Global solutions for a hyperbolic model of multiphase flow

Author(s):  
Debora Amadori ◽  
Andrea Corli
Author(s):  
Fuyi Xu ◽  
Xinliang Li

In this paper, we are concerned with the study of the Cauchy problem for a parabolic–hyperbolic model arising from chemotaxis in any dimension [Formula: see text]. We first prove the global existence of the model in [Formula: see text] critical regularity framework with respect to the scaling of the associated equations. Furthermore, under a mild additional decay assumption involving only the low frequencies of the data, we also establish the time-decay rates for the constructed global solutions. Our analyses mainly rely on Fourier frequency localization technology and on a refined time-weighted energy inequalities in different frequency regimes.


2020 ◽  
Vol 117 (6) ◽  
pp. 619
Author(s):  
Rui Xu ◽  
Haitao Ling ◽  
Haijun Wang ◽  
Lizhong Chang ◽  
Shengtao Qiu

The transient multiphase flow behavior in a single-strand tundish during ladle change was studied using physical modeling. The water and silicon oil were employed to simulate the liquid steel and slag. The effect of the turbulence inhibitor on the slag entrainment and the steel exposure during ladle change were evaluated and discussed. The effect of the slag carry-over on the water-oil-air flow was also analyzed. For the original tundish, the top oil phase in the impact zone was continuously dragged into the tundish bath and opened during ladle change, forming an emulsification phenomenon. By decreasing the liquid velocities in the upper part of the impact zone, the turbulence inhibitor decreased considerably the amount of entrained slag and the steel exposure during ladle change, thereby eliminating the emulsification phenomenon. Furthermore, the use of the TI-2 effectively lowered the effect of the slag carry-over on the steel cleanliness by controlling the movement of slag droplets. The results from industrial trials indicated that the application of the TI-2 reduced considerably the number of linear inclusions caused by ladle change in hot-rolled strip coils.


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