The present work provides a hybrid numerical–analytical solution through integral transforms for swirling laminar flows of a Newtonian fluid in an end-driven rotating cylindrical cavity. The top-end wall rotates at an angular velocity ω_u, while the bottom-end wall rotates at an angular velocity ω_b, with a fixed sidewall. The Generalized Integral Transform Technique (GITT) is employed to obtain a hybrid solution of the two-dimensional Navier–Stokes equations in the streamfunction-only formulation for steady-state incompressible flow. Results for the velocity components are presented for different aspect ratios (height-to-radius ratio) and Reynolds numbers. The numerical part of the solution is solved through the BVPFD subroutine from the IMSL Library, and the converged results are compared against fully numerical solutions available in the literature, with excellent agreement. In addition, it is shown that the GITT results are in overall agreement with experimental data from the literature. The physical behavior of the computed velocity field is consistent with the experimental flow visualizations regarding position and size of the breakdown bubbles. Finally, the results for both co- and counter-rotation configurations present flow patterns characterized by two symmetric regions that are in accordance with previous findings.

目前的工作通过积分变换为端部驱动旋转圆柱腔中牛顿流体的旋流层流提供了一种混合数值分析解决方案。上端壁以角速度ω _u旋转，下端壁以角速度ω _b旋转，有固定的侧壁。广义积分变换技术 (GITT) 用于在稳态不可压缩流的纯流函数公式中获得二维纳维-斯托克斯方程的混合解。速度分量的结果针对不同的纵横比（高度半径比）和雷诺数呈现。解的数值部分通过来自 IMSL 库的 BVPFD 子程序求解，收敛结果与文献中可用的完全数值解进行比较，具有极好的一致性。此外，还表明 GITT 结果与文献中的实验数据总体一致。计算出的速度场的物理行为与关于破裂气泡的位置和大小的实验流可视化一致。最后，同向和反向旋转配置的结果呈现出以两个对称区域为特征的流动模式，这与先前的发现一致。