Published in Proceedings of the 6th European Combustion Meeting, Sweden, 2013## Numerical simulation of lifted tribrachial |

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The parallel flow solver "NGA" [14], developed at Stanford University, is used to solve the transport equations. The solver implements a finite difference method on a spatially and temporally staggered grid with the semi-implicit fractional-step method [15]. Velocity and scalar spatial derivatives are discretised with a second order finite differences centred scheme. The time step size is calculated to achieve the unity CFL number. The solution of the Poisson equation on massively parallel machines is performed by the library hypre [16] with the preconditioned conjugate gradient iterative solver [17] coupled with one iteration of a multi-grid pre-conditioner [18].

Figure 1: Experimental and computational configuration and the tribrachial flame structure, the rich premixed flame (RPF), lean premixed flame (LPF) and diffusion flame (DF) are labeled. |

Figure 2: Comparison of experimental [19, 20], respectively, and computed laminar flame speed of n-heptane/air mixture at ambient pressure. |

Figure 3: Comparison of experimental [21] and computed oxidiser temperature at autoignition, T, as a function of the strain rate, _{2,I}a._{2,I} |

Moreover, the experimental results and calculations from the study on the mechanism of autoignition of n-heptane in opposed flow configuration [21] are compared with the present 97-species model, using CHEMKIN, in Fig. 3. The momenta of the opposed flow reac- tant streams at the duct exits are kept equal to hold the flame approximately in the middle of the two ducts [25]. Again, excellent agreement with the experimental re- sults is found, wherein the present model predictions fall within the uncertainty of the experimental measurements.

Table 1: Parameters used for the experiments and simulations, and the resulting experimental and numerical flame heights. |

Figure 4: Experimental and numerical height above the burner, H, as a function of the inlet temperature, T, with U = 1.5 m/s, _{jet}U = 0.4 m/s, _{coflow}X = 0.035._{n−hep,f} |

According to results summarised in Table 1, depending on the inlet temperature the flame lift-off height is between 24 <

Figure 5: The correlation between the heat release rate and the line-of-sight integrated CH*, with T = 625 K, _{0}U = 1.5 m/s, _{jet}U = 0.4 m/s, _{coflow}X = 0.035._{n−hep,f} |

Figure 6: Narrow-band (431 nm) filtered photograph of CH* (a) and numerical results, the mass fraction of CH* species after line-of-sight integration, (b), and the grayscale intensity values along the dashed lines in the CCD photograph compared with the numerical results of mass fraction of CH* (c), with T = 600 K, _{0}U = 1.5 m/s, _{jet}U = 0.4 m/s, _{coflow}X = 0.035._{n−hep,f} |

However, to compare the numerical results with the photographs, the spatially-resolved information has to be convoluted to the line-of-sight projection data [27, 28], see Fig. 5 showing the comparison of heat release rate and line-of-sight integrated CH*. In this study, the numerical results, namely the mass fraction of the CH* species, are post-processed (line-of-sight integrated and mirrored around the axis of symmetry to complete the full flame image) to be compared with the photographs of the flame taken through a narrow-band filter isolating the given frequencies. The CH* and OH* emit near 431 nm and 308 nm, respectively. The horizontal cuts, across the heat release rate and the line-of-sight integrated CH*, Figs. 5(a) and 5(b) respectively, show that the relative proportions between the rich and lean premixed wings are well correlated, as shown in Fig. 5(c).

Fig. 6(a) shows the CCD imagine of the tribrachial flame with initial temperature of 600 K, taken through narrow-band filter isolating the frequencies to near 431 nm. Using the same configuration, the "NGA" is used to obtain the equivalent results numerically. The output of the line-of-sight integration, post-processed numerical results, is shown in the Fig. 6(b).

The grayscale intensity values of the photograph are extracted along the dashed line depicted in Fig. 6(a) and compared with the computed values along the dashed line in similar position in Fig. 6(b). The Fig. 6(c) shows the comparison. The CCD distance, in Fig. 6(c), is converted from pixels to mm by taking the photograph of a ruler under the same configuration.

Figure 7: Narrow-band (431 nm) filtered photograph of CH*, with T = 700 K, _{0}U = 1.5 m/s, _{jet}U = 0.4 m/s, _{coflow}X = 0.035._{n−hep,f} |

Figure 8: Numerical results, the mass fraction of CH* species after line-of-sight integration, with T = 700 K, _{0}U = 1.5 m/s, _{jet}U = 0.4 m/s, _{coflow}X = 0.035._{n−hep,f} |

Comparing the photographs of the CH* and the CH* obtained computationally, also proves that the simulations are copying the actual reality with relatively high precision. The computations, as well as the actual photographs from the experiments, both show the same tendency that with increasing temperature the diffusion region of the flame becomes larger while the width of the flame is unchanged. Thus, this study indicates that the present 97 species mechanism predicts the peak CH* concentration with high accuracy.

Quantitative correlation between the chemiluminescence peak-intensity and the heat release rate is provided. Therefore, the chemiluminescence can be used as the heat release marker for the tribrachial n-heptane laminar flames. This is an inexpensive alternative to laser techniques that can provide an information with effective spatial-resolution for combustion sensing.

This study is a part of the ongoing effort to study the tribrachial flames in low temperature regimes. However, first the chemiluminescent diagnostic is observed for the high temperatures as presented here.

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