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arXiv 2005.08429physics.flu-dyncond-mat.soft
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屈服应力流体简单剪切流中球体沉降的数值模拟

Numerical simulations of a sphere settling in simple shear flows of yield stress fluids

Mohammad Sarabian, Marco E. Rosti, Luca Brandt, Sarah Hormozi

摘要:

我们进行了$3$ D数值模拟,研究了在具有弱惯性的屈服应力流体中存在和不存在简单的交叉剪切流的情况下单个球体的沉降。在我们的模拟中,沉降流被认为是主流,而线性交叉剪切流是具有主流的振幅$10\%$的二次流。为了研究载流流体的弹塑性对球体阻力及流体动力学的影响,采用\cite{saramito2009new}提出的弹粘塑性(EVP)本构关系对载流流体进行了建模。额外的非牛顿应力张量是完全耦合的流动方程和固体颗粒表示的浸没边界(IB)方法。我们的结果表明,前后不对称的速度是不太明显,负尾流消失时,施加线性横向剪切流。我们发现,在剪切屈服应力流体中的球沉降的阻力显着减少相比,否则静止的流体。更重要的是,由于简单剪切流和均匀流之间的非线性耦合,在存在二次剪切流时,球阻力不能由纯沉降阻力定律导出。最后,我们表明,在较高的材料弹性,主要是由于形式和粘性阻力的减少,在剪切屈服应力流体中的球体上的阻力减少。

英文摘要:

We perform $3$D numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross shear flow is a secondary flow with amplitude $10\%$ of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modeled using the elastovisco-plastic (EVP) constitutive laws proposed by \cite{saramito2009new}. The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary (IB) method. Our results show that the fore-aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly as compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross shear flow cannot be derived from the pure sedimentation drag law owing to the non-linear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield-stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction.

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