Flame propagation in a rotating tube

The steady propagation of premixed laminar flames in rotating circular tubes with adiabatic or isothermal walls is numerically investigated to study the effects of solid-body rotation on the flame shape and the flame propagation speed. Owing to the coupling of density variation across the flame and radial pressure gradient, the results show that the resulting baroclinic torque tends to make the unburned mixture ahead of the flame flow from the axis to the wall of the tube. This tendency intensifies with the increase in the tube rotation speed. Thereby, as the tube is rotated faster, the mushroom-shaped flame becomes more convex to the unburned mixture at the axis of the tube, resulting in larger flame surface and therefore a faster flame. On the other hand, the tulip-shaped flame becomes flatter at the concave portion near the axis, and turns convex to the unburned mixture, becoming a mushroom-shaped flame as the tube is rotated fast enough. Although tulip-shaped flame/mushroom-shaped flame transition is gradual in small tubes, in large tubes, it is catastrophic and a hysteresis behavior is observed. Since the tulip-shaped flame flattens near the axis as the tube rotation speed increases, its flame propagation speed in insulated tubes decreases during its transition to mushroom-shaped flame because of the decrease of its total flame surface. In isothermal-wall tubes, however, because its surface grows larger near the wall during the transition, its flame propagation speed increases slightly as the rotation speed increases.