Large eddy simulation (LES) is expected to be an efficient and accurate numerical method for predicting the behavior of non-Newtonian fluids. However, it has been reported that the LES results obtained using eddy viscosity subgrid-scale (SGS) models have a high dependency on the grid resolution for wall turbulence. In order to resolve this problem, in the present study, a mixed SGS model combining an isotropic eddy-viscosity model and a scale-similarity model, which is proposed by Inagaki and Abe (2017), is applied to non-Newtonian fluids obeying the power law. The model performance is tested in plane channel flows and pipe flows for the power-law index $n$ of 0.5–1.15, using a wide range of grid resolution. The results demonstrate that, whereas conventional eddy viscosity SGS models significantly depend on the grid resolution, the present SGS model successfully prevents such grid dependency and yields accurate results even with relatively coarse grids for both pseudoplastic and dilatant fluids, where the modeled SGS shear stress consistently compensates the damped grid-scale (GS) shear stress. When decreasing the value of $n$ (higher shear-thinning property), it has been recognized that the anisotropy of the turbulence is augmented. Since the present SGS model can express the anisotropy of the turbulence stress, the results from $n=1$ down to $n=0.69$ are in fairly good agreement with the DNS data, regardless of the grid resolution used, predicting the reduction of wall-friction drag, quantitatively. Upon further decreasing the value of $n$ to 0.5, most eddy viscosity models do not maintain a turbulent state, whereas the present model maintains turbulence and provides results that are in reasonable agreement with the DNS data. The validity of the present model is also confirmed for high-Reynolds-number flows up to $R{e}_{\tau }=750$, where the grid independency is retained. These results demonstrate that the present model can remarkably reduce the computational cost of LES for non-Newtonian fluids.

大涡模拟 (LES) 有望成为预测非牛顿流体行为的有效且准确的数值方法。然而，据报道，使用涡粘性亚网格尺度 (SGS) 模型获得的 LES 结果高度依赖于壁面湍流的网格分辨率。为了解决这个问题，在本研究中，Inagaki 和 Abe (2017) 提出的结合各向同性涡粘性模型和尺度相似模型的混合 SGS 模型被应用于服从非牛顿流体的非牛顿流体。幂律。模型性能在平面通道流和管道流中进行幂律指数测试$n$0.5–1.15，使用广泛的网格分辨率。结果表明，虽然传统的涡粘性 SGS 模型显着依赖于网格分辨率，但本 SGS 模型成功地防止了这种网格依赖性，即使对于假塑性流体和膨胀流体的网格相对较粗，也能产生准确的结果，其中模拟的 SGS 剪切应力始终如一补偿阻尼网格尺度 (GS) 剪切应力。当降低的值$n$（更高的剪切稀化特性），已经认识到湍流的各向异性增加。由于现有的 SGS 模型可以表达湍流应力的各向异性，因此从$n=1$ 向下 $n=0.69$与 DNS 数据相当一致，无论使用的网格分辨率如何，都可以定量地预测壁摩擦阻力的减少。在进一步降低的价值$n$到 0.5，大多数涡流粘度模型不保持湍流状态，而本模型保持湍流并提供与 DNS 数据合理一致的结果。还证实了本模型的有效性对于高达$\mathrm{电阻}{\mathrm{电子}}_{\tau }=750$，其中保留了网格独立性。这些结果表明，本模型可以显着降低非牛顿流体 LES 的计算成本。