Numerical simulation of angled-injected liquid jet breakup in supersonic crossflow by a hybrid VOF-LPT method

The breakup of angled-injected liquid jets in supersonic airflow is investigated numerically by a hybrid Volume of Fluid and Lagrangian Particle Tracking (VOF-LPT) method. A Multi-criterion adaptive mesh refinement (AMR) procedure and dynamic load balancing (DLB) algorithm are applied to improve the accuracy of interface and shock wave characteristics and reduce the use of computational resources and liquid mass loss. The flow characteristics of the spray field and penetration depth of the angled-injected liquid jet from the simulations agreed well with the experimental results. Under the supersonic crossflow conditions, the jet has momentum in the counter-flow direction that improves gas-liquid interactions. The penetration depth of the liquid jet increase with the increase of the injection angle. In particular, the penetration depth of the angled-injected liquid jet is given in the: $y/d=0.12·\sin \left(2\theta /3\right)·{\left(e^{\sin \left(2\theta /3\right)}\right)}^{3.185}·q^{0.389}{\left(x/d\right)}^{0.309}$. Moreover, the liquid jet at a larger injection angle has a larger spray spread angle and wider wake region due to the larger windward area. Furthermore, the total pressure loss of airflow increases with the injection angle increasing. Considering the total pressure loss for all injection conditions is lower than 14%, the total pressure loss caused by the injection angle increase can be negligible.