Stationary and time-dependent numerical approximation of the lid-driven cavity problem for power-law fluid flows at high Reynolds numbers using a stabilized finite element formulation of the VMS type
Stationary and time-dependent numerical approximation of the lid-driven cavity problem for power-law fluid flows at high Reynolds numbers using a stabilized finite element formulation of the VMS type
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DOI：
10.1016/j.jnnfm.2018.03.014
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发表时间：
2018-07-01
影响因子：
3.1
通讯作者：
Baiges, J.
中科院分区：
文献类型：
--
作者：
Aguirre, A.;Castillo, E.;Baiges, J.
在这项工作中，变分多尺度有限元公式被用来近似数值计算高雷诺数的盖驱动空腔流动问题。对于牛顿流体，许多作者已经广泛研究了低雷诺数和中等雷诺数（Re = 10，000）的基准情况，使用稳态和随时间变化的方法来代替稳态流动。对于更多的对流流动，解变得不稳定，描述振荡行为。用不同的数值方法，在小于或等于Re小于或等于35，000的7，300的宽范围内，定义了这种随时间变化的流体动力学的临界雷诺数。在非牛顿流场中，对于高雷诺数（Re > 10，000），特别是振荡时变流场中的空泡问题还没有得到深入的研究。VMS制定提出了使用现有的结果进行验证，以确定出现不稳定的流动条件，最后，建立新的基准解决方案，高雷诺数流体流动的幂律模型。所得结果与文献报道的结果吻合较好，并在非牛顿流体的情况下发现了与流动振荡行为有关的新数据。在这方面，随时间变化的流动表现出依赖于雷诺数和幂律指数，并已确定所有研究的情况下的非定常起始点。确定了定义牛顿流体流动的第一次霍普夫分叉的临界雷诺数（Re-c）的范围在小于或接近Re的8，100、小于或接近8，250之间，而对于幂律指数n = 0.5和n = 1.5，它是小于或接近Re的7，100、小于或接近7，200和18，250小于或接近Re，小于或接近18，500。
In this work, a variational multiscale finite element formulation is used to approximate numerically the liddriven cavity flow problem for high Reynolds numbers. For Newtonian fluids, this benchmark case has been extensively studied by many authors for low and moderate Reynolds numbers (up to Re = 10, 000), giving place to steady flows, using stationary and time-dependent approaches. For more convective flows, the solution becomes unstable, describing an oscillatory behavior. The critical Reynolds number which gives place to this time-dependent fluid dynamics has been defined over a wide range 7, 300 less than or similar to Re less than or similar to 35, 000, using different numerical approaches. In the non-Newtonian case, the cavity problem has not been studied deeply for high Reynolds number (Re > 10, 000), specifically, in the oscillatory time-dependent case. A VMS formulation is presented to be validated using existing results, to determine flow conditions at which the instability appears, and lastly, to establish new benchmark solutions for high-Reynolds numbers fluid flows using the power-law model. Obtained results show a good agreement with those reported in the references, and new data related with the oscillatory behavior of the flow has been found for the non-Newtonian case. In this regard, time-dependent flows show dependence on both Reynolds number and power-law index, and the unsteady starting point has been determined for all studied cases. It is determined that the critical Reynolds number (Re-c) that defines the first Hopf bifurcation for Newtonian fluid flow is ranged between 8,100 less than or similar to Re, less than or similar to 8, 250, whereas for power-law indexes n = 0.5 and n = 1.5, it is 7,100 less than or similar to Re, less than or similar to 7,200 and 18,250 less than or similar to Re, less than or similar to 18,500, respectively.