收敛-发散容器中的牛顿流
Newtonian Flow in Converging-Diverging Capillaries
摘要：
利用一维纳维-斯托克斯方程推导了五种不同收敛-发散轴对称毛细管中牛顿流体压力与体积流量关系的解析表达式。结果进行了比较，以前推导出的表达式相同的几何形状，使用润滑近似。一维Navier-Stokes方程的计算结果与无量纲数值因子下的润滑近似计算结果一致。通过与用数值积分离散化得到的数值解进行比较，也验证了导出的流动表达式。此外，他们已被证明是通过测试的收敛性的解决方案，收敛-发散几何接近极限直线几何。
英文摘要：
The one-dimensional Navier-Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids. The results are compared to previously-derived expressions for the same geometries using the lubrication approximation. The results of the one-dimensional Navier-Stokes are identical to those obtained from the lubrication approximation within a non-dimensional numerical factor. The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration. Moreover, they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.
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