Investigation of unsteady liquid nitrogen cavitating flows with special emphasis on the vortex structures using mode decomposition methods

Abstract

• Liquid nitrogen cavitating flows in a C-D nozzle were simulated by LES. • Thermal effects on the unsteady cavitation dynamics were investigated. • Vorticity transport equation was utilized to analyze the vortex structures and shedding dynamics. • Coherent structures and corresponding frequencies were investigated by mode decomposition methods. This paper presents the large-eddy simulations with significant thermal effects to investigate the evolution of cavitation dynamics in liquid nitrogen cavitating flows with special emphasis on the vortex dynamics and coherent structures. The liquid nitrogen cavitating flows in the converging-diverging nozzle under different flow conditions were numerically investigated and verified by the experimental data. The thermal effects on cavity structures and shedding dynamics were investigated by comparing the thermal and isothermal calculations. The cavitation dynamics of two typical thermal cavitation modes (the inertial mode and the thermal mode) were analyzed based on the temporal-spatial behaviors, the Fast Fourier Transformation (FFT), the Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) methods. The results show that: (1) The thermal effects could enhance the magnitude of the vorticity gradient inside the cavity. The detachment of the small-scale cavity is affected by the great vorticity gradient under the thermal condition. (2) For the inertial mode, the cloud cavity detaches due to the re-entrant jet and soon collapses, while for the thermal mode, the small-scale cloud cavity collapses slowly and the co-existing cloud cavities are observed. Three kinds of characteristic frequency for the inertial mode and thermal mode are obtained based on the temporal-spatial distribution of vapor volume fraction and the FFT analysis of the cavity area. The FFT power of the characteristic frequency for the single attached cavity process is not significant. This is because the cavity area processed by FFT cannot distinguish the attached cavity and the shedding cloud cavity. The characteristic frequencies in the thermal mode are much larger than those in the inertial mode. (3) The coherent structures of POD and DMD for the inertial mode and the thermal mode consist of the counter-rotating structures. The first four POD modes contribute more than 70% of the total energy. The first three modes with high energy obtained by the POD method have low frequencies. The locations of POD Mode 1 with the most energetic structure for two thermal cavitation modes are significantly different. The DMD algorithm can consistently extract the characteristic frequency for the single attached cavity process. The DMD modes with high frequency are characterized by the fragmented counter-rotating structures due to the co-existing shedding of cloud cavities, especially for the thermal mode. The obtained results between the inertial mode and the thermal mode including cavitation dynamics, frequency characteristics and corresponding coherent structures provide a reference for better understanding the cavitating flows in practical engineering applications.