Yongqing Zhao | Searcharxiv

arXiv2023

Continuous data assimilation for the three dimensional primitive equations with magnetic field

In this paper, the problem of continuous data assimilation of three dimensional primitive equations with magnetic field in thin domain is studied. We establish the well-posedness of the assimilation system and prove that the $H^2$-strong solution of the assimilation system converges exponentially to the reference solution in the sense of $L^2$ as $t\rightarrow \infty$. We also study the sensitivity analysis of the assimilation system and prove that a sequence of solutions of the difference quotient equation converge to the unique solution of the formal sensitivity equation.

math.AP↗

arXiv2018

Underlying burning resistant mechanisms for titanium alloy

The "titanium fire" as produced during high pressure and friction is the major failure scenario for aero-engines. To alleviate this issue, Ti-V-Cr and Ti-Cu-Al series burn resistant titanium alloys have been developed. However, which burn resistant alloy exhibit better property with reasonable cost needs to be evaluated. This work unveils the burning mechanisms of these alloys and discusses whether burn resistance of Cr and V can be replaced by Cu, on which thorough exploration is lacking. Two representative burn resistant alloys are considered, including Ti14(Ti-13Cu-1Al-0.2Si) and Ti40(Ti-25V-15Cr-0.2Si)alloys. Compared with the commercial non-burn resistant titanium alloy, i.e., TC4(Ti-6Al-4V)alloy, it has been found that both Ti14 and Ti40 alloys form "protective" shields during the burning process. Specifically, for Ti14 alloy, a clear Cu-rich layer is formed at the interface between burning product zone and heat affected zone, which consumes oxygen by producing Cu-O compounds and impedes the reaction with Ti-matrix. This work has established a fundamental understanding of burning resistant mechanisms for titanium alloys. Importantly, it is found that Cu could endow titanium alloys with similar burn resistant capability as that of V or Cr, which opens a cost-effective avenue to design burn resistant titanium alloys.

physics.app-ph↗