Level Set Modeling of Three-Dimensional Supersonic Liquid Breakup Using The Method of Characteristics

The advantages of using liquid fuels in aerospace propulsion are well known. While a large volume of studies has been devoted to the liquid breakup mechanism in low speed flows, its supersonic equivalent has not received enough attention. This paper proposes a method of characteristics (MOC) based algorithm to simulate breakup of liquid jet under supersonic conditions, wherein the level set (LS) method is used to track the interface between the supersonic gas flow and the subsonic liquid flow. Since the interface is marked by a high-density ratio (of a thousand or more), an LS formulation compatible with MOC is being developed. In the MOC based approach, the first-order hyperbolic Euler equations in the gaseous phase are reduced to the characteristic form and the compatibility equations which do not contain derivatives in the direction normal to the characteristic surfaces are obtained. Since MOC reduces the dimensionality of the problem by one, faster solutions can be obtained without compromising accuracy, when compared with standard finite difference (FD) or finite volume (FV) methods. To the knowledge of the authors, applying MOC on such a large scale has not been attempted before. Our preliminary results show that a strong shock wave is formed in front of the liquid column. Moderate shock waves are present ahead of the liquid ligaments formed during atomization. We expect to produce more results in the future by implementing the given procedure, as this work is very preliminary.