A spectrally accurate hybrid moment-of-fluid and level set method for multiphase flows

Florida State University, Tallahassee FL

Investigators

Abstract

State-of-the-art, highly accurate and efficient numerical algorithms will be developed for simulating multi physics and multi-phase flows of engineering and technological importance. These new numerical methods are also designed to be scalable with respect to an exceedingly increasing number of computer processors, and thus easily implemented on the current and immediately future high-performance computing platforms. They will constitute an enabling technology for use by practitioners in science, engineering, medicine, industry and military. The primary applications of this technology will be to the design of fuel injectors for diesel engines, the design of swirling flow injectors in modern aircraft gas turbine engines, the design of flat fan nozzles employed in combustion, painting, spray cooling, agriculture irrigating applications, the design of off-shore facilities for the conversion of natural gas into liquid state, patient specific drug delivery, and the design of aircraft wing anti-freezing devices. The high accuracy and efficiency of these methodologies will allow parameter studies and design optimization procedures, more sophisticated geometries and models, which have proved until now to be prohibitively expensive. A hybrid methodology coupling an adaptive mesh refinement, easily parallelizable, spectral-element method with the moment-of-fluid method will be developed for numerically simulating multi-phase flows. The principal investigators have already developed an adaptive, parallel, moment-of-fluid algorithm for incompressible and compressible multiphase flows. The primary objective of this proposal is to take the previous work of the principal investigators to a higher level, where each material has its own spectral-element representation, and a grid cell containing multiple materials will contain independent solution expansions for each material. A robust cell integrated semi-Lagrangian method will be implemented so that each material in each rectangular grid cell has a separate mapping from the departure region to the target region in such a way that the combination of all mappings tessellate the computational domain. A cut-cell spectral-element algorithm will be developed for numerically solving the pressure projection equation (a Helmholtz equation) and for numerically solving for the viscous forces in multi-material flows. The benefits of the new algorithm will be the greatly improved accuracy (without loss of robustness) in predicting the shape of deforming material boundaries where there are thin shear layers and/or thin thermal boundary layers.