论文标题
在简单的屈服应力流体中沉降的球体的数值模拟
Numerical simulations of a sphere settling in simple shear flows of yield stress fluids
论文作者
论文摘要
我们执行$ 3 $ d的数值模拟，以研究单个球体的沉积，而在没有弱惯性弱的屈服应力流体中简单的交叉剪切流动。在我们的模拟中，沉降流被认为是主要流量，而线性交叉剪切流量是幅度$ 10 \％$的二级流。为了研究携带流体对球体阻力的弹性和可塑性以及流动动力学的影响，使用\ cite {saramito2009new}提出的弹性塑料（EVP）构成定律对流体进行建模。额外的非牛顿应力张量与流动方程式完全耦合，固体粒子由浸入式边界（IB）方法表示。我们的结果表明，速度中的前AFT不对称性不太明显，当施加线性交叉剪切流动时，负唤醒消失了。我们发现，与原本静止的液体相比，在剪切屈服应力流体中沉降的球上的阻力显着减少。更重要的是，由于简单的剪切流和均匀流动之间的非线性耦合，因此在次级交叉剪切流程的存在下的球阻力不能源自纯沉积阻力。最后，我们表明，在较高的材料弹性下，在剪切的屈服压力中沉降的球上的阻力主要是由于形式和粘性阻力减少。
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.
