AbstractThe turbulent energy cascade in an upward or downward bubbly pipe flow with a Reynolds number of 1.5 × 104 was experimentally investigated in order to examine the effects of the flow direction on the turbulence modifications by bubbles. The bubble diameter was approximately 1 mm. The combination of a particle tracking velocimetry (PTV) system with Kolmogorov-order spatial and temporal resolutions and a shape projection imaging (SPI) system was used to simultaneously capture the liquid and bubble motions. The physical mechanisms of turbulence modification at each length scale, or in wavenumber space, were investigated by introducing a filtering-based scaling analysis, in which the filtering techniques derived from large eddy simulation (LES) were applied to the PTV measurements. The analysis can be used to examine the turbulent kinetic energy (TKE) exchange between bubbles and flows at each wavenumber. We observed significant differences in the flow statistics and turbulent energy budget of upward and downward flows, which are due to the sign of the relative velocity of bubbles. A negative relative velocity (downward flow) induces greater modifications in the energy budget than a positive relative velocity (upward flow), which suggests that the bubble-transport term of the turbulent energy is greater when the flow has to push down the bubbles. The flow provides more energy to the bubbles when it pushes them in the downward direction. The flow will also receive and dissipate more energy from the bubbles in a downward flow compared with an upward flow due to the greater transverse motion of the bubbles. The analysis introduced in the present study shows that the energy transfer from large to small scales is decreased in an upward flow and is increased in a downward flow. Similarly, the sign of the bubble term indicates that turbulent flow receives energy from bubbles in an upward flow, while it transfers energy to bubbles in a downward flow. We also observed that this energy transport is approximately 10 times larger in a downward flow than in an upward flow.
Proton Kinetic Effects and Turbulent Energy Cascade Rate in the Solar Wind
