LES stochastic modelling of cavitation with its applications in OpenFOAM
Cavitation is a vaporization process that commonly happens in high-pressure injector nozzles nowadays. It has been shown by previous studies that cavitation has a significant influence on the subsequent atomization process, the quality of which would in turn heavily affect the process of combustion. Injector nozzle designs nowadays are trending towards higher and higher injection pressure, making the knowledge on cavitation phenomena more and more relevant and necessary. Studies into cavitation phenomena have attracted a rapidly increasing amount of interest from both the academic and the industrial circle. However, due to the inherent difficulties, cavitation still renders itself a process that is hard to be quantified with the experimental facilities nowadays. On the computational side, some cavitation models have been developed and applied successfully. Lagrangian models have had much success in several studies. However, when it comes to applications of parallel computing, the inherent difficulty on computational load balancing could hinder the application of Lagrangian models in simulations of realistic injector nozzles. The Eulerian approach, on the other hand, is naturally conducive to a better computational load balance, for which a simple domain decomposition usually suffices. In the category of Eulerian modeling, the homogeneous equilibrium model (HEM) imposes less of a requirement to computational load, thus have been widely used in applications nowadays.
As much as HEMs have been widely applied in both academic studies and commercial computational tools, the stochastic feature of cavitation phenomena has been missing in the single Eulerian field models nowadays. With only one Eulerian field, only one bubble radius associated with the volume fraction is solved in any spatial location. However, physically, the vapor bubble sizes are highly fluctuating, hence can better be described by a probability density function (PDF). In order to solve the evolution equation of the PDF, a Eulerian Stochastic Field (ESF) model is developed in this work. Multiple Eulerian fields are used to represent a distribution of cavitation bubble radii.
The ESF method has been previously applied for cavitation simulations only in the context of a compressible flow solver. However, the solution of the compressible form of the Navier-Stokes equation is known to be computationally expensive for low Mach number flow. Therefore, whether the ESF model can be applied in combination with a pressure based solver became an interesting question. In this work, we coupled the ESF model to a pressure-based PISO algorithm, making the ESF model computationally efficient enough for studies of realistic injector nozzle geometries and standard operating conditions. Several simplified geometries, including one step-contraction throttle and two academic injector nozzle designs, are investigated using the novel cavitation model. Furthermore, we applied the ESF model on a realistic multi-hole injector geometry (spray G/G2 as defined by the Engine Combustion Network (ECN)) demonstrating that the ESF cavitation model can be applied in simulations of realistic nozzle injector geometries.
Eulerian Stochastic Field Method
Homogeneous Equilibrium Model