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<p>Direct numerical simulation is used to investigate the subcritical transition to turbulence in the counter-rotating Taylor-Couette configuration of axial aspect ratio of Γ = H/(R<sub>2</sub>-R<sub>1</sub>) = 4.7 and radius ratio η = R<sub>1</sub>/R<sub>2</sub> = 0.9 with the end-walls attached to the inner cylinder (the narrow gap flow case, R<sub>1</sub>, R<sub>2</sub> are radii of the inner and outer cylinder, H is the cylinders height). In all considered Taylor-Couette flow cases Reynolds number of the inner cylinder Re<sub>1</sub> = Ω<sub>1</sub>R<sub>1</sub>(R<sub>2</sub>-R<sub>1</sub>)/ν is increased along the Re<sub>1</sub> = Re<sub>2</sub> η/(Ω<sub>2</sub>/Ω<sub>1</sub>)&#xa0; line to reach ‘featureless turbulence’ area (Ω<sub>1</sub>,&#xa0;Ω<sub>2</sub>&#xa0;are angular velocities of the inner and outer cylinders, Re<sub>2</sub> = Ω<sub>2</sub>R<sub>2</sub>(R<sub>2</sub>-R<sub>1</sub>)/ν). Starting from this area the reduction of Re<sub>1</sub> is performed with the fixed Re<sub>2</sub> (Re<sub>2</sub> from − 1000 up to − 500). This leads finally to the appearance of aperiodic flow featuring interpenetrating spirals, and then to the Couette flow. For comparison, the computations are also performed for the wide gap flow case of η = 0.8 (Re<sub>2</sub> from − 1500 to − 500). In the (Re<sub>2</sub>, Re<sub>1</sub>) plane, the obtained turbulent-laminar critical line (η = 0.9) is located bellow the critical lines published in literature: bellow critical line obtained from the linear stability theory and bellow this obtained for the configuration with the end-walls attached to the outer cylinder. The results show the destabilizing influence of the end-walls attached to the inner cylinder on the flow dynamics. The radial profiles of the Reynolds stress tensor components illustrate quantitatively the changes occurring in the flow dynamics during considered processes. The Power Spectrum Density distributions are presented. The studied processes are visualized using the λ<sub>2</sub> method.</p>

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DNS of the shear flows between two counter-rotating cylinders, radius ratio eta = 0.9

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  • 发表日期：

    2025年10月2日

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  • Ewa Tuliszka-Sznitko

摘要

Direct numerical simulation is used to investigate the subcritical transition to turbulence in the counter-rotating Taylor-Couette configuration of axial aspect ratio of Γ = H/(R2-R1) = 4.7 and radius ratio η = R1/R2 = 0.9 with the end-walls attached to the inner cylinder (the narrow gap flow case, R1, R2 are radii of the inner and outer cylinder, H is the cylinders height). In all considered Taylor-Couette flow cases Reynolds number of the inner cylinder Re1 = Ω1R1(R2-R1)/ν is increased along the Re1 = Re2 η/(Ω2/Ω1)  line to reach ‘featureless turbulence’ area (Ω1, Ω2 are angular velocities of the inner and outer cylinders, Re2 = Ω2R2(R2-R1)/ν). Starting from this area the reduction of Re1 is performed with the fixed Re2 (Re2 from − 1000 up to − 500). This leads finally to the appearance of aperiodic flow featuring interpenetrating spirals, and then to the Couette flow. For comparison, the computations are also performed for the wide gap flow case of η = 0.8 (Re2 from − 1500 to − 500). In the (Re2, Re1) plane, the obtained turbulent-laminar critical line (η = 0.9) is located bellow the critical lines published in literature: bellow critical line obtained from the linear stability theory and bellow this obtained for the configuration with the end-walls attached to the outer cylinder. The results show the destabilizing influence of the end-walls attached to the inner cylinder on the flow dynamics. The radial profiles of the Reynolds stress tensor components illustrate quantitatively the changes occurring in the flow dynamics during considered processes. The Power Spectrum Density distributions are presented. The studied processes are visualized using the λ2 method.