In order to investigate H_{2} rich blowout limit at different blockage ratios and flow velocities, a CFD software FLUENT was used to simulate H_{2} burning flow field in bluffbody burner, and the software CHEMKIN was adopted to analyze the sensitivity of each elementary reaction. Composition Probability Density Function (CPDF) model was adopted to simulate H_{2} combustion field in turbulence flame. The numerical results show that reactions R2 and R9 possess the largest positive and negative temperature sensitivity. Temperature has a very important influence on these two reactions. When equivalence ratio is 1, the mixture is most ignitable, and the critical ignition temperature is 1550 K. There should be an optimal blockage ratio which can stabilize the flame best. When the blockage ratio remains unchanged, the relationship between H_{2} RBL and flow velocity is a logarithmic function. When the flow velocity remains unchanged, the relationship between H_{2} RBL and blockage ratio is a parabolic function. A complete extinction requires three phases: the temperature sudden decline in the main stream, the energy dissipation from the recirculation zone to the main stream, and the complete extinction of the flame.
Bluffbody stabilized combustion with triangular or cone stabilizers is common in afterburners of military aircraft. A central recirculation zone (CRZ) will form in the wake of the bluffbody burner [
Lots of researches on flame stabilized mechanism in a bluffbody burner have been carried out both in terms of experiment and theoretical treatment. Experimental researches on this problem are extremely important, but a largescale systematic mechanism analysis via experiments is both expensive and time consuming. The Volvo Aero Corp. [
On the other hand, computational fluid dynamics (CFD) has been widely used to study the turbulent reacting flows, fluid machinery, and combustion systems to predict device performance and optimize their structures. Many experiment studies are used to validate the simulation accuracy and to explain the flame extinction mechanism. For example, Giacomazzi et al. [
Even though there is a recirculation region in a bluffbody burner, the extinction will still occur if the stabilized ignition point was blown to the outside of CRZ. CRZ takes a very important effect on flammability. So the aim of the present work is to study the influence of flow velocity and blockage ratio on H_{2} Rich Blowout Limit (RBL) and finally summarize a formula for H_{2} RBL.
Figure
Geometry structure of bluffbody burner.
The calculation mesh.
Boundary conditions: mixture inlet temperature is 293 K, inlet pressure is 1 atm and inlet velocities are shown in Table
Outlet: pressure outlet.
Wall: adiabatic boundary.
Blockage ratio and gas flow velocities (1 atm, 293 K).
Bluffbody diameter 
20  30  40  50  60  70 
Blockage ratio 
0.2  0.3  0.4  0.5  0.6  0.7 
Gas velocity 
1  2  5  10  20  50 







The computations are repeated for different combinations of gas velocity and blockage ratio. The definition of Reynolds number based on the channel width has been given out as follows:
The blockage ratio
In combustion flows, conservation equations for mass, momentum, energy, and species are solved. The standard
Composition PDF Transport Equation (CPDF) is as follows:
The two terms on the righthand side represent the PDF change due to scalar convection by turbulent scalar fluxal and molecular mixing/diffusion, respectively.
The flow field researched in this paper is turbulence refer is to Re_{D} as shown in Table
CPDF transport equation cannot be solved by finite volume method; a Lagrangian Monte Carlo [
Table
Hydrogen chemistry reaction.
No.  Reaction 




1 
O_{2}+ H 

0.00  70.30 
2  OH + O 

0.00  3.52 
3  H_{2} + O 

2.67  26.30 
4  OH + H 

2.67  18.29 
5  H_{2} + OH 

1.60  13.80 
6  H_{2}O + H 

1.60  76.46 
7  OH + OH 

1.14  0.42 
8  H_{2}O + O 

1.14  71.09 
9  O_{2} + H + M 

−0.80  0.00 
10  HO_{2} + M 

−0.80  95.39 
11  HO_{2} + H 

0.00  4.20 
12  HO_{2} + H 

0.00  2.90 
13  HO_{2} + OH 

0.00  0.00 
14  HO_{2} + H 

0.00  7.20 
15  HO_{2} + O 

0.00  −1.70 
16  H + H + M 

−1.00  0.00 
17  OH + H + M 

−2.00  0.00 
18  O + O + M 

−1.00  0.00 
M  H_{2}O/6.5 O_{2}/0.4 N_{2}/0.4/  Third body efficiency  
Unit 

The studies on grid size and time step independence have been performed to determine the optimal grid and time step with a good accuracy for the simulation. Also, the kepsilonCPDF model was used.
Table
Grid size independence validation with time step 0.1 ms.
Grid size/mm 




Grid amount 

0.5  419  —  768  — 

0.8  420  1  760  8 

1.0  420  1  755  13 

1.5  415  4  707  61 

2.0  414  5  666  102 

Time step independence validation with grid size 1.0 mm.
Time step/ms 




Remark 

0.05  424  —  775  —  — 
0.10  419  5  755  20  Independent 
0.20  405  14  707  68  Worse 
0.50  402  22  604  171  Worse 
H_{2} RBL (volume concentration).




0.2  0.3  0.4  0.5  0.6  0.7  
1  0.775  0.782  0.783  0.786  0.779  0.777 
2  0.765  0.775  0.774  0.776  0.770  0.767 
5  0.753  0.763  0.763  0.765  0.757  0.754 
10  0.745  0.755  0.753  0.754  0.749  0.746 
20  0.735  0.743  0.743  0.745  0.740  0.737 
50  0.723  0.728  0.728  0.731  0.725  0.724 
Figure
Profiles of temperature on section
Grid size independence
Time step independence
Figure
Validation rig and calculation zone geometry.
Validation rig [
Threedimensional calculation zone
Vertical section—XOY
Geometry model and boundary conditions are as follows:
Length
Side length of bluffbody with the equilateral triangular crosssection: 40 mm;
Inlet condition of mixture of air and propane:
Outlet: pressure outlet;
Wall: adiabatic boundary;
Fuel oxidation was modeled by onestep global reaction:
The reaction rate is that proposed by Fluent Database according to Arrhenius Law [
The Reynolds number based on the bluffbody burner device and on the velocity at the bluffbody location is about 10^{5}. The flow field is simulated using compressible NS equations.
Figures
Profile of
Section
Section
Profile of
Section
Section
Profiles of temperature at sections (a)
Section
Section
Figures
Comparison of temperature field by different mathematical model.
Temperature field from Eugenio by FMLESEDC [
Instantaneous temperature by SLLESEDC model
Instantaneous temperature by kepsilonEDC model
Instantaneous temperature by kepsilonCPDF model
Mean temperature by kepsilonCPDF model of 10 periodic
In a word, the agreement observed between kepsilonCPDF model result and published classics experiment data is acceptable. The kepsilonCPDF combustion model can accurately predict the flame temperature, while SLLESEDC model can accurately predict the vortex structures and explain the extinction mechanism.
Figure
Comparison of recirculation zone between cold flow and combustion field.
Streamline
Figure
Streamline of cold flow field and combustion field.
SLLESEDC cold field
SLLESEDC combustion field
kepsilonCPDF cold field
kepsilonCPDF combustion field
Figure
Image of combustion experiment [
Figure
Discontinuous flame: when the equivalence ration is close to blow off, the flame temperature would decline rapidly, chemistry reaction would be slower, and the heat transfer and dissipation to the flame sheet can ignite the fresh mixture and, finally, induce the discontinuous flame. The first discontinuous position presents at the recirculation zone stagnant point.
Local extinction and reignition: if the cold mixture is heated up and reignited by flame kernel exactly, the flame is at critical blowout limit state of being acute and unstable. The local extinction and reignition will alternately appear in the recirculation zone. During the blow off, significant fragmentation of the flame occurred, with branches of flame remaining anchored in the bluffbody wake zone.
Global extinction: the fame pockets moved to the downstream of the recirculation and finally induced the global extinction. Overall blow off occurred with the gradual elimination of these flame fragments and local extinction [
Extinction process.
Discontinuous flame
Local extinction and reignition
Global extinction
H_{2} RBL is defined as the mole fraction of H_{2} in the mixture. It is the H_{2} mole concentration limit beyond which the extinction will occur. So, it is dimensionless (%) consider
Table
H_{2} RBL versus gas flow velocity and blockage ratio.
Linear coordinate
Curves of H_{2} RBL versus blockage ratio
Table
In a word, the H_{2} RBL will be improved by decreasing the gas velocity, or by increasing the blockage ratio before the optimal value. But if the blockage ratio increases when it has exceeded the optimal value, the H_{2} RBL will decline. So, when the surroundings remain unchanged in bluffbody burner, the H_{2} RBL is a function of gas flow velocity and blockage ratio. To investigate the relationship between gas flow velocity, blockage ratio, and H_{2} RBL, the gas velocity has been denoted by logarithmic coordinates (named, logarithmic velocitylg
Curves of H_{2} RBL versus gas flow velocity and fitting curve (the symbols are numerical results and the lines originate from the fitting formula).
Logarithmic coordinate
Linear coordinate
Linear fitting of the numerical data results by Least Square Method, and the value of
Fitting formulas about H_{2} RBL and gas flow velocity.

RBL fitting formula/100% 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

Figure
Slope and intercept of fitting function of H_{2} RBL versus blockage ratio
Slope fitting curve
Intercept fitting curve
Fitting the curve with a quadratic function by Least Square Method, then a formula for
Figure
Streamlines of recirculation zone.
Recirculation versus blockage ratio
Recirculation versus flow velocity
The simulation of ignition process is done in the condition of
Start ignition:
Ignition process:
Extinction process:
First half parts of Figure
Profiles of species average mass fraction and average temperature on section
O_{2}, H_{2}, Temperature
H_{2}O, OH, H
Temperature distribution from ignition process to extinction process.
Ignition process
Extinction process
Figure
It can be concluded that a successful ignition sequence in a bluffbody burner requires three phases: (1) the startup of ignition in the recirculation zone; (2) the energy accumulation in the recirculation zone; (3) the flame propagation from the recirculation zone to the main stream.
When
Latter half parts of Figure
During
In a word, CPDF model is accurate enough to capture the flame extinction. In terms of control of marine power, it can be concluded that the flame will extinguish as soon as the average temperature is lower than that at 800 ms. Feedback should be provided to fuel and air control system promptly to regulate fuel supply in order to avoid extinction.
So, a complete flame extinction process requires three phases: (1) the sudden decline of temperature in the burner because of the decline of fuel concentration; (2) the energy dissipation from the recirculation zone to the main stream; (3) the flame complete extinction.
The sensitivity analysis is a powerful tool in interpreting the results of computational simulations, and it can be used to research the influence of temperature, species concentration, and equivalence ratio on each elementary reaction [
To investigate the contribution of each elementary reaction to H_{2} burning, the software CHEMKIN [
For heatofformation sensitivity,
The equivalence ratio for calculation case in Figure
Temperature sensitivity for each reaction.
To investigate the influence of species concentration on chemistry reaction, the species sensitivity of intermediate species (H, O, and OH), reactants, and production were carried out. Figure
Temperature sensitivity for intermediate species of R2 and R9.
Profiles of intermediate species versus temperature.
Profiles of reactants and production versus temperature.
Rate of production versus temperature.
Figure
Figure
Temperature sensitivity coefficient of R2 versus equivalence ratio.
Temperature sensitivity coefficient of R9 versus equivalence ratio.
The numerical simulation on H_{2} premixed flame in a bluffbody burner has been carried out. The H_{2} flame ignition and extinction process is analyzed, and a function formula is summarized for H_{2} RBL. The results showed that kepsilonCPDF model is a reasonable method to capture H_{2} RBL. There should be an optimal blockage ratio, which can stabilize the flame best. The flame will take an “M” shape with reaction fronts inside the CRZ near the blow off condition. This research can provide theoretical instruction for bluffbody burner design, gas flow velocity control, fuel concentration matching, and the flame stability research. To systematically analyze the role of each elementary chemistry reaction taking place in the global combustion, CHEMKIN software was adopted to investigate the sensitivity of each elementary reaction. Other conclusions are as follows.
When the blockage ratio remains unchanged, H_{2} rich blowout limit is gas flow velocity’s logarithmic function.
When the gas flow velocity remains unchanged, H_{2} rich blowout limit is blockage ratio’s quadratic function.
The fitting formula of H_{2} rich blowout limit is
A complete extinction process in a bluffbody burner requires three phases, the suddenly decline of the temperature in the main stream, the energy dissipation from the recirculation zone to the main stream, and the flame complete extinction.
Reactions R2 and R9 possess the largest positive and negative temperature sensitivity. Increasing the rate of R2 will lead to a higher temperature, and increasing the rate of R9 will lead to a lower temperature. When equivalence ratio is 1, the mixture is most ignitable. The critical ignition temperature is 1550 K. Temperature has a very important influence on reactions R2 and R9.