Simulation of flame acceleration and DDT in H2-air mixture with a flux limiter centred method

Knut Vaagsaether, Vegeir Knudsen and Dag Bjerketvedt ICHS Pisa 2005 1

• Outline

– Introduction – Models and numerics – Physical experiments – Numerical experiments – Conclusion ICHS Pisa 2005 2

• The goal of this work is to simulate the explosion process from a weak ignition source through flame acceleration and DDT to a detonation • The simulation tool is based on large eddy simulation (LES) of the filtered conservation equations with a 2. order centred TVD method • Numerical results are compared to experimental results with pressure records ICHS Pisa 2005 3

• Filtered conservation equations of mass, momentum and energy   

t

  

x i

 

i

 0   

t j

  

x i

 

j

~

i

  

p



x j

  

x i

 

ij

  

u i u j

 ~

i j

    ~

E



t

  

x i

 

i

  ~

i



x j p

  

x i

   

T



x i

  

u i E

 ~

i

~

E

    ICHS Pisa 2005 4

• Turbulence model, by Menon et.al.

 

k



t

  

x i

  ~

i k

   

x i

   

t

Pr

t



k



x i

  

P



D P

  

ij

 ~

i



x j D



C

 

k

2  3 

ij

  2  

t

~

S ij

 1 3 ~

S kk



ij

 2 3 

k



ij



t



C s k

1 2  ICHS Pisa 2005 5

• In addition to the mass, momentum, energy and k, two other variables are conserved – Two reaction variables, α and z – α is a variable for the production of radicals where no energy is released – z is a variable for the consumption of radicals (exothermal reactions) ICHS Pisa 2005 6

– α is only solved for the unreacted gas – α keeps track of the induction time – If α is below 1, no exothermal reaction is taking place – If α reaches 1 an exothermal reaction occurs – The production term of α is an Arrhenius function and can be assumed to be 1/τ ICHS Pisa 2005 7

• The exothermal reactions are handeled in two ways – If the flame is a deflagration wave, a Riemann solver is used to calculate the states at each side of the flame – The Riemann solver use the burning velocity as the reaction rate – If the flame is a detonation wave or α reaches 1, another reaction model is used, presented by Korobeinikov (1972)

dz

 

k

2

p

2

z

2 exp

dt E

2

RT



k

3

p

2  1 

z

 2 exp 

E

2 

Q RT

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• Burning velocity as a function of velocity fluctuations, presented by Flohr and Pitsch (2000) • This model is developed for lean premixed combustion in gas turbine combustors

S t

 

S L

  1  A  Re  Pr  2 1 Da  1  4   Re  

u

   Da   

u

 

c

A  0 .

52 ICHS Pisa 2005 9

• Flame tracking with the G-equation 

G



t



v f



G



S T



G

• Where v f is the local particle velocity in front of the flame • G is negative in the unburned gas • The G 0 flame surface is set to be immediately in front of the ICHS Pisa 2005 10

• Solvers – A flux limiter centered method (FLIC) to solve the hyperbolic part of the equations, an explicit 2nd order TVD method – Central differencing for the diffusion terms – Godunov splitting for dimensions, diffusion terms and sub models – 4. order RK for ODEs ICHS Pisa 2005 11

• Experimental setup – 30% hydrogen in air – 1 atm, 20°C – Closed tube – 10.7 cm ID – Spark plug ignition at p 0 – 0.5 m between sensors – 1.5 between p 0 and p 1 – 3 cm orifice in obstacle ICHS Pisa 2005 12

• Experimental results, pressure records ICHS Pisa 2005 13

• Numerical setup – Same conditions as physical experiments – Assume cylindrical coordinates • 2D • Axis-symmetric – Carthesian, homogeneous grid – CV length 2 mm (~50 000 CV) – CFL number 0.9

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• Comparison of pressure history at sensor p 0 ICHS Pisa 2005 15

• Comparison of pressure history at p 2 ICHS Pisa 2005 16

• Density in a 240 mm X 107 mm area • Time difference is 0.025 ms • DDT occurs between image 1 and 2 ICHS Pisa 2005 17

• Mach number at center line behind the obstacle as the flame reaches the opening ICHS Pisa 2005 18

• Discussion and conclusion

– The pressure in the ignition end of the tube is simulated with some accuracy, even with these assumtions – The detonation wave is simulated very accurate compared to the experiments which means that the Korobeinikov model is good enough for this work – A DDT is simulated ICHS Pisa 2005 19

• Discussion and conclusion

– Some discrepancies between numerical and physical results in the ignition part (deflagration) • 2D • Boundary conditions for the G-equation • Burning velocity model – The DDT is simulated too late • 2D • Induction time • Errors in pressure from the ignition part • Is it possible with LES?

ICHS Pisa 2005 20

• Further work

– 3D simulation should be performed – Boundary conditions for the G-equation?

– Burning velocity model – Adaptive mesh refinement – A new model for the induction time ICHS Pisa 2005 21