59809 - A Semi-Analytical Model for Prediction of Wall Quenching Distances of Premixed Flames 

In order to predict the variation of the wall quenching distance of a premixed flame under different equivalence ratios and incoming flow velocities, a semi-analytical model has been derived based on the conservation of energy in the quenching zone. The flame is simplified as a cone, the annulus zone between flame base and the burner wall is the control volume. The height of the control volume is the quenching distance. According to the conservation of energy, in the control volume, the sum of the heat transferred from the flame and the heat released by chemical reaction is equal to the heat loss of the control volume.

The basic assumptions for derivation of the semi-analytical mode are summarized as follows: 1)    The flame is axisymmetric. 2) The gas is treated as ideal gas. 3)      Fuel and oxidizer form products in a single-step reaction. 4) The heat loss is assumed to be the heat conducted to the burner wall. The heat loss to the zone surrounding the control volume is small, and could be ignored. 5)      The temperature profiles are linear in the flow direction in the control volume. The influence of the temperature profiles in the radial direction in the control volume is ignored. 6) The flame base is treated as a point in the derivation. 7)       The influence of the pressure and temperature is not considered. The pressure and the temperature are in room condition. And the pressure keeps a constant during reaction. 8)   The influence of buoyancy is ignored.

In this model the flame surface radiation plays an important role. Factors influencing the radiation, including flame structure, flame surface area, flame temperature, radiation angle coefficient, radiation transmissivity and emissivity, have been analyzed, respectively.

In order to validate the model and obtain the experimental coefficients, a series of methane-air Bunsen flame wall quenching distance experiments have been conducted. In the experiment, the independent variables are the incoming flow velocity and the equivalence ratio. The equivalence ratios are 0.806, 0.911, 1.015, 1.112, 1.198, 1.222, 1.287, 1.308, 1.404, 1.406, 1.477, 1.616, 1.790, 2.037, 2.214, 2.404, 2.586, 2.744, and 3.021, respectively. The flow velocities (m/s) are 0.728, 1.019, 1.310, 1.602, 1.893, 2.184, 2.475, 2.766, and 3.058, respectively. Quenching distance is measured through analyzing visual photographs under different flow velocities and equivalence ratios. Each data has been repeated for at least 3 times under different equivalence ratios.

The conclusions are summarized as follows:

1) For equivalence ratio=0.8~1.2, quenching distance increases with the increasing incoming velocity. For equivalence ratio=1.2~1.4, quenching distance nearly keeps a constant. For equivalence ratio>1.4, quenching distance decreases with the increasing velocity.

2) For equivalence ratio<1.0, quenching distance decreases with the increasing equivalence ratio. For equivalence ratio=1.0~1.3, quenching distance increases with the increasing equivalence ratio. For equivalence ratio>1.3, quenching distance decreases again. For equivalence ratio>1.6, quenching distance nearly keeps a constant.

3) The comparison between the theoretical prediction and the experiment result shows that this semi-analytical model gives a good prediction of the quenching distance. The relative error of the quenching distance under different equivalence ratios and incoming flow velocities is less than ±15%.