Droplet trajectory

Droplet trajectories for limiting cases can be calculated by combining the equations of motion with the droplet evaporation rate equation to assess the likelihood that drops exit or hit the wall before evaporating. It is best to consider upper bound droplet sizes in addition to the mean size in these calculations. If desired, an instantaneous value for the evaporation rate constant may also be used based on an instantaneous Reynolds number calculated not from the terminal velocity but at a resultant velocity. In this case, equation 37 is substituted for equation 32 ... 

Oil Burners The structure of an oil flame is shown in Fig. 27-28, and Fig. 27-29 illustrates a conventional circiilar oil burner for use in boilers. A combination of stabilization techniques is used, typically including swirl. It is important to match the droplet trajectories to the combustion aerodynamics of a given burner to ensure stable ignition and good turndown performance. 

This is an important scaling consideration as the spray momentum is a controlling factor in the droplet trajectories. 

In the Lagrangian frame, droplet trajectories in the spray may be calculated using Thomas 2-D equations of motion for a sphere 5791 or the simplified forms)154 1561 The gas velocity distribution in the spray can be determined by either numerical modeling or direct experimental measurements. Using the uncoupled solution approach, many CFD software packages or Navier-Stokes solvers can be used to calculate the gas velocity distribution for various process parameters and atomizer geometries/configurations. On the other hand, somesimple expressions for the gas velocity distribution can be derived from... 

For agiven system of metal/alloy and atomization gas, the 2-D velocity distributions of the gas and droplets in the spray can be then calculated using the above-described models, once the initial droplet sizes and velocities are known from the modeling of the atomization stage, as described in the previous subsection. With the uncoupled solution of the gas velocity field in the spray, the simplified Thomas 2-D nonlinear differential equations for droplet trajectories may be solved simultaneously using a 4th-orderRunge-Kutta algorithm, as detailed in Refs. 154 and 156. 

Figure 5.7. Comparison of numerical modeling to high-speed video imaging of droplet trajectories in the spray during spray forming. Left, calculated droplet trajectories Right, high-speed video imaging of an actual spray. (Courtesy of Prof. Dr.-Ing. Klaus Bauckhage at University of Bremen, Germany.)...

Figure 16.6 Probability distributions for droplet trajectory angles at z = 10 mm at the spray centerline (left column) and spray boundary at r = 6.4 mm (right column) for (a) steam, (6) preheated air, and (c) normal air. I — D32 = 57.8 /rm, u = 17.383 m/s,...

Hall and Diederichsen (22) projected a stream of droplets (diameters 150 to 170 microns) from the periphery of a spinning disk up into a vertical furnace maintained at a sufficiently high temperature for ignition, 710° C. The spinning disk atomizer employed was capable of producing droplets of uniform, predetermined size. Drum photographic records were obtained of the luminous portion of the droplet trajectory and drop burning times were estimated therefrom. 

Spilhaus 8P) treats the shape of falling drops and the variation of the drag coefficient. Langmuir and Blodgett 6P) present a mathematical investigation of water droplet trajectories. 

The termination of droplet trajectories by a "micro-explosion" of this nature was observed for all of the synthetic fuels and fuel blends tested, but did not occur for the petroleum derived No. 6 oil. With this latter fuel, droplets were seen to bum to extinction and to result in the formation of a carbonaceous residue, usually in the form of cenospheres. The termination of individual droplets was observed, therefore, to be strongly dependent upon fuel type and could be characterized by three distinct types of behavior 1) large (1 mm) micro-explosions with a distinctly directional behavior (SRC process donor solvent blend), 2) smaller micro-explosions (SRC-II middle, heavy, middle/ heavy blend, DFM), and 3) carbonaceous residue formation (Indones-ian-Malaysian No. 6) without micro-explosions. High speed photographs show the micro-explosions to occur in a time span much faster than the camera framing rate (1/5000 sec). 

In addition to visual observations of a qualitative nature, a number of detailed sampling traverses were made to determine particulate and gaseous species concentrations within the soot sheet. The nature of the sampling system employed results in the sampled solid material being composed largely of soot since ceno-spheres and heavy solid material follow the droplet trajectories and are not captured by the probe. 

This model explains so the variety of droplet trajectories that can be met in real spraying systems. 

Langmuir, J. and Blodgett, K., Mathematical Investigation of Water Droplet Trajectories, Gen. Elec. Comp. Rep., July, 1945... 

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