侧墙对中等半径比同心旋转圆柱间Taylor-Couette流的影响——Ⅰ层流涡

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。

Effect of Endwall on Taylor-Couette Flow between Rotating Cylinders:I Iaminar Flow Vortex

Numerical simulation was made to study effect of the endwall on Taylor-Couette flow between the rotating cylinders.The radius ratio of model is 0.83,aspect ratio is 6,Taylor number is between 0 and 357.The inner cylinder is rotating and the outer is stationary.The result of the simulation shows that with no-slip boundary condition at the endwall,the endwall vortexes appear due to the endwall boundary layer below the critical Taylor number,and with the slip boundary condition at the endwall there is no vortex until the Taylor number is above the critical Taylor number.When the Taylor number is between 89 and 112,the maximum radial velocity is about 3% to 4% and 7% to 10% of the surface speed of the inner cylinder respectively with the stationary and the rotating endwalls.And the thickness of endwall boundary layer increases with the increase of the Taylor number when the endwalls are stationary,and it keeps constant when the endwalls are rotating.When the Taylor number is above the critical Taylor number,axial length of the endwall vortex increases or decreases with the increase of Taylor number respectively when the endwalls are stationary and rotating,but with slip boundary condition at the endwall,axial length of the endwall vortex equals approximately the gap of the cylinders.The critical Taylor number from laminar flow vortex to wave vortex with the three kinds of endwall boundary is bigger than that of with the periodic condition.