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Simulations and experimental study of DDT behind a single obstacle

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André Vagner Gaathaug

Knut Vaagsaether

Dag Bjerketvedt

Faculty of Technology

Telemark University College

Norway

- 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

- 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

Focus

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

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

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- 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.

- 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

- 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).

- 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.

- 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.

- 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.

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

Telemark University College – NTNU, 2010:221.

- 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 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 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.

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

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”

- 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.