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对有限长中等半径比同心旋转圆柱间Taylor-Couette流进行了数值计算,以研究侧墙对Taylor-Couette流的影响。圆柱的半径比为0.83,形状比为6,泰勒数在0~357之间。内圆柱旋转,外圆柱静止。数值计算结果表明,在无滑移侧墙边界条件下,在泰勒数低于临界泰勒数时,在侧墙边界层的作用下侧墙附近出现侧墙涡,而在滑移侧墙边界条件下,直到泰勒数大于临界泰勒数,轴间才出现明显的涡流。当泰勒数处在89~112之间,侧墙静止和侧墙旋转时产生的最大径向速度分别约为内筒表面线速度的3%~4%和7%~10%。侧墙静止时,随着泰勒数的增加,边界层的厚度也随之递增。侧墙旋转时,边界层厚度基本不变。在泰勒数大于临界泰勒数时,随着泰勒数的增加,侧墙静止和侧墙旋转时侧墙涡的轴向长度分别增加和减少,在滑移边界条件下,侧墙涡的轴向长度约等于轴间距。在3种侧墙边界条件下,层流涡向波动涡转捩的临界泰勒数变大。
The Taylor-Couette flow between a finite length medium radius and a concentric rotating cylinder is numerically calculated to study the effect of the sidewall on the Taylor-Couette flow. The radius ratio of the cylinder is 0.83, the shape ratio is 6, and the Taylor number is between 0 and 357. Cylindrical rotation, the outer cylinder stationary. The numerical results show that the sidewall vortex appears near the sidewall under the action of the sidewall boundary layer when the Taylor number is lower than the critical Taylor number under the condition of no-slip sidewall boundary, while under the condition of the sliding sidewall boundary Until the Tyler number is greater than the critical Taylor number, there was a significant eddy between the axis. When the Tyler number is between 89 and 112, the maximum radial velocities produced when the side wall is stationary and the side wall rotates are respectively about 3% -4% and 7% -10% of the linear velocity of the inner cylinder surface. As the sidewalls quiesce, as the Taylor number increases, the thickness of the boundary layer also increases. When the side wall is rotated, the boundary layer thickness is basically unchanged. When the Taylor number is greater than the critical Taylor number, the axial length of the sidewall vortex increases and decreases with the Taylor number increasing and the sidewall rotation decreasing. Under the slip boundary conditions, the axial length of the sidewall vortex About equal to the shaft spacing. Under the condition of three kinds of side wall boundary conditions, the critical Taylor number of laminar eddy fluctuation eddy 捩 becomes larger.