Nonlinear axisymmetric Taylor–Couette flow in a dilute gas: multiroll transition and the role of compressibility
Nonlinear axisymmetric Taylor–Couette flow in a dilute gas: multiroll transition and the role of compressibility
复制标题
稀气体中的非线性轴对称泰勒-库埃特流动：多辊转变和压缩性的作用
DOI：
10.1017/jfm.2020.897
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发表时间：
2020
影响因子：
3.7
通讯作者：
Meheboob Alam
中科院分区：
文献类型：
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作者：
Pratik Aghor;Meheboob Alam
本文数值求解了具有旋转内柱和静止外柱的理想气体的轴向有界Taylor-Couette流(TCF)的可压缩Navier-Stokes-Fourier方程，以了解可压缩性和有限长宽比对非线性Taylor涡产生的作用及相关的分叉情况。在宽间隙极限中轴对称情况下，长径比$\varGamma=h/\Delta$(其中$\Delta$是两个圆柱体之间的环形间隙，$h$是圆柱体的高度)通过改变圆柱体的高度准静态地改变，遵循Benjamin(Proc.R.Soc.朗德。A，第359卷，1978b，第27-43页)。对称的偶数($2，4，6，1点)涡旋在$varGamma\geq2$处被发现，而破坏中面$Z_2}$对称性的非对称双滚模(称为单滚模或反常模)在$varGamma\leq O(1)$处被发现。在($\varGamma，Re$)平面上确定了对称和非对称轧辊的相边界以及不同轧辊数量的共存区域。在有限马赫数($Ma)下，将这些相图以及相关的分叉图和各种模式与它们的不可压缩($Ma\to 0$)类似物进行了对比。结果表明，在可压缩TCF中，小长宽比圆柱体中的‘$1\leftrihtarrow 2$’滚转转变是亚临界的，而不可压缩圆柱中的分叉是超临界的。一般情况下，气体的可压缩性对非线性Taylor涡有稳定作用，因为($\varGamma，Re$)平面上的基本相图随着$Ma的增加而向更大的$Re$移动。可压缩性的稳定作用可以与向外喷流的减弱有关，而随着马赫数的增加，Ekman涡的增强则进一步帮助了这一作用。
Abstract The compressible Navier–Stokes–Fourier equations are numerically solved for axially bounded Taylor–Couette flow (TCF) of an ideal gas, with rotating inner cylinder and stationary outer cylinder, to understand the roles of compressibility and finite aspect ratio on the genesis of nonlinear Taylor vortices and the related bifurcation scenario. Restricting to the axisymmetric case in the wide-gap limit, the aspect ratio $\varGamma =h/\delta$ (where $\delta$ is the annular gap between two cylinders and $h$ is the height of the cylinders) is changed quasistatically by varying the height of the cylinders, following the experimental protocol of Benjamin (Proc. R. Soc. Lond. A, vol. 359, 1978b, pp. 27–43). The symmetric even-numbered ($2,4,6,\ldots$) vortices are found at $\varGamma \geq 2$, whereas the asymmetric 2-roll modes (called the single-roll or ‘anomalous’ modes), that break the midplane $Z_{2}$-symmetry, are uncovered at $\varGamma \leq O(1)$. The phase boundaries of both symmetric and asymmetric rolls and the coexisting regions of different number of rolls are identified in the ($\varGamma , Re$)-plane. These phase diagrams, along with related bifurcation diagrams and various patterns, at finite Mach numbers ($Ma$) are contrasted with their incompressible ($Ma\to 0$) analogues. It is shown that the ‘$1\leftrightarrow 2$’-roll transition in small aspect ratio cylinders is subcritical in compressible TCF in contrast to the supercritical nature of bifurcation in its incompressible counterpart. In general, the gas compressibility has a stabilizing effect on nonlinear Taylor vortices as the underlying phase diagrams in the ($\varGamma , Re$)-plane are shifted to larger values of $Re$ with increasing $Ma$. The stabilizing role of compressibility can be tied to the weakening of the outward jets, which is further aided by the strengthening of the Ekman vortices with increasing Mach number.
DOI：
--
发表时间：
2018
期刊：
影响因子：
--
作者：
Takafumi Akahori;Slim Ibrahim;Hiroaki Kikuchi;Hayato Nawa;Reika Aoyama and Yoshiyuki Kagei;名和 範人;名和 範人;Yoshiyuki Kagei and Naoki Makio;名和 範人;Yoshiyuki Kagei and Kazuyuki Tsuda;Yoshiyuki Kagei
通讯作者：
Yoshiyuki Kagei