Volume-Of-Fluid Lagrangian-Eulerian Models for Spray Simulations

Kuo, C.-W. Volume-Of-Fluid Lagrangian-Eulerian Models for Spray Simulations. University of Wisconsin-Madison, 2022.

A numerical tool to study the physics of sprays is Direct Numerical Simulation (DNS) via Volume- of-Fluid (VoF) methods. A noteworthy limitation of this method is its high computational power demand. In the cases of industrial sprays, the total number of computational cells required can be up to a trillion. Consequently, alternative strategies for alleviating the excessive computational burden of a DNS while still preserving a comparable level of solution fidelity are required.

One strategy is the Adaptive Mesh Refinement (AMR) method. The AMR serves to dynamically allocate high-resolution grids in the regions requiring them. Due to such a feature, the AMR is expected to provide a speedup benefit against a traditional static mesh. A detailed analysis of the AMR speedup promise for spray problems is performed. Results show that the envisioned advantage does not hold for high-velocity sprays, and two factors cause it. The first and obvious one is the number of AMR grids, which grows as the calculation proceeds. The second and less apparent factor is the decay of the cell-base speedup, which is related to the Frobenius condition number.

The other engineering approach is to combine VoF and Lagrangian-Eulerian (LE) strategies (VoFLE). In this method, the liquid bodies that local grids can characterize are numerically captured by VoF. The liquid elements that fall below the local mesh resolutions, i.e., unresolved structures, are transitioned into discrete Lagrangian droplets and handled in a LE fashion. We present a new VoFLE method by including the capabilities of computing potential further breakup of unresolved structures. The calculation of breakup is based on Maximum Entropy Formalism (MEF) conditional on the satisfaction of mass, momentum, and energy conservation constraints. Reasonable agreements are shown in the comparison between the predicted mean Sauter mean diameter and the experimental measurements.

Last, further expansion of the VoFLE solver for handling compressibility effect, heat transfer, and Lagrangian droplet vaporization is briefly addressed. This work is ongoing, and more detailed analyses and improvements are planned.