
  • Kinetic reaction rate ωK is relevant for detonations, where shock compression/heating is the dominante mechanism.

1

0

1. Vaagsaether, K., Modelling of Gas Explosions, PhD thesis, 2010,

Telemark University College – NTNU, 2010:221.

numerical results
Numerical results
  • Focus on the combustion behind the obstacle
  • Driver section (0 -> 1000 mm) challenge to reproduce
  • Several small explosions along the walls add up to DDT
    • Small scale mixing
    • Pockets of hot reactants
  • Very dependant on induction time model
  • Kinetic reaction rate is important
numerical results1
Numerical results

Numerical schlieren pictures from the simulation case with BR=0.84 and 35% H2 in air.

Frames are not equidistant in time. Induction model: del Alamo.

numerical results2
Numerical results

Numerical schlieren pictures from the simulation case with BR=0.84 and 30% H2 in air.

Frames are not equidistant in time. Induction model: del Alamo.

slide26
Film

Case with BR=0.75 and 30% H2 in air. Induction model: del Alamo.

numerical results3
Numerical results

Density gradient along top wall

  • Comparison of one case with two induction time models
  • One DDT, one without
  • Need to create large enough volume to explode.
  • Not too long and not too short induction time
  • “Draw to bow”
conclusion
Conclusion
  • Total run up distance from 1.1 m to 1.6 m in experiments.
  • Small explosions behind the flame front.
  • Onset of detonation at the walls, mostly top wall.
  • Simulations with two step combustion model.
    • Turbulent reaction rate for deflagrations.
    • Kinetic reaction rate for detonations.
  • Several small explosions along the walls.
  • Dependant on induction time model.