| A submerged vertical plane jet impinging onto free water surface will be excited into a flappingoscillation when the jet velocity, exiting the jet orifice, exceeds a critical value. The study on flappingmotion will provide a physical insight into the understanding of the mechanism of flapping motionand will be helpful for flow control and efficient mixing. Previous findings on flapping motion weremainly based on experiments and lacked detailed characterizations of this complex flow. In this paper,numerical investigations of free plane jet and impinging plane jet with flapping motion have beencarried out. The purpose of this study is to better understand the instability of free jet and the complexflow of flapping impinging jet.Firstly, a free plane jet at low Reynolds numbers has been investigated based on latticeBoltzmann method. Results show that there exist two flow states dependent on a critical Reynoldsnumber Recr. One is a stable flow state when Re<Recr, and the other is a flow state with periodicoscillation when Re>Recr. Due to the existence of periodic oscillation, the decay of mean centerlicevelocity is considerable faster than that of the steady jet. For the state of periodic oscillation, theproper orthogonal decomposition analysis of the steamwise velocity illustrates that the dominatedmode shows antisymmetric structure. With the increase of Reynolds number, the straining motiongradually dominates, which is a key issue associated with the jet instability.Secondly, the flapping motion of plane jets at low and moderate Reynolds numbers has beeninvestigated based on the free energy lattice Boltzmann method and large eddy simulation-VOFmethod. On the basis of reproducing the experimental phenomenon, the flapping motion has beenfurther characterized in detail in the present study. The feasibility of employing free energy latticeBoltzmnan method and large eddy simulation-VOF method to simulate flapping motion is verified bycomparing simulation results with experimental results.Results show that there exist two flow states for plane impinging jet. One is a stable flow state,and the other is a flow state with flapping motion. Compared with stable impinging jet, the meancenterline velocity decay is considerably faster and the entrainment rate is obviously higher forflapping impining jet, which will be beneficial for the enhancement of bulk mixing. The frequencycharacteristics for flapping flow state are obtained. The frequency of longitudinal velocity oscillationat the jet centerline is found twice of that of the transverse oscillation. Meanwhile, the surfacedisplacements of water surface oscillate with the same frequency as the flapping jet. The complex interactions of vortex/free water surface, vortex/jet shear layer and vortex/vortex give rise to higherturbulence fluctuations and larger momentum thickness in the near field region of flapping jet. Theflapping-induced velocity components are discussed. It is found that the flapping-induced velocitiesmagnitudes are as important as the turbulence fluctuations. The influence of dimensionless parameterson the flow pattern of submerged impinging jet has been discussed for different Froude numbers,Reynolds numbers and Weber numbers. It is found that Froude number could be used as a keyparameter for the onset of flapping motion. |
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