Spectral Analysis of Single- and Two-Phase Bubbly DNS in Different Geometries

The spectral analysis of turbulent single- and two-phase direct numerical simulation (DNS) data in flat plane channel, circular pipe, and reactor subchannel geometries is performed using the recorded DNS velocity fluctuations as a function of time and applying the fast Fourier transform. This results in an energy spectrum of the liquid turbulence in a frequency domain. The complexity of multiphase flow results in a mixed velocity time history coming from either the liquid or the gas phase. A modified single-phase signal that mimics the presence of bubbles ("pseudo-void') is developed to quantify the effect of the liquid signal intermittency as the bubble passes through a virtual probe. Comparisons of single-phase, pseudo-void, and two-phase results quantify the changes to the expected -5/3 slope of the energy spectrum for single-phase flows due to turbulent interactions caused by the wakes behind a bubble. The two-phase energy spectra show a slope close to 3 and similar shape in the different geometries while single-phase energy spectra exhibit the expected -5/3 slope. Pseudo-void results indicate that the change to the energy spectrum in bubbly two-phase flows is due entirely from liquid turbulence interactions with the bubble wakes. A comprehensive spectral analysis for different geometries and different Reynolds number flows at varying distances from the wall is an essential step in developing physically sound closure models for bubble-liquid interactions. The comparison between different geometries demonstrates the direct applicability of various models to reactor-relevant geometries.