Investigation On Characteristics Of Droplet Breakup Dynamics

Fuel spray in engines is a multi-phase,multi-scale and strongly nonlinear process which contains a series of microscopic phenomena such as the initial breakup of liquid jet,secondary breakup of droplets,droplet collision,wall impingement,and droplet evaporation.?ntrinsically,the macroscopic characteristics of spray are determined by these microscopic processes.A good knowledge of spray is of great importance for the development of high-efficiency and clean combustion.?n the present study,the breakup dynamics of a single droplet is studied numerically and theoretically.Furthermore,the study is extended to the interaction of droplet pair,considering droplet cloud behaviors in spray.Based on the open source code OpenFOAM,a simple coupled volume-of-fluid and level-set?S-CLSVOF?model is implemented,and the present numerical method based on the solution of the Navier-Stocks equations and S-CLSVOF model is tested by several typical two-phase problems.Results indicate that the present numerical method is able to capture the interface position and flow with high accuracy;furthermore,verification of the numerical method against experiment results and grid independency analysis are conducted on several breakup modes,in combination of the adaptive mesh refinement?AMR?technique.The results show that the present numerical method can effectively simulate the complex breakup modes.The sheet-thinning breakup of droplets is investigated based on the present numerical method and the AMR technique.The results show that the drag coefficient of droplets is determined by the recirculation due to the flow separation at the periphery of droplets.A stronger flow separation results in a larger recirculation,corresponding to a higher drag coefficient;the liquid-gas density ratio has a non-monotonic effect on the droplet deformation,which depends on the unstable conditions?We,Re?.?n highly unstable conditions?We>200,?,a lower density ratio results in a higher deformation rate and larger breakup structures,while a larger density ratio results in finer fragmentation;a qualitative relationship between the density ratio and the sheet-thinning instability is presented for droplets,indicating that the cross-stream thickness of droplets is relevant to the initial velocity of gas flow,droplet acceleration,and density ratio.The transition between various breakup modes is further studied.Considering the insufficiency of the experimental data of transition study for a high Oh number,the transitions of deformation/squeezing-bag breakup and bag to bag-stamen breakup modes for liquid droplets are studied numerically over a wide range of Oh up to 2.Based on the present simulation results,theoretical model based on Rayleigh-Taylor instability is further developed.The results show that the transition behaviors are directly determined by the ratio of the cross-stream diameter of the flattened droplet to the wavelength of most unstable RT wave?Df/?RT?.When the transition occurs,D_f/D₀ is almost independent of Oh number?a higher Oh corresponds to a larger We?;both D_f/D₀ and D_f/?_RTT should exceed the corresponding critical values for a transition.At low Oh numbers?Oh<0.1?,the bag and bag-stamen breakup begin at about We=9 and 15,respectively.The values of D_f/?_RT according to the formula ?_RT=2??3??/??₁a??1/2?for the transition ? and ? are in good agreement with present theoretical model;in a wide range of Oh numbers[0.001,2],the present theoretical model predicts the criticalities of the transition ? and ? with a higher accuracy by including the combined effect of the surface tension and viscosity simultaneously.By recognizing that spray is essentially droplet cloud behavior,which includes abundant interaction between droplet pairs,the interaction between the droplet shape and flow structure is studied under various breakup modes and the relative position of droplet pair.The results indicate that the interactions vary by the relative position of droplet pair.Specifically,the shearing between the high-speed flow of the gap between droplet pair and the merged recirculation is mainly the interaction for the droplet pair moving side by side.The smaller initial center distance?L=2,4D0?may lead to a repulsion between the droplet pair,and the larger initial center distance?L=6,8D0?results in an attraction of effect;for the tandem droplet pair,a smaller initial center distance may leads to a lower drag coefficient of the downstream droplet,and a higher drag coefficient of the upstream droplet due to the increase of recirculation;the interaction for the oblique case is complex:for the moderate initial center distance?L=4 D0,6D0?,the two droplets restrain each other due to their strong competition of recirculation and the drag coefficients of the droplet pair are less than or close to that of the single droplet case.?n contrast,for the case of L=8D0,the significant difference between the flow structures results in a higher drag coefficient of the upstream droplet than that of the single droplet case,and a lower one of the downstream droplet than that of the single droplet case.Furthermore,the increase of We number promotes the tendency described above.For the case of L=2D₀,the flow structures of the droplet pair are restricted,and the drag coefficients are lower than that of the single droplet case.