Momentum Coupling by Means of Lagrange Polynomials in the CFD Simulation of High-Velocity Dense Sprays

The discrete droplet model is widely used to describe two-phase flows such as high-velocity dense sprays. The interaction between the liquid and the gas phase is modeled via appropriate source terms in the gas phase equations. This approach can lead to a strong dependence of the liquid-gas coupling on the spatial resolution of the gas phase. The liquid-gas coupling requires the computation of source terms using the gas phase properties, and, subsequently, these sources are then distributed onto the gas phase mesh. In this study, a Lagrange polynomial interpolation method has been developed to evaluate the source terms and also to distribute these source terms onto the gas mesh. The focus of this investigation has been on the momentum exchange between the two phases.

The Lagrange polynomial interpolation and source term distribution methods are evaluated for non-evaporating sprays using KIVA3 as a modeling platform. This method is compared with the standard “nearest neighbor” method of KIVA3, and experimental data have been used to establish its validity. The evaluation criteria used include the liquid penetration, the drop size distributions and the velocity distributions for liquid and gas. It has been found that this new interpolation and distribution method leads to more realistic spray behavior and to an increased stability of the numerical solver.