scholarly journals Improved Bounds for Geometric Permutations

2012 ◽  
Vol 41 (2) ◽  
pp. 367-390 ◽  
Author(s):  
Natan Rubin ◽  
Haim Kaplan ◽  
Micha Sharir
Author(s):  
Wayne Strasser

Past work involving validated “cold-flow” CFD modeling of self-generating and self-sustaining pulsating transonic non-Newtonian slurry atomization elucidated acoustic signatures, atomization mechanisms, and the effects of numerics and geometric permutations. The numerical method has now been incorporated with exothermic oxidation reaction kinetics relations along with radiation, i.e. no longer cold-flow. These models provide substantially increased model rigor and allow for new pulsing thermal measures which help assess injector thermal stresses. Twelve models have been run for extended periods of time in order to assess the effects of dramatic changes in gas feed rate and prefilming (retraction) length. Given the new metrics and models, multiple statistically optimized designs are potentially available depending on the objective function(s) and their relative weightings in the overall value proposition to the project. In the case in which all metrics have equal value to the project and are simultaneously considered in a statistical model, the optimum design involves a mid-level of retraction and a mid-level gas feed rate. If, however, more relative weighting is placed on the importance of droplet size minimization and injector thermal management in lieu of feed passage pressure drop minimization, the optimum design involves a similar retraction but a very high level of gas feed rate.


Author(s):  
Wayne Strasser

The performance of a rather large-scale self-exciting coaxial three-stream airblast injector was studied experimentally and computationally by Strasser (International Journal of Multiphase Flow, 2010). Changes in the relative flow of the inner gas stream produced measurable responses in transient behavior and spray pattern. Particularly, above an inner gas momentum ratio of about 0.2, a transition occurred from a repeatable bursting pattern to one that exhibited a wide range of bursting events. In addition, the spray pattern shifted from unimodal to polymodal. Frequency domain analyses revealed distinct changes in the inner and outer air stream pulsations as a function of air feed rates. Since that work, efforts have progressed in studying the effects of injector geometry on spray characteristics and pulsating flow field response. Geometric features considered included inner nozzle retraction, stream meeting angle, outer annulus gap, and nozzle diameters. Changes to retraction produced the most profound, but not always monotonic, responses in the energy content and nature of the spray pattern. A flushed design was shown to have the strongest pressure pulsations, as well as having the spray bursts moved the farthest downstream of the injector, but only when the angle was moderate. Increases in the other geometric values also moved the ligament formation downstream and reduced the pre-filming dominant frequencies. In general, the time-averaged spray profiles were trimodal in shape and were focused or diffused by geometric permutations. The frequency responses of ligament production and feed pressures did not necessarily coincide; however, all but the highest retraction case exhibited frequencies that were multiples of approximately 200 Hz.


1987 ◽  
Vol 65 (3) ◽  
pp. 249-259 ◽  
Author(s):  
M. Katchalski ◽  
T. Lewis ◽  
A. Liu

1996 ◽  
Vol 75 (2) ◽  
pp. 187-197 ◽  
Author(s):  
Jacob E. Goodman ◽  
Richard Pollack ◽  
Rephael Wenger

2011 ◽  
Vol 59 (3-4) ◽  
pp. 327-347
Author(s):  
Johannes Böhm

2001 ◽  
Vol 11 (02) ◽  
pp. 239-242
Author(s):  
JOSEPH O'ROURKE

The recent result that n congruent balls in ℝd have at most 4 distinct geometric permutations is described.


1986 ◽  
Vol 1 (4) ◽  
pp. 371-377 ◽  
Author(s):  
M. Katchalski ◽  
T. Lewis ◽  
A. Liu

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