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高雷诺数粘弹性展向旋转平板Couette流动的流态转捩研究

TRANSITIONS IN HIGH-REYNOLDS-NUMBER VISCOELASTIC SPANWISE-ROTATING PLANE COUETTE FLOW

  • 摘要: 流态转捩问题一直是流体力学研究的重点之一.在粘弹性流体湍流中, 聚合物添加剂通过引入额外的弹性效应, 可显著改变流动状态, 导致截然不同于牛顿湍流的转捩现象.本研究针对粘弹性展向旋转平板Couette流动(RPCF), 结合FENE-P模型描述聚合物应力与构型张量间的本构关系, 采用三维并行谱方法进行直接数值模拟.通过固定高雷诺数(Re = 5200)和弹性效应, 进而改变旋转数(Ro = 0 ~ 1), 研究了旋转效应驱动的粘弹性RPCF流态转捩现象, 揭示了一条完全不同于牛顿湍流的转捩路径.结果表明, 转捩路径开始于减阻的惯性主导湍流( 0\leqslant Ro< 0.12 ), 途径增阻的惯性主导湍流( 0.12\leqslant Ro< 0.24 ), 最后到达增阻的弹性主导湍流( 0.24\leqslant Ro\leqslant 1 ). 对阻力特性的研究发现, 聚合物会通过抑制雷诺应力的产生进而降低湍流度, 而引入的聚合物应力又作为一个增阻源项, 这两种效应的耦合带来了丰富的阻力变化. 通过考察湍流场和粘弹性应力场的能量输运揭示了具有普适性的粘弹性RPCF能量关系图, 即科氏力项取代了以往的压力-应变项, 成为雷诺应力法向分量的主要能量来源. 特别地, 在 Ro = 1处流动再度湍流化, 此时聚合物分子链在科氏力产生的涡流作用下被剧烈拉伸, 导致聚合物应力的显著增大, 同时聚合物释放大量弹性能到湍流运动, 促进湍流的自维持过程.

     

    Abstract: The transition between flow states is a central topic in fluid mechanics. In viscoelastic turbulence, polymer additives introduce elastic effects that fundamentally alter the transition dynamics compared to Newtonian flows. This study investigates the viscoelastic spanwise-rotating plane Couette flow (RPCF) using the FENE-P model and direct numerical simulations based on a three-dimensional spectral method. At a fixed high Reynolds number (Re = 5200) and constant elasticity, the rotation number (Ro = 0–1) is varied to examine rotation-driven transitions. A distinct transition pathway is identified, evolving from drag-reduced inertia-dominated turbulence (0 ≤ Ro < 0.12), through drag-enhanced inertia-dominated turbulence (0.12 ≤ Ro < 0.24), to drag-enhanced elastically-dominated turbulence (0.24 ≤ Ro ≤ 1). Analysis shows that polymers suppress Reynolds stress generation while introducing additional drag via polymer stresses, leading to complex turbulent drag modifications. Energy transport analysis reveals that the Coriolis force replaces the pressure–strain term as the main energy source for Reynolds stress components, establishing a universal energy transfer map for viscoelastic RPCF. At Ro = 1, the flow is still turbulent as polymer chains are strongly stretched by Coriolis-induced vortices, releasing elastic energy that sustains turbulence.

     

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