| Droplet collision, as one of liquid fluid dynamics, is ubiquitous in nature and moderntechnology industry, such as raining, waterfall, atomization and spray of liquid fuel in internalcombustion engines and aero engines. As one of multi-physics of combustion and fluid flowin solid rocket motors with aluminized propellant, alumina droplet collisions have a greatinfluence on the ablation of internal insulation, nozzle erosion, slag accumulation insubmerged nozzles, as well as combustion instability. In order to understand all the details ofinternal flow field of the motors, guaranteeing the reliability, stability and efficiency, it isessential to study alumina droplet collisions and model it for large scale simulations.In the present work, direct numerical simulations have been performed by employing avolume of fluid method for tracking the interface and an adaptive mesh method for improvingthe calculation efficiency. First, the head-on and off-center binary collisions of tetradecanedroplet have been simulated with axisymmetric and3D method. And the results are in goodagreement with the experiments, which validates the accuracy of the present numericalmethod. Next, simulations of head-on and off-center binary collision of alumina droplets withequal-sized are carried out. The We-B map of the binary collision outcomes of aluminadroplets is captured, and the physics of different outcomes are presented. Besides, the head-oncollisions with different alumina droplet diameters, diameter ratios and gas pressures arenumerically investigated. Combining the numerical results with theoretical analysis, theeffects of above three factors and combustion temperature on the alumina droplet collisionsare obtained. Finally, alumina droplet collisions are modeled on the basis of physics of dropletcollision and the present numerical results. The major conclusions of this dissertation are asfollows:(1) For equal-sized alumina droplet collisions at D0=10μm, Oh=0.1151, We=1~800, B=0.1~0.7, six different outcomes are obtained: bouncing (II), coalescence after substantialdeformation (III), reflexive separation without satellite (IV), reflexive coalescence after a longextension (V), reflexive separation with satellites (VI), and stretching separation (VII). Sincethe van der Waals force model is not embedded in the present method, the coalescence afterminor deformation (I) cannot be captured. For head-on collisions, the critical Weber numbersduring outcome (II),(III),(IV),(V),(VI) are40,239,318,355, respectively. The outcome ofhead-on collisions at We>355is reflexive separation with satellites. At355<We <500, the mechanism of separation is end-pinching mechanism, and the collision results in three similardroplets. While collisions at We>600, the mechanism of separation is capillary waveinstability mechanism, inducing several different small droplets. For off-center collisions at B=0.1,0.3,0.4,0.5, the critical Weber numbers between outcome (II) and (IV) or (VII) are307,224,94,59, respectively. Moreover, the deformation processes and physics of outcomes arediscussed by analyzing droplet deformations and energies.(2) For equal-sized alumina droplets with diameters D0=10μm,100μm,200μm, theOhnesorge number is0.1151,0.0364,0.0257. The bouncing critical Weber numbers afterhead-on collisions are40,26and25, respectively. And the critical Weber numbers ofreflexive separation after head-on collisions are239,45and34, respectively. The changes ofdroplet diameter and propellant combustion temperature mainly affect the Ohnesorge numbersof droplets. With the decrease of droplet diameter, the Ohnesorge number increases, and thecritical Weber numbers of bouncing and reflexive separation gradually get larger, whichresults in the slight increase of bouncing area and greatly extension of coalescence area, andreflexive separation only happens at high Weber number. While increasing the propellantcombustion temperature, the Ohnesorge number decreases, and the decreasing rate getssmaller as well. The result is that the critical Weber numbers of bouncing and reflexiveseparation gradually get smaller, leading to the decrease of bouncing area and greatlylessening of coalescence area, and reflexive separation area moves to low Weber number. It iseasier to happen for droplet breakup. For equal-sized droplet collisions, the Ohnesorgenumber determines the outcome distributions in We-B map and the critical Weber numbers.While the Weber number and impact parameter determine the deformation process and resultof collision. The Ohnesorge number can be the parameter of similarity criteria for studyingequal-sized droplet collisions. Besides, The critical Weber number model of Gotaas et al.[110]can be used to predict the critical Weber number of reflexive separation of binary collision ofalumina droplets with equal-sized.(3) Unequal-sized alumina droplets with γ=1,2,3and small diameter10μm, after head-oncollisions, the bouncing critical Weber numbers are40,26and21, respectively, and thecritical Weber numbers of reflexive separation are239,267and390, respectively. Thedeformations of unequal-sized droplets are totally different from the equal-sized droplets.With the increase of diameter ratio γ, the difference of droplets increases, causing that thebouncing area decreases and the coalescence area greatly expands. The area of reflexive separation moves to the high Weber number.(4) Under the pressure3,6,9MPa, equal-sized alumina droplets with diameter100μm, afterthe head-on collisions, the bouncing critical Weber numbers are28,26and26, respectively,and the critical Weber numbers of reflexive separation are48,45and45, respectively. Underthe low pressure (≤11.7atm), with increasing the pressure, the bouncing critical Webernumber gradually gets larger. However, under high pressure (≥3MPa), pressure has noinfluence on the collision and bouncing critical Weber numbers of alumina droplets.Furthermore, reflexive and stretching separations are not affected by the pressure either.(5) Combined physics of different outcomes with theoretical analysis of energy anddeformation of droplet collision, alumina droplet collisions are modeled with numericalresults and considing viscous dissipation, including model of coalescence after minordeformation, bouncing model, reflexive separation model, stretching separation model, aswell as model for calculating droplet parameters after separation. |
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