Simulation of flame acceleration and DDT in H2-air mixture with a flux limiter centred method
description
Transcript of Simulation of flame acceleration and DDT in H2-air mixture with a flux limiter centred method
ICHS Pisa 2005 1
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 2
• Outline– Introduction
– Models and numerics
– Physical experiments
– Numerical experiments
– Conclusion
ICHS Pisa 2005 3
• 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 4
• Filtered conservation equations of mass, momentum and energy
0~
ii
uxt
jijiijij
iji
j uuuuxx
puu
xt
u ~~~~~
EuEu
x
T
xx
puuE
xt
Eii
iij
ii
i
~~~
~~~
ICHS Pisa 2005 5
• Turbulence model, by Menon et.al.
DPx
k
xku
xt
k
it
t
ii
i
Pr
~
j
iij x
uP
~
2
3
kCD
ijijkkijtij kSS 3
2~
3
1~2
2
1
kCst
ICHS Pisa 2005 6
• 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 7
– 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 8
• 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)
RT
QEzpk
RT
Ezpk
dt
dz 2223
2222 exp1exp
ICHS Pisa 2005 9
• 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
4
1
2
1
DaPrReA1Lt SS
u
Recu
Da 52.0A
ICHS Pisa 2005 10
• Flame tracking with the G-equation
• Where vf is the local particle velocity in front of the flame
• G is negative in the unburned gas
• The G0 surface is set to be immediately in front of the flame
GSGvt
GT
f
ICHS Pisa 2005 11
• 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 12
• Experimental setup– 30% hydrogen in air
– 1 atm, 20°C
– Closed tube
– 10.7 cm ID
– Spark plug ignition at p0
– 0.5 m between sensors
– 1.5 between p0 and p1
– 3 cm orifice in obstacle
ICHS Pisa 2005 13
• Experimental results, pressure records
ICHS Pisa 2005 14
• 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
ICHS Pisa 2005 15
• Comparison of pressure history at sensor p0
ICHS Pisa 2005 16
• Comparison of pressure history at p2
ICHS Pisa 2005 17
• 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 18
• Mach number at center line behind the obstacle as the flame reaches the opening
ICHS Pisa 2005 19
• 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 20
• 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 21
• 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