Lagrangian simulation of evaporating droplet sprays

Abstract

Listen

Translate article

In this paper we present the purely Lagrangian approach for the high fidelity simulation of evaporating sprays as a potentially advantageous alternative to the widely used Lagrangian–Eulerian approach. We motivate our arguments using analytical solutions which we derive from a set of simplified spray (droplet and vapor) equations, albeit ones that retain key physical complexities of the two-phase flow. These solutions are obtained for two model flows: the stagnation point flow and the point vortex flow. By comparing numerical results with these analytical solutions we demonstrate limitations of the Lagrangian–Eulerian approach in providing solutions that are consistent with the governing equations. The problem alluded to here is specific to evaporating sprays and is over and above the well known issue of the point source approximation. Moreover, while it is related to the presence of interpolations between the disperse and continuous phases, it is not inherent in them—an interpolation scheme that effectively eliminates this problem is identified. Rather it has to do with the fact that in the Lagrangian–Eulerian approach the evaporated volume information is lost and is substituted with an arbitrary, with respect to the evaporation process, grid related volume. The result is grid dependency of the solution and the inability to satisfy physical constraints on both the intensive and extensive properties as dictated by the governing equations. To alleviate these problems, we present the first of a potential family of purely Lagrangian numerical schemes. The scheme is three dimensional and unsteady and naturally captures the key physics inherent in the spray equations. Moreover, it is able to properly resolve the vapor scales that are smaller than the flow dynamical scales. Comparisons of results from this model with the analytical solutions demonstrate the correctness of the approach. The model is also implemented in the simulation of a shear layer flow seeded with evaporating droplets. In these simulations the velocity field is obtained using the Lagrangian vortex element method thus yielding a completely grid free and naturally adaptive computation of an evaporating spray.