通过在分数阶拉普拉斯耗散的正则化效应和 Coriolis 力的色散效应之间建立新的平衡,我们证明了三维广义 Navier-Stokes-Coriolis 方程组柯西问题在 Besov 空间中的整体适定性。特别地,当旋转速度足够快时,允许初速度任意大。By striking...通过在分数阶拉普拉斯耗散的正则化效应和 Coriolis 力的色散效应之间建立新的平衡,我们证明了三维广义 Navier-Stokes-Coriolis 方程组柯西问题在 Besov 空间中的整体适定性。特别地,当旋转速度足够快时,允许初速度任意大。By striking new balances between the regularizing effects of the fractional Lapla-cian dissipation and the dispersive effects of Coriolis force, we prove the global well-posedness of Cauchy problem for the three-dimensional generalized Navier-Stokes-Coriolis equations in Besov spaces. Particularly, it is shown that initial velocity can bearbitrarily large provided that the speed of rotation is sufficiently high.展开更多
The vertical centrifugal-casting technique is widely used in the manufacture of various irregularlyshaped castings of advanced structural alloys with thin walls, complex shapes and/or large sizes. These castings are u...The vertical centrifugal-casting technique is widely used in the manufacture of various irregularlyshaped castings of advanced structural alloys with thin walls, complex shapes and/or large sizes. These castings are used in the increasing applications in aero-space/aviation industries, human teeth/bone repairs with nearnet shaped components, etc. In a vertically rotating casting system, the mold-filling processes of alloy melts, coupled with solidification-heat transfer, may be much more complicated, because they are driven simultaneously by gravity, centrifugal and Coriolis forces. In the present work, an N-SNOF-equations-based model, solved using a SOLA-VOF algorithm, under a rotating coordinate system was applied to numerically investigate the impacts of centrifugal and Coriolis forces on metallic melt mold-filling processes in different vertical centrifugal-casting configurations with different mold-rotation rates using an authors＇ computer-codes system. The computational results show that the Coriolis force may cause remarkable variations in the flow patterns in the casting-part-cavities of a large horizontal-section area and directly connected to the sprue via a short ingate in a vertical centrifugal-casting process. A ＂turn-back＂ mold-filling technique, which only takes advantage of the centrifugal force in a transient rotating melt system, has been confirmed to be a rational centrifugal-casting process in order to achieve smooth and layer-by-layer casting-cavities-filling control. The simulated mold-filling processes of Ti-6AI-4V alloy melt, in a vertical centrifugal-casting system with horizontally-connected plate-casting cavities, show reasonable agreement with experimental results from the literature.展开更多
文摘通过在分数阶拉普拉斯耗散的正则化效应和 Coriolis 力的色散效应之间建立新的平衡,我们证明了三维广义 Navier-Stokes-Coriolis 方程组柯西问题在 Besov 空间中的整体适定性。特别地,当旋转速度足够快时,允许初速度任意大。By striking new balances between the regularizing effects of the fractional Lapla-cian dissipation and the dispersive effects of Coriolis force, we prove the global well-posedness of Cauchy problem for the three-dimensional generalized Navier-Stokes-Coriolis equations in Besov spaces. Particularly, it is shown that initial velocity can bearbitrarily large provided that the speed of rotation is sufficiently high.
基金supported by the NNSF of China(key program,grant No.50291012)a National Key Project.
文摘The vertical centrifugal-casting technique is widely used in the manufacture of various irregularlyshaped castings of advanced structural alloys with thin walls, complex shapes and/or large sizes. These castings are used in the increasing applications in aero-space/aviation industries, human teeth/bone repairs with nearnet shaped components, etc. In a vertically rotating casting system, the mold-filling processes of alloy melts, coupled with solidification-heat transfer, may be much more complicated, because they are driven simultaneously by gravity, centrifugal and Coriolis forces. In the present work, an N-SNOF-equations-based model, solved using a SOLA-VOF algorithm, under a rotating coordinate system was applied to numerically investigate the impacts of centrifugal and Coriolis forces on metallic melt mold-filling processes in different vertical centrifugal-casting configurations with different mold-rotation rates using an authors＇ computer-codes system. The computational results show that the Coriolis force may cause remarkable variations in the flow patterns in the casting-part-cavities of a large horizontal-section area and directly connected to the sprue via a short ingate in a vertical centrifugal-casting process. A ＂turn-back＂ mold-filling technique, which only takes advantage of the centrifugal force in a transient rotating melt system, has been confirmed to be a rational centrifugal-casting process in order to achieve smooth and layer-by-layer casting-cavities-filling control. The simulated mold-filling processes of Ti-6AI-4V alloy melt, in a vertical centrifugal-casting system with horizontally-connected plate-casting cavities, show reasonable agreement with experimental results from the literature.
