Flame trajectory of a non-vertical turbulent buoyant jet flame

This paper presents a theoretical and experimental study on the flame trajectory of a non-vertical turbulent diffusion flame in still air. A series of propane turbulent flame tests (inner diameter of the burner: d=13 mm) with different initial Froude numbers Fr0 (31.4, 125.5, 282.3, 501.8, and 784.1) and initial flame angles θ0 (60∘, 45∘, 30∘, 15∘, 0∘, −30∘, and −45∘) are performed. The flame motion is physically described based on the Favre-averaged governing equations. The effects of buoyancy and streamline curvature on turbulent mixing are characterized by the mixing length theory. By theoretical derivations, a Richardson number (Ria) is proposed to characterize the flame asymmetry, and a flame trajectory predictive model coupled with the effect of flame asymmetry is established. Experimental results indicate that under the same conditions, the flame curvature first increases and then decreases (eventually tends to be zero) with the continuous increase of Fr0, and increases gradually with the decrease of θ0. A flame intermittency fitting method and a temperature fitting method based on the normal bi-Gaussian distribution are proposed to determine the flame trajectory under different flame asymmetry. These methods are validated by experimental data. It is found that in the near field where the flame is curved, the peak trajectory deviates from the flame midline. In the far field, as the flame recovers to be symmetric, the peak trajectory tends to coincide with the flame midline. Furthermore, experimental data verify that the proposed model can accurately predict the flame trajectory under different flame asymmetry. Finally, results indicate that, under the same conditions, the effect of flame asymmetry on the flame trajectory first increases and then decreases (eventually disappears) with the continuous increase of Fr0, and increases continuously with the decrease of θ0. Comparison between model prediction and experimental data verifies that Ria is the key parameter for the flame asymmetry.