Effect of liquid and air swirl strength and relative rotational direction on the instability of an annular liquid sheet

Instability of a swirling annular liquid sheet in swirling inner and outer air streams has been investigated by a temporal linear stability analysis. The effects of the swirling and axial motion of the liquid and the air streams, as well as the effects of relative inner and outer air swirl orientation with respect to the liquid swirl direction on the instability have been investigated. Results show that for a non-swirling liquid sheet axial inner air stream is more effective than axial outer air stream in enhancing the sheet instability. This is opposite of a swirling liquid sheet where axial outer air is more effective in promoting sheet instability compared to axially moving inner air stream. The liquid swirl has a destabilizing effect at the outer interface but has a stabilizing effect at the inner interface. At high liquid swirl Weber number, the outer air (with axial and swirl velocity components) is more effective in enhancing sheet instability compared to the inner air (with axial and swirl velocity components). To understand the effect of air swirl orientation with respect to liquid swirl direction, four possible combinations with both swirling air streams with respect to the liquid swirl direction have been considered. Results show that at high liquid swirl Weber number a combination of counter-rotating-inner air stream and co-rotating-outer air stream has the largest most unstable wave number. However, at low liquid swirl, co-inner/counter-outer combination has the largest most unstable wave number. The combination of inner and the outer air stream co-rotating with the liquid has the highest growth rate. In many combustion applications, the liquid sheet is injected in high pressure environment where the effect of high ambient pressure results in increased aerodynamic interaction due to high air density. Hence the effect of high ambient pressure is studied in terms of the dimensionless parameter of air-to-liquid density ratio. Results show significantly higher disturbance growth rates at high air pressure. However, the qualitative sheet stability behavior is similar to that at atmospheric pressure.